A 523088
THE TESTING
OF
MATERIALS
OF
CONSTRUCTION
UNWIN
TA
410
U62
LONGMANS & CO.
LIGERETVRT
AUDIT
KABINETTA NA
G

ARTES
LIBRARY
1837
*HINA-
VERITAS
UNIVERSITY OF MICHIGAN
E PLURIBUS UNUM
TUE BUR
SCIENTIA
OF THE
SI-QUAERIS PENINSULAM AMOENAMI
CIRCUMSPICE
NINJAJAJAJNIKAOS
GONZAGO
DEPARTMENT
OF
GİNEERING
༢༠༣༢
YENERAL LIBRARY.
}
1
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THE TESTING
OF
GEN, LIBRARY.
MATERIALS OF CONSTRUCTION
1
TA
410
.262
2
3
PRINTED BY
SPOTTISWOODE AND CO., NEW-STREET SQUARE
LONDON
▸


AUTOTYPE
Plate I.
3.BUCKTON
LEEDS
1.TON
ENGINEERING
BUCKTON
& COLP
LEEDS
LABORATORY AT THE CENTRAL INSTITUTION
OF THE GUILDS OF LONDON.
THE TESTING

OF
7 22 27
MATERIALS OF CONSTRUCTION
A TEXT-BOOK FOR THE
ENGINEERING LABORATORY AND A COLLECTION OF
THE RESULTS OF EXPERIMENT
BY
WILLIAM CAWTHORNE UNWIN, F.R.S.
M. INST. C.E.
PROFESSOR OF ENGINEERING AT THE CENTRAL INSTITUTION OF THE CITY
AND GUILDS OF LONDON INSTITUTE: FORMERLY PROFESSOR OF
HYDRAULIC AND MECHANICAL ENGINEERING AT THE
ROYAL INDIAN ENGINEERING COLLEGE
LONDON
LONGMANS, GREEN, AND CO.
AND NEW YORK: 15 EAST 16th STREET
1888
All rights reserved
/Teala ES
PREFACE.
THE present work is a treatise on the Strength of the
Materials used in Construction, considered in connection
with the instruments and methods by which the pro-
perties of materials are investigated experimentally.
The data on which the engineer relies in designing
structures cannot be fully understood without some
knowledge of the methods by which they are ascertained.
But for several reasons a knowledge of the methods of
testing has become of late of greater importance. With
the introduction of new materials the engineer has been
forced to make greater use of the testing machine, both
in estimating the constructional value of materials and
to escape the danger of employing material which is
unsuitable. A considerable advance has been made in
the construction of all the apparatus used in testing,
and the operations of testing are carried out with more
care and skill. Lastly, the establishment of Engineering
Laboratories in connection with Schools of Engineering
72221
vi
TESTING OF MATERIALS OF CONSTRUCTION
has made experimental investigation an essential part
of engineering education.
Bud
The following treatise consists of three parts. In
the first, the mechanical properties of materials are ex-
plained—that is, the phenomena of elasticity and plasti-
city, and the relations between stress and deformation, so
far as they have been scientifically ascertained. In the
second, the apparatus used in the engineering laboratory
is described. The author has had opportunities of ex-
amining nearly every form of testing machine, and of
using very nearly all the subsidiary measuring and other
apparatus here described. Lastly, the third part contains
a collection of the most complete and trustworthy results
of testing, of all the ordinary materials of construction.
This third part, no doubt, traverses ground occupied
by several excellent treatises. Nevertheless, it will be
found to contain a large amount of information, either
new or at least not easily accessible to English readers.
The mass of data accumulated in the last forty years
is enormous, and in the selection of results of testing
for the present work some definite principles have been
steadily kept in view. Where laws were established first
by careful and adequate experiment, it seems historically
just to reproduce the original investigation. When,
as in some of Hodgkinson's experiments, very simple
PREFACE
vii
means of measurement were used, accurate enough for
the purpose in view, this adds value to these early
results. But beyond question more recent investiga-
tions have, on the whole, been carried out with better
appliances, and with greater skill and knowledge. In
selecting amongst these, the point of greatest importance
seemed to be that the investigations should be complete.
That is, that all the facts useful to observe about a
material should have been ascertained. If the tenacity
of one sample of a material is determined, the shearing
strength of a second, the crushing strength of a third
-these results are less instructive than if one sample
of material had been tested in all three ways. In giving
tables of results they have all been reduced to common
units, so as to be most easily understood and compared.
It will be noted that a large number of the results.
are borrowed from German and American sources.
The establishment of Testing Laboratories, supported by
Government, in Berlin, Munich and Vienna, and more
recently at Watertown in the United States, is perhaps
a procedure not likely to be followed in this country.
But it can hardly be doubted that those laboratories
have in a very important degree assisted foreign
engineers and manufacturers. No mechanical investi-
gations of the properties of materials at all comparable
viii TESTING OF MATERIALS OF CONSTRUCTION
in completeness to those undertaken in the Berlin
and Munich laboratories have been carried out in this
country. Whether or no the minuteness and delicacy
of measurement and elaboration of method have been
pushed beyond practical needs there may be difference
of opinion. But everyone who studies the memoirs
issued by the accomplished directors of the Continental
laboratories must admire the patience and insight and
skill which they exhibit. It is perhaps true that the
full and unreserved publication of methods and results,
so necessary for scientific progress, is hardly possible
except in the case of public Institutions directed by
men of acknowledged eminence.
Results obtained by the author himself have been
introduced sparingly, and chiefly where they filled gaps
in the information available.
Kensington February 1888.
;
CHAPTER
INTRODUCTION
I. MECHANICAL PROPERTIES OF BODIES ACTED ON
STRESSES
II. PLASTIC PROPERTIES OF MATERIALS
III.
STRESS-STRAIN DIAGRAMS
IV.
TESTING MACHINES
V. SHACKLES FOR HOLDING TEST BARS
VI. MEASURING INSTRUMENTS
VII.
VIII. ELASTIC CONSTANTS FOR METALS
IX. CAST IRON
X. IRON AND STEEL
XI. COPPER, COPPER ALLOYS, AND MISCELLANEOUS TESTS
OF METALS
12.
CONTENTS.
AUTOGRAPHIC RECORDING APPARATUS
XIII. TIMBER
XIV. STONE AND BRICK
XV. LIMES AND CEMENTS
90
XII. EXPERIMENTS ON REPETITION OF STRESS. ENDURANCE
TESTS
INDEX
BY
3
·
•
a
PAGE
1
17
45
56
106
171
192
228
246
259
276
339
356
394
410
441
483
LIST OF PLATES.
PLATE
I. ENGINEERING LABORATORY AT THE CENTRAL INSTITUTION
OF THE GUILDS OF LONDON INSTITUTE
II. 100-TON TESTING MACHINE OF MESSRS.
BUCKTON & Co. .
III. OLSEN AND GRAFENSTADEN TESTING MACHINES
IV. GENERAL VIEW OF THE WATERTOWN 450-TON
TESTING MACHINE
V. PLAN AND ELEVATION OF THE WATERTOWN
TESTING MACHINE
Frontispiece
to face 136
""
PAGE
""
""
142
160
160
→
Erratum.
Page 159, line 8 from bottom. For one per cent.' read 'one-tenth
of one per cent.'
1
$
t
4.
;
THE TESTING
OF
MATERIALS OF CONSTRUCTION.
INTRODUCTION.
THE arts of construction probably arose out of simple
need of shelter, and in house-building men were first
driven to apply natural materials to purposes involving
the consideration of their mechanical properties. As
communities were formed and social relations became
more complex, the builder's art developed and extended.
Roadways were necessary for traffic, temples for wor-
ship, fortresses for defence.
Now, in all works of construction are involved
questions of the strength of materials. In the rudest
house-building, materials must have been selected
because they were strong, and proportioned with some
reference to the forces to which they would be sub-
jected; with every increase of size and complexity in
the structures erected reconsideration was necessary of
the materials available, and more attention would be
given to securing adequate strength. Other considera-
tions would have weight. Granite might be chosen for
B
C
2
TESTING OF MATERIALS OF CONSTRUCTION
durability, marble for polish, bronze for lustre, gold for
costliness, metal to be beaten, wood to be carved. But
in no case could considerations of strength be entirely
ignored. The forms which give character to mediæval
architecture—arch, buttress, groin, and tracery— are due
to the desire to obtain great structural strength consis-
tently with other requirements. And amongst those
other requirements one must always have been to
economise the amount of material used.
It is, however, under the pressure of quite modern
necessities that the problem of using materials to the
greatest advantage in securing strength has come to be
before all other considerations in the mind of the
designer. In modern structures and machines, what-
ever other objects are in view, the designer has always
to consider what are the straining actions to which the
structure will be subjected, and what is the safest
material, and the best disposition of it, and the least
amount of it necessary to resist those straining actions.
The cause may be the increased value of labour, or
the greater use in construction of artificial or manu-
factured materials, or the greater scale of modern works,
or the commercial conditions under which they are
undertaken. Whatever the cause, the modern engineer
or constructor has always to consider what is the least
amount of material required to give adequate strength.
The simplest mode of ascertaining the safety of a
structure, say of a railway bar, or a bridge, is to apply
to it a testing-load greater than the maximum load to
INTRODUCTION
3
which it is likely to be subjected. To a certain extent
this testing of completed structures is, and always will
be, carried out. Before a boiler is put under steam it is
tested by hydraulic pressure; before ordinary traffic
passes over a railway bridge, a heavy testing-load is
placed on it. Such tests sometimes reveal unknown or
unsuspected sources of weakness. But little informa-
tion is derivable from tests of completed structures, from
the necessary limitation of the testing-load. No load
can be applied likely to injure or deform the structure,
unless it is quite seriously ill-proportioned or ill-con-
structed. And an extreme testing-load may damage
a structure, such as a boiler or bridge, without any
possibility of the injury being detected at the time.
It would also be very inconvenient if structures were
erected at hazard with a chance of breaking down
under the testing-load. Such tests of completed struc-
tures have become to a great extent superfluous. They
are useful as affording a final guarantee of security, but
they do not supply very important or specific informa-
tion as to the margin of safety which exists. In by far
the largest number of cases no testing-load can be
applied except the ordinary working load.
It is here that purely theoretical studies come to the
assistance of the engineer. For the materials he uses,
the deformations due to the stresses are small, and
within working limits of stress they are very nearly
proportional to the stresses. Assuming the deforma-
tions to be small and proportional to the stresses, it is
B 2
4
TESTING OF MATERIALS OF CONSTRUCTION
possible to reduce the straining actions in the most
complex structures to comparatively simple straining
actions in their separate members. With that part of
applied mechanics which deals with the determination
of the simpler straining actions on the members of
complex structures we have not in this treatise to deal.
Supposing, however, this reduction made, then experi-
ment on pieces of material subjected to such simple
straining actions will show how the members of complex
structures should be proportioned. Hence, for a hundred
years or more, engineers have been constantly experi-
menting on small pieces of different materials subjected
to simple straining actions. Experiments of this kind
are called tests of the strength of the material, and the
machines for making these tests are called testing
machines.
There are two distinct objects in view in subjecting
materials to mechanical tests. The one is scientific,
the other commercial. When the object is scientific, the
experimenter aims at the determination of the physical
constants of the material and at verifying the assump-
tions on which theoretical calculations proceed. When
the object is commercial, the experimenter endeavours
to ascertain whether samples of a material comply with
certain more or less arbitrarily chosen standards of
quality. That the methods of testing for scientific and
for commercial purposes more or less coincide should
not be allowed to obscure an essential difference.
Absolute results are wanted in scientific testing, rela-
INTRODUCTION
5
tive results in commercial testing. What is the elastic
limit, the modulus of elasticity, the working limit of
stress in given conditions of a given material, are ques-
tions in the one case. Which of two samples of mate-
rial is the better sample on the whole, is the kind of
question in the other case.
Scientific Testing.-The object of scientific testing
being to determine the physical constants for a material,
it will be useful to enumerate those which for the pur-
poses of the engineer are most important.
The definite physical constants required in the ap-
plication of theories of the resistance of materials are
as follow:
1. The density or heaviness. A great part of the
straining action in most structures is due to the weight
or inertia of the structure itself. Besides this, in many
materials the density is directly connected with other
properties of the material.
2. For some purposes and for certain materials
it is useful to determine the hardness or resistance to
abrasion.
3. Certain co-efficients of elasticity or ratios of stress
to strain. For practical purposes it is usually accurate
enough to assume a material to be elastic, homogeneous,
and isotropic. In that case its deformation by any
straining action can be determined if two elastic co-
efficients are known-the co-efficient of elasticity of
form, and the co-efficient of clasticity of volume. But,
for application, other elastic co-efficients dependent on
6
TESTING OF MATERIALS OF CONSTRUCTION
these are also convenient. These co-efficients are re-
quired for two reasons. A structure must be designed
so that not only does it resist the straining action
without breaking, but also without prejudicial deforma-
tion, and the elastic co-efficients are required to deter-
mine the deformations from the stresses. Next, in
many cases the stresses depend on the deformations and
the co-efficients of elasticity appear in the equations for
determining the stresses.
4. Limits of Elasticity.-Certain materials, like cast-
iron, are not perfectly elastic in their initial condition
for any straining action. They are permanently de-
formed, or take a permanent set with very small loads.
But many materials are almost perfectly elastic, and
most important materials of construction become so for
a certain range of stress. It is only within that range
of stress that the ordinary rules of strength of materials
are applicable. The limits of elasticity must be known
to determine the extent to which the rules can be
trusted.
If the limits of elasticity of a material were fixed by
the conditions of its manufacture, the modulus of elas-
ticity and limit of elasticity, once directly ascertained by
experiment, would furnish all the data necessary to the
engineer in applying the theory of elasticity and fixing
the working limits of stress. That, however, is not the
It has long been known that the elastic limit of
a bar is not a fixed limit. By loading and straining a
bar in one direction the elastic limit for that kind of
case.
INTRODUCTION
7
stress is raised. More recently it has been shown that
if the bar is loaded and strained in different directions
the elastic limit may be lowered.
One of the most ordinary conditions of a structure
or machine is that it is subjected to reiterated working
stresses, all lying between a minimum and maximum
value, or between a maximum stress of one kind and a
maximum of the opposite kind. In such conditions,
new elastic limits are produced differing from the
original or primitive elastic limits. The determination
of what those limits are in given circumstances is the
object of remarkable and difficult researches, which are
beyond the range of ordinary testing.
No doubt it is accurate enough to treat ordinary
structures and machines as perfectly elastic and to
determine the distribution of stress on that assumption,
for experience has fixed the limits of working stress
far within the primitive elastic limit. But it is by
no means clear that the working stress is commonly so
fixed as to secure equal safety in different cases, and,
if the proper working stress is to be determined on
rational principles, the study of the conditions in which
the elastic limits change becomes essential.
5. Breaking Stresses.-In the case of some materials
an increasing load produces simply an increasing defor-
mation. Generally, however, a limit is reached at which
the bar suddenly fractures. Under defined conditions
of loading—for instance, with a gradually increasing
statical load applied in a short time-the breaking stress
8
TESTING OF MATERIALS OF CONSTRUCTION
„PÉSZTAŁE ZELAN
is a perfectly definite constant for a material, and is
nearly independent of the form and dimensions of the
bar tested.
As ordinarily stated in tables of strength of materials,
the breaking stress is a somewhat fictitious quantity.
Most materials commonly tested are ductile. Suppose
the bar subjected to tension. With such materials a
maximum load is reached before the bar breaks. At
that point the elongation becomes very rapid and the
section rapidly diminishes. The bar will no longer
support the maximum load, and it finally breaks with
a load 10 or 20 per cent. less than the maximum
load. What is ordinarily understood as the breaking
stress is the maximum load divided by the initial sec-
tional area of the bar. That is, it is a load which is not
the breaking load, estimated on an area which no longer
existed when the bar broke. There are, of course,
reasons of convenience for estimating the breaking
stress in this way, and no error need arise if the mode
of estimating the breaking stress is remembered.
But, further, the early experiments of the Railway
Commission, the experiments of Fairbairn for the Board
of Trade on a small plate girder, the splendid series of
researches by Wöhler, continued by Spangenberg and
Martens, and confirmed by similar experiments of Bau-
schinger and Baker, all show that bars subject to contin-
ually varying stress break with loads of from one-half to
two-thirds the statical breaking stress. The greater the
range through which the stress varies and the greater
INTRODUCTION
9
the number of repetitions, the lower is the breaking
stress. These results are explainable if it is supposed
that, instead of fixed limits of elasticity, these limits.
depend on the range and kind of variation of stress,
and that, if the range of perfect elasticity possible in
given conditions is exceeded, deformations are produced
which, accumulating with successive repetitions of load,
finally lead to fracture. General experience accords
with this conclusion. Under a purely statical stress a
bar not too ductile would probably be safe with seven-
eighths of the ordinary so-called breaking stress. But
with a varying load no working stress as high as that
would be safe. If the range of variation is small, the
working stress may still be comparatively high. The
Conway Bridge, in which the rolling load is small
compared with the permanent weight of the bridge, is
subjected daily to stresses reaching 7 tons per square inch,
or nearly one-third of the breaking stress. But ordinary
iron bridges with a larger proportion of rolling load,
and therefore a greater variation of stress, are not sub-
jected to more than 5 tons or at most a quarter of the
statical breaking stress. Even this limit proves to be too
high for bridges of very short span, in which the range of
variation of stress is greater. Ordinary shafting and
axles are rarely loaded beyond 4 tons to the inch, and
in many parts of machines subjected to alternating ten-
sions and compressions the stress does not exceed 2 tons
per square inch, or one-twelfth of the breaking stress.
It has been common to assume that the margin
-
10 TESTING OF MATERIALS OF CONSTRUCTION
between the calculated working stress and statical
breaking stress, as determined by ordinary testing, is
merely an allowance for contingencies. But it is in no
way clear that in cases where this margin is in practice
greatest the probability of the working stress being
exceeded is greatest also. Further, the need of an
allowance of 400, 600, or 1,100 per cent. for mere con-
tingencies neglected in calculating the stresses in the
structure is incredible. It is much more probable that
the elastic limit really fixes the safe limit of working
stress, and that this varies with the range of variation
of stress.
Hence, besides the ordinary so-called breaking
stresses determined in ordinary statical testing, it is
distinctly one object of scientific testing to determine
the breaking stresses under conditions of variation of
stress, and especially to ascertain the conditions of time
under which such variations of stress are effective in
altering the breaking stress.
But besides these dynamical conditions which affect
the physical constants of a material, it is the object of
scientific testing to determine how far different con-
ditions of manufacture, of mechanical treatment in the
forge, of chemical constitution, of temperature, and so
forth, affect the physical constants of the material, and
inferentially its value as a material of construction. It
is by researches of this kind that guidance is obtained
in seeking the improvement of any given manufacture.
6. The Yield Point.-In iron and steel, and perhaps
-
INTRODUCTION
11
other rolled or hammered materials, at a stress exceed-
ing more or less the elastic limit, there occurs a large
and almost sudden increase of deformation in the
ordinary method of testing, and the deformation is per-
manent or plastic deformation. For greater stresses
the plastic deformation increases, and it amounts, before
fracture is reached, to many hundred times the whole
elastic deformation. The point at which this almost
sudden augmentation of plastic deformation occurs is
termed the yield point or breaking-down point. It is
obvious that a general plastic yielding of a structure
would ruin it for practical purposes, hence the yield
point seems to fix a limit of stress independent of that
determined from considerations of safety against frac-
ture, which the working stress should not exceed. The
yield point is raised by loading, which exceeds the
primitive yield point, but it is not usually practicable to
raise the yield point of a material artificially before using
it in a structure, and consequently the primitive yield
point due to the mechanical operations of manufacture
fixes with respect to deformation the dangerous limit of
stress. Professor Kennedy has especially insisted on
the yield point as fixing the greatest working limit of
stress.¹ But the case is not quite so simple as at first it
appears. In almost all actual structures the maximum
stresses are confined to very limited portions of the
structure. It is not quite clear that a riveted joint is
either sensibly deformed or permanently injured, even
1
¹ Professional Papers of the Corps of Royal Engineers, vol. x. 1884.
12 TESTING OF MATERIALS OF CONSTRUCTION
I
if the yield point at the dangerous section is exceeded.
In testing large riveted girders the deflections are
regular and proportional to the loads, almost to the
breaking weight, and show no indication of a yield
point.
By careful scientific testing most of the constants
enumerated above have been determined for the various
materials which are used by the engineer. But a ques-
tion arises which should not be entirely passed over.
How far do such tests as have been made afford a
trustworthy foundation for the wide extension which is
given to their results by the aid of applied mechanics?
It is, perhaps, desirable at least to point out some of
the differences between the conditions of even the most
careful testing and those which obtain in engineering
structures. In the first place, most experiments have
been made on test specimens of very small size; and it
is not always safe to infer that the material in the small
test-bar, and that in the large structure, are of identical
quality and in precisely similar conditions. In the case
of timber, for instance, Professor Lanza's experiments.
show a wide discrepancy between small and large
specimens. In another respect, at least, there is still a
considerable difference between engineering structures
and ordinary test-bars. Engineering structures are
almost always compound structures made up of me-
chanically connected parts. To what extent a com-
pound structure of that kind can be taken to be
equivalent to a simple homogeneous structure is at
INTRODUCTION
13
present, at least, so far as direct experiment is con-
cerned, very imperfectly known. Happily, the very
defect of elasticity in ordinary materials tends to dimi-
nish the variation of stress in compound structures
which is due to imperfection of the mechanical connec-
tions. But it is probable, and, to a certain extent, it is
in accordance with practice, that the limiting stress
should be rather lower in a compound than in a
simple structure; that stresses, for instance, are safe
in a simple railway bar or axle, which under similar
conditions would be unsafe in a riveted girder. The
differences between ordinary tests and actual structures
as to time and frequency of repetition of load have
already been spoken of. Lastly, in many actual cases
in practice, the parts of a structure are subjected to
combined stresses, and but little progress has been
made experimentally in determining the effect of such
combined stresses.
Commercial Testing. The materials used by the
engineer are natural or artificial products, and generally
several sources of supply are available. It is important
to be able to distinguish the quality of the materials
coming from different localities or from different manu-
facturers, or which differ considerably in quality or
cost. A manufacturer may be skilful or careless; may
use good raw materials or bad raw materials; or acci-
dental circumstances may interfere with the processes of
manufacture. The conditions involved in the success
of a manufacture are numerous and complex. No mere
P
14 TESTING OF MATERIALS OF CONSTRUCTION
supervision of the processes or examination of the re-
sulting product is an adequate guarantee of quality.
Now, the engineer requires to know if he is getting
material good of its kind, and suitable for the purpose
intended. To determine this no method is so convenient
or safe as the selection of sample portions of the mate-
rial, which are then subjected to appropriate tests, and,
since a rapid and definite judgment is required, more or
less arbitrary standards of quality must be accepted.
Qualitative or comparative testing of this kind
may be
called Commercial Testing, to indicate its character
without any intention of depreciating its importance.
Since the physical constants of a material really
determine its value for constructive purposes, com-
mercial tests may be made to approximate as closely as
is practicable to tests for scientific purposes. But this
is by no means always convenient. Shorter and readier
methods are often sufficient for comparative purposes.
What the user of a material requires to know is whether
a material supplied is as good as material previously
employed in similar cases; or, of two materials equally
available, which is the better. Generally he is content
to adopt one or two easily applied tests, and to judge
by comparison of the results of these alone. All that
needs to be noted at present is that these commercial
standards of quality are often arbitrary to an extent
which has been too much overlooked.
In testing steel, for instance, it has been common to
look to the breaking stress and the ultimate elongation
INTRODUCTION
15
as marks of quality. Admitting that a steel of 30 tons
tenacity and 30 per cent. elongation is better than a
steel of 28 tons tenacity and 25 per cent. elongation,
the results are relative merely, and give no absolute
measure of the difference in constructional value of the
two materials. If one steel has 30 tons tenacity and
25 per cent. elongation, and the other 28 tons tenacity
and 30 per cent. elongation, it even remains doubtful
which is the better material. Neither the breaking
stress nor the elongation represent conditions of stress
or deformation which can be even approached in the
actual application of the material.
Again, it is sometimes convenient to make chemical
analyses of materials instead of mechanical tests.
No
doubt the physical properties of a material are often
closely connected with, and can, to a certain approxi-
mation, be inferred from its chemical composition.
Particular defects, such as adulteration, are better de-
tected by chemical analysis than by mechanical tests,
and in some cases particular constituents have a defi-
nite effect on quality. Sulphur and phosphorus are
prejudicial when present in iron. The physical pro-
perties of steel depend somewhat closely on the amount
of carbon, silicon, and manganese it contains. Lime
and gypsum are sometimes mixed with cement, and
injure its quality. But, in fact, the engineer has to do
with the mechanical properties of materials; and the
indications furnished by chemical analysis, though
valuable, are indirect, and not for the engineer's pur-
16
TESTING OF MATERIALS OF CONSTRUCTION
pose completely reliable. Steels made from the same
raw materials, and having identical chemical consti-
tuents, may, from difference of mechanical treatment
and other causes, have differences of quality of im-
portance to the engineer.
The engineer is, therefore, in most cases obliged to
use mechanical tests in discriminating the quality of his
materials. Then there arises the question, what are
the mechanical tests most readily applied and most
trustworthy in their indications? Complete experiments
on the physical properties of the material are in general
too laborious and costly. Certain physical properties
must be selected as marks of good quality. For practical
purposes, limited tests of this kind have been established,
and contracts are made for the supply of material under
specified test conditions.
What tests of this kind are commonly applied will
be discussed later on. At present it is only necessary
to point out that, in proportion as the test is limited to
a few properties of the material, and especially when it
differs widely from the conditions in which the material
is used, it is an empirical test of quality and sometimes
misleading. Examples are not wanting of the general
adoption of commercial tests which have tended to pre-
vent the production of the best material, and to retard
the progress of a manufacture.
S
PROPERTIES OF BODIES ACTED ON BY STRESSES 17
CHAPTER I.
MECHANICAL PROPERTIES OF BODIES ACTED ON BY
STRESSES.
THE systems of forces to which bodies are subjected,
due to their weight or to the loads they support, or to
other causes, are termed stresses.
These stresses pro-
duce in the body on which they act alterations of size
or of shape, and these alterations are termed strains.
One of the principal objects of testing materials is to
determine the relation between stresses and the strains
they produce. Very commonly stress is considered as
the mutual action of two bodies at their plane of con-
tact, or the mutual action of two parts of a body at an
imaginary plane of division. A hanging chain carrying
a load is in a condition of stress due to the upward re-
action at the point of support and the downward pull of
the load. Each link is in a condition of stress due to
the upward and downward pull of the two neighbour-
ing links; and if a link be considered divided by a
horizontal plane, the stress at that plane is the upward
and downward action of the half link on either side.
1. Elastic and Plastic Materials.-The most important
с
18 TESTING OF MATERIALS OF CONSTRUCTION
distinction between bodies, from a mechanical point of
view is that some are elastic and others non-elastic or
imperfectly elastic. Elastic bodies recover their form
after the stress is removed; non-elastic bodies or imper-
fectly elastic bodies undergo a permanent change of
shape when a stress is applied. The most important
materials of construction are nearly perfectly elastic for
a certain range of stress, and imperfectly elastic for
greater stresses.
But there are materials which can be
greatly changed in form without losing continuity or
breaking into fragments. To these we give the names
malleable, ductile, or plastic, according to the mode of
application of the stress. Gold is beaten into leaves,
copper is drawn into wire, clay is moulded by pressure.
The word which best expresses the property of
suffering an indefinitely large deformation is the word
plastic. A material is termed brittle if it breaks under
an increasing stress before any great permanent de-
formation is caused. It is called tough if, under an
increasing stress, it becomes plastic and undergoes a
large permanent change of shape.
2. Summary of the Elastic Properties of Materials.-
When a body is subjected to the action of external
forces, it undergoes a deformation which is either a
deformation which disappears if the load is removed
(elastic deformation), or a deformation which remains
after the load is removed (plastic deformation). Ac-
cording to the best experiments, and especially those of
Bauschinger, all the materials used in construction,
PROPERTIES OF BODIES ACTED ON BY STRESSES 19
except perhaps hard tool steel, show a small amount of
permanent set after loading the first time, even if the
loads are comparatively small. But in many materials,
and up to a certain limit of stress called the elastic limit,
the permanent sets are very small, and may perhaps
rather be ascribed to initial want of straightness of the
bars tested or to small defects of homogeneousness than
to any inherent property of the material.
6
Within the limit of elasticity a very simple relation
holds between the stresses or deforming forces and the
strains or deformations. This law was published in 1676
by Robert Hooke, in the form of an anagram: The
true theory of elasticity or springiness, ce iii n o sss tt uu.'
The key to this anagram was given, two years later, in
the phrase, 'Ut tensio sic vis; the
power of any spring
is in the same proportion with the tension thereof.'
Using more modern terms, we say the stress is propor-
tional to the strain. Later it will be shown to what
extent actual materials conform to this law and behave
with sensibly perfect elasticity. At present it is enough
to assume that with most materials, and for straining
actions within the elastic limit, the plastic or permanent
deformations are so small that they may be neglected,
and that the temporary or elastic deformations conform
to Hooke's law.
-
3. Tension and Compression. When a prism is sub-
jected to a stress parallel to its axis and uniform on
cross-sections perpendicular to the axis, it extends in
length and diminishes in section or shortens and in-
c 2
20
TESTING OF MATERIALS OF CONSTRUCTION
creases in section. Let p be the stress reckoned on
unit of area, and a the extension or compression reckoned
per unit of length. Then, by Hooke's law-
1
(1).
This constant is termed the coefficient of direct elasticity,
or Young's modulus. It has the same value for tension
and compression.
4. Poisson's Ratio.-When a bar is extended or com-
pressed by a simple longitudinal stress of the kind de-
scribed above, it contracts or dilates laterally. If±a is
FIG. 1.
1
2
??
λ
I
* - d (1-1)· »
1
=
E, a constant
λ
Į (1 + ^)
I
wy
G
a
ਸ


d(2+)
7 不
​1
V(1-^)
the longitudinal extension or compression, reckoned per
unit of length, then the contraction or dilation trans-
versely is a/m, where 1/m, the ratio of lateral con-
traction to longitudinal extension, is a constant termed
Poisson's Ratio. For most solid bodies m has values
between 3 and 4, and for metals its most general value
is nearly 4; for india-rubber, m = 2 nearly, when the
deformation is small.
Hence a simple longitudinal stress, p, per unit of
PROPERTIES OF BODIES ACTED ON BY STRESSES 21
area produces a longitudinal strain, λ =p/E, and a
transverse strain, - λ!m = - p/m E.
M
It might be questioned whether a should be reckoned
per unit of original or per unit of stretched length of
the bar. For ordinary solids a is so small that it makes
no sensible difference, and a is calculated per unit of
original length. But for india-rubber, equation (1) is
much more nearly satisfied if a is calculated per unit
of stretched length. If a is the elongation per unit of
original length, is the elongation per unit of
stretched length.
7
1+ λ
5. Change of Volume under simple Direct Stress.—
Suppose the prism has initially the length and cross-
section a. Subjected to a longitudinal tension, the
length becomes 1 (1 + x), and the section a (1-2)²?
กาว
Consequently the initial volume al is changed to al
(1 + 2 − 2) very nearly, since the deformations are
small. The change of unit volume is a 22/m.
Thus, if m = 4, as for metals, the change of volume
of one cubic unit is, the volume being increased
by longitudinal tension; if m = 2, as for india-rubber,
there is no change of volume. Similarly, for com-
pression, the change of unit volume is a for metals,
the volume being diminished.
Work done in Extending or Compressing a Bar.-If
the stress is gradually increased from zero to a limit p,
-
22
TESTING OF MATERIALS OF CONSTRUCTION
since equal increments of stress produce equal incre-
ments of strain, the mean stress is p/2, and the work
per unit volume done on the bar is
Material
(2).
6. Numerical Values of the Constants.-In order to
have some idea of the numerical importance of the
quantities which are under discussion it is desirable to
examine a few cases. The following are values of the
modulus E in tons per sq. inch, and the extension a
and lateral contraction a/m per unit length for each
ton per sq. inch for some materials :
Wrought iron
Mild steel
Cast iron
Glass
Bronze
Yellow deal
•
W = 1 p a
2
•
·
E
13,250
12,200
14,400
13,250
6,250
10,020
3,530
4,400
715
Extension per
ton per sq. inch
per unit length
·000075
•000082
'000069
•000075
·00016
·00010
•00028
⚫00023
·00139
-
1
Lateral con -
traction per
ton
per sq. inch per
unit width
·000019
*000020
•000017
·000019
⚫000040
⚫000025
•000071
·000058
Taking ordinary Bessemer steel, such as is used in
riveted work, the elastic limit will not be below 10 tons
per sq. inch. Up to that limit the extension will be
0007, or about Tooth of its initial length. Hence the
lateral contraction will be about th of its initial
width. The increase of volume when stretched will be
aboutth. The work in stretching the bar up to
1
56
PROPERTIES OF BODIES ACTED ON BY STRESSES
23
1
10 tons per sq. inch will be (10 × 2240) 1400×12
of a foot-pound per cubic inch of the bar.
FIG. 2.
7. Superposition of Two simple Direct Stresses at Right
Angles. Consider a small
cube, of unit length of
side, with simple stresses
normal to two pairs of
faces and parallel to
the third pair. Under
the action of p₁ there
P1
will be the following
strains :
Pr
parallel to OC,
Adding the parallel strains,
parallel to OC, 21
0
C
OA, 23 =
ag
P1
E
parallel to OB and OA,
Under the action of p2, the strains are :
parallel to OB, P
E
parallel to OA and OC,
P₁
E
OB, λ₂ = p²
E
A
P2
mE'
P1
mE'
Pi
B
P1
ME'
P1 P2
mE ME
Pi
P2
mE
P2
alm

شر
24
TESTING OF MATERIALS OF CONSTRUCTION
Now let the stresses P1, P2, be of equal intensity, P,
but opposite sign. The strains become
or putting
1-λ
V
P
p
(1 + 1); - (1+1) and 0... (3),
い
​E
E
m
the lengths of the sides of the cube will be
1+λ; 1-2; and 1
and the volume neglecting a² is unchanged.
Fig. 3 shows the distorted cube. A
A square traced
on the side of the original
cube will be distorted into a
rhombus, the angles of which
are greater and less than a
right angle by the equal
amount 0.
Now
FIG. 3.
-1+A
S
1-λ
1+2
Or, as is small,
// (1 + 1) = x,
P
E
K
1
لا
F
tan 1
2
(3 - 0)
(
-
Ө
1
2
P
tan
1 + tan
and 0 = 2λ
A
2
Mag
2
(4),

(5).
8. Isotropy.-A material is quite conceivable which,
tested by a direct tension for instance, should give one
PROPERTIES OF BODIES ACTED ON BY STRESSES 25
value of E for a stress in one direction and a different
value of E for a stress in another direction. The
materials used in construction are produced by processes
of forging, rolling, &c., in which the mechanical actions
have definite directions with reference to the piece pro-
duced. The pressure of the rolls on a bar is perpen-
dicular to its axis, and while the bar is squeezed down
vertically it has different degrees of freedom of expan-
sion in all horizontal directions. It is quite conceiv-
able that this mechanical action should make the elastic
properties in the direction in which the bar was com-
pressed different from those in the direction in which
it expanded. The bar would then be said to be not
isotropic.
Now, fortunately, most of the mechanical operations
in producing iron and steel are effected at temperatures
at which the material is almost perfectly plastic, and
they do not produce such great differences in the elastic
properties in different directions as similar operations
at lower temperatures would do. We may for most
purposes treat ordinary materials as isotropic, always
remembering that the assumption can only be approxi-
mate. The extent to which there are variations of
isotropy in ordinary materials has hardly been experi-
mentally examined.
9. Normal and Tangential Components of Stress.—
Shearing Stress.-Suppose a simple stress, P, applied
parallel to the axis of a bar, so that the distribution on
cross-sections perpendicular to the axis is uniform. If
26
TESTING OF MATERIALS OF CONSTRUCTION
a is the area of such a cross-section the intensity of
stress is
a
p
(6).
To find the stresses on an oblique section, a b, it is con-
venient to resolve P into normal and tangential compo-
nents. Let be the
angle between the nor-
mal to the section and
the axis of the bar, then
N = P cos 0 and T =
P sin 0. As the tan-
gential stress T tends
to cause sliding at the
section, it is called the
shearing stress, while
the normal component is often termed the direct stress.
The area of the oblique section a b is a sec 0. Hence
the intensities of normal and tangential stress on a bare
(7).
(8).
N
π
P
2:
T
FIG. 4.
Normal stress = Pn =
Tangential stress = p,
α
Р
α


-0 for 0, we get
P cos 0
a sec o
b
P sin 0
a sec o
For an oblique section at right angles to a b, substituting
p cos 20.
= p sin 0 cos 0.
Normal stress = p'₂ = p sin 2 0.
Tangential stress = p = p sin cos 0.
0
PROPERTIES OF BODIES ACTED ON BY STRESSES 27
So that the intensity of tangential stress is the same
on two oblique sections at right angles. The shearing
stress is greatest and = p for planes at 45° with the
1
2
axis.
Now let us consider a case in which the stresses can
be reduced to simple shearing stresses.
angle A B C D represent a parallel-
Let the rect-
opiped, the stresses on which can
be reduced to tangential stresses
on two pairs of the faces.
it can be shown that the stresses
on the faces at right angles are
equal. For the lengths of the sides represent the areas
of the faces, so that the total stresses on the faces are
P₂ × A B and p₁ × AD. Equating the moments of the
P1
two couples, p₂ × AB × BC = î₁ × AD × A B, that
21
is, P2= P1.
2
Let Fig. 6 represent a cube of unit length of side,
subjected to equal shearing stresses
on two pairs of faces at right angles A
in directions parallel to the third
pair of faces. The effect of these s
stresses will be to distort the square
face of the cube into a rhombus,
each angle being altered by an
amount 0. Assuming Hooke's law,
8 = C 0
A
Pi
Then P
D
D
FIG. 5.
P2
FIG. 6.
S▾
.S
B
C
B

C

(9),
where C is a modulus of elasticity of a somewhat dif-
ferent kind from that already described. For Young's
28 TESTING OF MATERIALS OF CONSTRUCTION
D
modulus applies to a case where there is a change both
of volume and figure. In this case there is a distortion
of shape only. C is called the modulus of transverse
elasticity or coefficient of rigidity.
FIG. 7.
1552
The tangential stresses here assumed as acting on
the faces of the cube are equivalent to a tension and
compression along its dia-
gonals. For obviously half
the stresses on each adjacent
pair of sides is equivalent to a
stress S✓2 along a dia-
gonal, and the shearing stress.
on the four faces is therefore
equivalent to a tension along
one diagonal and an equal thrust along the other.
But the section of the cube along the diagonals is 2.
Hence the intensity of the tension and thrust is p= s.
4552
い
​The case is, therefore, identical with that previously
treated, in which a tension and thrust at right angles
were superposed. In that case it was found that
0 = 2λ
-S52
st
S

Therefore
S
یں
S
\\-S√2
7
Ө
(10).
But by the definition of the coefficient of rigidity,
remembering that the shearing stresses and direct
stresses to which they are equivalent are equal,
Ꮯ Ꮎ .
P
E' ( 1 + 1/12).
m2 + 1
m
2 p
E
PROPERTIES OF BODIES ACTED ON BY STRESSES
29
Hence
с
c = ?
พ
Ꮎ
For metals in which m = 4,
2
C = E.
=
124
mE
m + I
K = /
V
10. Coefficient of Elasticity of Volume.-When a
body is acted on by a stress uniform all round, like a
fluid pressure, its volume is increased or diminished.
Let v be the change of volume reckoned per cubic unit
of the body under a stress, P, per sq. unit of area.
Then
(12)
is called the coefficient of elasticity of volume. All
systems of stress acting on a body may be resolved into
distorting or shearing stresses, which do not alter the
volume, and a fluid stress.
P-P
. (11).
The relation between K and the other constants is
easily found. For suppose a cube of unit length of side
acted on by a longitudinal stress,
3 p, on two opposite faces. It
will in no way alter the condi-
tion of stress to introduce stresses,
+ p and -p, on each of the
remaining four faces. Considering
the stress shown in the figure, a
+p on each horizontal face and
a -p on opposite vertical faces
together form a shearing or distorting stress; simi-
FIG. 8.
iP
ip
tp

be
to
tp
JL L
30 TESTING OF MATERIALS OF CONSTRUCTION
larly, another + p on each horizontal face, and a p
on the two other vertical faces. These produce no
change of volume. There remains, therefore, a stress
+p on every face, together constituting a fluid stress
of intensity, p.
But it has already been shown that a longitudinal
stress, 3p, would produce a change of volume equal
to 3(2 – 22). Therefore, discarding the distorting
stresses, a simple longitudinal stress, 3 p, produces the
same change of volume as a fluid stress, p. Hence-
M
K=
or since
But
E
K
ทาว
K
=
2
(2-2)
2
λ = p/E
Em
3m 6
S
2C (m + 1)
በጊ
2C (m + 1)
3m 6
mandag g
6K + 2C
3K-20
;
A
(13).
According to the view generally adopted in this country
C and K are the fundamental coefficients in the theory
of elasticity of isotropic bodies.
11. Examples of the Value of Constants.-The follow-
ing short table gives values of the constants discussed
above in tons per square inch :-
-
PROPERTIES OF BODIES ACTED ON BY STRESSES 31
Water
Flint glass
Brass
Steel
Wrought iron
Cast iron
Copper
COEFFICIENTS OF ELASTICITY.
Volume
elasticity
K
Simple
rigidity
C
141
2,204 to 2,636 1,492 to 1,524
6,363 to 6,890 2,185 to 2,560
11,690
5,200
9,245
4,883
6,123
3,378
10,690
2,794 to 2,839
splat
Ma
Young's
modulus
E
3,645 to 3,829
6,020 to 7,112
12,820 to 15,560
12,470
8,567
7,442 to 7,836
B
12. Torsion. When a prismatic bar is fixed at one
end and a couple is applied at the other end, in a plane
at right angles to the axis of the bar, it suffers a de-
formation termed torsion, which gives rise to simple
shearing stresses in the bar. The theory of torsion of
prismatic bars in general
is difficult. It is sufficient
for testing purposes to con-
sider a cylindrical bar, the
theory of which is simple.
FIG. 9.
In such a bar A A, B B,
each plane transverse sec-
tion remains plane after
twisting and its dimensions
are unaltered. The dis-
tance between two trans-
verse sections is un-
changed, so that the length
of the bar is unaltered. A
longitudinal strip on the surface of the bar initially
parallel to the axis becomes a helix in the twisted bar.
b
el
ロ
​ні у
Reciprocal of
Poisson's Ratio
*-10
B
a
4.1
3.0
3.25
3.6
3.7
2.6
1
}
In

1
J

32
TESTING OF MATERIALS OF CONSTRUCTION
Any small square on the surface of the bar becomes a
rhombus, ef gh. This deformation corresponds to that
produced by equal shearing forces on the opposite sides
of the square e f g h, or to stresses of tension and com-
pression of equal intensity with the shearing stresses
along the diagonals of e f g h-that is, at 45° with the
axis of the bar.
Hence the general condition of stress in the bar is
that there are shearing stresses on transverse sections
and on radial longitudinal
sections. Or there are ten-
sions and compressions
along helixes drawn on
concentric cylindrical sec-
tions at an inclination of
45° with the axis.
Let be the angle
through which the bar is twisted, per unit of length,
That is, if a b is the arc
surface of the bar at the
expressed in circular measure.
through which a point on the
radius ¹ turns, then--
2
e
FIG. 10.

"V
π
180
dating
Τι
Ө
a b
2.11
Mag
[If n is the torsion angle per unit length of bar in
degrees,
n.]
Consider the slice between two transverse sections
at a distance dl. One twists relatively to the other
through an angle fofdl. A square, ef gh, on the
PROPERTIES OF BODIES ACTED ON BY STRESSES 33
surface of the slice becomes a rhombus, ef' g' h. Now
the arc ff'
=rdl. For any intermediate cylindrical
section of the slice at radius r, the corresponding de-
formation is kk' rol. The angle of deforination
of the rhombus on the surface of the bar is ff' /eƒ = 1
= 1; and the corresponding angle of deformation of
a rhombus on the cylinder of a radius » is $ = ‚· 6.
π5
Now consider the stress on a ring between radii
and r + dr at the end of the slice. The area of the
ring is 2 dr. If f is the stress per unit of area, the
whole stress on the ring is 2 fr dr, and the moment
of this stress about the axis of the bar is 2 fr² dr.
Hence the whole moment of stress on the end of the
bar, which must be equal to the external twisting
moment, must be—
π
and at radius r
=
But in shearing, the relation of stress and strain gives,
at the surface of the bar,
Hence-
T = 2 = √ ƒ r² dr.
75
Å
ƒ₁ = C &₁ = Cr, 0,
1
ƒ = C & = C » 0.
T = 2 π CO √ √³ dr
= 1 π Cor₁₂+
O
1
(14).
Or putting in fi the shearing stress at the surface of
the bar,
3
1
T = { # fir³·
(15).
D
34
TESTING OF MATERIALS OF CONSTRUCTION
When the section of the bar is not circular, the
determination of the relation of the moment of torsion,
greatest stress, and angle of twist is difficult. The
greatest stress is in the cases most likely to occur at
those points of the boundary of the section which are
nearest the centre. The following are the equations
obtained by St. Venant :-
Let A be the area of the section.
I the polar moment of inertia of the section
relatively to its centre of gravity.
where
I' the moment of inertia relatively to an axis
through the centre of gravity, and coinciding
with its greater diameter.
a, b, the greater and less semi-diameters if the
section is elliptical, the greater and less half-
lengths of the sides if rectangular.
fi the greatest stress.
Then
Ө
fr
k
TI
CA¹
T
γ
I'
b
k = 42 for elliptical sections,
(15α),
7 = 0.5 for elliptical sections,
= 0.75 for rectangular sections.
(156),
40 approximately for rectangular sections;
PROPERTIES OF BODIES ACTED ON BY STRESSES
35
It may be pointed out that experiments on torsion,
in which the stresses are within the elastic limit, afford
the easiest means of determining the coefficient of trans-
verse elasticity C.
13. Determination of C by Torsional Vibrations.-
When the value of C is required for thin cylindrical
bars or wires the method of torsional vibrations may
be used. It can be shown that torsional vibrations of
a wire fixed above and supporting a weight are nearly
isochronous, and that the time of a single oscillation
is given by the relation
t = π
T
π
2
с
I
where t is the time in seconds, I the moment of inertia
of the vibrating system about its axis of rotation, and
T the twisting couple when 16 = 1. Hence, since
с
י'
T
2:3
ין
2 π I l
ť² jot
(16).
14. Bending Stress.-A bar is subjected to simple
plane bending when the following conditions are satis-
fied: (1) the unstrained bar is straight, and has a
longitudinal plane of symmetry; (2) the bending
forces are applied in that plane normally to the axis.
These conditions are easy to obtain, and the deforma-
tion which occurs is one of the easiest to observe.
Hence materials are often tested by bending.
D 2
36 TESTING OF MATERIALS OF CONSTRUCTION
The nature of the stresses to which the bending
forces give rise is not difficult to trace. Suppose a
prismatic bar (Fig. 11),
fixed at one end and
loaded with W at the
other. If the bar were
divided at a b, equilibrium
might be re-established
by introducing a vertical
force-S, equal to W, and
a pair of equal horizontal forces F,-F, forming a tension
and thrust, and having a moment Fh equal and opposite
to the moment WI of the couple formed by W and S.
This illustration serves to show that at a cross-
section of a bent bar, normal to the axis, the molecular
forces must in general consist of a shearing stress cor-
responding to S, and of direct stresses of tension and
compression having resultants corresponding to F F.
The existence of these direct tensions and compres-
sions at the upper and lower edges of the bar is easily
shown, thus:-
F+
F
FIG. 11.

Thoma
Sigm
2
ㅈ
​W
FIG. 12.


е
Suppose a rectangular bar of wood to have thin
pieces of steel fitted in grooves in its top and bottom
PROPERTIES OF BODIES ACTED ON BY STRESSES 37
surfaces. Let these be fixed to the bar at one end, but
otherwise free to slide longitudinally. If the bar is
now bent it will be found that the bar has shortened a
distance c on one side and lengthened a distance e on
the other, as shown by the projection or retraction of
the thin steel plates. Further, the compression c will
be equal to the extension e if the bar is symmetrical
above and below its axis.
C
The following table gives measurements made in
this way by M. Morin and M. Tresca on a deal bar,
8 inches deep, 5 inches wide, and 152 inches long,
between supports. It was loaded in the middle.

Load in lbs.
440
880
1,320
1,760
2,204
2,644
Bar reversed
Again reversed
Deflection in ins.
Total
•1056
•2160
•3840
*4352
•5360
*6512
•
per 220 lbs.
*0528
*0544
*0640
*0472
*0524
*0576
Means
""
""
Compression,
per 220 lbs.
с
·01036
•01020
·00992
·00968
•01000
*00984
•01000
*00944
•01012
Extension,
per 220 lbs.
e
·01020
*00992
*00972
·00928
*00976
•00984
·00980
·00976
•01048
These observations suggest a conception of the
action which occurs in bending, which proves to be
exact enough for nearly all purposes. Suppose that
plane parallel transverse sections of the unstrained
bar remain plane after bending, and then radiate to
the axis of curvature. It follows, since the bar is
lengthened on one side and shortened on the other,
that at some intermediate surface, termed the neutral
38
TESTING OF MATERIALS OF CONSTRUCTION
surface, the material is neither lengthened nor shortened.
Further, for other parts of the material, the elongation
or shortening (parallel to the longitudinal axis) will be
proportional to the distance from the neutral surface.
The stresses will therefore also be proportional to that
distance.
15. Generally, as has been shown, there is a shear-
ing force at the transverse sections of the bar, and the

p
K
-
a
*
P
FIG. 13.
ed
ab
FIG. 14.
1
り
​D
2π (p + ?)
275
P
P

moment of the bending forces varies along the bar. In
one particular case the action is simpler (Fig. 13).
Suppose equal couples of moment Pa applied at the
ends of the bar, then between A and B the bending
moment is uniform and the curvature circular, Let
P
be the radius of curvature measured to the neutral
surface a b. Then a fibre of the length a b before cur-
vature has the length c d after bending. But
рту
P
a
V
PROPERTIES OF BODIES ACTED ON BY STRESSES 39
and the extension (or compression, if y is negative) is
/p per unit of length.
Hence, if ƒ is the stress at a distance y from the
neutral surface,
= E
EY
(17).
P
On an element of area a the stress is fa, and the
total stress on the whole section of the bar is, therefore,
Σ (fa) = Σ (E ¼ a).
Y
P
f
But, since the pressures and tensions across the section
form a couple,
(E 2 a) = 0 ;
P
Σ (Ε
or, since E/p is constant, y a = 0.
Σ
This equation is only true if the distances y are
measured from a line passing through the centre of
gravity of the section. Hence the neutral surface of
the bar passes through its longitudinal axis of figure.
The moment of the stress fa about the neutral axis
of the section (intersection of neutral surface with the
section) is fay=
Ey2a The total moment of the couple
P
formed by the tensions and pressures at the section is-
2
Σ (Ex² a)
or
E
P
Σ
a y².
Now, the quantity a y² is known as the moment of
inertia, or second moment of the section, and is usually
denoted by I. Hence, putting M for the moment of
40
TESTING OF MATERIALS OF CONSTRUCTION
the forces on one side of the section, which is equal to
the moment of the molecular forces at the section,
M
(18),
which expresses the relation between the bending
moment and the curvature of the bar. Let f and f be
the tension and pressure at distances y, and y, from the
neutral surface.
Then
f
E
M
P
EI
P
____
Y₁r fo
fe
fi
I
E
(19).
Generally it is necessary to consider the greatest
tension and pressure at any point of the cross-section.
Then
Yt and y must be taken as the distances of the
parts of the section furthest from its neutral axis. It
is convenient to call the quantities I/y, I/y, the moduli
of the section for tension and compression. If Z, Z.
are put for these moduli,
M = f₁ Z₁ = fc Zc
Y
P
fo
I
Y
Yo
(20),
which gives the relation of the bending moment to the
stresses induced.
If the bending moment varies along the beam the
radius of curvature also varies. Then Eq. 18 gives p
P
for the section at which the bending moment is M. If
I varies, then Eq. 18 gives different values of M or
at different sections.
f
16. Deflection of a Beam.--Let a be a point on the
PROPERTIES OF BODIES ACTED ON BY STRESSES 41
neutral axis, and b a neighbouring point; let x and y
be co-ordinates of a, c the centre of curvature, and a c
= p. Then a cbd is equal to the angle between
||
0,
!
Ө
0
the tangents to the neutral surface at a
increment of slope of the beam. Let ab
and, since ds = de very nearly,
=
Y
FIG. 15.
do
dx
Ꮯ
ido

1
Р
=fdx=/da
(21),
which can be integrated when M and I are expressed
in terms of x.
Further, if the deflection of O below a = y, dy/dx
(22),
which again is integrable.
iy
M
EI
=
= So dx.
and b, or the
ds =
d s = p d 4,
}
!
42
17. Application to the Simplest Cases occurring in
Testing. The value of I and Z for the simplest forms
of section is as follows:-
TESTING OF MATERIALS OF CONSTRUCTION
B
H
h
S
S
B
050
Hollow rectangle, or I,
with equal flanges
1
h H
I
يلا
Area, A.
b h
Π
شمار ہیں
A4
d²
BH-bh
Moment of
Inertia, I.
1
12
b h³
1
12
π
64
$1
d¹
B H³ -- b h³
12
I = 0.126 A h²,
Z = 0.2525 A h.
Modulus of
Section, Z.
1
10
6
=
·b h²
1
6
دری
Τ
32
·0982 d³
d³
BH³-bh3
6 H
For irregular sections, such as rail sections, the area
and moment of inertia must be determined by well-
known graphic methods. But the following approxi-
mation is suitable for ordinary rails.
Let A be the area of section, h the height of the
rail. Then
PROPERTIES OF BODIES ACTED ON BY STRESSES 43
The greatest bending moment for the simplest
modes of loading is as follows :--
I. Beams encastré at one end, length 7.
Load W at the free end I from support-
M at support W l.
Load w per unit of length uniformly distributed-
M at support 1/12/12 20
w 12.
II. Beams supported at each end, span l.
Load W in centre-
1 W 7.
4
M at centre
Load w per unit of length uniformly distributed—
M at centre
// w 12.
The greatest longitudinal tension or compression for
a given bending moment and section is-
Rectangular section f
Circular section
I section
11
б
11
1 W 73
3 EI
6 M
bh2.
10.2 M
d³
3
The greatest deflection & is as follows for beams of
uniform section :
6 HM
BH³ - bh³°
3
I. Beam encastré at one end, length 7.
Loaded at free end with W-
at the free end.
44
TESTING OF MATERIALS OF CONSTRUCTION
Loaded uniformly with w per limit of length-
าย
б
1 w 14
8 EI
II. Beam supported at each end, span /.
Loaded at the centre with W
8
at the free end.
W13
48 EI
at centre.
Uniformly loaded with w per unit of length--
5 w 14
384 EI
E
at centre.
If there is a concentrated and distributed load, the
deflections due to each may be added.
-
18.-Determination of Young's Modulus by Experi-
ments on Bending.-If a uniform prismatic bar is en-
castré at one end and loaded at the other with a weight
W, and the deflection è is measured,
E
1 W 73
381
(23).
sup-
Similarly, if a prismatic beam of uniform section is
ported at the ends and loaded at the centre with W,
(24).
It is assumed, of course, that the stresses do not
exceed the elastic limit, and that the observations are
repeated often enough and the measurements sufficiently
delicate to give trustworthy values of the deflection.
W 73
4881
45
CHAPTER II.
PLASTIC PROPERTIES OF MATERIALS.
19. Plasticity in materials has long been recognised,
and the terms malleable (capable of being hammered
into sheets), ductile (capable of being drawn into wire),
plastic (capable of being moulded), have been used with
more or less clearness to denote the property of under-
going an indefinitely large deformation and retaining it
permanently. The characteristic of plasticity is not the
largeness of the deformation but its permanence when
the stress is removed. Cork may be compressed to
one-eighth of its volume by a fluid stress, but it recovers
its original volume again if the stress is removed, so
much so that it has been proposed to use cork in gun
compressors to absorb the force of recoil and restore
it again. Cork is compressible in volume, not plastic.
Indiarubber can be extended to eight times its original
length with little change of volume, but it recovers its
figure when the tension is relaxed. It has a long range
of somewhat imperfect elasticity. But iron at welding
heat takes any figure given to it in the rolls or under
the hammer and retains it. It is almost perfectly plastic.
In a paper by M. Henri Tresca, who first studied
scientifically and carefully the plastic properties of
46
TESTING OF MATERIALS OF CONSTRUCTION
solids, there is a passage which precisely indicates the
relation of the phenomena of plasticity to those observed
in ordinary testing :-¹
1
'For all bodies two distinct periods are recognised :
the period of perfect elasticity, which corresponds to
variations of length proportional to the forces applied;
and the period of imperfect elasticity, during which, on
the contrary, the changes of dimension increase more
rapidly than the forces producing them. If the second
phase of deformation be alone considered, it is easily
understood that it tends towards an ultimate condition
in which a given force, sufficiently great, would continue
to produce deformation, so to say, without limit-as
may be observed in the process of drawing lead wire.
This particular condition, in which the deformation is
indefinitely augmented under the operation of a suffi-
ciently great force, constitutes in fact the geometrical
definition of a third period, which has been designated
by the author as the period of fluidity. The period of
fluidity is more extended for plastic substances; it is
more restricted, and will even disappear altogether, for
some vitreous or brittle substances. But it is perfectly
developed and extremely extended in the case of clays
and of the most malleable metals.'
M. Tresca observed in early experiments with lead
G
1 Proc. Inst. of Mechanical Engineers, 1878, 'The Flow of Solids,' by
M. H. Tresca. See also a paper in the same Proceedings in 1876. Also
Cours de Mécanique Appliquée, professé à l'École Centrale, by H. Tresca.
Also numerous Mémoires sur l'Ecoulement des Solides in the Comptes
Rendus.
PLASTIC PROPERTIES OF MATERIALS
47
and similar plastic metals that the large plastic defor-
mation was unaccompanied by any sensible change of
density. Assuming a deformation without change of
volume, M. Tresca has chiefly studied the geometrical
conditions of the phenomena of plasticity. There is
another feature of plastic deformation, however, and
that is the dependence of the deformation on time.
Even within the elastic limit there is an internal mole-
cular friction or viscosity resisting deformation of shape,
and greater as the rate of deformation is greater. But
the time influence is very much more marked in plastic
deformation. Under a stress producing plasticity the
deformation gradually increases, either indefinitely or at
a diminishing rate, as the time during which the stress
acts is indefinitely prolonged.'
The following simple cases of nearly pure plastic
deformation, selected chiefly from M. Tresca's Memoirs,
will serve to indicate the geometrical laws of the defor-
mation.
20. Suppose a cylindrical block of plastic substance
supported on a die-block and perforated by a punch.
It will be found that the height of
the punching or wad (Fig. 16) is in
general much less than that of the
FIG. 16.
block. Thus with a block 10 c.m.

H
↓
h
止
​high, through which a hole, 2 c.m.
diameter was punched, the wad was only 3 c.m. high.
1 See the article on Elasticity' in the Encyclopædia Britannica, by
Sir W. Thomson, F R.S.
48 TESTING OF MATERIALS OF CONSTRUCTION
FIG. 17.
A precise determination showed that there was no
increase of density in the wad. Consequently during
punching seven-tenths of the metal must have flowed
laterally into the block. A partially-
punched nut (Fig. 17) showed a wad
having a thickness visibly less than the
penetration of the punch. Some super-
posed discs of lead punched similarly and then divided
showed the appearance sketched in Fig. 18. The wad,
FIG. 18.
like the original block, con-
sisted of a series of discs,
the lowest being nearly of
the thickness of the original
discs and the higher ones
thinner. Of the metal
forced laterally, therefore,
the higher layers furnished
the larger part. What hap-
pens in punching thick blocks is therefore now
obvious. The metal under the punch becomes plastic
and flows, till the remaining metal is so thinned that its
resistance to shearing is less than the pressure on the
punch.
21. Formation of a Jet by Plastic Flow.-Suppose
a series of lead discs are placed in a strong cylinder
(Fig. 19) and subjected to pressure in an hydraulic
press. If the pressure exceed a certain limit, and if there
is an orifice in the bottom of the cylinder, the lead will
flow like a liquid, forming a jet exhibiting contraction.



PLASTIC PROPERTIES OF MATERIALS
49
Each disc originally superposed in the box contributes
to form part of the jet. Let the
thickness of the layers originally
in the box be H, and let this be
diminished after flow to h, while
the jet attains a length ; let R
be the radius of the box, and r that
π
R² (H−1) = = 12 1
1
H-h
R2
222
F
H
| h
of the jet; then from the con-
stancy of density of the lead, we obtain the equation—
с
a
C
FIG. 19.

Concentric Contraction of Central Cylinder.-Imagine
in the block a cylinder of radius → (Fig. 20) forming
a prolongation of the jet, so
that the lead in the chamber
FIG. 20.
۔ ہم
|-
1.
consists of an annulus of radii R
and r,
and a cylinder of radius
When the thickness of the
metal in the chamber diminishes
by a c = dh, the material forced
out of the annulus can es-
cape neither towards the piston
nor towards the sides of the
chamber. It must necessarily
flow into the space occupied by the central cylinder.
From symmetry that cylinder will remain a cylinder, "
diminishing to r-dr. Equating the volume forced
I
I
}
-
-
T
;--p-
-R
d
-
E
(1).
r
16
¿

→

50
TESTING OF MATERIALS OF CONSTRUCTION
out of the annulus to the diminution of volume of the
central cylinder--
vend
π (R² −7·2) d h = 2 hr dr,
75
dh
h
(2).
Proportional Contraction of Cylinders forming the
Central Cylinder.-Let Fig. 20 represent in plan a sec-
tion of the central cylinder. When that cylinder changes
radius from to r-dr, from matter forced in from the
external annulus, any other cylindrical space of radius
must also diminish in radius. It is natural to sup-
pose that the areas diminish proportionally, so that---
Integrating,
2 r dr
R2-2.2
2 πrdr_ 2 πpdp
To giz
πρά
dr
グ
​(3).
Transformation of Central Cylinder.--Let p be now
the radius of the cylinder which was initially of
radius 7.
From (2)
Replacing d r from (3),
dh
h
log h
d p
Р
dh
2rdr
h R2-72
27.2
R2-29
27.2
R2-7.2
d
P
P.
log p+c.
PLASTIC PROPERTIES OF MATERIALS
51
Let H, as in (1), be the initial height of the layers
in the chamber.
For h = H, pr.
Then,-
log H
Eliminating c,
log
h
H
P
"
27.2
R2-7.2
2.2
R2 — p²
(1/4)
A
C
log r+c.
~
R2
(4).
Which gives the radius p of the portion of the central
cylinder initially of radius r after any amount of flow
into the jet.
If A B (Fig. 21) is the original surface of the lead,
CD the surface after
ā
9
log?
1'
2 r
the flow of the jet
cdgh, then the matter
initially occupying the
central cylinder abcd
will be found occupy-
ing the space ef gh, ef
being the diameter to
which the original cen-
tral cylinder is now
reduced. Also klis
the value of when so
P
much of the jet was
formed that kl was at c d, and Ok = λ was then the
length of the jet.
J
e
ir
1
FIG. 21.
I
f
h
d
D
B

I
h
H
1
I
1
1
Τ
E 2
52
TESTING OF MATERIALS OF CONSTRUCTION
Now, in the equation
R
t = (44) "
2' H
اد
р
let p be the radius
length of the jet is l.
h = H ·
W
22
of the central cylinder when the
But from (1)
1.2
R2
when 72 R2 72, or r =
=
–
*
?= (1 - 1/1/11)
R2 H
ጥ
of the second degree. If r =
R2
G
(5),
which is the equation to the curve fh, p being the
abcissa when the ordinate measured above O X is l.
If that
pi
2.2
The curve varies with the value of
2
.
R² - 7.2°
quantity is greater than 2 the curve may be regarded as
a parabola of a higher degree.
R
√2
If it is equal to 2,
the curve is a parabola
R
√3
27.2
the curve reduces
to a straight line.
M. Tresca has experimentally verified the law; the
verification proved entirely satisfactory.
22. Pressure of Fluidity.-These experiments show
that a ductile body is deformed when the pressure
exceeds a certain amount according to geometric laws,
and permanently, so that there is no indication of
elasticity or tendency to return to the primitive shape.
PLASTIC PROPERTIES OF MATERIALS
53
M. Tresca designates by the term 'pressure of fluidity'
the stress necessary to induce this state.
23. Application to the case of Prisms subjected to
Tension or Compression.-M. Tresca perceived perfectly
well that, in testing, a bar passed from the elastic state
through an imperfectly plastic state to an almost per-
fectly plastic condition, but he has not investigated the
phenomena which occur in testing. There is, however,
a general relation deducible on the assumption of a
condition of perfect plasticity which will be useful
hereafter.
Suppose that in the deformation of a plastic bar the
volume does not change. Let be the initial length
7
and d the initial diameter of a bar which, when elongated
plastically, has the length 1 + λ and the diameter d − ò.
From the constancy of volume we get-¹
1
Hence,
75
2
I d² l = = ( 1 − s)² (1 + x)
4
4
4
2
7.
(1² = ³)² = 1 = x
(1-3)
+
Now, the contraction of area is-
K
7
I d² - (d = 8)² } = = d² + x
-
4
4 ι λ
contraction of area
initial area
So that for a perfectly plastic material the percentage
1 This deduction was given in the Engineer, May, 1885.
2
1+ λ
54 TESTING OF MATERIALS OF CONSTRUCTION
of contraction of area is not proportional to the per-
centage of elongation calculated on the original length
of the bar, but to the percentage of elongation calculated
on the stretched length of the bar.
Now, during plastic elongation the intensity of the
stress remains constant. Hence, the initial load on the
bar when the plastic condition is reached is, if p is the
pressure of fluidity—
P₁
Hence,
π
4
d² p.
Similarly, when the elongation is λ,
75
2
P = (d — 8)² p.
4
2
Р
P₁ = (d¹² = ³)² = 1/4 x
(1-2) 1+
1
the load diminishing as the bar stretches. It will be
seen that this phenomenon occurs in the last stage of a
tensile test.
If the stress is compressive,
dilatation of area (d + d)²
original area
d²
1
Τηλ
||
-
P
P₁'
the load increasing as the prism shortens, as occurs in
crushing short prisms.
24. Work done in Plastic Deformation.-Consider
the case of a prism which shortens a length da while
PLASTIC PROPERTIES OF MATERIALS
55
the load increases from P to P + d P. The work done
in compression is P da. But
But P₁
prism,
P d λ = P₁ l
Hence the work in compression from an original length
I to a length 1-2 is-
W = f. P₁ /
αλ
レーズ
​αλ
1 - λ
- P₁l log. T
W = p V logε ī
ι
レーズ
​π
d² p, and, putting V for the volume of the
4
Z
1-%
56
TESTING OF MATERIALS OF CONSTRUCTION
Chill
25. Suppose a cylindrical bar of uniform diameter
placed in a testing machine, and the load gradually
increased while measurements are made of the length
of a marked portion of the bar. For every value of
the stress there will be a corresponding value of the
strain. The strains may be plotted as abcissæ and
the stresses as ordinates, and points will be obtained
on a curve giving the rela-
tion of stress and strain
for the whole test. This
may be called the stress-
strain curve for the bar.
For a perfectly elastic.
bar the stresses are pro-
portional to the strains.
Hence the curve is a
straight line, such as AOB.
F
By setting off compressions to the left, extensions to
the right, thrusts downward and tensions upward, a
continuous line is obtained representing the relation of
COMPRESSIONS
L
FIG. 22.
TENSIONS
10
B
C
STRESS-STRAIN DIAGRAMS.
0
CHAPTER III.

5
E
EXTENSIONS
10
A THRUSTS
D
STRESS-STRAIN DIAGRAMS
57
stress and strain for the whole range of perfect elasticity
of the bar.
P₁ = P
For a perfectly plastic bar, the load would have to
attain some value, POC or -POE, these being
the so-called 'pressures of fluidity,' before plastic de-
formation commenced. In a bar in compression the
section increases as it shortens. Hence, since the pres-
sure per unit of area in a plastic material is constant,
the load must increase. In a bar in tension the section
contracts as the har elongates, and hence the load must
be diminished as the elongation increases, if it is to be
kept in equilibrium with the resistance of the bar.
Hence curves giving
the relation of stress.
and strain during
plastic deformation
are curves such as
CD or E F.
It has been shown
that the relation of
stress and strain dur-
ing plastic deforma-
tion is-
V
7
1 ± 2
where P, is the load
1
which causes a de-
G
I
1
1
!
1
1
1
}
H
2-.
F
о
FIG. 23.
E
D
X
formation ±a in a length 7. This shows that the
curves CD, EF are parts of hyperbolas having OX
58 TESTING OF MATERIALS OF CONSTRUCTION
and GO' H as asymptotes, where G O' II is at a dis-
tance from COE.¹
Before examining some stress-strain diagrams for
different materials it may be pointed out that quite
similar diagrams are obtained by plotting moments
of torsion and angles of twist, or bending moments
and deflections.
26. Stress-strain Curves for a Brittle Material.-A
brittle material may be defined as a material which
breaks without any considerable plastic deformation.
Cast metals may be taken as examples of materials
approaching to this description.
The right-hand curve in Fig. 24 shows the stress-
strain diagram from Hodgkinson's experiments on
long cast-iron bars. No part of the curve, except a
short portion, perhaps, near the origin, is quite
straight. Materials like cast iron take a sensible
though small set even with comparatively small loads,
and the set increases regularly with the loads. Such
materials have, strictly speaking, no elastic limit when
first subjected to stress. Further, in materials like cast
iron or steel castings the bar breaks before any great
plasticity is exhibited. The curve runs to the break-
ing-points in tension and pressure without any great or
significant change of curvature.
¹ An account of stress and strain diagrams, indicating the different
character of the elastic and plastic portions of the curve, was given by
the author in the Engineer for May 22, 1885, and also in a lecture at
the Society of Arts on Autographic Diagrams, February, 1886.
STRESS-STRAIN DIAGRAMS
59
0.002
Load
in
tons
per
sq. in
30
29
28
0-001
Compressions.
Tension.
27
65
~~~~~
26
25
24
23
22
21
19
18
17
16
5432 -
15
14
13
12
496665&M ~
8
7
3
2
1
23456789-23456
ན
12
13
14
15
16
∞ a
18
19
20
21
~~~
22
23
24
25
Held Point -26
0.001
Compression
FIG. 24.

Field Point
·003 ·002 ·001
Compressions
0.002 0.003
Extensions.
7
5
3
רא
Tons
per sq. inch
ہے۔
3
4
5
6
7
-8
9
10
-
+2
13
15
HE
17
18
19
.002
Extensions
20
21
22
23
24
·001
Stress-strain Curves for Cast Iron and Mild Steel.
Bruke
60 TESTING OF MATERIALS OF CONSTRUCTION
The following short table gives a comparison of
the extensions and compressions for different loads :
Load
in tons
per
sq. in.
123420
6
7
9
12
Extension per
unit length
·000166
⚫000347
•000544
*000765
·001021
⚫001338
Compression per
unit length
·000174
·000351
·000531
·000714
·000899
·001090
·00128
·00167
*00229
Increase of Exten-
sion per ton per
unit length
·000166
•000181
·000197
⚫000221
⚫000256
⚫000317
Increase of Com-
pression per ton
per unit length

•000174
·000177
⚫000180
·000183
⚫000185
·000191
·000190
·000195
⚫000207
27. Elastic Stress-strain Curve.-Most rolled materials
are almost perfectly elastic, both for tension and com-
pression, for a considerable range of stress. The left-
hand curve in Fig. 24 gives the stress-strain curves,
up to points just beyond the elastic limits in tension
and compression, for two bars of mild steel, tested by
the Committee of Civil Engineers.' The steel was cast
steel suitable for piston rods. The bars were 1 inch
diameter, and the deformation was measured by verniers
in a length of 10 feet.
The numbers given in the following table are taken
from a plotting of the results to a large scale. The
steel broke at 41.85 tons per sq. in. in tension.
It will be noticed that the deformation per ton per
sq. in. is nearly constant and nearly the same for ten-
sion and compression. Hence the results plot nearly
into a continuous straight line. Beyond 26 tons per
¹ Experiments on the Mechanical and other Properties of Steel. By a
Committee of Civil Engineers, 1870.
STRESS-STRAIN DIAGRAMS
61
Stress
in tons
per
sq. in.
sq. in. the elastic limit in tension and compression is
passed, and the deformations quite abruptly become
larger.
7
10
15
20
25
30
Extension per
unit length
Means
⚫00054
•00076
·00112
·00150
·00192
*U0583
Compression per
unit length
⚫00050
⚫00072
·00108
·00146
·00188
STRESSES
TENSION
COMPRESSIONS
Extension per ton
per sq. in. per
unit length
•000077
⚫000076
⚫000075
*000075
•000077
EXTENSIONS
·000076
28. Stress-strain Diagram for Indiarubber.-India-
rubber supplies an example of a solid in which the
deformations are not small compared with the origi-
nal length. It has besides great incompressibility
FIG. 25.
Compression per
ton per sq. in. per
unit length
·000071
·000072
*000072
·000073
·000075
·000073

PRESSURE
The strong line shows the immediate strain. The dotted that after
some minutes.
of volume, so that under considerable alterations of
form its volume is nearly constant. Dr. Winkler has
62
TESTING OF MATERIALS OF CONSTRUCTION
given the following results of experiments on india-
rubber in tension and compression :-
p
is the load in kilograms per sq. cm.
a is the elongation or compression of unit length.
a' is the elongation or compression when the load
has been some time on the bar.
signs refer to compression; the signs to
The
tension :--
P
-0.5
1.0
1.5
2.0
2.5
3.0
Compression
λ
-.036
·076
109
•139
·163
•185
λ'
Ei
-.036
·082
•115
•147
173
•198
P1
2
P
+ 0·5
1.0
p
1.5
2.0
3.0
4.0
5.0
6.0
Tension
1+ λ
7
λ
Fig. 25 shows these results plotted. It will be seen
that the stress-strain curve is without any straight
portion, the elongations increasing faster and the com-
pressions less fast than the stresses. The modulus of
elasticity Ep/a, calculated in the ordinary way, is
therefore extremely variable. The section contracts so
that the volume of the bar remains constant. Then
the real stress in the bar is p₁ = p(1+a). Then the
modulus of elasticity, calculated from the real stress
and the elongation per unit of initial length, is-
M
+ 046
•121
•207
316
•548
•859
1.309
1.794
λ
E + P ;
+ '052
·137
.264
•396
*698
1.135
1.572
2.110
K
STRESS-STRAIN DIAGRAMS
63
and the modulus, calculated from the real stress and the
elongation λ, per unit of stretched length, is--
Load
p
- 3.0
- 2.5
- 2.0
- 1.5
- 1.0
-0.5
0
+0.5
+1.0
+1.5
+2·0
+3·0
The following table gives values of E, E1, and E2.
It will be seen that for a considerable range of stress
E₂ is even more constant than E1, and both are more
constant than E :
2
+ 4·0
+5·0
+6·0
E₂ = P₁
E2
71
Real stress
Pi
2.45
2. 09
1.72
1.34
•92
'48
0
•52
1.12
1.81
2.63
4.64
7.44
11.55
16.76
E₁ (1 + λ)
1
= E₁ + P₁
= E + p (2 + 2).
E
2
p (1 + x)²
λ

16.2
15.3
14.4
13.8
13.2
13.9
10.9
8.3
7.2
6.3
5.5
4.7
3.8
3.4
E1
=E+ P
13.2
12.8
12.4
12.3
12.2
13.4
11.4
9.3
8.7
8.3
8.5
8.7
8.8
9.4
E2
E₁ + Pi
15.6
14.9
14.11
13.6 Mean
13.1 13.7
13.9
11.9
10.4
10.5
10.9
13.1
16.1
20.3
26.2
Mean
11.4
D
29. Stress-strain Curve for Ductile Materials. - In.
soft wrought iron and steel the stress-strain curve has
the form shown in Fig. 26. Between the elastic limits
A and C the curve is a straight line. The parts A B
and CD correspond to a partly plastic condition of the
material in which the larger part of the deformation is
64 TESTING OF MATERIALS OF CONSTRUCTION
▼
E
permanent. In tension a maximum stress is reached
at D, but the deformation can be continued with a
diminishing stress till the bar breaks at some point E.
During the part DE the curve falls very rapidly,
because generally a local
drawing out begins, and
the deformation is confined
to a small portion of the
bar. In the compression
curve A B there is a more
gradual change of curvature,
because nothing like local
deformation occurs. Up to
the points A and C there
is almost immediate equili-
brium between the stress
FIG. 26.
TENSION
COMPRESSIONS O
A
D

EXTENSIONS
PRESSURE
B
and strain. But in the parts A B and C D the deforma-
tion is gradual, and requires time for its completion.
The deformation hardens the material, and at last ceases.
In the part D E probably no definite relation of stress
and strain is reached, and the deformation increases
without limit.
Yield Point, or Breaking-down Point in Tension.-
It is somewhat remarkable that, amongst the ordinary
materials used in construction, a tolerably perfect
straight clastic line is chiefly found in the case of mate-
rials, like wrought iron or rolled steel, which have been
subjected to severe mechanical pressure in manufacture.
For such materials, up to some point A, the line O A is
STRESS-STRAIN DIAGRAMS
65
extremely straight, and the stresses and strains are
almost exactly proportional. Between A and B a
sensible, but slight, curvature appears in the diagram,
and a sensible, though small,
deviation from proportion-
ality begins to appear in the TENSION
FIG. 27.
stresses and strains. Bau-
B
A
D

schinger calls the point A the
limit of proportionality, but
it would be better to call it
the elastic limit. A little
beyond the elastic limit, at
B, there is, for some rolled o
(
or hammered materials, a very singular and marked
jump, or inflection B C in the stress-strain diagram.
This point is very clearly marked in the diagrams
of the Committee of Civil Engineers appointed to
make experiments on steel,¹ and is shown in Fig. 24,
which is a plotting of two of their experiments on
steel. The Committee call this point the yielding
point.' The behaviour of the material at this point
was very accurately described by Bauschinger in
1879,2 and he adopted for it the term 'Streck grenze.'
Bauschinger indicated the very great suddenness of the
increase of extension, lateral contraction, and tempera-
ture. In 1881 Prof. Kennedy, in a Report on Riveted
Joints to the Institute of Mechanical Engineers, called
attention to this peculiarity in rolled steel, and gave to
с
E
1 Experiments on Steel, 1870. 2 Civilingenieur, Bd. xxv. s. 81.
F
66
TESTING OF MATERIALS OF CONSTRUCTION
the point A the name 'breaking-down point.' On the
whole this term seems very suitable, if by breaking
down is understood a breaking down of the primitive
molecular arrangement.
The phenomenon of breaking down is not due to
any action of the testing machine, for it is shown in
diagrams from a machine in which the load is auto-
matically adjusted to the resistance of the bar, and in
machines in which the loading is effected entirely by
hydraulic pressure. Probably the breaking-down point
is a kind of physical record of the condition of constraint
in the bar at the moment of rolling or hammering. Not
that the stress at the breaking-down point is identical
with the stress in rolling, for the temperature conditions
are different in rolling and testing. But still, it is pro-
bable that at the breaking-down point a mechanically
produced condition of aggregation is passed, and the
artificially-created rigidity suddenly gives way.
Beyond the inflection at the breaking-down point
the partly plastic, partly elastic, extension proceeds
regularly, again. But the precise extension for any
load between B and C depends more or less on the
time during which the load acts. During any pause in
this part of the curve the extension increases without
increase of load, and when the load is increased again
the rigidity of the bar is found to be greater than before,
and the curve becomes steeper (Figs. 35, 39). Next
to the breaking-down point the most important point
to observe is the point D, where the maximum load is
STRESS-STRAIN DIAGRAMS
67
10.8
reached. For this point it would be convenient to have
a name, and, by analogy with elastic limit, the term
'plastic limit' may be proposed. This implies, what
seems to be the case, that at the point C the pressure of
fluidity is reached for the part of the bar at which frac-
ture ultimately occurs. It is probably at the point C, i
or very near it, that the local contraction begins which
is so characteristic of the last stage of testing of ductile
materials.
D
30. Form of the Stress-strain Curve at the Yield Point.
The form of the stress-strain curve near the yield
2.5
3
a
a
2.C
FIG. 28.

19/
CO
Extensions in inches.
0-1
13·0
B
12
2
TONS OF
TOTAL PULL
18
15
point is very variable, being greatly affected by small
stress differences and by differences in the time rate of
extension. Further, in most autographic arrangements
12
6
F 2
68
TESTING OF MATERIALS OF CONSTRUCTION
the record of stress is affected, when the specimen is
yielding rapidly, by the inertia of the load. In Professor
Kennedy's autographic apparatus the effect of the inertia
of the load is eliminated, and Fig. 28 gives some auto-
graphic diagrams taken in this apparatus. It is difficult
to believe, however, that the irregular curves near the
yield point are not due to time differences, or perhaps
to small stress differences arising out of the inertia of
the elastic system formed by the test bar and testing
machine. The diagrams are, however, the most satis-
factory autographic diagrams yet obtained.¹
31. Behaviour of a Ductile Material when broken by
Tension; Local Drawing Out, or Local Contraction.-A
bar or plate of ductile material such as soft steel is
placed in the testing machine and subjected to a gradu-
ally increasing stress till it is broken. At first, as the
extensions are small, it is easy to keep the lever of the
testing machine floating with almost any rate of loading.
At the yielding point, however, the stretching suddenly
becomes rapid, and with most testing machines it is not
possible to keep the lever floating. The lever can only
be kept floating if the pumps which work the hydraulic
press are capable of moving the press ram as rapidly as
the rate of increase of stretch. With a single-lever testing
machine the author finds it possible in most cases, but
not always, to just keep the lever floating during the
4
¹ In Professor Kennedy's diagrams the ordinates are curved :—a is a
diagram for a Swedish iron bar; b, Shelton bar iron; c, Swedish iron;
d, Landore rivet steel; e and f, Landore steel plate; g, cast steel; h,
mild-steel bar.
STRESS-STRAIN DIAGRAMS
69
stretching at the yielding point, but to do this it is often
necessary to run the weight back a little to diminish the
stress. When the rapid stretch at the yielding point is
ended, and the bar has again become capable of sup-
porting an additional stress, it is quite easy, in general,
to adjust the rate of loading so that the press just takes
up the stretch, and the lever remains floating almost
without movement. And this continues till the maximum
load is reached. Beyond that point the drawing out of
the specimen at a restricted portion of its length begins,
and the reduction of area is so rapid that the stress
must be diminished. It is here again difficult to keep
always the lever floating. Finally, the bar breaks sud-
denly with a load considerably less than the maximum
load it was sustaining just before the local drawing out
commenced.
Suppose the bar ruled with straight lines at right
angles to the direction of the stress. As the bar
stretches the distance between these lines increases, but,
so far as can be judged, they remain straight and
parallel during the increase of stress till the maximum
load is reached. During the local drawing out the
lines become curved in the part which is drawing out.
The line exactly at the centre of the part which is draw-
ing out, however, remains straight. Professor Kennedy¹
has inferred from this curvature of the lines that the
stress becomes very ununiform on the section of fracture,
being greatest at the centre of the bar. Some slight
1 Proc. Inst. Mech. Eng. 1881, p. 218.
70
TESTING OF MATERIALS OF CONSTRUCTION
variation of stress probably is produced, but the author
doubts if the variation is at all large. In fact, the ex-
tension measured along the curved edges of the bar is
not very different from the extension at the centre, and
if the material is plastic great variation of deformation
is possible with small variation of stress.
-
Fig. 29 is from photographs of a strip of mild-steel
plate taken during the process of testing. A was taken
just when the maximum load was on the bar. No be-
ginning of the drawing out is visible, and the lines
drawn on the bar are still straight, as far as can be ob-
served. Fig. B was taken just after the drawing out
became visible, and when the stress on the bar had been
a little diminished. At the centre of the part drawn
out the line is still accurately straight, but the lines on
each side are curved. Fig. C was taken at the very
moment before fracture. The drawing out is here more
considerable. Fig. D is the bar after fracture.
32. Distribution of Drawing Out along the Bar.-If
a bar is divided into inch lengths before testing, and
these are measured again after the bar is broken, the
plastic extension in each inch length will be determined.
It will be found that the amount of extension is more
or less irregular along the bar. In the inch length in
which local contraction and fracture occur the exten-
sion is very great. On either side it diminishes, at first
rapidly, afterwards more slowly, and is least near the
enlarged ends at which the specimen is held. But there
are irregularities, showing that there are differences of
STRESS-STRAIN DIAGRAMS
71

A
B
FIG. 29.
Drawing out of Mild Steel.
C
W
D


72 TESTING OF MATERIALS OF CONSTRUCTION
plasticity along the bar, and in rare cases two local
contractions form at different parts of the length. It
is possible that some of the irregularities are due to the
fact that the elongation is usually measured on one side
of the bar only. It is desirable that the measurements
should be taken on opposite sides of the test bar and
averaged.
The following table gives some measured values for
different materials :-
ELONGATIONS IN ONE INCH LENGTH OF BAR AT DIFFERENT DISTANCES
FROM THE FRACTURE.
(The elongation in the division in which fracture occurred is indicated in
italic type).
Lead
Brass
Material
↑
Wrought iron;
Angle iron
Channel iron
Rivet iron
Square bar
Flat bar
Steel:
•
Steel plate
Steel axle
Steel tire
1
2
Co
3
Inches along the Bar
4.
4 | 5 | 6
Q
0.18 15 30 17 14 22
0.23 20
7
9 10
16 17 1·01
2030 21 22 24 21 21 21
❤
O
0·05·06 |06|06|·06 |·065| 07 | 08 || 135·08
009 11 08 10 23 141110 10 09
0·17·195 23 51 26 2325 23 23 18
. 0.24 22 22 22 21 27 5050
0 11 16 14 10 10 10
26
10
10 10
19 19 15 15 16
་
070 30 22
0.16 17 21 21 18 17 21 65
0·02-06
0·02 06·08 21 67 22 05 02
11
12
18 17 17'
46
17 13 102
03
03 0608·122
It follows that the ultimate extension, reckoned as a
percentage of the length of the bar, varies as the length
is greater. Thus, taking the square wrought-iron bar,
¹ H. R. Towne,
2. Steel Committee. The other measurements are the author's.
STRESS-STRAIN DIAGRAMS
73
and taking lengths symmetrically situated with respect
to the fracture, the ultimate extension per cent. is-
In two inches, including fracture.
In four inches
six
""
""
""
""
""
eight
ten
twelve,
""
;>
""
•
+
Extension in fourth inch (fracture).
Extension in divisions 1, 2, 3, 5, 6, 7
Double extension in division 8
Extension in division 9 .
50 per cent.
38
32
29
27
26
Extension in ten inches symmetrical with fracture
Elongation per cent., 25·35.
""
">
""
""
""
""
""
""
>"
""
But not only does the ultimate extension depend
the length measured, it depends also, in bars of a given
length, on the position of the fracture. It is desirable
for comparative purposes to calculate the extension for
all bars in such a way as to give the nearest approxi-
mation to the extension of a bar which broke at the
centre of the measured length. Thus the ultimate ex-
tension of the rivet-iron bar in a length of ten inches is
best obtained thus-
0.51
1·335
0.46
0.23
2535
This has not been the usual method of calculating
the ultimate extension, but it obviously gives results
more comparable than the usual method, and it has
been recommended for adoption by the German testing
laboratories. Further results on the variation of ex-
tension with distance between gauge points will be given
in the chapter on the form of test pieces.
74
TESTING OF MATERIALS OF CONSTRUCTION
Extension in Each Inch
•80
•70
-60
.50
·40
.30
⚫20
.10
с
6
Distribution от
Drawing out.
4
FIG. 30.
a. Lead.
b. Brass.
c. Angle Iron.
d. Channel Iron
e. Steel Plate.
f. Steel Axle.
Rivet Iron.
2
0
2
Distances from Fracture in Inches
4
5
g
6
the bar is obtained by plotting the extensions per inch
A good idea of the distribution of drawing out along

STRESS-STRAIN DIAGRAMS
75
as ordinates at the centre of each inch length, and con-
necting the points by a curve. Fig. 30 shows some of
the results so plotted.
It may easily be seen that the length of the part in
which local contraction occurs must depend in some
way on the sectional dimensions. The local contraction
will be longer for a larger bar. Hence it might be ex-
pected that two bars of the same material and the same
length, but differing in section, would draw out differ-
ently, and give different values of the ultimate elonga-
tion. The following results obtained by M. Barba show
that this is so :-
Diameter,
inches
DIFFERENCES OF ELONGATION IN BARS WITH DIFFERENT PROPORTIONS
OF LENGTH TO DIAMETER.
*787
•394
(Pieces cut from bar of soft steel rolled to 14 inch diameter and annealed. Also on a
harder steel.)
•197
*787
·394
•197
Length
between
gauge points
in inches
3.94
3.94
3.94
3.94
3.94
3.94
Length
Diameter
092492
5
10
5
10
Limit of
elasticity,
tons per
sq. in.
15.85
15.72
16.00
21.90
21.25
20.94
Breaking
stress, tons
per sq. in.
23.47
23.40
23.85
37.CO
37.67
38.05
Elongation
per cent.
37.5
30.2
A
25.0
25.9
21.0
17.0
Similar Test Bars (Barba's Law).-M. Barba inferred
that to get identical values of the drawing out from dif-
ferent pieces of the same material they must be either of
identical dimensions or of similar form. This law can
76
TESTING OF MATERIALS OF CONSTRUCTION
hardly be considered to have been absolutely established,
but the following results show that it is at least a good
approximation
IDENTITY OF PERCENTAGE OF ELONGATION IN SIMILAR BARS (BARBA).
A billet of extra soft steel was hammered to an octagon of 34 × 34 inches, rolled to
a bar 14 inch diameter and annealed. Three test pieces gave the following results:-

Diameter,
inches
*787
·394
•197
Means
Diameter,
inches
•272
*407
•543
*679
.815
•950
1.090
1.22
Means
*272
*407
•543
*697
·815
•950
1.090
1.22
Lengths be-
tween gauge
points, inches
Means
7.87
3.94
1.97
Lengths be-
tween gauge
points
1.97
2.95
3.94
4.92
5.91
6.89
7.87
8.86
Length
Diameter
1.97
2.95
3.94
4.92
5.91
6.89
7.87
8.86
999
10
10
EXPERIMENTS ON TWO HARDER QUALITIES OF STEEL, ROLLED TO BARS
1 INCH DIAMETER AND ANNealed.
9
16
10
Length
Diam.
1 to
7.24
Limit of
elasticity, tons
per sq. in.
1 to
7.24
15.72
15.68
15.72
15.71
Limit of
elasticity,
tous per sq. in.
15.22
15.22
15.34
15.16
15.10
15.22
15.28
15.22
15.22
20.76
23.21
22.65
24.10
25.76
24.16
24.16
Breaking
stress, tons per
sq. in..
23.53
26.77
26.65
26.70
26.45
26.40
25.95
25.40
25.11
Breaking
stress, tons
per sq. in.
26 20
23.85
23.35
23.90
41.11
41.20
40.50
40.17
40.30
39.34
40.10
23.70
40.35
Contrac-
tion per
cent.
69.3
69.0
69.7
68.6
69.2
69.7
68.8
69.5
69.2
Elongation
per cent.
36.5
38.0
37.4
38.4
31.8
35.8
34.4
36.1
31.0
30.5
31.4
31.0
Elonga-
tion per
cent.
32.8
33.2
33.0
33.5
33.6
33.2
33.0
34.0
33.3
20.0
18.8
18.2
18.1
18.0
18.1
19.5
18.6
STRESS-STRAIN DIAGRAMS
77
Dimensions of
test bar
Width Thickness
.787 •197
1.575 ·394
2.362 •591
EXPERIMENTS ON PLATES.
Width
Thickness
4 to 1
Length
between
gauge
points
1.97
3.94
5.91
Limit of
Length elasticity,
tons per
area
sq. in.
10 10 10
Breaking
stress,
tons per
sq. in.
10.67 23.60
10.86 24.25
13.14 24.70
Elonga-
tion per
cent.
39
39
39
33. Suppression of the Drawing Out.-The drawing
out in ordinary test bars is measured on a portion of
uniform section, and the measurements are not extended
quite up to the enlarged ends by which the specimen
is held. The enlarged ends diminish the drawing out
of the parts nearest them, and if the part between the
enlarged ends is very short the drawing out, contrac-
tion, and strength are all affected. For the present,
cases will be considered in which the change of section
is gradual not abrupt.
1
A plate perforated with a row of holes, or formed
like B or C (Fig. 31), is virtually a very short test bar.
In reporting on riveted joints for the Institute of
Mechanical Engineers, the author noticed that in some
cases a perforated plate was stronger than a plain test
bar of the same material. Shortly after, this was shown
more distinctly in some experiments of the Board of
Trade on riveted joints,2 and in experiments by Professor
Kennedy for the Institute of Mechanical Engineers.
In these last experiments, perforated steel plates inch
1 Proc. Inst. of Mech. Engineers, 1881, p. 319.
2 Experiments on Steel. Memorandum of the Board of Trade, 1881,
P. 18.
78 TESTING OF MATERIALS OF CONSTRUCTION
thick were 10.7 per cent. and 3-inch plates 11.9 per
cent. stronger than plain test bars of the same material.¹
PERFORATED PLATES. BOARD OF TRADE REPORT, 1881.
Mild-steel plates.
Unperforated
Punched
Punched and annealed
Punched and bored to size
Drilled
Unperforated
Punched
Punched and annealed
Punched and bored
Drilled
Ultimate or breaking stress per sq. in.
of initial net section, in tons
3" plate
27.84
22.94
29.31
28.81
30.23
•
"plate
30.17
28.32
31.6
31.23
31.46
"/
4″ plate
53.3
24.1
41.3
24.0
36.6
plate
1
It will be seen that the punched plates lose from
6 per cent. of strength in 1-inch plates to 25 per cent. in
1-inch plates. But in all other cases there is a gain of
strength in the perforated plates. This amounts to about
4 cent. in the 1-inch plates, 10 per cent. in the -inch
per
plates, 5 per cent. in the 2-inch plates, and 23 per cent.
in the 1-inch plates. That this is due to the diminution.
of contraction the following table shows. In punched
plates the contraction is diminished, but the metal is
also injured by the process of punching.
27.69
25.33
29.39
30.86
31.37
Contraction of arca per cent.
"plate 3" plate
50.0
19.1
37.4
28.9
32.7
1" plate
28.17
21.26
29.12
29.15
28.43
39.4
13.0
30.7
19.4
32.1
¹ Proc. Inst. of Mech. Engineers, 1881, p. 215.
1" plate
388
5.4
24.7
15.9
33.2
STRESS-STRAIN DIAGRAMS
79
Some experiments by Mr. Strohmeyer¹ illustrate
very clearly the dependence of the breaking stress, es-
timated in the usual
way by dividing the
breaking load by the
initial section, on the
amount of drawing
out before fracture.
Form
A
B
с
Dimensions
Width Thickness
ს
t
mm.
mm.
35
46.8
31.8
18.0
12.5
The test bars of
the forms shown in
Fig. 31 were all cut from the same plate, and the holes
were in all cases 24 mm. (0.96 inch) diameter. The
width b varied in different test bars.
54.0
44.0
34.0
28.4
23.3
18.6
13.0
7.6
12
2222 22
12
12
12
12
12
12
12
12
12
12
12
12
Ratio
b
d
B
1.94
1.32
0.75
0.52
2.25
1.83
1.42
1.18
0.97
0.77
0.54
0.32
d
m
50
40
273
21
54
50
46
>
Elongations per cent.
of hole
in in 200
50 mm.
mm.
413
37
33/
25
21
FIG. 31.
?

26
18
14
12
را

28
26
22
22
20
16
14
10
Ċ
25
m
44.0
Ab

Breaking stress,
kilos. per sq. mm.

47:4
48.0
47.7
48.0)
46.6
47.0
45.8
45.0
48.8
45.2
45.5
45.1
Mean
47.8
Mean
45 7
It will be seen that form B is 9 per cent. and form C
4 per cent. stronger than the simple test bar A. This
is the effect which the author attributes to diminution
1 Prcc. Inst. of Civil Engineers, 1884.
80
TESTING OF MATERIALS OF CONSTRUCTION
of the contraction of area by the neighbourhood to the
breaking section of less strained material. Now, as the
breadths at corresponding points of B and C are exactly
equal, it looks, at first sight, as if B and C ought to
behave exactly alike, whereas, apparently, in the ex-
periments B is stronger than C. It will be seen, how-
ever, that the material near the point of fracture is not
in identical conditions in the cases B and C. Suppose
two bars of the form D are placed back to back and
broken. The material at the place of fracture is now
identically in the same state as in form C, and contrac-
tion takes place not only round the semicircular holes,
but along the edges m m. Weld together the pieces
along this line, and the contraction along m m can no
longer occur. The piece is then identical with form B,
it has less contraction than C, and ought to be stronger
The experiments show that it is so.
~
Mr. Richards made a very interesting series of ex-
periments at the Barrow Company's Steel Works on
test bars similar to Mr. Strohmeyer's bars A and B.
The material was mild steel made by the Siemens pro-
cess. The plate was inch thick. Two pieces had
parallel sides like ordinary test bars. The other speci-
mens were indented on each side by a semicircular.
drilled hole, leaving a section between of varying width.
The results are given in the following table.
Here the plates of form B, equivalent to perforated
plates, are on the average 12.6 per cent. stronger than
the parallel-sided bars of form A, and the strength is
STRESS-STRAIN DIAGRAMS
81

Form
A
B
Width
b
inches
1
1
•645
•650
·995
•995
1.47
1.46
2.28
2.27
Thickness
t
*495
·490
495
·500
*502
·495
•502
•50
*495
·495
•
Contrac
tion of
area
per cent.
52.5
53.5
129999995
45
46
47
42
31
36
42
43
Contrac-
tion of
width
per cent.
27.0
27.5
19
19
11
12
8
10
9
8
Contrac-
tion of
thickness
per cent.
33.3
35.9
32
33
37
34
26
30
36
37
Breaking
stress in
tons per
sq. in.
32.01
32.47
36.64
36.52
36.82
37.05
36.18
35.88
35.72
35.72
very uniform considering the different widths of the
specimens. The contraction of area in form A is 53
per cent., while in form B it is only 41 per cent., so
that there is a diminished contraction to account for
the increase of strength. Further, while the con-
traction of thickness is nearly the same in form A and
form B, the contraction of width, which is what would
be affected by the form of the specimen, is 27.2 per
cent. in form A, and only 11.9 per cent. in form B.
The shortest possible bar is formed by turning a
groove with a very slightly rounded bottom. The
following experiment on two bolts of Whitworth com-
pressed steel gives the strength of a bar of extremely
tough material thus shaped. The heads and nuts of the
bolts were turned to fit spherical seatings, so that the
stress was quite fairly applied. A groove, a little rounded
at bottom, precisely like a Whitworth screw thread, was
turned in the body of one bolt as at A (Fig. 32), and
the other was turned in the form shown at B.
G
-
82
TESTING OF MATERIALS OF CONSTRUCTION
Form A
B
2 4
A
""
B elongated 60 per
area was 54.6 per cent.
FIG. 32.
----
~
سرامهر
→→
Diameter
1.560
1.487
244
Plain bar
Collar bar
1호
​С
B
Grade P
•
+
Decrease
Breaking load, Breaking stress, in
tons per sq. in.
in tons
101.77
62.35
extension of other metal near it. If the material were
perfectly elastic the stress at any re-entrant angle would
be infinite, but the plasticity of all ordinary materials
diminishes very greatly the inequality of stress. Never-
theless the inequality exists, and it counteracts the gain
of strength due to suppression of drawing out.
Two pieces of the same cast iron were tested, one
in the form of an ordinary test bar, the other with a
square collar in the middle of its length. The re-
entrant angles at the collar were virtually nicks. The
breaking weights were-
•
cent., and the contraction of
For A the elongation and
contraction were practically
nil.
34. Abrupt change of Sec-
tion-Nicked Specimens.-At
any abrupt change of section
the stress on cross sections
cannot be uniform. The less
strained metal hinders the
13.875 tons per sq. in.
11.980 99
1·895 ""
showing a loss of 13.6 per cent. of strength, due to
·
53.25
35.87


""
""
STRESS-STRAIN DIAGRAMS
83
the inequality of distribution of stress caused by the
collar.
Mr. Baker made some interesting experiments on
steel plates with artificially produced cracks." A fine
saw-cut was made at one or both edges of the
specimen, and then, raising the specimen nearly to
welding heat, the saw-cut was closed up so far as to be
rendered invisible. Fig. 33 shows a set of specimens
of the same steel. Specimen a was an ordinary test
a
FIG. 33.
b
XOX
31.40
24·70
32.50
36.30
e

28.00
bar
b
d was a bar with semicircular notches, so that it
was virtually a short bar; was a bar with a saw-
cut or crack on both sides; e a bar with a saw-cut
or crack on one side; e a bar perforated with a crack
on each side of the hole.
The breaking weights in tons per sq. in. are
given under the figures. It will be seen that the
short bar d is stronger than the plain test bar a by
3.8 tons, or 12 per cent. ; but the nicked bar bis
weaker by 11 ton, or 34 per cent.
short bar, b should have carried as
Considered as a
much as d, the
¹ Minutes of Proc. of Inst. of Civil Eng., vol. lxxxiv. p. 165.
G 2
84 TESTING OF MATERIALS OF CONSTRUCTION
G
inequality of distribution of stress has therefore re-
duced its strength by 15 per cent. Similarly e is
weaker than d by 8 tons, or 22 per cent.
It is clear,
therefore, that, in the case of nicked bars, the increase
of strength which would result from the virtual short-
ness of the bar is more than counteracted by the
inequality of stress on the section of fracture. Mr.
Baker found with specimens of indiarubber a loss
of strength in nicked specimens of 60 or 70 per cent.,
and that is probably due to the fact that india-
rubber, although it deforms enormously, is really less
plastic than steel, and consequently the variation of
stress is greater.
Relation of ultimate Elongation to Contraction of
Area. It is now common, in testing iron and steel by
tension, to record the ultimate elongation in a length of
8 or 10 inches, and the contraction of area at fracture,
as data useful for deciding on the value of a material.
Both the ultimate elongation and the contraction are
supposed to indicate the ductility of the material, and
a good deal of confusion arises from the discrepancy
between these two quantities.
It has already been shown (§ 23) that for a per-
fectly plastic material
contraction of area
initial area
2
i+a'
polare supper)
that is, the percentage of contraction is equal to the
percentage of elongation, calculated on the stretched
STRESS-STRAIN DIAGRAMS
85
·
Material
length of the bar. Hence, a definite relation between
the elongation and contraction will only be found for
the short length of the bar, which becomes almost per-
fectly plastic, and draws out during the last stage of
the test. That a definite relation does exist between
the elongation and contraction in the immediate neigh-
bourhood of the fracture is easily shown. From the
experiments on steel by a Committee of Civil En-
gineers, Tables A, B, C, D, it is possible to get the
elongation in a length of 1 inch or 2 inches of the bar
in the neighbourhood of the fracture, and to compare
it with the contraction of area.
Bessemer steel
Crucible steel
Means
No. of bar
943
1,194
1,285
1,028
1,174
1,305
923
1,038
1,184
1,295
1,275
1,255
1,265
873
1,078
1,147
1,068
Length, in
inches
ι
2011 QI d O ON IN THI∞
2
1
1
2
2
2
1
1
1
2
Contraction
Initial area
W
Ω
•32
·55
·44
•58
•56
•37
•47
•50
⚫44
·41
•34
•42
*09
•44
•37
•54
*03
·40
Elongation
Stretched length
λ
1 + λ
•22
•31
•35
•34
·36
*30
•35
•42
•32
•27
•27
•30
*09
•29
•25
⚫40
⚫03
•28
Here the agreement is as close as could be expected,
the percentage of elongation (estimated on the stretched
length) being three-fourths of the percentage of con-
.
86
TESTING OF MATERIALS OF CONSTRUCTION
traction of area. Had it been possible to measure the
elongation in, say, a 4-inch length, the approach to
agreement would, no doubt, have been closer.
The following numbers are from some measurements
by the author-
Iron bar
""
""
""
Angle iron
Iron plate.
Steel plate
Delta metal
99
Material
•
•
M
•
Length
NNNNNNNNN
2
2
2
2
2
2
312
•24
•28
•42
•15
•12
•39
·09
•27
<<
λ
•20
•20
.27
•15
•11
$29
·07
⚫32
If there is this near agreement in the contraction
and elongation in the short, plastically-yielding part of
the bar near the fracture, then there can be no agree-
ment in the contraction and elongation in greater
lengths of bar. The contraction does measure in a
definite way the plasticity of the material under the
breaking stress. The ultimate elongation in an 8- or
10-inch length measures partly the plasticity of a short
length under the breaking stress, partly the plasticity
of the rest of the bar before drawing out commenced.
The two measures of the ductility are only in agreement
when the elongation is taken for a very short length of
bar near the fracture.
35. Influence of Time on the Stress-strain Curve.-It
has been seen that plastic yielding is gradual, either
increasing indefinitely or at a diminishing rate under a
STRESS-STRAIN DIAGRAMS
87
given stress. Hence it might be expected that the
plastic part of the stress-strain curve would be flatter
the slower the rate
of loading. Professor
Ewing gives the
stress-strain curves
shown in Fig. 34 for
two similar pieces of
soft-iron wire, one
loaded to rupture in
minutes,
four
the
other at a rate about
5,000 times slower.
In the same way,
in taking autographic
stress-strain diagrams
there is a notch in
the diagram at any pause in the increase of loading.
Fig. 35 shows a diagram for a manganese steel bar,
tested with a pause of five minutes at each successive
ton.
20
Stress, Tons per sq. in.
010
0
Falst
Slow
FIG. 34.

20
10
Extension Fer Cent
30
Fig. 36 shows the stress-strain curves for four pieces
of wrought iron cut from the same bar. For bar 319
the extensions were measured on a length of 4 inches;
for the other bars on a length of 9 inches. In the case
of bars 319 and 154 the extension increased at a nearly
uniform rate during the plastic stage. In the case of bar
313 there were four-minute pauses at each successive
ton, and the diagram is notched. In the case of bar
88
TESTING OF MATERIALS OF CONSTRUCTION
►
•
Load
Tons
20
15
10
Fons
20
15
10
5
6
1
Extension
39
1
1
FIG. 35.

r
2 Inches.
in 8 inches.
FIG. 36.

313
164
2 Inches
314
314 the load was taken off and a pause of six minutes
allowed at each successive ton. It may be noticed that
STRESS-STRAIN DIAGRAMS
89
▸
the breaking-down point is more marked with the
longer bars. The following table gives a summary of
the tests:
No. of bar
319
154
313
314
Tons per sq. in.
Yield point
12.97
14.37
13.68
14.23
Maximum load
22.19
22.10
22.34
22.47
Elongation per cent.
34.7
25.8
29.5
28.2
36. Influence of Time on the ultimate Elongation.-
Some remarkable experiments of Colonel Maitland at
Woolwich¹ show that, contrary to a common prejudice,
the ultimate elongation is increased by very rapid load-
ing. Colonel Maitland experimented on a steel which, in
unhardened specimens of 2 inches in length between
shoulders, broke in the testing machine at 26 tons per
sq. in. and with 27 per cent. of elongation. A specimen
was then screwed into blocks arranged so as to fall ver-
tically in a slide. After a certain height of fall the top
block was arrested by stops and the specimen broken by
the momentum of the lower block. Broken in this sudden
way the ultimate elongation was 47 per cent. Specimens.
were then screwed into plugs fitting a strong tube and
broken by exploding gunpowder and guncotton between
the plugs. The plugs were driven out in opposite
directions, breaking the specimen connecting them.
Under these circumstances the ultimate elongation was
'The Treatment of Gun Steel.' Proc. Inst. of Civil Engineers, vol.
lxxxix. p. 120.
90
TESTING OF MATERIALS OF CONSTRUCTION
from 47 to 62 per cent. The explanation of these
results appears to be that with very rapid increase of
stress there is not time for the formation of a short
local contraction, but the general extension continues up
to the breaking point.
1
Hardening Effect of long-continued Stress.-Experi-
ments on the influence of time on the extension and
breaking stress of wires have been made by Mr. J. T.
Bottomley in Sir W. Thomson's laboratory. Eight
specimens of soft-iron wire were tested by gradually
increasing stress, applied in ten minutes of time in each
case. They broke with 43 to 46 lbs. (mean, 45.2 lbs.),
with elongations varying from 17 to 22 per cent.
Another specimen, left with 43 lbs. hanging on it for
24 hours and then broken by gradual increase of stress
during 25 minutes, broke with 491 lbs., with 15 per
cent. elongation. Another, left for 3 days with 43 lbs.
hanging on it and then broken by increasing stress, bore
51 lbs. and elongated 14-4 per cent. A bar, loaded
first with 40 lbs. and broken by gradual addition of load
during two months, broke with 57 lbs. The slower
loading had therefore increased the strength by nearly
27 per cent. The increase of breaking stress and
diminution of elongation is commonly attributed to a
hardening effect of long-continued stress. But the
result seems complicated by the influence of time on
the local drawing out in the neighbourhood of the
fracture. Generally the more slowly the load is applied
¹ Article 'Elasticity,' in the Encyclopædia Britannica.
STRESS-STRAIN DIAGRAMS
91
the shorter is the local contraction and the less the
contraction of area.
37. Correction of the Stress-strain Diagram to show the
actual Stress in the Bar.-In ordinary stress-strain dia-
grams the loads are plotted as ordinates, and the elonga-
C
I
TONS!
45
40
35
30
25-
d
20
15
10-
5
0
8"---*
te
a
•
#
9.3″
FIG. 37.

π
#
1
2"
1
1
Steel Plate!Nº 75
Area ·904 sq. in.
h
k
1
រ
1
I'
X
tions of the bar between two gauge points initially
marked on the bar as abcissæ. By a mere alteration
of vertical scale the ordinates represent equally the
stress per sq. in. of the initial section of the bar.
Thus, in Fig. 37 a represents the elongation la
in 7 inches length of bar which has extended a per inch
when the load is that represented by ab. If the bar is
92
TESTING OF MATERIALS OF CONSTRUCTION
w sq. ins. section, ab will measure on a scale o times
that for the loads the stress per sq. in. of initial section
of the bar. Up to the yield point the section of the
bar changes very little, but beyond the yield point the
deformation is so large that the section sensibly changes.
Then ab does not represent the stress per sq. in. of the
actual section of the bar at the moment. To find this
it is approximate enough to consider that the change of
density is small compared with the deformation. Hence,
so long as the deformation is general over the marked
length of bar-that is, up to the maximum load point i,
the section of the bar can be found from the measured
length.
Let 1, wo be the length between gauge points and sec-
tion of the bar initially, and / (1 + 2) and w, the length and
section when the load is P. Then, w / = w₁ / (1+2),
(0)
@ 1
Pi
If p is '/w, the stress reckoned on the initial section,
then the real stress on the actual section is-
p (1 + 2).
In the diagram take OC to the same scale as
7
that on which O a = 12. Draw bd horizontal. Through
d draw C'de, cutting ab in e. Then ae represents P1,
the actual stress on the reduced section, to the same
scale as that on which ab represents p, the stress calcu-
lated on the initial section. If several points are thus
(0)
1 + λ
P
Wy
STRESS-STRAIN DIAGRAMS
93
found we get a curve feg, lying above the ordinary
stress-strain curve and extending to the point of maxi-
mum load. This is sometimes called the curve of true
cohesive strength. It is simply a curve giving the
relation of the actual stress and strain.
Beyond the point of maximum stress the construc-
tion fails, for the extension becomes chiefly local and
the in the formula above is no longer the length
between the gauge points. But another point in the
curve may still be found. If the contracted section is
measured after the bar is broken, then the breaking
load hk divided by that section gives the real stress
km at the moment of fracture. It is obvious, however,
that the part gm of the curve is distorted, for while the
abcissæ
up to the point i represent extensions of a fixed
length 1, the abcissæ from i to h represent extensions
of an undetermined portion of l. The real elongation
per unit of length at the moment of fracture in the part
which is drawing out is given by the equation-
λι
W
W 1
W1
▬▬▬
and if Ok' is taken equal to la₁, and k' m' set off equal
to km, the general form gm' of the final portion of the
real stress-strain curve is determined. It is quite
possible to measure the contracted section at inter-
mediate loads between i and h during testing and to
calculate intermediate points along gm'. So far as can
be judged from one or two instances, the portion gm' of
94
TESTING OF MATERIALS OF CONSTRUCTION
the curve shows a regular increase of tenacity with
increasing strain without the abrupt inflection of the
distorted curve gm.
38. Stress-strain Diagrams for nearly Plastic
Materials. When very ductile materials are loaded
with pressures which approach or reach the pressure
of fluidity the strains follow approximately the plastic
law, and the stress-and-strain curve becomes nearly a
hyperbola.
In tension experiments a difficulty arises from the
extension becoming local instead of general. It is im-
possible after local contraction sets in to determine
what length of bar is being elongated, and hence the
strain per unit length cannot be determined. In com-
pression experiments this difficulty does not arise. But,
on the other hand, it is difficult to keep long bars
straight during compression, and hence experiments
must be made on short cylinders, for which accurate
measurements are more difficult. Besides this, in short
cylinders a barrel-shaped distortion occurs, due partly,
no doubt, to friction at the ends against the plates
which apply the pressure. Nevertheless, these results
are interesting as showing an approach to a perfectly
plastic condition. Fig. 38 shows the stress-strain
curves for short cylinders of lead, copper, and wrought
iron. The lead curve is from an experiment by Prof.
Kick.¹ The cylinder was initially 50.05 mm. diameter,
•
1 Proc. Inst. of Civil Engineers, vol. 1. p. 188. The lead curve is
plotted with loads on specimen as ordinates, not stress per sq. in.
STRESS-STRAIN DIAGRAMS.
95
Pressure in Tons
per sq. inch 01
10
20
30
40
50
60
70
80
90
100
1
1
0.2
Hyperbola
FIG. 38.
Compressions
0.3

Wrought Iron
-0-
Lead
O
Copper
---0--0--0--0--Q
0:4
0--2--0
D
"
0.5
0.6
96
TESTING OF MATERIALS OF CONSTRUCTION
and 64.4 mm. in height. The following table gives the
loads and compressions :-
CRUSHING OF A LEAD CYLINDER (Kick).
Load, in tons Height, in inches
2.9
3.25
3.35
3.45
3.95
5.65
2.576
2.312
1.904
1.716
1.636
1.376
1.128
Compression,
in inches
*264
*672
•860
·930
1.200
1.448
Diameter at
centre, in inches
2.00
2.16
2.40
2.52
2.60
2.84
3.16
Stress, in tons
per sq. in. of
central area
¹ Industries, March 25, 1887.
•79
.72
*67
.65
.62
.72
It appears that the pressure of fluidity was reached
at about 0·75 tons per sq. in., and the stress remained
approximately constant notwithstanding the large de-
formation.
Fig. 38 shows a similar curve for a wrought-iron
cylinder. The experiment was made by Fairbairn, and
the results are discussed in
are discussed in Cotterill's
Cotterill's Applied
Mechanics,' p. 418.
1
24
1
Plastic Compression of Copper Cylinders.-Small
copper cylinders made of the softest and purest copper
are used in crusher-gauges for determining the powder
pressure in the bore of the gun. The copper cylinders
are made in two sizes, 4 sq. in. and sq. in. in
section, and the initial length is 05 inch. Tables
have been published¹ giving the compression of these
cylinders when compressed by hydraulic pressure, the
compressions being measured by a Whitworth measur-
ing machine.
Iz
STRESS-STRAIN DIAGRAMS
97
Compression,
in inches
λ
•10
•11
•12
•13
•14
•15
•16
∙17
•18
•19
•20
•21
•22
•23
•24
•25
Cylinder initially 0.5 in. long and 2 sq. in. area
24
Compressed
length, in inches
ι
λ
*40
•39
.38
•37
⚫36
*35
⚫34
•33
•32
•31
*30
•29
*28
•27
•26
•25
Pressure, in lbs.
P
2,091
2,225
2,359
2,494
2,628
2,763
2,897
COMPRESSION OF SOFT-COPPER CYLINDERS.
3,031
3,162
3,296
3,431
3,565
3,700
3,834
3,968
4,103
Pressure per sq.
in. of compressed
area, in tons
17.9
18.7
19.3
19.8
20.3
20.7
21.1
21.4
21.6
21.9
22.1
22.2
22.2
22.1
22.1
22.0
Compression,
in inches
ለ
•10
•11
•12
•13
•14
•15
•16
•17
•18
•19
•20
•21
•22
•23
•24
•25
*26
.27
•28
Cylinder initially 0.5 in. long and sq. in. area
*29
30
31
Compressed
length, in inches
λ
ι
M
*40
*39
*38
*37
.36
•35
•34
•33
⚫32
31
•30
•29
•28
*27
*26
*25
*24
•23
*22
*21
*20
•19
Pressure, in lbs.
P
4,000
4,333
4,666
5,000
5,333
5,666
6,000
6,333
6,666
7,000
7,333
7,666
8,000
8,333
8,666
9,000
9,333
9,666
10,000
10,333
10,666
11,000
Pressure per sq.
in. of compressed
area, in tons
17.1
18.1
19.0
19.8
20.5
21.2
21.8
22.3
22.8
23.2
23.5
23.8
23.9
24.0
24.0
24.0
24.0
23.7
23.5
23.2
22.8
22.4
:
II
98
TESTING OF MATERIALS OF CONSTRUCTION
The preceding table gives the compressions 2, com-
pressed length - λ, and observed pressure producing
7
the compression. Neglecting the barrel-shaped distor-
tion the stress reckoned on the deformed prism is-
pl - a
Pi
"
ωι
No. of
bar
and the values of this have been calculated and placed
in the tables. When the material is completely plastic,
P₁ is the pressure of fluidity.
1
It will be seen that for compressions exceeding
two-fifths of the original length the pressure on the
actual deformed section is nearly constant. Further,
the numbers for the cylinder of sq. in. area are
almost exactly double those for the cylinder 4 sq. in.
area. According to both tables the pressure of fluidity
for soft copper must be about 22 tons per sq. in.¹
24
1
39. Raising the Elastic Limit by Stress.-It has
long been known that for iron, steel, and other metals
a load exceeding the elastic limit raises that limit.
Thus, Bauschinger gives the following results of ex-
periments on five gun-metal bars, of a section about
2.8 × 0.5 inches. The elongations were measured in
-
8 inches by the mirror apparatus :—
123 LO
4
5
Original elastic
limit, in tons
per sq. in.
Stress applied,
in tons per
sq. in.
6.56
6.10
6.56
5.85
6.02
Permanent
set, in inches
Raised elastic
limit, in tons
per sq. in.
⚫00061
'00061
*00067
⚫00054
•00057
Tenacity, in
tons per sq.
in.
4.62
3.82
3.84
3.50
3.77
1 See also Treatise on the Manufacture of Guns (official), p. 92.
6.15
5.74
5.77
5.80
5.66
14.2
14.9
13.3
12.9
13.2
-
STRESS-STRAIN DIAGRAMS
99
Load
in Tons
23
In these experiments the second loading was effected
only a few minutes after the first loading.
Bauschinger noticed that if a bar after loading
beyond the elastic limit was left for twenty-four hours
O
21
19
f
ια
0
с
FIG. 39.

α
I IN.
Extensions.
2 IN,
چه
or more at rest it recovered partially the set previously
taken, and if then the elastic limit was again determined
H 2
Uor M
100 TESTING OF MATERIALS OF CONSTRUCTION
it was in some cases raised not only up to but beyond
the load previously applied.
Fig. 39 shows a stress-strain diagram of a piece
of steel plate, taken autographically by apparatus
which will be described. The yielding point, or break-
ing-down point, is strongly marked at a load of about
18 tons. At 19 tons, 21 tons, and 23 tons the load
was almost completely removed, the pencil tracing
downwards and retracing upwards almost exactly
straight lines parallel to the primitive elastic line.
Thus, at 19 tons the pencil described while the load was
removed and replaced the straight line a b. The distance
ob represents the permanent set produced by the load
of 19 tons, and the stress-strain diagram for the material
altered by loading is the line bac.... Similarly for
the other points at which the load was removed. The
peculiarity specially to be noted, and which indeed is
only shown in such autographic diagrams as this, is the
steepness and almost straightness of the curve at a
The material is not only nearly perfect in its elasticity
in the reimposition of the load up to the point a, corre-
sponding to a load of 19 tons, but is nearly perfect in
elasticity to the point f, corresponding to a higher load.
More accurately, ƒ is a new yielding point in the material
altered by loading.
Viscosity of Solids. Elastic After-Working.-If a
wire carrying a heavy vibrator is set in vibration tor-
sionally within its limits of elastic stress, the vibrations
subside more rapidly than can be accounted for by
-
STRESS-STRAIN DIAGRAMS
101
external causes or by heating effects. There must,
therefore, be an internal molecular friction or viscosity.
In a wire kept vibrating constantly more molecular
friction is found than in one allowed to rest between
each experiment' that is, the arc of vibration dimin-
ishes more rapidly.2 This is due to an 'elastic after-
working,' by which the strained metal recovers its
original condition gradually during a period of rest. If
the limit of elasticity has been exceeded, there is a still
more marked change of the material after straining and
during subsequent rest, due to elastic or plastic after-
working.
3
40. Bauschinger's Experiments on the Influence of Rest
after Drawing Out on the Elastic Limit.-Bauschinger first
indicated that, by drawing out a metal by stress beyond
its elastic limit, the elastic limit is raised, not merely
during the continued action of the load, but during a
period of some days after the load is removed. The
elastic limit may in certain cases rise above the stress
corresponding to the load imposed.
In a later paper¹ he gives a series of experiments on
different metals loaded successively up to a point at
which yielding just began. In one series, the successive
¹ Sir W. Thomson, Proc. Roy. Soc., vol. xiv. 1865, p. 289. Article,
Elasticity,' in Encyclopædia Britannica, § 34.
2 Mr. Tomlinson states that this fatigue of elasticity does not occur if
the stresses are kept well within the elastic limit.—Trans. Roy. Soc., vol.
clxxvii. part 2, 1886.
3 Dingler's Journal, Bd. 224, s. 5.
4 Ueber die Veränderung der Elasticitätsgrenze,' Civilingenieur, 1881,
s. 290.
102
TESTING OF MATERIALS OF CONSTRUCTION

20
1.5
Tons per Sq: inch.
Note
O
·002
=
e
"
Ingot Iron.
>= Flastic limit.
• = Yield point.
-
"
· 004'
===
B
رے
002”
·0'02'
ezee a
- 006°
#
·004"
اقدام
-008
22.0
H
"
FIG. 40.
Extensions.
·006′
· 010
·008′
//
A
1.014"
A. Reloaded without
interval.
B. 1 - First loading
2
3
4
010
51 hours after 1
47
2
46
-012"
"
·014'
""
""
3
-016
STRESS-STRAIN DIAGRAMS
103
loadings followed each other immediately; in the other,
a pause of one or more days was allowed after each
loading before again loading. Generally the results
were of the character indicated in the plotting of two
series of the results in Fig. 40. Four stress-strain
curves for cach series are shown, plotted to a very large
scale for the extensions, and each line extends up to
the point (marked by a dot) at which yielding just
sensibly commenced. The elastic limit (or exact limit
of proportionality) is shown by a circle marked e.
In the series A the bar was reloaded without any
sensible interval of time. The yield point rises at each
loading but the elastic limit falls, in the second loading
almost to zero. In series B an interval of about
fifty hours was allowed between each loading. In this
case the yield point rises as before, but the elastic limit
rises also at each successive loading. Comparing the
two series, it appears that the elastic or plastic recovery
during the fifty-hour pause (unloaded) raised the elastic
limit from the positions shown in A to those shown in
B. Bauschinger's results seem to be expressed in the
following conclusions :—
If a material is strained to or beyond the yield
point, unloaded, and again immediately loaded :-
(a) The breaking extension is diminished, and the
breaking load somewhat increased.
(b) The clastic limit is lowered sometimes to zero,
and the modulus of elasticity is a little
diminished.
104
TESTING OF MATERIALS OF CONSTRUCTION
(c) The yield point is raised to the stress corre-
sponding to the previous load.
If after the first loading a period of quiescence is
allowed before the second loading:-
(a) The clastic limit rises sometimes above its
initial value.
(b) The yield point rises gradually above the
stress corresponding to the previous load.
41. Use of the Stress-strain Diagram in estimating the
Work done on the Bar.-Let Fig. 41 be a stress-strain
diagram, the ordinates
being as usual loads, in
tons, on the section a of
o the bar, and the abcissæ
extensions of a length 7
between
gauge points.
Draw verticals through
B, C, D. Then, the work
done on the bar up to the
yield point is the area
OBE, work done up to the
and work done in break-
The areas are easily mea-
sured by a planimeter. If m inches = 1 ton, and n
inches
O E
plastic limit is OBC F,
ing the bar is OBCDG.
1 inch of extension, then-
B
1
FIG. 41.

}
1
F
I
Ꮐ
Work in inch tons =
S
area of diagram in sq. ins.
M N
STRESS-STRAIN DIAGRAMS
105
By dividing by the volume al of the bar we get
the work per cubic inch of material. From what has
already been said the elongation at rupture varies for
the same material with the length between gauge points,
and to a certain extent with the section of the bar. It
is only with similar test bars that the work in breaking
the bar, estimated per cubic inch of material, will
furnish comparable numbers. But further, the part
CD of the diagram is in most diagrams, if not in all,
somewhat badly determined, and at any rate is ex-
tremely affected by time differences in the rate of exten-
sion. The work represented by FCDG is almost
entirely work expended in local drawing out of the bar.
If this is discarded, the area OBCF represents the
work up to the plastic limit, at which, so far as carry-
ing a load is concerned, the bar is virtually destroyed.
If this is divided by the volume of the bar, values are
obtained nearly independent of the dimensions of the
bar, and therefore affording a good measure of its joint
strength and ductility.
106
TESTING OF MATERIALS OF CONSTRUCTION
CHAPTER IV.
TESTING MACHINES.
A TESTING MACHINE is simple or complex according as
it is intended for a few or a greater number of purposes.
If the machine is to be used for determining the quality
of one kind of material subjected to one kind of strain-
ing action it may be of very simple construction. In
that case it will be desirable that all the test pieces
should be of one size and form, and this simplifies the
construction of the machine. In an ordinary cement
testing machine simplicity is obtained by the limitation
of the purposes for which it is available. If, however,
a testing machine is to be used for varied investigations
on many materials, under different kinds of straining
action, for specimens of different shapes and sizes, then
the machine must be more complicated, and accessory
apparatus must be provided. In the adaptation of a
machine to diverse purposes there must be some sacri-
fice of convenience, some compromise between conflict-
ing requirements. Hence, there is no testing machine
absolutely preferable to all others. Almost
Almost every form
of testing machine has special merit for some particular
kind of work.
TESTING MACHINES
107
It must be remembered that, with every increase of
complexity in the machine, and with every addition to
the accessory apparatus, greater difficulty in using the
machine, more care in adjustment, and more loss of
time in adapting it to particular experiments is involved.
Hence, the extent to which it is desirable to combine
different functions in a single machine is a matter for
careful consideration in any given case. Some testing
machines are like special tools in a workshop, doing one
kind of work only, and with these the rapidity of work
is greatest, and the liability to errors of oversight or ill-
adjustment is least.
-
42. The simplest mode of testing is to apply a dead
load directly to the test bar. Many of the earlier
experimental investigations were made in this way, and
the method is still used in testing the weaker materials.
It is, however, laborious and inconvenient to have to
handle a load equal to the stress required. By using a
lever between the load and specimen the weight to be
handled is diminished in the ratio of the lever arms.
Many of the earlier testing machines were little more
than a lever for applying the stress. But here a prac-
tical inconvenience arises. If the specimen is held
between a fixed abutment and the lever, the position of
the lever alters as the specimen deforms, and so much
the more the greater the ratio of the lever arms. Some
arrangement must be made for neutralising the effect
of the deformation. The abutment must be moved to
keep the lever horizontal. In some machines a screw
108
TESTING OF MATERIALS OF CONSTRUCTION
and nut afforded the only means of adjustment. In
these cases it was necessary to remove or reduce the load
while the adjustment of the abutment was made. Some-
times the load was lifted by a crab and tackle while the
nut was screwed up.
To escape some of the difficulties of a lever arrange-
ment a hydraulic press has been used to produce the
stress in the specimen. The specimen being held at one
end by a fixed abutment, the other is strained by attach-
ment to the ram of the press, the movement of which
takes up the deformation. In such machines the stress
in the specimen must be inferred from the fluid pressure
on the plunger, indicated by a pressure-gauge. Then,
an allowance must be made for the friction of the cup-
leather or packing of the ram. As this allowance is
large, and varies with the condition of the ram and the
packing, machines of this type are not susceptible of
great accuracy.
Katt
According to experiments of Mr. John Hick, the
friction of a press cup-leather on a ram d inches diameter,
with a pressure of p lbs. per sq. in., is—
F = cdp,
π
4
where c is a constant. But the whole pressure on the
ram is 1 d2p. Hence, the fraction of the load on the
ram expended in friction and not transmitted to the
specimen is 4 c/ d; that is, it decreases as the diameter
of the ram is greater. Hence, the proportional error
likely to be introduced by miscalculation of the cup-
75
TESTING MACHINES
109
leather friction is less as the size of the ram increases.
Machines of this type are, therefore, most suitable for
testing test pieces of large section. However, the law
of cup-leather or packing friction is not really known,
and its amount is certainly extremely variable.¹
It next appeared possible to combine the advantages
of the hydraulic press machine and the lever machine in
this way. The test bar was placed between a hydraulic
press and a lever, or system of levers, acting as a steel-
yard. Roughly speaking, it may be said that in such
a machine the stress is applied by the hydraulic press
and measured by the steelyard. All good modern
machines are essentially arranged in this way, though
in some screws and gearing are substituted for the
hydraulic press, and in others a manometric arrangement
is substituted for the steelyard.
2
43. Machines for Testing in various ways Iron, Steel,
and other Strong Materials.-Machines for general testing
purposes almost always now consist of:-
(1) A lever, or system of levers, with weights,
forming a complete weighing apparatus. This is con-
nected with one end of the specimen, and its purpose is
to indicate from moment to moment the exact stress
applied to the specimen. In a few cases, in place of
the lever and weights a manometric apparatus is em-
1 The friction in testing machine rams is certainly greater than Mr.
Hick's formula gives. Probably the friction is greater at very slow speeds
than it was in his experiments.
2 This arrangement appears to have been first used by Bramah, in a
machine constructed for Woolwich Dockyard, earlier than 1837.
110 TESTING OF MATERIALS OF CONSTRUCTION
ployed, the stress being balanced by fluid pressure,
which is measured by a mercury column or a pressure-
gauge.
(2) A system of shackles for holding the specimen to
be tested, so guided that the straining action is exactly
of the kind required. Shackles must be provided suit-
able for the different sizes and forms of specimens to be
tested, and different shackles for each different kind of
straining action to be applied.
(3) To neutralise the effect of the deformation of the
specimen on the position of the weighing apparatus, a
movable abutment must be provided to hold one end
of the specimen. This is most commonly the ram of a
hydraulic press, which can be actuated by a pump, a
screw-compressor, or an accumulator. In other cases,
worm-gearing acting on a nut and screw, or even a
sliding-wedge driven by mechanism, has been used.
The object of all these arrangements is to take up
regularly and smoothly the deformation of the speci-
men, so that the point of attachment of the weighing
apparatus is practically immovable.
44. With regard to their general arrangement,
testing machines may be divided into-(a) Horizontal
testing machines, in which the stress is exerted hori-
zontally; and (b) Vertical machines, in which the stress
is exerted vertically. The difference is one of con-
venience chiefly. Where very long specimens have to
be tested the machine must be horizontal. All chain-
cable testing machines, for instance, are horizontal.
TESTING MACHINES
111
But there is a difference of action not entirely unim-
portant in horizontal and vertical machines. In hori-
zontal machines the weight of the shackles and other
parts connected with the specimen acts transversely to
the load applied by the machine. If not neutralised by
guides the weight would produce straining actions not
measured by the weighing apparatus. No guides can
quite perfectly prevent this transverse action, though
they may render it comparatively harmless. And the
guides themselves introduce some frictional resistance
which gets measured as part of the stress. In vertical
machines, on the other hand, the weight of the shackles
acts in the direction of the load, and can be balanced,
without guides, so as not to affect the measurement of
the stress.
45. In designing a testing machine the qualities to
be aimed at are as follows:
(1) The machine must have adequate sensitiveness-
that is, the power of indicating decisively and accurately
small differences of stress. To obtain sensitiveness in
a lever machine, the fulcrum on which the lever rests
and the supports of the shackles and weight are hard
steel knife-edges acting on hard steel planes. The sen-
sitiveness depends on the smallness of radius of the
knife-edges and their accurate straightness. If initially,
or under the action of the load, the knife-edge bends,
it virtually becomes broader, and the sensitiveness is
diminished. Now, the amount of sensitiveness required
in a good machine is not a quantity which can be
M
112 TESTING OF MATERIALS OF CONSTRUCTION
may
definitely assigned, nor is it easy to measure in an
actual machine, except in the case of an unloaded
machine. But there is no doubt that the sensitiveness
attained in good machines is in excess of practical
requirements. This point will be discussed later; but
it be pointed out that two specimens cut from the
same plate quite commonly differ in strength by more
than 1 per cent. Supposing the strength of the test
bar to be 20 tons, 1 per cent. of this would be 4 cwt.,
and a reasonably good machine indicates differences of
stress of far less amount than this. In most machines,
probably, the sensitiveness varies with the load and
increases as the load is greater. That is, the ad-
ditional stress required to distinctly move the weighing
apparatus becomes a less fraction of the load as the
load increases. In a good 100-ton machine, carrying
its full load, the lever will be distinctly moved by an
addition to the stress of ton. That is, the sen-
1
10000
sitiveness is such that Too of the load is indicated.
This is equal to the sensitiveness of a good chemist's
balance. The sensitiveness of machines with mano-
metric apparatus may be made still greater.
(2) The machine must be accurate in the indications
given that is, the stress indicated by the machine must
differ very little from the real stress. A sensitive
machine may be inaccurate if the ratio of the leverage is
imperfectly known, and it must be inaccurate if, from
any flexure of the parts, the leverage changes with the
load. Hence, it is of much more importance than has
1
100
TESTING MACHINES
113
generally been supposed that a testing machine should
be so arranged that it can itself be tested. The weights
used to load the lever can, of course, easily be stan-
dardised. But in many machines the leverage, or ratio
of the weight applied to the stress on the specimen, has
only been determined by measurement of the distances
between the knife-edges, and very generally the original
determination of the leverage by the maker is accepted
as sufficient, however long the machine may have been
in use.
It is clear that, however carefully the leverage
was determined in the first instance, the wear or dis-
placement of the knife-edges may seriously alter it in
course of time. If the fulcrum distance is 2 inches, a
displacement of inch would introduce an error of
1 per cent. into all measurements made by the machine
on the assumption that the leverage had remained
50
constant.
C
The determination of the leverage of the machine
by measurement of the knife-edge distance only is not.
satisfactory, and in machines used for scientific pur-
poses direct means of testing the leverage by weighing
should be provided.
(3) Facility of adjustment for different kinds of
straining action, and for specimens of different dimen-
sions. The importance of this quality in a machine
depends very much on the kind of work it is intended
to do. But it should be remembered that the shackles
used for different kinds of stress are somewhat heavy
and cumbrous, and the operation of changing the
I
114 TESTING OF MATERIALS OF CONSTRUCTION
arrangements for various kinds of work is somewhat
laborious.
(4) Capability of easy and rapid manipulation
during a test. In commercial testing it is of great
importance that the testing should be accomplished
rapidly. The means of gripping the specimen must be
convenient, and often the manipulation of the weighing
and hydraulic apparatus can best be effected by engine
power.
(5) Autographic apparatus for registering the
results is very convenient, and is a safeguard against
errors in recording the results. Some machines are
adapted, and others are not adapted, for the addition of
autographic apparatus.
(6) It is very objectionable if, during a test, the
specimen is subjected to shocks and vibrations.
Shocks or vibrations may arise either in the weigh-
ing apparatus (in adding loads, for instance); or in
the hydraulic press (by the action of a pump); or,
lastly, from the energy acquired by parts of the machine
which move when the specimen more or less suddenly
takes an increment of deformation.
Suppose a cubic inch of water suddenly forced into
the hydraulic press by the pump. If the lever and
weights had no inertia, no harm would result. But, in
fact, the movement of the press ram induces a movement
of the whole system, and the stress in the specimen is
for the moment increased by the inertia of the whole
system connected with it. If the specimen suddenly
TESTING MACHINES
115
1
1000
extends 16 inch, the weights on the lever move
through a not inconsiderable distance. They acquire
energy in falling, which again is expended in momen-
tarily increasing the stress on the specimen.
The question whether a machine with small leverage
or large leverage is likely to produce greater stresses in
the specimen in consequence of its inertia has been a
good deal discussed. If a specimen is loaded with a
dead weight M, the inertia of the load reckoned at the
specimen is M. But if the same specimen is put in a
machine with a leverage n, with a load M/n producing
the same stress, the inertia of the load reckoned at
the specimen is (M/n) n², or Mn. Hence it has been
argued that the stresses due to shock increase directly as
the leverage of the machine. All that the calculation
shows is that, with a given velocity of movement at
the specimen, the stored energy of the load liable to be
expended in straining the specimen increases with the
leverage. But the inference ignores the practical con-
ditions in which testing machines are used. In propor-
tion as the leverage of a machine is greater, its movements
are more narrowly limited by the stops at the free end
of the lever. The greater the leverage the more easily
is any tendency to acquire velocity in the machine
detected and controlled. Hence, practically, it is
probable that the greater the ratio of the leverage, the
less is the liability to unknown and prejudicial stresses
due to inertia of the machine. In the Buckton machine
the maximum leverage is 50 to 1; in the Werder
I 2
116
TESTING OF MATERIALS OF CONSTRUCTION
machine it is 500 to 1; while in some compound-lever
machines it is 20,000 to 1, or more. If the mere amount
of leverage produced so serious an effect as that inferred
above it would long ago have been detected in the use
of the machines. In fact, however, in skilful hands,
each machine is used in a manner suited to its construc-
tion and so as to reduce any action of this kind to a
negligable amount.
46. Arrangement of the Lever or Steelyard and Weights.
-In the oldest form of lever machine a bent lever
FIG. 42

IV
(Fig. 42) was used, the three principal knife-edges being
in one straight line. The object of this arrangement
was to secure a constant leverage notwithstanding some
change of position of the lever. The leverage is the
ratio of the perpendiculars from the fulcrum f on the
directions of the load w and stress s, and if the knife-
edges are not in one straight line the ratio of those dis-
tances sensibly changes with the alteration of inclination
of the lever. In more modern machines the lever is
left straight, and is formed of sufficiently rigid side
plates (Fig. 43), between which are the knife-edges, fixed
in rigid cross supports.
TESTING MACHINES
117
In the older machines and in some modern machines
the loading is effected by placing separate weights in a
scale-pan. Unless the leverage is large this is laborious,
and, unless the lever is supported when weights are
FIG. 43.


I
added, shocks are produced on the specimen. Two
modes of overcoming this difficulty have been found.
In one the separate weights are successively added by
mechanical arrangements; in the other a single travel-
ling, or jockey, weight is rolled out along the lever. In
the former, the leverage is constant; in the latter, the
leverage varies as the jockey weight is rolled out.
Fig. 44 shows diagrammatically these arrangements.
At A is the ordinary lever and scale; B and C are two
arrangements in which jockey weights are used. In C
the weight is so contrived that its centre of gravity lies
in the line through the knife-edges. In order that the
variation of position of the lever may not affect the
stress on the specimen the centre of gravity of the lever
must be on the line through the knife-edges, and the
jockey weight must either have its centre of gravity on
that line or must be hung from a knife-edge which
travels on that line. At D is shown the mechanical
118 TESTING OF MATERIALS OF CONSTRUCTION
The
arrangement for adding weights to the lever.
weights are carried by a frame which can be raised or
O
ロ
​Mi
O
FIG. 44.
A
B
C
D
Pla
-6-
·u*

Comunio
E
lowered by a screw. As the frame is lowered the weights
are deposited in succession on projections upon the rod
connected with the lever.
In Fig. 45 this mode of carrying the weights is
shown in more detail. The central rod a is suspended
from the lever. The side rods b, b are connected with a
screw raising or lowering arrangement; w, w are the
carefully-adjusted weights. When not in use the weights
rest on lugs on the side rods b, b. By lowering b, b the
weights are successively dropped without shock on the
corresponding lugs on a.
TESTING MACHINES
119
FIG. 45.
a
1
There is one other arrangement of the lever which
should be mentioned. In the testing machines of
Thurston, Michaelis, and Polmeyer, a
bent pendulum lever is used (E, Fig. 44),
carrying a single heavy load. As the
pull on the specimen is increased, the
pendulum - bob moves outwards and
upwards. If a and b are the perpendicu-
lars from the principal fulcrum on the
directions of the load and stress, the
varying leverage is the ratio b/a.
47. Principal Types of Testing Ma-
chines. It is proposed in the following
paragraph to indicate the principal types
of testing machine which have been used
as a key to the more detailed description
of some of these machines which will
be given later. It must be understood,
however, that the figures are merely
diagrams.
It will be seen that the most obvious arrangement
is to place the weighing apparatus at one end of a speci-
men and the straining apparatus at the other. In fact,
a large number of machines are thus constructed. Later,
it appeared that certain advantages were obtainable by
placing both weighing and straining apparatus at the
same end of the specimen.
Simplest of all arrangements, probably, is that
adopted first in a complete shape in the testing machine

I'
b
TINE
(01
b
W
W
120 TESTING OF MATERIALS OF CONSTRUCTION
at St. Chamond, and later adopted by Wicksteed,
Martens, and Michaelis. In this machine (Fig. 46)
the specimen s is held between a shackle attached to
a horizontal weighing lever above and the ram of a
es
S
P
FIG. 46.

-
Wicksteed
Martens
Michaelis
hydraulic press below. The weighing of the stress is
effected by rolling out a jockey weight along the lever,
or, in the Martens machine, by the arrangement shown
in Fig. 45.
Somewhat similar is the arrangement of the test-
ing machine of Messrs. Fairbanks & Co., of New York
(Fig. 47). In this case a worm-wheel and screw are
substituted for the press. The Fairbanks machine is
virtually an ordinary platform weighing machine adapted
TESTING MACHINES
121
to the purpose of testing. It should be pointed out
that, instead of the simple-lever system shown in this
diagram, the actual Fair-
banks machine has a com-
pound-lever system, involv-
ing the use of nine levers
and twenty-seven knife-
edges, the object being to
gain so enormous a lever-
age (in some cases 24,000
to 1) that the stress is
balanced by very small
weights. Fig. 48 shows
diagrammatically the
Thomasset machine, the

(O
(0%
S
FIG. 48.
Thomasset
1J
FIG. 47.
O
Fairbanks
S
d
WW

general arrangement of which is the same, but in which
a manometric arrangement d is substituted for the
122
TESTING OF MATERIALS OF CONSTRUCTION
weights used in other machines. The end of the lever
presses on what is virtually a frictionless diaphragm
supported by fluid pressure. A
pressure-gauge or mer-
cury column, indicating the amount of fluid pressure
mmm!
S
Tľ
FIG. 49.
w.w
Grafenstaden
26t
?
T

on the diaphragm, gives data for determining the stress
when the area of the diaphragm and leverage is known.
Fig. 49 shows the machine of the Grafenstaden
Company at Mulhouse, which has a peculiarity adopted
in the testing machines of Riehle Brothers, extensively
used in America. In order to get a very short knife-
edge distance on the main lever the fulcrum is not
placed in the lever itself but in a subsidiary lever
below, connected to the main lever by links. The
TESTING MACHINES
123
W ι
X
distance x is the virtual fulcrum distance, or the short
arm of the lever. It is obvious that this may be made
as small as desired on this arrangement without intro-
ducing any mechanical difficulties of construction.
Fig. 50 shows the arrangement of the testing
machine of Messrs. Greenwood & Batley, of Leeds,
d
FIG. 50.
Greenwood
Yo

S
is
which has perhaps been more generally adopted than
any other in this country. It is adapted to give a
horizontal pull, and has a compound-lever system. This
involves the use of a bent lever between the weighing
lever and specimen.
Fig. 51 is a sketch of the Maillard machine, in which
manometric arrangements are substituted for a lever

FIG. 51.
Emery
P
system. To a certain extent this is also the arrange-
ment of the great 500-ton testing machine at Water-
town Arsenal.
Lastly, Fig. 52 shows the Werder machine, which
1
124 TESTING OF MATERIALS OF CONSTRUCTION
has been adopted very extensively in Germany. This
differs from all the preceding machines in this, that
both the weighing and straining apparatus are at one
S
P
FIG. 52.

ι
Werder
W
end of the specimen. Hence, the expensive parts of the
machine being all at one end, arrangements can be
made to take in specimens of almost any length, by
prolonging the bed of the machine, without much extra
expense. All the German Werder machines take in
specimens in both tension and compression 30 feet in
length, a result not obtained in any other type of
testing machine except that at Watertown, and there
only with greater difficulty, as the press must be
movable. In the Werder machine the hydraulic press
acts on the short arm of a single bent lever l. This
lever is carried by the specimen, so that the other end
of the specimen requires only a fixed abutment. By
the action of the press the lever is kept horizontal,
notwithstanding the deformation of the test bar. The
Werder machine may be described as a machine in
which the principal lever is supported on a moving
fulcrum. The great advantage of having only a fixed
abutment to provide for the back end of the specimen
is obvious. Another advantage in this machine is, that
TESTING MACHINES
125
1 6
the short arm of the lever can be reduced as much
as one pleases without shortening the knife-edges. It
will be shown presently that actual Werder machines
for testing specimens up to 30 feet in length, and up to
a load of 100 tons, have a short lever arm of 4 m.m.,
or inch in length only. Thus a leverage of 500 : 1
is easily obtained, and the loads to be handled are small.
On the other hand, these very considerable and practi-
cal advantages are not obtained without some sacrifice.
The sensitiveness of the main lever is so great that it
must be adjusted by a spirit-level. Further, the ratio
of the leverage must be determined by direct experiment
with a control lever and weights.
48. The Woolwich Dockyard 100-ton Machine.-
This machine, which embodies nearly every feature of
importance in modern testing machines, is described and
figured in the first edition of Barlow's Strength of
Materials,' and must therefore have been constructed at
a very early date.¹ It was intended chiefly for testing
cables, but was used for ordinary testing also. Barlow
describes its principle thus:-'The Admiralty have
had constructed in Woolwich Dockyard for testing iron
cables a machine in which the strain is brought on by
hydrostatic pressure, but its amount estimated by a sys-
tem of levers, balanced on knife-edges, which act quite
independently of the strain there is on the machine,
and exhibit sensibly a change of pressure of ton,
1
'
Treatise on the Strength of Timber and Iron. By P. Barlow, F.R.S.
London, 1837, p. 237.
126
TESTING OF MATERIALS OF CONSTRUCTION
The
even when the total strain amounts to 100 tons.'
machine, which was constructed by Bramah, had a hori-
zontal cast-iron frame of 104 feet in length. On
one end of this was a hydraulic press, the position
of which could be adjusted by gearing. At the other
end was a system of levers, taking the pull and weighing
it. The first lever was a bell-crank lever, as in most
horizontal testing machines, and there were two other
levers. The total leverage was 2,240 to 1, so that
1 lb. in the scale-platform balanced 1 ton of stress.
The hydraulic press was worked by pumps, arranged
with great ingenuity to suit the varying pressure re-
quired. Friction-grip shackles are shown for ordinary
test bars, to which reference will be made later. The
distinctive features of this machine reappear in all
modern testing machines.
49. Fairbairn's Machine.-The testing machine con-
structed by Fairbairn and used in many of Eaton
Hodgkinson's experiments, consisted of a heavy wrought-
iron lever, with arms in the ratio of 8 to 1 and of the
bent form (Fig. 42). The lever rested on a short knife-
edge at the top of a box-shaped casting, and at its free
end carried a scale-platform. There was no hydraulic
press, and the deformation of the specimen was taken up
by a nut on a screwed rod. The lever was used in
several ways both for tension and crushing
1
J
P
1 This lever machine, which has a certain historical interest from the
importance of some of the researches made with it, is figured in its original
form in Fairbairn's paper on the ‘Strength of Wrought-iron Plates and
Riveted Joints,' Phil. Trans. 1850; Useful Information for Engineers,
TESTING MACHINES
127
Creusot 30-ton Machine.- This is a single-lever
machine, arranged very similarly to the Fairbairn ma-
chine in its original form. But worm-gear is added to
neutralise the effect of the deformation of the speci-
men, and a ram is placed under the lever to lift the load
off the specimen when necessary. The leverage is
17 to 1.
Machine of Major Wade.-In tests of cast iron for
guns in America in 1855 a machine was used designed
by Major Wade, and a similar machine was used for
many years at Woolwich. It is chiefly noticeable for
being one of the first compound-lever machines. One
lever had a ratio of 20 to 1, and the second lever, to
which the specimen was attached, a ratio of 10 to 1.
Consequently, the loads on the specimen were two hun-
dred times the applied weights. It was only adapted for
very short specimens.²
Machine at St. Chamond, for tensions up to 50 tons.³
This rather remarkable single-lever machine has some
peculiarities adopted in more modern machines. The
lever is constructed of two I-beams of wrought iron,
about 14 feet long and 12 inches deep. A rigid knife-
Fairbairn, p. 252. The same machine, somewhat altered in arrange-
ment, and in the form in which the author often used it between 1855
and 1865, is figured in a paper on 'The Strength of Iron at Different
Temperatures,' Brit. Assoc. Report, for 1856. See also Downing, Practical
Construction, pp. 3, 68, and Plate I.
¹ Lebasteur, Les Méteaux, 1878, Plate I.
2
'Report on Metal for Cannon,' by the American Ordnance Depart-
ment, pp. 305, 315.
9 M.M. Denizeau and Lechien, Mémorial de l'Artillerie et de la
Marine, 1883.
128
TESTING OF MATERIALS OF CONSTRUCTION
edged bar fixed between these side beams rests on the
top of a strong iron standard. At 0.6 inch only from
the fulcrum knife-edge is the knife-edge supporting the
shackle. The lever is prolonged backwards, and carries
a counterweight for putting it in balance initially. A
travelling jockey weight runs along the lever, which is
virtually a steelyard, and so balances the strain in the
specimen. A peculiar arrangement is adopted to take
up the deformation and keep the lever horizontal. This
is a wedge, sliding in guides, and driven by a screw and
gearing. As this arrangement produces no shock, it
is probably very meritorious, at least for light machines.
SINGLE-LEVER MACHINES.
50. The Werder 100-ton Testing Machine.-In 1852
a testing machine was designed for the Railway Com-
mission of Bavaria by Ludwig Werder, and con-
structed by Messrs. Klett & Co., of Nuremberg.
Similar machines have been built for the Government
testing laboratories at Berlin and Munich, for the
Polytechnic Schools at Zurich and Vienna, and for
several manufactories and railways. Probably it is not
too much to say that by far the largest part of the
original mechanical investigations carried out in the
last fifteen years has been accomplished by the aid of
Werder machines. In the hands especially of Dr.
Bauschinger, of Munich, tests of materials have been
made with this machine with a precision and accuracy
never before attained.
TESTING MACHINES
129
The Werder machine is a horizontal testing machine
with hydraulic press worked by pumps and single-lever
weighing apparatus. By an ingenious arrangement the
press and lever are kept on the same side of the specimen.
All the complicated and expensive parts of the machine
being thus brought to one side of the specimen, com-
paratively simple and inexpensive arrangements can be
made for extending the machine to take in specimens
of very great length. Usually the Werder machine is
made to test specimens both in tension and compression
up to 30 feet in length.
The general principle of the arrangement of this
machine has already been indicated. Fig. 53 shows a
sectional elevation of the more important working parts,
and detailed drawings will be found in the treatises
- cited below.1 R is the hydraulic press ram, which acts
against a knife-edge on what is really a bent lever L₁.
The crosshead C₁, which holds one of the shackles S₁,
is connected by the long bolts t, t with a crosshead car-
rying the other knife-edges which support the lever. If
the specimen stretches, C, moves to the right, and the
lever falls; if the press ram is then moved to the right
the lever is again lifted. The back crosshead C₂, which
holds the other shackle S2, slides on a cast-iron railway
behind the machine. It is spaced at any distance from the
fixed frame of the machine by the loose distance pieces d, d.
¹ Mittheilungen a. d. mechanisch-technischen Laboratorium in Mün-
chen, Heft 1 & 3. Maschine zum Prüfen der Festigkeit der Materialien
und Instrumente zum Messen der Gestaltsveränderung der Probekörper.
München, 1882. Also Lebasteur, Les Métaux.
K
130 TESTING OF MATERIALS OF CONSTRUCTION

FIG. 53.
Da
m
C₁₁
P
d
C₁₂
L₁₂
L₂
17
g
201
JP Mimanais.
4 PT
At s is a tension test-bar,
and m is Bauschinger's mirror
arrangement for measur-
ing extensions. In testing,
weights are placed on the
scale platform of the lever
L₁, and then by the pumps
the ram R is moved out till
the lever is in balance.
To obtain a high ratio of
leverage, so that the weights
to be handled may be small,
the short arm of the lever L₁
is reduced to the extraordi-
narily small distance of 4 mm.
or inch. The lever is of
-
3
16
such a length that the lever-
age is 500: 1. Of course
the short-arm length of the
lever cannot be directly mea-
sured with accuracy enough
to determine the leverage of
the machine. Hence a second
lever (control lever) L, is
provided, acting on the cross-
head C₁. This lever has
a ratio of 10:1, and its
arms can be accurately
measured.
TESTING MACHINES
131
By putting weights acting on L, in balance with
weights acting on L, the leverage of the principal lever
L, is determined. With so small a fulcrum distance as
13/65 inch the width of the knife-edges is a quantity com-
parable with the short arm-length of the lever. It is
necessary, therefore, that the lever L, should have an
R₁ R
a
с
=2
A
FIG. 54.

t
t
Y
L₁
l-
extremely small range of motion.
placing a spirit-level on the lever.
returning the press ram after a test.
The arrangement of the hydraulic press and lever
will be better understood from the diagrammatic sketch,
Fig. 54. Here R, is the press cylinder cast in one with
This is secured by
g is hand-gear for
**
K 2
132 TESTING OF MATERIALS OF CONSTRUCTION
the frame of the machine, and R, is the press ram. The
press ram, cased in gun-metal, is 12 inches diameter.
The hand-pumps for working the press have rams of 1.2
and 0·4 inch diameter. The ram R₂ carries a horn a,
with cross-shaft, from which the great lever L₁ is sus-
pended by links, and also the crosshead C connected
with the front shackle. The back part of the lever L₁
is a large U-shaped casting, partly surrounding the
press, so that the centre of gravity is near the knife-
edges. It carries a scale platform and adjusting weight.
The pair of crossheads C pass through the lever, and
are connected each by two longitudinal tie-rods t to the
shackle crosshead. The press ram carries in front a
hard steel prism 14 inches long, against which one
knife-edge on the lever acts. The crossheads C each
carry a prism 75 inches long, against which the other
knife-edges act (shown dotted). The distance between
the upper and lower knife-edges, reduced to inch in
the actual machine, is the short-arm length h of the bent
lever, the long arm being 1.
16
Fig. 53 shows the arrangement of the machine for
testing bars in tension. For crushing cubes and short
specimens the space between C, and the back of the
press is utilised, proper seatings being introduced.
Longer specimens can be crushed between C, and C2,
the tie-bars t, t being then extended to the cross-head
C2.
Convenient arrangements for transverse testing
and for torsion are also easily fixed.
51. Single-lever Testing Machine of Messrs. Buckton
TESTING MACHINES
133
and Co., of Leeds.—This machine was described at the
Leeds meeting of the Institution of Mechanical En-
gineers.¹ The machines then constructed were 50-ton
machines for testing ordinary short commercial test-
bars. It appeared to the author in 1883 that a larger
machine, capable of taking in moderately long speci-
mens, could be constructed on the same general plan.
In correspondence with Mr. Hartley Wicksteed, plans
were made for a 100-ton machine, which would take
specimens 6 feet long. Two very satisfactory machines
were built of this size, under the author's direction, for
the engineering laboratories at Cooper's Hill and at
the Central Institute of the Guilds of London. Other
machines of the same power have since been made.
Considered as an instrument of general scientific re-
search, the Buckton machine, even on the larger scale,
is inferior to the Werder machine. But it is more
handy for ordinary testing, and probably it is more easily
kept in trustworthy adjustment.
-
Fig. 55 shows the general arrangement of the 50-ton
Buckton machine. H is a rigid cast-iron standard
bolted to the foundations, and having at top a horn pro-
jecting back to carry the principal knife-edge or fulcrum
of the lever. The great lever L, L, with its jockey-
weight W, forms the weighing apparatus, and the
hydraulic ram F, F takes up the deformation of the
specimen. A tension specimen is shown at S, between
the friction-grip shackles A, B. The knife-edges of the
1 Proc. Inst. of Mech. Eng., 1882.
134
TESTING OF MATERIALS OF CONSTRUCTION

FIG. 55.
A
11
MARUSTUSVANAKOVAT
CARI PETRTINJUAL
T
H
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A
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H
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B
TUMBLRAU
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W
TESTING MACHINES
135
lever L, L are 3 inches apart, one resting on the
standard H, the other supporting the shackle A. To
support the knife-edges and prevent flexure, they are
gripped by rigid castings bolted between the side plates
of the lever. The hydraulic press F has a stroke of
6 inches to take up elongation and slip of the test-bar
in the grips. The press is worked by means of a 'quiet
compressor.' This is a press with a ram driven by a
pair of screws, which again are driven by gearing and
belting. This secondary press, which is a substitute
for the pumps ordinarily employed, forces water into
the main press F quietly and without shock, and works
very satisfactorily indeed. More power, however, is
required than with pumps. The press is so used that
the lever is kept 'in balance'—that is, floating freely
between the stops which limit its motion. The jockey-
weight weighs exactly one ton, and can be moved along
the lever by a screw driven at will, either by belting or
by the hand-wheel in front of the standard. Before a test
the jockey-weight is run back till the lever is in balance
with the test-bar free. A vernier, attached to the
jockey-weight, is set to zero on a scale running along
the lever. Then the specimen is fixed, and the jockey-
weight moved out along the lever, while the press is used
to keep the lever horizontal. Each 3 inches of movement
of the jockey-weight adds a ton to the load on the speci-
men, and the vernier easily reads on the scale to 1 ton.
100
52. 100-ton Testing Machine of Messrs. Buckton and
Co.-The photographic frontispiece shows a general
136
TESTING OF MATERIALS OF CONSTRUCTION
view of the engineering laboratory at the Central In-
stitute, with the 100-ton testing machine. Plate II. is
a general elevation of the same machine. F, F is the
main standard of such a height that moderately long
specimens can be tested. To the foot of this standard
is bolted the principal hydraulic press R, the ram of
which acts downwards on a crosshead c₁, connected by
adjusting side screws to an upper crosshead c₂, to which
the lower specimen shackle S₂ is attached. There is
worm-gearing to the side screws to adjust the length
between the shackles S1, S2. The press-ram is kept
home by the balance-weight B, attached to it by spring
shackles. To work the press there is a second press or
compressor C, the ram of which is driven by the twin
screws s₂ and gearing 92. The crossed belts b, and
fast-and-loose pulleys behind the standard drive the
compressor ram in or out, and so force water into or
allow it to flow back from the main press R. r₂ is a
hand-lever to the fork actuating the belts b₂, which
drive the compressor.
The great main lever L, of wrought-iron side-plates,
rests on the top of the standard F, F by means of a
knife-edge, and a second knife-edge behind this supports
the upper shackle S₁. These knife-edges are 20 inches
long, and are formed of hardened steel ground into a
rectangular groove in steel bars 4 inches in diameter.
These bars are further supported by castings bolted to
the side-plates. The distance between the knife-edges
is 4 inches. The free end of the lever plays in a space
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TESTING MACHINES
137
in the supporting pillar P. J is the jockey-weight,
weighing one ton, and straddling the lever so that its
centre of gravity is as nearly as possible on the plane
through the knife-edges. This runs on four rollers on
rails fixed each side of the lever, and is moved by the
long screws, S. The jockey-weight can be put in
motion either by the crossed belts by connected with
the reversing handle ri, or by the hand-wheel hand
countershaft k, if very slow motion or fine adjustment
is required. Along the lever is the graduated scale a, a,
and a vernier v on the jockey-weight indicates the posi-
tion of the jockey-weight. Initially the lever is put in
balance, and the vernier set to read zero on the scale.
Then each 4 inches the jockey-weight moves adds a ton
of stress on the specimen. The scale is 200 inches
long, so that with the jockey-weight at the end of the
lever a stress of 50 tons is measured.
For greater
stresses the jockey-weight is run back to zero, and the
25-cwt. load W is attached to the lever by a screw
coupling. As this hangs at a leverage of 40, it balances
a stress of 50 tons. The jockey-weight is then run out
again. The vernier easily reads to ton. Although
the arrangement of a double weight may seem cumbrous,
it is not so in practice, and the author prefers it to the
plan of making the jockey-weight 2 tons. In three-
fourths of ordinary testing, or more, the stresses do not
exceed 50 tons, and the coupling up of the extra load
is very easily managed.
1
200
The tension shackles S1, S2 are shown in place, and will
138 TESTING OF MATERIALS OF CONSTRUCTION
be described in a later chapter. The lower crosshead is
guided by a slide on the frame F, F. For compression
tests a table guided by the same slide is hung from
the upper knife-edge by four long suspension rods, and
specimens are crushed between this table and the lower
side of the crosshead C2.
It will be seen that, standing by the standard, the
experimenter has complete control of the machine. The
specimen is in sight on the left; the floating of the lever
can be seen to the right, and the two handles to the
belt-gear r₁, r, and the hand-wheel hare within reach
71, 72
without moving.
The author has now had considerable experience in
the use of this machine, and has found it extremely
convenient and accurate. The specimen is very con-
veniently placed for measurement during a test, and
specimens of a considerable range of size and form can
be tested. The sensitiveness of the lever on its knife-
edge is such that although, with the jockey-weight, it
weighs about five tons, it is very perceptibly moved by
half a pound placed on the shackle.
53. 50-ton Single-lever Machine of the Société Alsa-
cienne of Grafenstaden, Mulhouse.-A larger compound-
lever machine made by this firm was described in
Engineering,' June 25, 1880. The neatly arranged
machine shown in Plate III., Fig. 2, is a single-lever
machine of the type shown in Fig. 49. The specimen
is held between the shackles A1, A2. The
upper shackle
is connected to the straining mechanism, which in this
6
TESTING MACHINES
139
case is a screw having on it a long nut, driven by
gearing G. The screw is prevented from rotating by a
slide. The lower shackle is attached to the main lever
F at a knife-edge. This lever is connected by links to
the subsidiary beam F1, which carries the fulcrum
knife-edge. The links have knife-edges at the points
at which they rest on F and F₁. A jockey-weight
runs on the graduated lever F. The lever F₂ carries a
counterweight to put the main lever in balance. The
Grafenstaden machines are said to be in use at Essen,
Creusot, and Terrenoire.
2
COMPOUND-LEVER MACHINES.
54. 100-ton Testing Machine of Messrs. Adamson
and Co., of Hyde, near Manchester.-The machine
shown in Fig. 56 is a compound-lever horizontal
machine.¹ Mr. Adamson attaches great importance to
getting a fairly large distance between the principal
knife-edges, and at the same time to having a very great
leverage. Hence a compound-lever system is necessary.
This machine is specially designed for use in large
iron and steel works, where specimens are required to
be tested for commercial purposes, rather than for very
accurate scientific work, although with care and pre-
cision on the part of the operator very good results may
be obtained.
The machine, with all its appliances, is entirely self-
contained; it is mounted on a heavy cast-iron founda-
Engineering, June 17, 1887.
1
140 TESTING OF MATERIALS OF CONSTRUCTION

FIG. 56.
UTIZOSI d
FRAUMS
AUGU
***
**
$10.
TESTING MACHINES
141
tion, which requires no bolting down. It is capable of
testing all kinds of materials in tension, compression,
and bending; by a special arrangement it inay also be
used for torsion. The testing stress is obtained by an
hydraulic cylinder and ram 63 inches in diameter. The
cylinder is of forged steel, and is intended to carry a
working pressure of about three tons per square inch.
The pressure is obtained by a small double cylinder
pump, driven by cranks, and is provided with a fly-
wheel, pulleys, and handle for hand or power driving.
The plungers are made on the compound principle, one
small one working inside an annular plunger. When
it is required to pump rapidly at low pressures both of
them are coupled together, forming one large plunger;
but for high pressures the inner one only is used: then
the speed has to be sacrificed for pressure. This
arrangement permits two men to pump up to the full
power of the machine, viz. 100 tons. The pressure on
the ram is transmitted to a substantial cast-steel cross-
head by means of two steel ties, 3 inches in diameter,
running along either side of the machine. These ties
are screwed at the ends to allow of the crosshead being
adjusted for various lengths of specimens.
The gripping-jaws for holding the specimens are
turned on the outside and then fitted into a circular
hole. This arrangement insures the perfect gripping of
bars or plates having tapered cross-sections.
In or-
dinary rigid jaws the thick side is gripped first, and
consequently a tearing action is produced instead of a
-
142 TESTING OF MATERIALS OF CONSTRUCTION
fair and uniform pull. The other end of the bar is
similarly held by a second crosshead which is attached
to a set of three levers, and a steelyard provided with a
travelling weight, the position of which indicates the
load on the specimen under test. The leverage obtained
is 15,000 to 1, so that a very small travelling weight
can be used, viz. 4 lbs. ; when greater loads are required,
other weights of 3 lbs. each are hung on the end of the
steelyard.
All the levers and steelyard are arranged in a case
to protect them from dust and injury. The handle for
adjusting the traversing weight is placed outside of the
case, so that it never need be opened except for clean-
ing; the steelyard is visible through a glass door.
By means of very simple attachments this machine
may be adapted for testing specimens in compression or
bending. The hydraulic ram is provided with a chain.
and weight to bring it back to its original position after
the fracture of the specimen. All the knife-edges on
the levers are of hardened steel, and specially arranged
to prevent warping in hardening. This machine is
very conveniently arranged for getting at the specimens
when under test; it is also very compact.
55. Olsen Compound-lever 100-ton Testing Machine
Plate III., Fig. 1).—This is of the type largely adopted
in America, the mechanism being in principle the same
as that of a platform weighing machine. Four columns
on the platform E carry the steel plate B, to which one
end of the specimen is attached. Four straining screws
Plate III

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A₂
F
A 2
FLOOR
8 FEET
TESTING MACHINES
143
carry the plate C, to which the other end of the speci-
men is attached. The columns supporting B rest on
the lever system F, F. The straining screws carry the
large driving-nuts H, which are put into action by the
gearing below the levers. The nuts abut against the
frame through roller bearings, to diminish friction.
The platform E rests on three main levers, acting as
a single lever. Beyond the platform the three levers
act through a stirrup on the second lever F2, and this
again is connected with the third lever or graduated
steelyard F. A small poise or jockey-weight gives the
measurement of stresses from 0 to 5,000 lbs. ; a larger
poise, stresses from 5,000 to 100,000 lbs. ; and an addi-
tional weight on the end of the lever adds 100,000 lbs.
The screws and driving-nuts take the place of the
hydraulic press used in other machines. A crossed belt
on the pulley T, and open belt on the pulley U, drive
the gearing. A friction clutch engages either pulley
with the driving-shaft. There is also a slow motion
by friction-gear V.
SIMPLE HYDRAULIC PRESS MACHINE.
56. 600-ton Testing Machine of the Union Bridge
Company, at Athens, Pa.-This machine was constructed
with the object primarily of testing the full-size eye-
bars which are so largely used in American bridge
construction.
Two horizontal riveted girders B, B (Fig. 57)
60 feet in length, supported by cross-girders on five
144 TESTING OF MATERIALS OF CONSTRUCTION

FIG. 57.
PLAN
H
B
B
ŏ
Si
S₂
R
©
с
B
CIVALUMAIL
ELEVATION
آنها
90
о
с
ین
R
O
ა
с
с
(),
O
с
C
a
Q
Q
·A·
SLOP
10 FEET
5
masonry piers,
form the frame of
the machine. At
one end of the
frame is a large
hydraulic press
cylinder R, with a
freely moving pis-
ton. This has four
to
piston - rods,
which is attached
a crosshead carry-
ing shackles S₁ for
one end of the test-
There is a
bar.
movable tail-piece
C, which can be
attached
point in the length
of the frame, which
at any
carries a similar
crosshead
and
shackle S, for the
other end of the
test-bar. The cross-
heads are carried
on accurate wheels
r, r, running on a
track fixed to the
sdag
TESTING MACHINES
145
lower flange of the frame girders. The tail-piece having
been fixed to the girders at a suitable distance from
the hydraulic press, the specimen is introduced. Then
pressure is applied to the piston of the press, and in-
creased till the specimen breaks. The pressure on the
piston is measured by a Shaw mercury column and by
a spring pressure-gauge. The load on the specimen
is taken to be equal to the pressure on the press
cylinder. It will be seen that in this very large and
important machine the principle of construction is
simple, the lever weighing apparatus being dispensed
with.
The hydraulic press cylinder R is of cast steel,
4 feet 3 inches bore and 6 feet 0 inch long. It has
an area of 2,039 inches, and an effective stroke of
4 feet 11 inches. The maximum water-pressure for
which provision has been made is 600 lbs. per square
inch. The cylinder is secured to the girders by bolts,
and its back end is left open, so that the piston can be
seen.
The main girders B, B are of wrought iron, 60 feet
long, 3 feet 6 inches high, built of plates and angle
bars, rolled in one length. Holes, 6 inches diameter
and 18 inches apart, are bored through the web for the
bolts of the tail-block. Along this part of the web it is
2 inches thick.
The tail-block C is a steel casting, which may be
attached to the main girders by two pins each side,
fitting the 6-inch holes. Geared steel nuts g give a
L
146 TESTING OF MATERIALS OF CONSTRUCTION
further adjustment of the distance of the shackle from
the tail-block.
To provide for recoil between the shackle and tail-
block there is a rod attached to the shackle passing
through a friction-clamp on the tail-block. The eye-
bars are attached to the shackles by a 7-inch pin in
an elongated hole 7 x 9 in the shackle. This permits
the specimen to recoil independently of the shackle.
When smaller pins must be used collars reduce the size
of the pin-hole.
The shackle attached to the hydraulic press piston
is similar. The piston has a gland and hemp packing,
and the piston-rods also pass through stuffing-boxes.
The piston-gland is tightened till the leakage, with
maximum pressure, is reduced to a thin film of water
discharging uniformly round the piston. After a spe-
cimen is broken a discharge-cock is opened to a tank
4 feet 6 inches below the cylinder. The small vacuum
thus formed, equivalent to 1½ lbs. per square inch on
the piston, is found sufficient to move it home. Hence
it has been assumed that 3,000 lbs. represents the
maximum allowance to be made for the friction of the
hydraulic press. For practical purposes this allowance
is disregarded.
The pressure is obtained by a pump with three
single-acting plungers, 24 inches in diameter and
10 inches stroke, working at slow speed. An engine
with two cylinders, 8 inches diameter and 8 inches
stroke, works the pumps.
TESTING MACHINES
147
Main girders.
Steel castings
With a maximum load the stresses on the parts of
the machine are as follows:-
""
Connecting rods
Bolts
7,100 lbs. per sq. in. compression.
15,000,,
13,000
15,000
12,000,,
""
""
""
""
""
""
""
tension.
""
shear.
All these stresses are for the net effective sections,
and the margin of safety appears to have proved suffi-
cient under the shock of sudden release of load. Bars
varying from 5 to 18 square inches section have been
broken in the machine. It is intended to construct
compression apparatus for this machine.
The machine was designed by Mr. Charles Kellogg.
The idea involved in its design is thus stated by Mr.
Macdonald :-'It is not contended that this is an instru-
ment of precision, or that in sensitiveness or accuracy
it is the equal of the testing machine at Watertown
Arsenal. Mr. Kellogg would be the last person to in-
vite comparison in that respect with the superb inven-
tion of Mr. A. Emery. What he has accomplished has
been the construction of a machine at moderate cost
which will test to destruction full-sized sections as they
are required for structural purposes, with rapidity and
reasonable accuracy.'
¹ The Railroad and Engineering Journal, vol. Ixi. p. 71.
C
The particulars and description of this machine
have been taken from a paper read before the American
Society of Civil Engineers by Mr. Charles Macdonald,
M.Am. Soc.C.E.¹
L 2
148
TESTING OF MATERIALS OF CONSTRUCTION
MANOMETER MACHINES.
57. The Thomasset Machine¹ (Fig. 48).-M. H.
Thomasset, of Paris, constructed, apparently about 1872,
a machine differing in its mode of action from previous
machines in two ways. (1) To force water into the
hydraulic press a 'quiet compressor' ('compresseur
sterhydraulique'), like that used in oil presses, is em-
ployed instead of pumps. It has the advantage of
convenience, and of preventing the pulsatory action pro-
duced by pumps. However, it requires more power to
drive it. (2) In the weighing apparatus the pressure of
a liquid column acting on a large diaphragm, which forms
a virtually frictionless piston, is employed to balance
the stress on the specimen. This has the advantage of
convenience, cumbrous weights being dispensed with.
It has the further very important advantages that the
inertia of the weighing apparatus becomes very small,
and that the load adjusts itself perfectly automatically
to the stress. The slightest variations of stress are
indicated by the rise of the liquid column, which
balances the stress independently of any manipulation
by the operator. Apart from the question of the suc-
cess of M. Thomasset in overcoming the difficulties of a
new problem, his machine has very great merit from a
theoretical point of view. Other makers have proceeded
on the same lines, and probably the Thomasset machine
1 Lebasteur, Les Métaux, p. 52.
;
TESTING MACHINES
149
is in some degree the parent of the great machine at
Watertown.
One shackle of the machine being attached to the
ram of a press, the other is attached to the short arm of
a knee lever. The longer arm presses on the centre of
a diaphragm covering a circular cistern of mercury, or
of water communicating with the cistern of a mercury
The diaphragm is a vulcanised rubber
sheet fixed round its edge by a ring, and receiving the
load from the lever on a loose circular metal plate only
slightly less in diameter than the cistern.
manometer.
Let be the area of the circular diaphragm in sq.
centimeters; P the stress on the specimen in kilograms;
n the leverage of the bent lever. The total pressure 'on
the diaphragm is P/n kilograms, and the pressure in
the cistern is P/2n kilograms per sq. c.m. But if
h is the height in c.m. of the mercury column in the
manometer, measured from the level of the cistern (or,
strictly, from the point where the mercury stands with
no stress on the specimen),—
h
76
P
Ως η
;
1
If = 5,000 sq. c.m. (about 2.6 feet) in diameter
n = 5; then a column of mercury 1 meters (5 feet)
high will balance 50,000 kilograms (50 tons) of stress.
As the section of the mercury column is only 3000 of
the area of the diaphragm, the whole movement of the
diaphragm for a load of 50 tons is only half a millimeter
(0.02 inch).
150
TESTING OF MATERIALS OF CONSTRUCTION
58. The Maillard Testing Machine (Fig. 51).—A
very interesting machine,¹ based on the same principles
as the Thomasset machine, was designed by Colonel
Maillard for use in the French arsenals, and one of
these machines is now in daily use at Woolwich.
Broadly speaking, it is a Thomasset machine in which
the lever is got rid of, and the pull taken directly on
the diaphragm. This involves an enlargement of the
size of the diaphragm, and some other changes. The
machine as hitherto constructed is only suitable for
short specimens, and is only arranged for tension.
In this machine the specimen is held horizontally
between shackles, one attached to the ram of an hydraulic
press, the other to a crosshead which pulls on a dia-
phragm in a cistern containing fluid. This short
cylindrical cistern has the same axis as the hydraulic
press, and necessarily the diaphragm which receives the
pressure is on the side furthest from the test-bar, so
that the crosshead is forked to surround the cistern.
The diaphragm is of caoutchouc, protected by a metal
plate. The cistern communicates by a pipe with a
Galy-Cazalet manometer, or a mercury manometer.
The cistern is carried on trunnions upon a carriage
sliding horizontally. By means of a screw and hand-
wheel the position of this carriage can be adjusted to
suit different lengths of specimen.
The stress in the test-bar, transmitted through the
shackle and crosshead to the plate or piston at the
1 Lebasteur, p. 53.
G
TESTING MACHINES
151
back of the cistern, is exactly balanced by the fluid
pressure. The diaphragm moves at most only a small
fraction of a millimeter, so that the friction and bending
resistance of the diaphragm is quite negligable. Con-
sequently, if the graduation of the manometer is correct,
the stress is determined with great accuracy. If P is
the stress on the bar, h the rise of the mercury column
in the manometer above the zero at which it stands
when no stress is applied, & the density of the mercury,
S the area of the diaphragm, s, and s, the large and
small areas of the manometric piston,—
1
P = hd S $1.
S2
To eliminate errors due to uncertainty as to the areas of
the diaphragms, to capillarity, and so on, the manometer
is graduated by experiment. The cistern is removed
from the machine, laid horizontally, and loaded with
standard weights.
In a good manometer the tube must be at least
3 centimeters in diameter (14 inches); with a smaller
column, drops of mercury remain attached to the tube
when the column falls. The manometric piston in
the manometer used is so arranged that the centi-
meter rise of column corresponds to the kilogram per
square centimeter on the smaller piston, and conse-
quently on the diaphragm of the main cistern of the
testing machine. Hence if n is the rise of column in cen-
timeters, and S the area of diaphragm in centimeters,
P = n S.
152
TESTING OF MATERIALS OF CONSTRUCTION
In the machine at the Ruelle Foundry the diameter of
the large diaphragm is 9 feet.
59. Wire-testing Machine of Messrs. W. H. Bailey and
Co., of Salford.-Fig 58 shows a very nicely arranged
small tension machine, on the same principle as Col.
Maillard's. One end of the specimen is held in friction-
grips in a shackle attached to a screw and hand-wheel,
which takes up the elongation. The other shackle is
attached to crossheads and links, which surround the
diaphragm chamber, and apply the load on the back of
the diaphragm. The pressure in the diaphragm chamber
is transmitted to a pressure-gauge and to a mercury
column, either of which can be used. There is a valve.
on the pipe allowing flow towards the pressure-gauge
or mercury column, but preventing back flow. This
holds the gauge at the maximum pressure, and
and prevents
injury when the specimen breaks and the load is sud-
denly removed. A small hand-wheel
A small hand-wheel opens this valve
and lets off the pressure slowly. The machine will
give a tension of 4,500 lbs.
EMERY MACHINES.
60. The 450-ton Emery Testing Machine at Water-
town Arsenal, U.S.A.-In 1872 a committee of Ameri-
can engineers was formed to urge on the Government
of the United States the importance of a thorough and
complete series of tests of American iron and steel.
Subsequently, by direction of the Government, a Board
was constituted for the purpose of carrying out tests
TESTING MACHINES
153
S
AIG
FIG. 58.

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154
TESTING OF MATERIALS OF CONSTRUCTION
of iron, steel, and other metals, and an appropriation
was made of 75,000 dollars for the construction of the
necessary apparatus. In 1875 a contract was made
with Mr. A. H. Emery for the construction of a testing
machine capable of exerting a stress of 800,000 lbs.,
and of taking in specimens for testing 30 feet in
length. In 1879 the machine was completed satisfac-
torily, and it is probably the largest and most accurate
testing machine in the world.
Before acceptance by the Board, a link of hard
iron, 5 inches in diameter, was placed in the machine,
and slowly strained in tension till it broke at 722,000 lbs.
Without any readjustment, a horse-hair was then fixed
in the machine, and broken at an indicated stress of 1 lb.
No other testing machine would have permitted the
observation of so great a range of stress.
To give an idea of the sensitiveness of the weighing
apparatus of the Watertown machine, it may be com-
pared with a delicate chemist's balance. A good assay
balance will carry 1 gram, and turn with of a milli-
gram, or 1oooo of the load. A fine balance exhibited
at Philadelphia, with 1 lb. in each scale, would turn
10
10000
1
1
500000
1
with 3000 of its load.¹ Ordinary fine balances
weighing to 1 lb. will turn with 1 grain, or 7000 of
the load. Now before the Emery machine was com-
pleted it was arranged as a balance. In seven weigh-
ings of a load of 100 lbs. the greatest difference in the
observed weights was 175000 of the load. In nine
1
¹ Mechanics, November 3, 1883.
TESTING MACHINES
155
weighings of 200 lbs. the difference between the
greatest and least observed weight was only 235 0 0 0 0
1
of the load.
Since the construction of the Watertown testing
machine, smaller machines of the same kind have been
made by the Yale and Towne Manufacturing Company
of Stamford, U.S.A. The ingenuity displayed in the
mechanical arrangement of these machines, the perfec-
tion of their workmanship, and the delicacy and pre-
cision of their indication of the smallest differences of
stress are so remarkable, that it is difficult to speak of
them without seeming to exaggerate. In a 75-ton
machine, which the author examined in Paris, every
half-pound of load was precisely and instantly indi-
cated, whatever the stress the machine was exerting.
At the same time, in no other machine is the stress
exerted in such a purely static manner. It is almost
impossible for any shock or inertia stress to be exerted
on the specimen. As a machine of precision the Emery
machine is far in advance of any other. It may seem
that the delicacy of the machine must be such as to
unfit it for ordinary rough commercial testing. On this
point the author cannot speak from personal experience,
but, so far as he can judge, this is not the case. Igno-
rance and want of skill are certain to lead to false results,
even when the roughest machine is used. Granted a
reasonable amount of skill in the operator, the Emery
machine may be used for ordinary rough testing as
easily and safely as machines of less precision.
156 TESTING OF MATERIALS OF CONSTRUCTION
The Emery machines differ essentially in principle
from any others. They are really compound lever
machines, with an hydraulic press acting on one end of
the specimen, and a lever weighing apparatus on the
other end. But their greatest peculiarity is that a
kind of hydraulic lever is introduced between the speci-
men and the weighing apparatus. The pull of the
specimen is taken on an 'hydraulic support,' the action
of which is like that of the diaphragm in the Maillard
machine. The fluid pressure in the hydraulic support,
which is exactly proportional to the stress on the test-
bar, is transmitted through a very small pipe to act on
a frictionless diaphragm of comparatively small size, and
it is the pressure on this diaphragm only which has
to be balanced by the lever weighing apparatus. The
weighing apparatus can therefore be made of small size,
and of the utmost refinement and accuracy.
In the 75-ton machine the ratio of areas of the dia-
phragms is 20 1, so that the lever weighing apparatus
has to balance 3.75 tons only with the full load. There
are three levers with ratios of 1 : 20, 1 : 20, and 1 : 40,
so that the resultant leverage is 320,000 to 1.
The action of the Emery machine may, perhaps, be
made clear by the diagrammatic sketch of a vertical
machine (Fig. 59). A tension specimen is shown
between the shackles S1, S2. The upper shackle is held
by the ram of the hydraulic press, which can be adjusted
on the guide-screws G, G. These screws are fixed on
the frame F, F of the machine. The lower shackle is
TESTING MACHINES
157
attached to a yoke or frame Y, Y, which transmits the
load to the hydraulic support. At s is a thin circular
brass sac, filled with alcohol and glycerine, supported
over all its area, except a ring inch wide at its cir-
cumference, by the strong and rigid crossheads P1, P2.
1
8
When the machine
is acting as shown
in tension the yoke
transmits the load
to the crosshead P,
and thence through
the sac s to P₁,
which rests against
the stops a, a on the
frame. For com-
pression the yoke
presses downwards
on P₁, through s to
P₂, and P₂ then rests
on the stops b, b.
The whole play of
the crossheads be-
tween the stops a and
b is only 50 inch.
2
1
00
The movement of the yoke and compression of the
hydraulic support is determined by the amount of
motion permitted in the lever weighing apparatus.
With the 75-ton machine, when the indicating lever
moves 4 inches (2 inches above or below mean position)
29
a
6
ADCETROGI GEOONSGOT
G
FIG. 59.
HILIIST
Y
Y
1

BOHINOOR!
S₂
F
P₁
P
F
COMODALODOVODBOLDS
G
THE
a
7
158 TESTING OF MATERIALS OF CONSTRUCTION
1
8000
1
4000
200
10
the greatest compression of the sac s is only gooo inch.
The movement of the smaller diaphragm and of the
fulcrum of the first lever is 40 inch; the free end of
the first lever moves inch, and that of the second
lever inch. Mr. Henning assures me that it is easy
to keep the indicating lever within inch of its mean
position, and the movements of the system are then
only of the amounts just stated. It is on the small-
ness of the movement that the exactitude of the action
of the hydraulic support depends.
It is a peculiarity of the lever weighing system that
knife-edges are replaced by an arrangement more sen-
sitive and exact, and less liable to injury by wear. In
FIG. 60.
a
石
​

11021
place of the knife-edge Mr. Emery uses a thin flat blade
of steel rigidly fixed in the lever and its support. If
the lever moves, this bends. But the resistance becomes
insensibly small if the motion of the lever is small and
the blade of steel thin. Fig. 60 shows two arrange-
ments of these substitutes for knife-edges.¹ In a the
steel blades are in tension; in b they are in compression.
The steel is 0.004 to 05 inch thick, and the blades are
1 A somewhat similar device seems to have been proposed by Weber
at Gottingen in 1841, and by M. Taurines in 1867.
TESTING MACHINES
159
so wide that the stress in the steel does not exceed 18 to
30 tons per sq. inch. The blades are fixed by forcing
them into grooves by hydraulic pressure, about three
times as great as the working load.
A somewhat similar arrangement is adopted to get
rid of all sliding friction in the moving parts of the
testing machine (Fig. 59). The yoke and crossheads
do not slide in the frame, but are free. They are guided
without friction, and for a minute amount of motion
without sensible resistance, by four flat flexible plates
attached to each piece and to the frame.
In the vertical machine the change of arrangement
from tension to compression or transverse stress is
extremely simple. Gripping wedges of a new pattern
for test-bars not machined are used, which are designed
to ensure a perfectly fair pull, and to ensure the speci-
men not breaking inside the clips. In some cases the
lever weighing apparatus is dispensed with, a very large
and accurate pressure-gauge being used instead. This
pressure-gauge has a pressure diaphragm and lever
system made on the same plan as the lever weighing
apparatus, The accuracy of the pressure-gauge to one tenth on
per cent. is guaranteed. The machine can be easily
calibrated by placing a standard weight on the lower
shackle and weighing it by the weighing apparatus.
7
Plate IV. gives a general view and Plate V. a plan
and elevations of the Watertown Emery machine. The
bed of the machine consists of a long track, built in
sections set on masonry. At the right hand is the
160 TESTING OF MATERIALS OF CONSTRUCTION
any
hydraulic press 1569 (Fig. 1), with its shackle or holder
1475. At the left is the hydraulic support, the cross-
heads of which are seen at 1455, 1456, with the other
shackle 1475. The frame at the left end is connected
with the press by the guide-screws 1450. The hydraulic
press
is carried on a four-wheel truck, and can be set at
distance from the hydraulic support, to suit different
lengths of test-bar. The guide-screws are 48 feet long
and 8 inches diameter, and are driven by the geared
nuts 1569 and the gearing at the extreme right of the
figure. When the gearing is not acting the press is
locked to the screws. The press has a 20-inch ram, with
a piston-rod 10 inches diameter. The press is worked
by accumulators, and acts in both directions, according
as tension or compression is required.
In each of the test-bar holders there are two 14-inch
hydraulic presses, which grip the specimen with a force
of 500 tons.
The space for the ends of the specimen is 10 inches
deep in the middle and 5 inches at the sides, and it is
30 inches wide.
The hydraulic support rests on a longitudinal slide,
its motion being controlled by powerful buffer-springs,
which absorb the recoil when the specimen breaks. In
ordinary conditions the buffer-springs merely hold the
hydraulic support in its middle position.
When a
specimen breaks, the press and hydraulic support recoil
in opposite directions, the forces developed being op-
posed by the guide-screws. But as the recoiling forces
Plate IV
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TESTING MACHINES
161
are not exactly balanced, the buffer-springs come into
play and gradually bring the machine to rest. In ten-
sion, the pull is transmitted from the test-bar holder,
through a great central link, to the back crosshead
1455, and so through the brass sack and front crosshead
to the frame. In compression, the thrust comes first on
the crosshead 1456.
The fluid pressure in the hydraulic support is trans-
mitted through a small pipe to the pressure-gauges
1708, and also to the secondary diaphragm and the
lever weighing apparatus in the case 1705.
In the general view (Plate V.) the hydraulic support
is on the right, and the press and lever weighing
apparatus on the left.
SPECIAL TESTING MACHINES.
G
61. Torsional Testing Machines.- In some testing
machines a special shackle is used for torsional stresses.
But an ordinary large testing machine is too clumsy for
a comparatively delicate test of this kind, and some of
the shackles used in this way are defective in arrange-
ment. For torsional tests a special small machine is
desirable, but hitherto no sufficient attention seems
to have been given to the best arrangement of such a
machine. A very neat little machine of this kind, by
M. Thomasset, is figured in Lebasteur.¹
One end of the specimen is turned by worm-gear,
while the other acts through a lever on a diaphragm and
¹ Les Métaux, Lebasteur, Plate V.
M
162 TESTING OF MATERIALS OF CONSTRUCTION
manometer. This seems to contain the essentials of a
perfect torsion machine, but the shackle arrangements
for holding torsion specimens do not seem as yet to have
been fully thought out. Prof. Kennedy gives details of
a small torsional machine.1
Thurston's autographic torsional machine will be
described in a later chapter.2
62. Machines for Transverse or Cross-breaking Tests.
-Shackles for cross-breaking are provided with most
large testing machines, and will be described in the
next chapter. For transverse tests of cast iron small
special testing machines are useful. Bars of cast iron
3 feet × 2 inches × 1 inch, laid on supports 3 feet
apart, with the deeper side vertical, break with from 25
to 40 cwts. placed at the centre, so that the loads to be
dealt with in tests of this kind are not very great.
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FIG. 61.

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الدليل الأسد
MEMANATIO
HO
Fig. 61 shows a small machine, made by Messrs.
Tangye Brothers, for tests of this kind. The bar rests
on knife-edges on the base-plate, and is loaded at the
1 6
Engineering Laboratories.' Proc. Inst. Civil Engineers, vol. lxxxviii.
2 First described in Proc. Am. Soc. of Civil Engineers, 1874, p. 350.
TESTING MACHINES
163
centre by a lever and jockey weight. Somewhat similar
machines are made by Messrs. W. H. Bailey & Co., and
probably by other engineers.
4
M. Kuhlmann has introduced a machine of rather
more elaborate construction for breaking cylindrical
test-bars inch in diameter and 8 inches in length.
It is suggested that small test-bars of this kind can be
more easily and accurately cast, can be cast vertically,
and arc, if desired, easily turned in the lathe, so as to
be quite accurate in form. The pattern for casting
them is a polished metal bar. There is an arrangement
in the machine for indicating deflections.
Another convenient arrangement, known as the
'Balance Monge,' is in use in some gun factories. It
consists of a bracket
(Fig. 62), fixed to a wall,
having two opposed
knife-edges. By a bridle
and block a scale-plat-
form is attached to the
bar.
FIG. 62

63. The Bending and
Temper Test.-A very
convenient practical test of the ductility of a material is to
bend a strip about 1 inch wide over a corner of small
radius, and observe the angle at which it cracks on the
extended side. Sometimes the test is made on strips in
the condition in which the material is received. In the
case of steel, strips are heated to cherry red and plunged
M 2
164 TESTING OF MATERIALS OF CONSTRUCTION
in water of a temperature of 80° before bending. This
shows whether the steel tempers or hardens by sudden
cooling. Sometimes the strips are simply sheared strips.
At other times the edges of the strips are planed or the
strips annealed, and they then bend to greater angles
before cracking.
The roughest plan of bending is to put the strip of
plate over a V-block, and bend it by blows of a heavy
swage; the bending is continued by light endway blows
of a steam hammer. A press for bending angle iron
may be used in a somewhat similar way, the pressure
being applied first transversely, then endways. In
experiments by Prof. Kennedy,¹ bars 11 inch square
were supported on knife-edges 6 inches apart. A load
was applied steadily on a central bearing-piece of
13 inch radius. When the angle reached 90° the bear-
ing-piece was reduced to inch radius. In experiments
for the Board of Trade, strips were placed on supports
10 inches apart and bent by hydraulic pressure to an
angle of 90° by a ram with a rounded end of 2 inches
radius. The bending was then continued till the strip
cracked or the angle reached 180° by quiet pressure ap-
plied at the ends, in the testing machine. Mr. Stroh-
meyer2 clamped pieces between a steam hammer and its
anvil, hammering the projecting end till the strip was
bent through an angle of 45°. It was then reversed and
7
-
1
The Use of Steel Castings,' Parker. Journal of the Iron and
Steel Institute.
2 'The Working of Steel,' Strohmeyer. Proc. Inst. of Civil Engi-
neers, vol. lxxxiv.
TESTING MACHINES
165
bent in the opposite direction, and the bendings con-
tinued till fracture occurred. The number of bendings
is taken as a measure of the ductility of the material.
To ensure accurate bending to a given angle, an anvil
mould, with a radius of curvature of 13 inch, was used
below the test piece.
4
A lever apparatus for quietly bending strips of plate
is described in the work cited below. Fig. 63 shows
a small apparatus of this kind introduced by Mr. A.
FIG. 63
TRU.
M

H. Kuhlmann. It has a screw worked by a handwheel
or by a ratchet lever. The piece to be tested is bent in
the middle, and the angle measured subsequently. It
will bend strips 2 inches wide and 2 inch thick.
4
64. Testing Pipes. As water mains of cast iron are
ordered in very large quantities, special arrangements
for testing them before delivery are generally adopted.
The general quality of the metal used is determined
by testing sample bars cast once or twice a day from the
same metal as the pipes. These are most commonly
bars 2 ins. × 1 inch × 40 ins., which are broken trans-
¹ Die Eigenschaften von Eisen und Stahl. Wiesbaden, 1880.
166 TESTING OF MATERIALS OF CONSTRUCTION
versely on supports 36 inches apart. In some cases,
however, a tension test is made; and this is no doubt
the more rational proceeding.
A
4
Next to this, the regularity of form of the pipes is
tested. The thickness is tested by callipering, long cal-
lipers of special construction being used. A variation
of inch in thickness is the most generally allowed. A
pipe with inch variation in thickness should be re-
jected unless the working pressure is light. In rolling
the pipes they usually come to rest with a thin side
uppermost, and this is some guide in determining the
thickness. Ordinary callipers are 18 inches in length;
special callipers have been made up to 6 feet in length,
but these, from their springiness, require a good deal of
care and skill in use. Deviation in weight is also noted.
Usually pipes with a deviation of 2 to 5 per cent. are
rejected. Socket and spigot gauges for the inside of
the socket and outside of the spigot are also used. A
disc with a long handle passed through the pipe is
used to show deviations from cylindrical form. The
disc is usually inch less in diameter than the nominal
bore of the pipe. This disc should pass fairly through
the pipe while held square.
The most important test, however, is the hydraulic
pressure test. The testing machine consists of two
standards on a frame, carrying discs which are pressed
against the ends of the pipe. One disc is fixed, the other
movable. A grummet, consisting of an iron ring
served with tarred rope or yarn, is inserted between the
1
4
TESTING MACHINES
167
discs and pipe to make a joint. The movable head is
forced up by a screw, which exerts considerable pres-
sure. Water is then run in till the pipe is full from a
cistern, the air escaping by an air-vent. The air-vent
and supply-pipe are then closed, and a pressure pro-
duced by a small force-pump. A weighted valve and a
pressure-gauge show when the pressure required for
testing is attained. For pipes of 30 inches or more in
diameter 4 to 5 lengths can be tested per hour. The
pressure prescribed is usually double the working pres-
sure. While under pressure the pipes are struck hard
with a hammer of 5 to 7 lbs. Leakage through the
pipe is indicated by the fall of pressure shown by the
gauge. If proved before coating with tar or asphalte
defects are more easily seen.
64 a. Calibration of a Testing Machine.-Experi-
mental verification of the accuracy and sensitiveness
of a testing machine is absolutely necessary, both in the
first instance and at intervals afterwards. It will be
sufficient to describe the process of verification adopted
for the 100-ton Buckton testing machine. The stress
in this machine is weighed by a jockey weight, and the
first point to verify is that this jockey weight is exactly
1 ton. The jockey weight was adjusted at the
Standards Office, and certified by the inspector. It is
not difficult to verify this weight from time to time by
lifting it, with one of the convenient steelyard weigh-
ing machines interposed between the crane-hook and
weight.
168 TESTING OF MATERIALS OF CONSTRUCTION
Adjustment to Zero of Scale.—The adjustment is easily
effected, and is necessary after any change of the shackles
used. The jockey weight is run back till the lever rests
in absolute equilibrium midway between the stops. The
vernier attached to the jockey weight is then set to zero
on the scale.
Verification of the Jockey Weight by the use of the
Lever. A very simple test of the accuracy of the
jockey weight is made in this way. A uniformly
graduated scale runs along the lever. Division 5 co-
incides with the principal knife-edge on which the lever
rests, and at division 45 a subsidiary knife-edge has
been fixed. Bring the lever to balance, and set the
vernier to zero. Then run back the jockey weight to
1 on the scale. A weight of 56 lbs., hung at divi-
sion 45, or forty divisions from the fulcrum, ought to be
in balance with the jockey weight moved one division
back. If it is not, the jockey weight is not a ton. This
simple test, which can be made in ten minutes, is suffi-
cient at any time to check the accuracy of the jockey
weight to about 12 lbs.
Verification of the Agreement of the Scale Divisions
with the Short-arm Length of the Lever.-The fulcrum
distance in this machine is 4 inches, and the unit of the
scale must be 4 inches also. The agreement of the
scale unit with the short-arm length is best determined
by weighing. For this purpose a standard 1-ton weight,
made of a suitable form, is hung from the shackle of
the machine. The lever is balanced, and the vernier
TESTING MACHINES
169
set to zero. The ton weight is then hung in the shackle,
and balanced by the jockey weight. The vernier ought
then to read 1 ton on the scale. If it does not, the
fulcrum distance must be altered, as it is inconvenient
to alter the scale. Perhaps it is still more accurate to
balance 56 lbs. at a leverage of 40 by the ton weight in
the shackle without moving the jockey weight.
Test of Sensitiveness.-In this machine the lever and
jockey weight, with the parts attached to them, weigh
altogether about 5 tons, and this is therefore the
minimum weight on the knife-edge. With this weight
resting on the knife-edge there is a perceptible move-
ment of the lever when lb. is placed on the shackle,
and a return if the weight is removed. If the friction
of the knife-edge is assumed to be proportional to the
load, the error in 100 tons of stress would only be
10 lbs.
Probably a greater sensitiveness than this could be
obtained if necessary. The knife-edge of this machine
is of the exceptionally great length of 22 inches. Any
initial or induced flexure virtually broadens the knife-
edge and reduces the sensitiveness. Hence a very long
knife-edge, though more durable, is likely to be less
sensitive than a shorter one.
Test of Neutrality of the Lever.-The centre of gravity
of the lever and jockey weight should be on the line
passing through the knife-edges. If it is not so, the
leverage alters, either decreasing or increasing as the
inclination of the lever alters. The author has tested
170 TESTING OF MATERIALS OF CONSTRUCTION
this directly by ascertaining the pull, with the lever in
different positions, by a weighing machine suspended
in the shackles. The following tests were made by first
placing weights on the shackle and taking them off;
afterwards, by repeating the operation with weights on
a small scale suspended from the long arm of the lever.
Throughout the whole of these tests the lever was
absolutely untouched, so that no vibration or swing
was given to neutralise any friction in the machine.
The weights placed on the shackle were, of course, at
4 inches from the fulcrum; the weights on the other
side are reduced to equivalent weights, also at 4 inches.
from the fulcrum. The figures are the mean of the rise
and fall in two series of tests taken at different times;
the rise and fall in the two series of tests differed
very
little:

Weight on
shackle,
in lbs.
1
2
7
Movement of
end of lever,
in inches.
*09
•26
*48
1.10
1.53
Movement
per lb.
*09
•13
•16
•22
22
Weight on
long arm
1.4
2.9
5.7
8.6
11.5
Movement of
end of lever,
in inches
•12
•52
1.21
1.98
2.49
Movement
per lb.
*08
•18
•21
•23
•21
SHACKLES FOR HOLDING TEST BARS.
I. TENSION SHACKLES.
65. The load required to fracture a bar varies with
the mode of holding it in the testing shackles. The
proper form of test bars to ensure comparable results in
different tests will be discussed later. But the follow-
ing general remarks may serve as an introduction to
the examination of the methods of holding test bars in
the machine.
a
Let o be the section of a bar A (Fig. 64), which
breaks at ab with a tension T normal to a b. Then, if
the direction of T passes through the centre of figure of
T
CHAPTER V.
T
171
A
FIG. 64.
P
1813
P
с
D



P
P
B
a c


bi id
E
ab, the stress is uniformly distributed, and T/w is the
real tenacity of the bar. But, if these conditions are
not satisfied, the stress is not uniformly distributed, and
172
TESTING OF MATERIALS OF CONSTRUCTION
T/w is the apparent tenacity, which may be less than
the real tenacity to almost any extent.
(1) The stress on the cross section will cease to be
uniform if the resultant of the load P (Fig. 64, B), does
not pass through the centre of figure. The stress is
then a varying stress, varying uniformly so long as the
elastic limit is not passed, and according to some other
law if it is passed. The specimen tears from the edge
where the stress is greatest. At C the load is also
eccentric, and this indicates how non-uniformity of
stress may be produced by unhomogeneousness of the
material itself. A patch of material of different extensi-
bility from the rest produces a similar effect to a hole.
(2) The stress on cross sections may be rendered
non-uniform by the local action of contiguous material.
Thus, bars of the form D are known to break with a
low apparent tenacity. The unstrained material a pre-
vents the elongation of the adjoining material b, and
virtually renders the material unhomogeneous. In the
form E a similar action occurs; but here the less strained
material on either side of the section of fracture hinders
contraction so much as to raise the apparent tenacity
(see § 33).
66. Pin Grips.-The oldest way of holding plate
specimens is to drill a hole at each end and narrow the
bar in the middle by slotting or milling. The test bars
are then of the form A (Fig. 64). A steel pin in the
jaws of the testing machine shackles passes through
each pinhole in the specimen. This method of holding
SHACKLES FOR HOLDING TEST BARS
173
plate specimens is convenient and satisfactory, especially
when the test bar is of large size.
The pinholes must be accurately on the axis of the
narrowed part of the bar to ensure uniformity of stress.
But, besides this, it is important that the pins should be
so large as not only to be safe against shearing, but so
that the crushing pressure on the surface of the pin-
holes is not great enough to largely deform them. If
this is not attended to the bar will almost certainly
break from the pinhole across the enlarged ends, even
when these are considerably larger than the narrow part
of the test bar.
Let a be the area of section of the bar at ab, and d
the diameter of the pin. Then, the shearing section of
the pin will be sufficient if
FIQ
2
d² f₁ = k f, a,
where f, and f, are the tearing and shearing resistances
of the plate and pin, and k a factor of safety not less
than 3. If f, =ƒ1,
d = 1·38 √a.
α.
Thus, for breaking specimens of 4 sq. ins. area, a pin
is required of 23 inches diameter.
Now let t = thickness of test bar, and f. the pressure
at which it crushes. Then, in order that the pinhole
may be safe against deformation,
f a must be less than f. dt.
174 TESTING OF MATERIALS OF CONSTRUCTION
Suppose the pinhole is safe if the crushing pressure is
not greater than f, then
d
2α
t
;
or d must be twice the width at the narrow part of the
bar. This gives a very large diameter to the pin, much
more than has generally been allowed. The calculation
is of course based on assumption, but it indicates why
plate specimens with pinholes often give trouble by
breaking through the ends.
With cast-iron test pieces the ends may be thickened,
and then a smaller diameter of pin suffices. With
wrought iron, cheeks may be riveted on.
Sometimes a number of smaller pins are used instead
of one large pin. The objection to this is the great
difficulty of drilling a number of holes so accurately
that all the pins bear equally. Some specimens tested
in this way break through the pinholes at sections very
much larger than the middle of the bar, clearly showing
a want of uniformity of bearing of the pins.
67. Friction Grips.-In the 'Journal of the Society
of Arts,' vol. li. 1837, there is a description of what
are termed 'nippers' for iron bars by Mr. J. Kingston,
of Woolwich Dockyard. These nippers appear to be
precisely the friction grips used at the present time for
holding test bars. The shackles consisted of two iron
blocks with a rectangular hole, having the two opposite
sides inclined. Two gripping pieces, or wedges, fitted
SHACKLES FOR HOLDING TEST BARS
175
in the mortice gripped the specimen. As the tension
on the bar increased, the pressure of the gripping pieces
increased proportionately, in consequence of their sliding
down the inclined surfaces of the shackle. The inside
of the gripping pieces was formed like a coarse screw-
thread to give greater bite. The paper contains in-
teresting details of experiments on copper, Muntz metal,
and iron bars made with these nippers.¹
About 1860 the author used at Sir W. Fairbairn's
suggestion some wedge grips of a similar kind. These
were for cylindrical bars, and were made in three parts,
like the cone keys at one time used for fixing pulleys on
shafts. The wedges had a taper of 1 in 8, and fitted
in a conical hole in the shackle. Of late, pairs of flat
wedge grips have been very generally used in testing
plate specimens.
Fig. 65 shows a shackle for wedge grips designed
by Mr. Wicksteed, and not unlike the shackles used
in many machines. The hardened-steel wedges with
serrated faces are seen at w, with the test bars between
them. These wedges have a slope at the back of 1 in
6. They are held in slots in two conical pieces b which
fit a conical hole in the shackle. These seatings allow
the wedges to swivel, so as to hold test bars with faces
not quite parallel. For round and square bars V-shaped
grooves are formed in the face of the wedges.
1 Mr. Trueman Wood pointed out this very early record of testing
appliances to the author. The grips are figured also in the 1837 edition of
Barlow's Strength of Materials.
176 TESTING OF MATERIALS OF CONSTRUCTION
8
MIN
S
W
8
FIG. 65.


11
"
es
!
18

Fig. 66 shows the arrangement of the wedge-grip
shackles in the Werder Machine. This shackle differs
from those most used in this country-(1) in the short-
SHACKLES FOR HOLDING TEST BARS
177
ness of the wedges; (2) in the slot in the shackle being
open at the ends, so that any width of plate can be held.
On the other hand, there is no provision for fairly
B
Ş
FIG. 66.

Q
5
|

holding test pieces the faces of which are not parallel.
Perhaps this is less important when the wedges are
short. For with short wedges the serrations bite deeply
into the bar, and so to a certain extent adjust themselves
to a small defect of parallelism in the faces.
Richle's Wedges.—In order to ensure the coincidence
of the tension with the axis of the specimen, Messrs.
Riehle Brothers, of Philadelphia, adopt a plan different
from that used in this country. The shackle has a
rectangular recess, so that the wedges which grip the
specimen cannot swivel. There would, therefore, with
ordinary flat-faced wedges be a likelihood that the
wedges would grip the specimen more on one side than
N
178 TESTING OF MATERIALS OF CONSTRUCTION
the other; in fact, if the specimen were thicker on one
side they would inevitably do so. To avoid this the
wedges are made with a round face.
Ⓡ Fld
B
mil
B
FIG. 67.


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B
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FIG. 68.
The shackle is shown at A (Fig. 67), and the round-
faced wedges at C, C, with the specimen between them;
e is a pin used to adjust the specimen
between the wedges. Fig. 68 shows on
a larger scale the form of one of Riehle's
wedges.

Shackles of the Emery Testing Machine.
These are as original and ingenious as
the other details of the machine, and
more nearly comply with the conditions
required for perfectly holding a test bar
than
any other shackle. Fig. 69 shows the shackle. g
is the end of the press ram, or yoke, to which the shackle
is to be attached. f is a nut forming part of the shackle.
In the shackle two oblique cylindrical holes are bored,
forming the seats for the sliding wedge pieces b. In
these wedge pieces are fitted the various gripping
SHACKLES FOR HOLDING TEST BARS
179
pieces c, to suit flat plates of different thicknesses or
round or square bars. The wedges b slide so that their
faces are perfectly paral-
G
lel. The gripping pieces
are cylindrical, so that
they can adjust them-
selves to plates of un-
equal thickness. The
wedges b are not, as in
other machines, loose,
but form a permanent
part of the shackle; a
toothed rack is formed
on the side of them, en-
gaging a pinion driven
by the shaft h, so that
they can be moved for-
ward to grip the test
piece. A ratchet and
click prevents the slack-
ing back. The wedges
are traversed by a bar d
carried by the rod e,
which is pressed by a
spring, against which
the rotation of the shaft h
moves them. Under fis
an elastic packing to pre-
vent injury by shock.
-
b
FIRES!!
*
e
FIG. 69.

a
ale
te
4
a
a
ん
​
h

h
N 2
180 TESTING OF MATERIALS OF CONSTRUCTION
The gripping pieces c are each in two parts, the back
part being roughened with teeth, the front part plain.
This allows a certain stretch of the specimen in the
length of the gripping pieces, and at the same time
holds them by a double bite. This prevents fracture
of the test piece inside the shackle.
68. Colonel Maillard's Grips.- In the Maillard
machine very convenient grips are used in the form of
FIG. 70.


n
n
ޔކ
two half-rings n, n, screwed on the outside. The test
bar is formed with shoulders at the ends. A pair of
grips enclose the shoulder, and these are then screwed
into the shackles of the machine. Fig. 70 shows these
grips, which are extremely simple and convenient to use.
69. Shackles with Spherical Bearing-surfaces.-For
very accurate experiments, especially for experiments
on the modulus of elasticity, the coincidence of the ten-
sion with the axis of the bar is of great importance.
It is best secured by carrying the bar on bearing-
surfaces which are spherical. This has been done in
several testing machines for round bars, but has not
been accomplished for plates.
The easiest way of supporting round bars is to form
SHACKLES FOR HOLDING TEST BARS
181
a screw-thread on the ends, and then fix on the bar a
steel nut with hardened spherical face. Fig. 71 shows
two arrangements the author has used, and found both
convenient and simple. The
screwing of the end of the
test bar, which should be
done in the lathe, is tolerably
inexpensive. The steel nuts
may have the forms shown,
and they rest on steel rings
which drop into the conical
recess of the ordinary shackles.
Cast-iron specimens are con-
veniently tested in this way,
the screwed end being made
rather extra large.
Spherical Seatings for Bars
with Shouldered Ends.-Pro-
FIG. 71.

1
вечето порно
====="
WHAT IS IN

bably the most satisfactory
form of test bar for very accurate tension experiments
is that adopted as the standard form in Germany. The
round bar is turned in the lathe, leaving square shoulders
at each end. As a seating for these shoulders two half-
rings may be used, as shown in Fig. 72. The author
has used both forms. In one the displacement of the
half-nuts during the test is impossible. But even with
the other form, which is simpler, displacement does not
The half-rings should be of hardened steel.
Fig. 73 shows the shackles used in the machine of
occur.
182 TESTING OF MATERIALS OF CONSTRUCTION
the Grafenstaden Engine Co., of Mulhouse. Two hinged
boxes
grasp the test bar, which is formed with shoulders.
FIG. 73.
FIG. 72.
+



Cual
B
es
TO 20

Between the shoulders of
the bar and the boxes
half-rings with spherical
seats are inserted, so that
the bar may swivel into
the line of pull.
Of
70. Bauschinger's Ten-
sion Shackle for Specimens of Wood.-Fig. 74 shows a
cast-iron shackle for specimens of timber used in
Bauschinger's researches. The dovetailed end of the
shackle fits into the ordinary tension shackle of the
SHACKLES FOR HOLDING TEST BARS
183
The shackle is in two halves, and the
In order to get
testing machine.
specimen is centred by the set screws.
JUECOLD
LOURDOND
S
FIG. 74.
「

es
S
a uniform distribution of stress in the neighbourhood
of the shoulders, two thin wedges, or keys, are driven
in at the back of the specimen.
71. Kortum's Patent Rope Attachment.-Ropes are
amongst the most difficult of materials to hold satisfac-
torily in the testing machine. Fig. 75 shows a form of
attachment which appears to have been used satisfac-
torily both for hemp and wire ropes. The figure shows
an ordinary attachment, and not one made specially for
testing. But shackles of precisely this kind, made some-
what more strongly, have been used in the testing
laboratory at Berlin for testing ropes. By any process
of splicing or knotting the rope is injured, or at least
bending stresses are introduced which weaken the rope
in the neighbourhood of the shackle.
184
TESTING OF MATERIALS OF CONSTRUCTION
FIG. 75.
Kortum's shackle consists of a conical shell or
thimble, provided with a hook or loop, and having
internal gripping wedges k
which compress the rope be-
tween them. The wedges
are so formed as to compress
the rope concentrically, and,
having a greater taper than
the thimble, the pressure is
greatest at the free end of
the rope and least near the
mouth of the thimble. Hence
the bite on the rope increases
regularly from the mouth
backwards. The wedges have
teeth on the inside, which indent the rope without
sensibly injuring it near the mouth of the shackle.
They are easily fixed, and adjust themselves automatic-
ally as the tension comes on the rope.

a-b
a
II. SHACKLES FOR OTHER TESTS.
72. Fig. 76 shows a crushing shackle, designed by
the author for short specimens. There s is the speci-
men, a cube of stone, for instance, which rests between
the two parts of the shackle. The pull on the shackles
exerts a crushing force of equal amount on the stone.
The shackles are guided by the side bolts, so that the
opposite faces remain parallel. To distribute fairly
the load on the stone block, which may be, to a small
SHACKLES FOR HOLDING TEST BARS
185
extent, out of truth, a cup-and-ball distance piece, with
well lubricated surfaces, is placed between the upper
face of the stone and the shackle.
FIG. 76.




73. Kennedy's Torsion Shackle. - Fig. 77 shows a
form of friction grip used by Prof. Kennedy for holding
specimens subjected to torsion; s is the specimen, held
between two V-shaped fixed jaws and a third movable
jaw. This last is centred eccentrically to the curvature
of its surface, so that the slight rotation of the specimen,
186
TESTING OF MATERIALS OF CONSTRUCTION
I
tending to turn the jaw, produces a considerable fric-
tional grip.¹
FIG. 77.
74. Transverse or Cross-breaking Shackles.-Fig. 78
shows shackles for transverse tests supplied with the
machine of Messrs. Buckton. A
vertical machine lends itself less
conveniently to transverse test-
ing than a horizontal machine,
but, on the other hand, no slides
interfere with the accuracy of
the test. The shackles shown are


steel castings. The specimen s s (in the figure a rail
bar) is shown supported between two standards a a,
fixed on the lower shackle, and the centre shackle b.
The standards a a can be adjusted through a limited
range for different lengths of
span. There are rough knife-
edges at the points of sup-
port. The shackle shown is
intended for loads up to 50
tons.
S
FIG. 79.

1
T
[C
B+0
the Werder machine.
be held in the ordinary tension shackles. The rivet or
bolt to be sheared is in double shear.

75. Shearing Shackles.-
Fig. 79 shows a simple form
of shearing shackle used in
The shackle is formed so as to
'Iron and Steel,' by P. V. Appleby. Proc. Inst. Mech. Eng.
vol. lxxiv.
SHACKLES FOR HOLDING TEST BARS
187

FIG. 78.
୪
b
20
S
S
"
B
OD
Blood
Exp
D
с
日
​
TE
76. Shackle for Indenting Bars to determine the Hard-
ness. It is for certain purposes necessary to determine
the relative hardness of different specimens. For this
188
TESTING OF MATERIALS OF CONSTRUCTION
FIG. 80.
purpose the plan generally used is to indent the speci-
men by a given load, and measure the depth of indenta-
tion. Major Wade used a hardened-
steel pyramidal point, or knife-edge,
as shown at A (Fig. 80), held in a
guide-block which could be placed
in the testing machine. A A pressure
of 5 tons was used to force the point
or edge into the specimen, and the
relative hardness was taken to be
proportional to the volume of inden-
tation. Colonel Rosset has improved
this arrangement by adopting the
form of point shown at B. The
point consists of two knife-edges
inclined at 163°, the angle of the knife-edges being 90°.
Mr. Turner has used a quite different method. He
fixes a diamond in a wooden lath, so that it rests nor-
mally on the specimen. The weight in grams which
must be placed on the lath to cause the diamond to
scratch the specimen is taken to be proportional to the
hardness.

A
B
ida
77. Forms of Test Bars for Tension.-In Fig. 81, a
shows the old form, used by Hodgkinson for cast iron,
with pin shackles; b shows a form suitable for cast
iron, used by Professor Kennedy. For cast iron the
author prefers the form k, with screwed ends and nuts
with spherical seatings.
For ductile materials, such as wrought iron and soft
SHACKLES FOR HOLDING TEST BARS
189
36"
I
8"
·
12"-
__
I..
→
答
​k---4
* FULL SIZE
α
25
2
13 25 2"
321
ટદ
k---oor--
* 564
——
dist
ស
100
FIG. 81.

-4"-
* 40 *
←35→
-3"
1
*-50-*30*
25 dia.
\
← 12 to 15 rad
25-2050 20
"
192
4
25.23
16"
b
200-
с
- 10″-
d
16 to 18
e
10" to 12
/03
f
-240-
h
9
7
k
m
15/00
200
~*
20 dia
"}
10 to 12
Less
240 rad.
-
-2종
​4
32
-30-
+50+20-251
<
AUDONO
+1½

steel, the forms c, d, e, f, g, h, k, l are used, and the
ordinary size of these is marked in metric or English
190 TESTING OF MATERIALS OF CONSTRUCTION
dimensions. c, d, e are ordinary forms for plates, the
two last being for wedge grips. The recessed form d is
better than e, but in ductile materials the form e, which
is cheaper, may be adopted without much fear of the
specimen breaking in the shackles ; ƒ is a form for round
bars, held in wedge grips with V-shaped recesses in the
faces; g and h are standard forms in the German Imperial
testing laboratories; k is a very convenient form, the
ends being chased to a screw-thread in the lathe-nuts
are put on when the specimen is
tested; 7 is the general form for which
the shackles of the newer American
machines are adapted, and is often made
of greater length; m is the form adopted
by Bauschinger for wood.
FIG. 82.
Fig. 82 shows the most usual form of briquette for
tension tests of cement. The briquette is made in a
mould. Stone and similar materials may be tested for
tension in wedge grips, and test specimens are then
generally simple prisms.
78. Shearing and Torsion Test Specimens.-Fig. 83
shows a specimen prepared for shearing of the form
*
I
·
-1-1883
99
a
22
--
-

16
FIG. 83.
← 2 →
k-2-d
FIG. 84.
.6 25

← 1′* 1'
"
b
used by Professor Kennedy. Two narrow grooves are
cut, so that the shearing planes are defined. Fig. 84
SHACKLES FOR HOLDING TEST BARS
191
shows Thurston's form of torsion test piece, the ends
being square to fit the shackles and the centre part
cylindrical.
Test Specimens for Crushing.- Fig. 85 shows the
ordinary forms of test specimens for compression. For
metals such as iron, steel, cast iron, or brass, small
FIG. 85.

a
b
-12-
-P
4 cube-
3%
4.
33-
6
*སྙལ
с

cylinders a are used. For cement, stone, &c., cubes, as
at b. For wood, Bauschinger has found it to be de-
sirable to protect the ends with a metal plate, a sheet of
paper being interposed. The form he adopts is that
shown at c.
192 TESTING OF MATERIALS OF CONSTRUCTION
·}
CHAPTER VI.
MEASURING INSTRUMENTS.
ORDINARY graduated measuring instruments are re-
quired in the engineering laboratory to determine the
dimensions of test bars. In some cases the deforma-
tions (elongations, deflections, &c.) can be measured
accurately enough by the same instruments. For the
more accurate measurement of strains, however, special
measuring instruments are required.
79. The Graduated Straight-edge.-Steel straight-
edges of different lengths, graduated on the edge, are
used for several purposes. For the rougher tests dimen-
sions may be callipered, and the callipers placed on the
graduated straight-edge. Extensions of ductile ma-
terials can be measured in a similar way. Two slight
centre punch-marks are made on the bar, and the dis-
tance between these is taken by a beam compass, which
is then placed on the graduated straight-edge. The
differences of successive measurements are the elonga-
tions. The most convenient graduated straight-edges
are made by the Brown & Sharpe Manufacturing
Company, of Providence, U.S.A. These have gradua-
My
MEASURING INSTRUMENTS
193
tions into inch and inch, and into millimeters
10
and fifths of millimeters.
ساسيالسيليسيلسياسالمسلسلسيليسيا
1
100
80. The Straight Vernier Calliper.-The beam com-
pass of the draughtsman is very commonly graduated
along the beam, and a vernier is fixed on the sliding
head. The fault of the beam compass, however, is the
springiness of the points, and want of perfect truth of
the sliding surfaces of the beam. A straight vernier
calliper is, in fact, a beam compass with very rigid points
and a metal beam. Fig. 86 shows the construction of
CAME
FIG. 86.

CUBA TEEMAMO
اللسان
B
120 15 10
in
10:
Ices
a vernier calliper as made by Messrs. Brown & Sharpe.
A steel straight-edge of very accurate form is bent
down at b to form one leg. On this slides very accu-
rately the sliding head B, carrying the second leg a.
For more accurately adjusting the position of the sliding
head B there is a third slide C, which can be clamped
to the bar, and from which the position of B can be ad-
justed by a fine-pitched screw. The face of B is cut
away to show the scale, and the bevelled face of the slot
is graduated as a vernier.
The most convenient graduation for English mea-
sures is for the scale to be divided into tenths, and each
O
194
TESTING OF MATERIALS OF CONSTRUCTION
tenth into quarters. A quarter-tenth reads twenty-five
thousandths. If now on the vernier a length of twenty-
five quarter-tenths is divided into twenty-five, the vernier
will read off thousandths of an inch.
The outside diameter, or width, of bars is obtained
by placing them between the jaws a b, and sliding the
moving head till contact with gentle pressure is obtained.
The calliper should be held lightly in both hands, and
by slight movements it is easy to determine if the jaws
are square with the bar to be measured. No excessive
pressure must be used or the instrument will be injured.
Inside diameters of rivet-holes and similar measure-
ments may be obtained by using the rounded outsides
of the jaws a b. There is then a fixed quantity to be
added to the reading on the scale. Some callipers, how-
ever, have two verniers, so placed that one reads out-
sides and the other insides.
-
The steel vernier callipers of Messrs. Brown &
Sharpe are extremely useful and trustworthy, and will
even bear moderate rough usage without much injury.
The shortness of the jaws is, however, sometimes incon-
venient.
Instruments of the same kind, somewhat more finely
graduated, and with longer jaws and heavier slides, are
made by Messrs. Holtzapfel and Messrs. Elliott
Brothers.
81. The Screw Micrometer.-This instrument (Fig.
87) is a kind of calliper, and is useful for determining
the dimensions of the smaller test bars. At one end of
MEASURING INSTRUMENTS
195
a bent frame is a fixed abutment, at the other a cylin-
drical bar C, moved by a fine-pitched screw. By
turning the sleeve D, the bar C advances to or retires
from the abutment. An object to be measured is placed
с
FIG. 87.

α
10
D
in the jaws, and C is advanced till there is contact with
gentle pressure. Some tact is required, and it should
be remembered that a force applied to the sleeve pro-
duces a much greater pressure between the jaws. There
is a graduation along the straight cylinder at a into
tenths of an inch and quarter-tenths, and the edge of
the sleeve D is itself graduated into twenty-five divi-
sions, each of which corresponds to a movement of the
1
Τ
jaw of Too inch. As the divisions are open, it is quite
possible to read the scale by estimation to one-fifth
of 1000 inch. But although this reading is easy,
it is not equally easy to ensure the delicacy of
touch required for so great accuracy. In the Brown
& Sharpe micrometer calliper the adjustment to zero,
if the instrument wears, is effected by withdrawing the
sleeve D, and applying a small wrench to a nut inside.
•
0 2
196
TESTING OF MATERIALS OF CONSTRUCTION
The instrument should be tried occasionally to see
whether, when screwed home till the faces of the jaws
touch, the scale really reads zero. If not, adjustment is
required. The accuracy of this instrument depends
entirely on the accuracy with which the fine-pitched
screw is cut. When obtained from a really trustworthy
maker the screw can generally be relied on to read
accurately to the nearest To'so inch. Beyond this
degree of accuracy, however, no screw can be trusted
which has not been independently tested. Usually
these instruments take between the jaws either 1 inch
or 2 inches at most.
1
1000
82. Professor J. E. Sweet's Screw Micrometer.-This
instrument (Fig. 88) is made by the Syracuse Twist
FIG. 88.

falfa teftifie
Drill Company. It has a ratchet-threaded measuring
screw, the working face of the screw-thread being
MEASURING INSTRUMENTS
197
wear.
normal to the axis of the screw, and the back face
inclined. The tops of the thread, both in screw and nut,
are removed, so that after wear a perfect bearing is still
obtained by closing the split-nut. A slight looseness
of the nut will not affect the measurement, on account
of the square bearing of the thread. The screw and nut
are of equal length (3 inches), to ensure equality of
The screw is moved by a sleeve provided with a
milled head and held between washers, one of steel and
the other of felt, to produce an adjustable friction, so
that equal pressure may always be obtained between the
measuring points. The index-bar projecting over the
divided circle is adjustable. The pitch of the most
carefully made screw is more or less variable, and no
two screws are absolutely of the same pitch. This
error is corrected by inclining the index-bar forward
for a screw of too fine pitch, backward for one too
coarse. Each instrument is adjusted by the makers to
a standard 1-inch distance-piece. The index-bar is
mounted on a split-sleeve, threaded upon the extended
end of the measuring nut with a thread of correspond-
ing pitch. This allows the index-bar to be thrown
backward or forward to a convenient position for read-
ing, or even turned a half-revolution, if desired, to
measure work on the lathe, and read the dimension in
that position. The above, which may be termed the
head-gearing, is used only for determining the fractional
parts of an inch. Whole inches are measured by the
aid of standard distance-pieces, furnished with the
198 TESTING OF MATERIALS OF CONSTRUCTION
1
1000
1
64
instrument. The tail-spindle is unclamped, drawn
back, and a distance-piece inserted, and the spindle again
clamped. No special pains need be taken to do this
accurately, as the final adjustment is effected by setting
the index-bar and its sleeve. The milled head is double,
being graduated for Too inch, and for binary fractions
as small as 4 of 32, or 2048 inch. The milled head
by which the screw is turned is mounted freely on the
spindle, and held between a washer of felt and one of
steel dowelled upon the end of the spindle, and tightened
by an adjusting screw. The friction thus produced
secures uniform pressure between the measuring points,
and eliminates the 'personal equation.' A variation of
10000 inch can be recognised. The capacity of the in-
strument is 0 to 4 inches.
83. Whitworth's Millionth Measuring Machine and
Workshop Measuring Machine.-These are fixed instru-
ments, of heavier and much more accurate make than
the ordinary screw micrometer. The screw has 20
threads to the inch, the screw wheel 200 teeth, and the
micrometer wheel is divided into 250, so that each
division represents 1000000 inch. The end of the fast
headstock and the end of the movable headstock are
true parallel planes. The ends of the piece to be mea-
sured must also be true parallel planes. In measuring
to an accuracy beyond 1000 a feeling-piece is used.
This is a piece of steel about 2 inch thick, with parallel
faces. It is introduced between the bar to be measured
and the fast headstock. When proper adjustment has
1
MEASURING INSTRUMENTS
199
been reached, the movement of one division of the
micrometer wheel will set fast the feeling-piece. Without
the feeling-piece it is said that a movement of 40 000
inch can be distinctly felt and gauged.
Fig. 89 shows a machine of this type of American
construction (Richard's machine), with a standard
test piece in the jaws. The machine consists of a solid
THOMAE
amanda.app.mklaasi padains
FIG. 89.

KOHTELIAIMLEREating me da EULARn van deLIDIN DAN
bed, something like a lathe-bed, with two headstocks,
one fixed, the other moved by the accurate fine-pitched
screw. The screw has a graduated head, and sometimes
with a vernier also. The machines are guaranteed to
be correct to 1000 inch. They will read to 25000 inch,
but, without special means of ascertaining the pressure
at the point of contact, such accuracy of reading is
stated to be fallacious.
INSTRUMENTS FOR MEASURING STRAINS.
84. In almost all experiments on the elastic proper-
ties of materials it is necessary to measure the strains
or deformations which correspond to different stresses.
Thus, in tensile tests the elongations are measured, in
torsional tests the twist, in bending tests the deflection.
200 TESTING OF MATERIALS OF CONSTRUCTION
50
In ordinary commercial tests of the quality of ductile
materials, such as wrought iron and steel, only the
ultimate permanent deformation is measured, and since,
in such cases, this deformation is considerable, compara-
tively rough measurements are sufficient. Thus, if a
soft-steel bar is broken by tension, the permanent
stretching of an 8-inch length may amount to 2 inches.
An error of even inch in measuring this would be
only 1 per cent. of the elongation, and that is accuracy
enough for practical purposes. Of course, for somewhat
more rigid material, such as wrought-iron plates, the
extension is less, and it is desirable to make the
measurement more closely. But even in that case no
very refined measurement is practicable, because of the
difficulty of fitting together the broken pieces. To
ascertain the strains in ductile materials during the
progress of a test, after the elastic limit is passed, some-
what rough measurements are also sufficient. But it
is altogether different in observing the strains within
the elastic limit. A mild-steel bar, 10 inches long, is
stretched less than inch when the elastic limit is
reached. For an accuracy of 1 per cent. the error of
measurement must, therefore, not exceed 1000 inch;
and measurement to this degree of accuracy is more
difficult than is commonly supposed. If the true
elastic limit is to be determined, measurements to at
least 100000 inch are necessary. The smallness of this
quantity may be realised by the aid of an illustration
due to Sir J. Whitworth: 100000 inch is only 400 of the
1
100
1
MEASURING INSTRUMENTS
201
thickness of a sheet of thin foreign letter-paper. In
the case of standard measures of length, with bars of
the most suitable form, the measurement, even to this
degree of accuracy, is comparatively easy. But mea-
surements of deformation have to be made on test bars
of a form less suited for measurement and under con-
ditions of some difficulty. Hence special methods are
necessary, and instruments specially arranged for the
purpose.
FIG. 90.
In the case of test bars, a difficulty of measurement
arises out of the occurrence of a change of curvature of
the bar during the test. The bar may initially have a
small curvature, and be straightened by the load; or, if
the load does not act accurately along the axis of the bar,
it may become curved during
the test. Suppose a bar curved
like the bar in Fig. 90 in the
plane of the paper. If the bar
straightens by loading, the dis-
tance between a and b will in-
crease, not only by the amount
of the elongation, but by the
difference of the chord and arc
length ab. Suppose two clips
fixed on the bar normal to its axis, and measurements
taken between two points 2, b2. By straightening of
the bar the clips will become parallel, and the distance
a b₂ will be lengthened by the alteration of inclination
of the clips still more seriously. It is important to

~
(
b3
(2
1
202 TESTING OF MATERIALS OF CONSTRUCTION
notice that if the points a, b, had been taken on the
other side of the bar, an opposite error would have
arisen, the distance being shortened by the straighten-
ing of the bar. Consequently, we may infer at once that
the mean of measurements on opposite sides of the bar
will be much more free of error due to curvature than
any single measurement.
Suppose a, b are two points on the axis of a bar
initially bent in the plane of the paper. Let arc length
a b = 2c, chord ab = 2 a, versed sine h.
=
h. Then-
C =
= √(a² + }} h²), nearly.
50
If now measurements are taken on a straight scale
between a and b, and the bar straightens by tension, it
will have an apparent elongation 2 (c-a), due merely
to change of curvature, and this will enter as an error
into the measurement of the extensions. For instance,
suppose the chord length a b is 10 inches, and the
versed sine of the curve inch. The bar would then
have a curvature probably as great as could occur in a
reasonably good test bar. Then the arc length would
be 10.000026 inches, and an error might arise, from the
straightening of the bar during a test, of 0.000026 inch.
This, however, is a quantity too small to be of import-
Con-
ance in any ordinary measurements of extension.
sequently, if measurements were really made between
points on the axis of the bar, it does not appear that
serious error would arise from any probable amount of
initial curvature of the bar.
MEASURING INSTRUMENTS
203
In fact, however, in all measuring instruments the
measurement is made at a distance from the axis of the
bar. Under the best circumstances the bar would be
measured at two points a, b, on its surface, which, in
the straightening of the bar, would move apart to a
distance equal to the arc length ab, the lines o a, ob
becoming parallel. In most measuring instruments the
case is much worse; the measurements are made between
two points, such as a₂, b₂, rigidly connected with the
bar, and the error introduced into the measurements is
the difference of the length a, b, and the arc length ab.
Since, as has been shown, the difference of the arc and
chord length ab is very small, it will be a sufficient
approximation to say that the error of measurement
will be the difference of the straight lengths a, b, and
ab. Let a a₂ = ∞, and o a = r.
Then-
a2 b₂
a b
?? x
??
a² + h² - 2 h x
a² + h²
If, as before, ab
10 inches, h =
10 inches, h =
inch, and
Then, if by
X
9.968 inches.
2 a
2 a =
x = 2 inches, then a b₂
the straightening of the bar the lines o a, ob become
parallel, an error is introduced in the measurements of
0.032 inch; a very appreciable quantity, even in rough
measurements of elongation. The error is more than
1,000 times as great as it would be if the measurements
were really taken directly at the axis of the bar. If
the measurements are taken on the surface of the
bar at a₁, b₁, the error will be less. Thus, if a α₁ = x
1
50
204
TESTING OF MATERIALS OF CONSTRUCTION
= 0.375 inch, we get a b₁ 9.994 inches, and the error
due to straightening would not exceed 0.006 inch; a
quantity much less, but still large enough to be of con-
sequence in elastic measurements. If measurements
are taken at points symmetrically placed on either side
of the bar, the error due to curvature is nearly elimi-
nated, the lengthening of the distance on one side being
compensated by shortening on the other.
85. The Wedge Gauge.-The wedge gauge is a tri-
angular plate, with sides sloping at 1 in 10, graduated
FIG. 91.

a
¿
а
3
FIG. 92.
along the longer side. If this is pushed between two
pins, or shoulders, the distance between them can be
read off on the scale, magnified by the ratio of the
sloping sides ten times. Professor
Eaton Hodgkinson used wedge
gauges, and the author also used
wedge gauges, for measuring ex-
tensions, about 1856. Two loose
picces, a, b (Fig. 92), were clamped
on the test bar, and the wedge
gauge pushed between them. They
were made to bite into the test bar
سلسل السلسال
2
M
IN
ŏ


-
slightly at two points on the test bar, at a distance l.
As the test bar extended, the wedge gauge slipped
MEASURING INSTRUMENTS
205
1
500
further in, and the differences of readings gave the elon-
gations to inch.
86. Micrometer Screw Extensometer.-A screw is
equivalent to a wedge gauge in a more convenient form.
It is virtually a wedge gauge wrapped
round a cylinder. If p = pitch of screw,
d = diameter of graduated head of the
on which readings are taken,
the distance to be measured parallel
to the axis of the screw, A the dis-
screw
8
tance on the circumference of the head which corre-
sponds to an axial movement à, then-
Δ
100
πα
P
= π dò/p.
πα
A =
"
FIG. 93.

1
20
Let the screw have 25 threads to the inch (p = 0·04),
and the head be about 2 inches
in diameter, and
1
2500
F
1
ΤΟ 00
divided into 100 parts of about inch each. Then
each division corresponds to inch, and can be
read by estimation to quarter-divisions, or Tooo inch.
The accuracy of the instrument depends on the uni-
formity of pitch of the screw, which is often less accu-
rate than it is intended to be. A difficulty also arises
in consequence of the elasticity of the instrument.
Differences of pressure at the point of contact cause
differences of reading.
1
Professor Thurston ¹ appears to have first used an
¹ Materials of Engineering. Thurston. Vol. ii. p. 369.
206 TESTING OF MATERIALS OF CONSTRUCTION
instrument with two micrometer screws placed symme-
trically on each side of the axis of the test bar. These
screws were carried in a clamp fixed on the test bar,
and were brought into contact with steel pins fixed on
a second clamp. By using twin micrometer screws the
error due to curvature of the bar is nearly eliminated ;
for if the straightening of the bar, by tilting the clips,
lengthens the distance on one side, it shortens it equally
on the other. To get rid of the error of different pres-
sures at the point of contact, Professor Thurston con-
nected the two clips with the poles of a battery, so that
contact of the micrometer screw and abutment completed
circuit and gave a signal. It is not quite clear, however,
that circuit is always established with just the same
pressure, and the clips were of very imperfect form,
leaving uncertain the length which was extending.
87. Electric Contact Screw Micrometer, by Messrs.
Henning & Marshall. The micrometer shown in
Fig. 94 is probably the most accurately and carefully
designed screw micrometer which has hitherto been
used. It is described in a paper read before the American
Society of Mechanical Engineers in 1885, and the instru-
ment was made by the Brown & Sharpe Manufacturing
Company.
It consists of two clips, or carrying frames, A and B,
which grip the specimen s symmetrically between two
steel points and two knife-edges on each clip. As the
distance between the clips increases with the extension
of the specimen, the increment is measured by two
-
1
MEASURING INSTRUMENTS
207
symmetrically placed micrometer screws m m, carried
by one clip, and brought into contact with a pair of
plugs g g on the other clip. The pointed screws which
grip the test bar are at hh, and the spring-pressed
knife-edges at c c. The bars d d are used in fixing
7
g
f
QUIÛIJAM
PLAČILA ZELF LEAST DIE AL MARE AS THEI
m
!
A
B
n
CMMANER
N
TILBU
STEFNIRJINAN
kn
τ
2
Li
RUDEL
S
C
S
S
FIG. 94.

h
d
n
BACK VITALO
FLUKE FREE
TIME
ι
บ
UJ
g
LV
FLAME
m
the clips initially at the right distance apart. They are
then moved out of the way while the instrument is in
use. Vertical scales ee are provided, as well as the
graduation on the heads of the micrometer screws mm.
Each of the frames is connected with an electric bell,
a circuit being established when the point f of either
micrometer screw touches the contact-plug g. To
208
TESTING OF MATERIALS OF CONSTRUCTION
ensure proper adjustment in a plane normal to that of
the micrometer screws, the centring screws hh are
brought to bear on the surface of the test bar, after the
rods dd have been thrown into gear, and the points of
the micrometer screws placed over the centre of the
contact-plugs. Then the centring screws are forced
slightly into the test piece, so as to hold securely. After
this, the side bars d d are gently removed, and the
electric wires attached. The plane of contact of the
micrometer screws and contact-plugs is in the middle
of the measured length.
It is claimed for this apparatus that :---
(1) Its construction is symmetrical.
(2) It is applicable to various shapes of test bar.
3) It can be adjusted with certainty, so that the
screws are symmetrical with the test bar.
(4) The micrometer screw-heads are of large size,
giving readings of small extensions.
88. Screw Extensometer with Levels.'-Fig. 95 shows
diagrammatically an arrangement the author has adopted,
and which obviates most of the difficulty of employing
a micrometer screw. Two clamps grip the specimen
between pointed set screws, a a and bb, at points on a
plane passing through the axis of the bar. The lower
clip carries the micrometer screw e, on the hardened
point of which the upper clip rests. If, then, the clips
can be kept exactly normal to the axis of the test bar,
the micrometer screw measures the distance between
Proc. Physical Society, vol. viii. p. 178.
MEASURING INSTRUMENTS
209
C
two points on the axis of the test bar-namely, the points
on the intersection of a a and b b with the axis. Or, to
put it another way, the micrometer screw being at the
middle of the width of the clips, it measures the mean
extension of the two sides of
the bar. Now to set the clips
accurately normal to the axis
of the bar they are provided
with delicate levels. Before
taking a reading these are ad-
justed. The lower clip is first
set level by the adjusting screw c
d. Next, the upper clip is set
level by the micrometer screw
e; lastly, the reading is taken
on the graduated head of the
micrometer screw. Fig. 96 is
a general view of the instru-
ment applied to a flat test bar.
C1 C2 are clips; ll levels; m the
micrometer screw;r a bar of
adjustable length to suit dif-
ferent test bars. The instru-
ment is very easy to use; the
pressure on the micrometer screw is constant, being the
weight of the upper clip; and lastly, the measurements
are virtually measurements made on the axis of the bar,
so that errors due to curvature are nearly eliminated.
The instrument constructed reads to 10 inch.
с
1
FIG. 95.

MEDIT
لسلسلسلبيلسا
e
е
d
COO
P
210 TESTING OF MATERIALS OF CONSTRUCTION
an
FIG. 96.
89. The Cathetometer. The cathetometer is
instrument for determining the difference of level of two
points by a telescope sight. It may therefore be applied
to determining the elonga-
tion of a bar under stress by
reading the length between
two fine diamond scratches
before and after the stress is
c applied.
It consists of a telescope
with cross wires, carrying a
sensitive level, and sliding
on a very accurately formed
vertical slide. The slide is
carried on a support, round
which it can rotate. Suppose
the axis of rotation adjusted
accurately vertical, and the
slide adjusted accurately
parallel to the axis of rota-
tion. Lastly, let the axis of
the telescope be adjusted to
the horizontal by the aid of
its level-tube. Then if the
し
​LOKALAMA
m
T
7
Pllana, pana wonde
7
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A g

telescope be set in succession on two points, and readings
taken on a scale attached to the telescope-slide by a
vernier attached to the telescope, the difference of the
readings will be the difference of level of the points.
The cathetometer is for certain purposes extremely
MEASURING INSTRUMENTS
211
valuable. The readings are taken from any convenient
distance, without its being necessary to touch or even
approach the bar to be measured. The measurements
are taken directly on an accurate scale, and are absolute
measures, not needing any reduction, and not depending
on any other measurements. On the other hand, in
determining elongations or deflections the cathetometer
is laborious in use. The need of taking two vernier
readings for each measurement of the bar wastes a good
deal of time.
The author has used a cathetometer by Breithaupt,
of Cassel. This has a cylindrical central support, which
can be set by a circular level indicating to 10 seconds.
The prism on which the telescope slides is of cast iron,
with an inlaid silver scale 1 metre in length, divided
into millimeters. This prism is balanced by a weight
on the other side of the axis of rotation. To adjust
this prism accurately vertical a special separate adjusting-
level of great sensitiveness is provided. The telescope,
fixed in Y's on a brass slide-block, is reversible, and
carries a striding-level, also reversible. By a clamp
and tangent screw the telescope cross wire can be
brought into accurate coincidence with the object. The
block carrying the telescope has a vernier reading
on the silver scale on the prism to mm. (or 30
inch).
500
1
20
By means of a micrometer eyepiece a cathetometer
may be used to read to obʊ inch. In connection
with one of the testing machines at Berlin there is a
1
10000
P 2
212 TESTING OF MATERIALS OF CONSTRUCTION
cathetometer with two telescopes, having micrometer
eyepieces, so that both marks on the bar can be read on
the cathetometer at the same time.
90. Touch Micrometer.-Every mechanic is accus-
tomed to take dimensions in callipers with very great
accuracy. Hence it appeared that a process equivalent
to callipering would be delicate enough even for mea-
suring small elastic extensions. The author constructed
an instrument of this kind in 1883 which proved simple
and convenient.
Suppose two clips fixed on a test bar in some way
which strictly defines the length of bar which in extend-
ing carries the clips. Let there be on the clips case-
A
C
B
be
(-
you
FIG. 97.

(D
WWE
JUL (3
hardened plugs in pairs opposite each other. If the
distance between these plugs is callipered during a test
the amount of extension can be determined.
Fig. 97 shows a kind of micrometer calliper. It
consists of a frame having a sliding-piece A, which
slides without shake, and can be fixed by a set screw.
MEASURING INSTRUMENTS
213
The piece D is merely an adjusting piece, ordinarily
clamped, which can be replaced by a longer piece if
necessary, to suit different lengths of test bar. Both
the sliding-pieces A and D have hard-steel plugs at
their ends. In use the instrument is held in the hand
between the clips on the test bar, and the steel plugs
brought into contact with those on the clips with gentle
pressure. The slide is then clamped, and the reading
taken.
The sliding-piece has two scales, A and B. The
scale A is read by sight against a vernier on the frame
to hundredths of an inch; the other scale is read
through the microscope micrometer. Fig. 98 shows the
field of view in the microscope: ab is a fixed cobweb,
corresponding with the zero on the
scale A. In the field is rather more
than a tenth of an inch on the scale
B, the tenths being divided into fifths
of tenths (or fiftieths) of an inch.
From the reading on the scale A the
precise tenth in the field of view is
known. Suppose that e reads on the fixed scale 2.2.
Between e and the zero g are two fiftieths and a fraction
of a third. The point ƒ therefore reads 2.24, and it
only remains to measure the distance fg. This is done
oy bringing the crossed cobwebs to ƒ by means of the
graduated head C of the micrometer, when the number
of tenths of thousandths of an inch which measure
FIG. 98.
77
Ap

ď
f g
is read off on the graduated head. The process is
214 TESTING OF MATERIALS OF CONSTRUCTION
tedious to describe, but it is extremely simple in
practice. Further, as the same tenth of an inch usually
remains in view for the whole period of a test in which
the elastic extension is measured, it is in general only
necessary to note the reading on the graduated head C
after the first reading.
The instrument is simple; the readings are taken
on a finely graduated scale, and the errors of the micro-
meter screw are virtually reduced, because an enlarged
image of the scale is measured. The author has found
it easy to read to
to read to ʊʊ inch, with an error of not more
than 5th, and even more delicate reading is possible.
It is also more rapid to use than without experience
would be expected. Two or more readings on different
sides of the bar can be taken if desired.
1
500
Cowper's Extensometer.-Mr. Cowper has described
an extensometer used in testing long bars for the Kieff
Bridge in 1850. It consisted of a light iron tube about
4 feet long, with a small brass fork at each end which
fitted against pins attached to the test bar. One fork
slid on an accurate slide and carried a vernier. This
fork was pushed home against the pin by a spiral
spring. For comparatively rough measurements the
author has used a vernier extensometer of the same
kind on short 8-inch or 10-inch bars. It gives readings.
to To inch.
1
1000
91. Lever Extensometers.-Many instruments have
been used in which the extensions of a bar are me-
Proc. Inst. of Mechanical Engineers, 1878, p. 256.
MEASURING INSTRUMENTS
215
chanically magnified by a lever. The defect of such
instruments is that the extension is measured between
clips often attached to the bar in an unsatisfactory way,
and that, to obtain sufficient magnification, the short
arm of the lever is so short that the range of indication
is very small.
Col. Paine's Lever Extensometer.-In Mr. A. V.
Abbott's work¹ on testing machines there is described
a neat and simple form of lever
extensometer shown in Fig. 99.
This was used by Col. Paine
in tests made at the East River
Bridge. The apparatus con-
sists of two bars, A and B,
arranged to slide parallel to
each other. At one end of
each bar there is a knife-edge
F in a brass slide, and initially
these knife-edges are adjusted
to a known distance apart.
The instrument is clamped to
the test bar K by springs
G G, which press the knife-
edges into small indentations
N
N
A
FIG. 99.

H
K
DU
E
PTTTTT
G
in the bar. A lever C is fixed on the bar B. Its
short arm bears on a projection O on the bar A, while
its long arm moves a vernier D, which slides in the
projecting guide E.
Abbott, Testing Machines (Van Nostrand's Science Series), p. 86.
216 TESTING OF MATERIALS OF CONSTRUCTION
Kennedy's Lever Extensometer.-Prof. Kennedy has
designed and very largely used the simple lever extenso-
meter shown in Fig. 100. This consists of a light frame
C
i
FIG. 100.

i
f
S
с
W

พ
f carrying a simple lever i.
The two steel points, one
on the frame ƒ, the other on the lever i, are 10 inches
apart. These are placed in centre punch marks on the
¹ Proc. Inst. of Civil Engineers, vol. lxxiv.; also lxxxviii. p. 24.
MEASURING INSTRUMENTS
217
specimens, the apparatus being held in position by elastic
bands cc, a weight w helping to preserve the balance.
The lever i turns on two set screw points, and the other
end moves over a plane covered with section paper,
attached rigidly by an arm to the frame on the test bar.
As the piece extends the steel points move apart, turn-
ing the lever round its axis. The leverage is 100 to 1,
and readings can be taken to 10 inch. The ratio
of magnification was determined by measurement with
vernier callipers.
10000
Dupuy's Extensometer for Actual Structures.-The
object of this apparatus is to ascertain by direct
measurement the alterations of length of different mem-
bers of iron structures by loads. Assuming that a bar
of iron is elongated or shortened Tobooth part of its
10000th
length by stress in tension or compression of 1.27 ton
per sq. in., it is possible to calculate from the observed
alterations of length the stresses in the bars produced
by the loads. To the bar to be tested a fulcrum pin is
attached, on which works a lever arm, with a leverage
of 20 to 1, terminating in a pointer moving over a
graduated arc carried by the fulcrum piece. To the
short end of the lever is jointed a bar 1 metre (3.28 feet)
in length, a pin at the other end of this bar being also
attached to the bar to be tested. With the proportions
adopted, each millimeter of movement of the pointer
on the scale corresponds to a stress of a kilogram
1 Ann. des Ponts et Chaussées, 5th series, vol. xiv. p. 381.
218 TESTING OF MATERIALS OF CONSTRUCTION
per sq. mm. in the bar to be tested (0.635 ton per
sq. in.)
92. Differential Cathetometer. This instrument was
exhibited by Dr. Heinrich Streinitz, of Gratz, at
South Kensington in 1876,¹ and appears to have been
used by him some years earlier in researches on the
FIG. 101.
elasticity of wires. Dr.
Streinitz appears to have
originated a method of
measurement which is ex-
tremely delicate. Fig. 101
shows the principle of the
apparatus: a a is a stout
glass rod carried by a
heavy foot; on this are
clamped the two frames
bb; cc are rods sliding
in the frames bb, and dd are jointed prolongations,
serving to adjust the instrument; mm are light touch
levers, which by weights or springs are kept in contact
with the bar s to be measured.

a
MALAD
LAB
b
C
SATUAJ
FIN
d
d
m
m
These levers rotate in the plane of the sketch on
pins at the ends of the bars dd, and each lever carries
a mirror m perpendicular to the plane in which it
rotates. Every movement of either end of the bar s
will cause a rotation of the corresponding mirror. Now,
suppose a telescope and scale so placed that the gradua-
¹ Catalogue of the Special Loan Collection of Scientific Apparatus at
South Kensington Museum, 1877, p. 60.
MEASURING INSTRUMENTS
219
tions of the scale are seen after reflection at the mirror
in the telescope. Then, as either mirror rotates, the
graduations will move in the field of the telescope.
Now let be the movement of one end of the bar to
be measured, and ▲ the corresponding change of scale
reading. Let L be the distance of telescope and scale
from the mirror, and r the radius of the lever m to the
point of contact with the bar s. Then-
2 L
Δ
GS
I'
1
Now, as can be made as small as one centimeter, and
L as much as 5 meters, the movement can be magnified
1,000 times. If a good telescope is used, tenths of milli-
meters can be read on the scale, and consequently the
movement of the end of the bar can be determined to
100 millimeter. The difference of the movement of
the two ends of the bar gives the change of length of
the bar. It is obvious that the method of measurement
is one of extreme delicacy. The apparatus in no way
interferes with the free movement of the bar. There is
some labour in taking the two readings and computing
the difference, and perhaps some difficulty in deter-
mining with sufficient accuracy the small radius of the
lever r. Dr. Streinitz determined r by using a sphero-
meter. The rod a a is of glass on account of its small
coefficient of expansion. Moreover, the glass tube may
be filled with water, and the temperature ascertained by
thermometers. A correction for any change of tem-
perature can then be applied.
C
Uor M
220
TESTING OF MATERIALS OF CONSTRUCTION
In 1879 Prof. Kennedy exhibited at the Institution
of Civil Engineers a two-mirror arrangement similar in
principle to that of Dr. Streinitz.¹ But he has given
up its use in favour of the lever extensometer already
described.
93. Bauschinger's Roller and Mirror Extensometer.2
To Prof. Bauschinger belongs the credit of first sys-
tematically taking double measurements on opposite
sides of a test bar. A pair of clips, formed like parallel
vices, are clamped on the bar at a and b (Fig. 102).
FIG. 102.

e1
->
b
J1

92
di
dz
2
C1
C2
a
a
These grip the bar between knife-edges. The clip b
carries a pair of hard ebonite rollers d1, d2, on accu-
rately centred spindles. The spindles are prolonged
upwards and carry the mirrors J1 J2, which rotate in the
plane of the figure as the spindles rotate. The rotation
of the mirrors is measured by reading-telescopes (1, 2,
(
1 Engineering Laboratories,' Kennedy. Proc. Inst. of Civil Engineers,
vol. lxxxviii. p. 22.
2 Maschine zum Prüfen der Festigkeit der Materialien, construirt von
Ludwig Werder, und Instrumente zum Messen der Gestaltsveränderung der
Probekörper, construirt von Joh. Bauschinger. München, 1882. Also
Mittheilungen a. d. Mech. Techn. Laboratorium in München, Hefte
1 und 3.
MEASURING INSTRUMENTS
221
t
2
and scales f at a distance of 10 or 15 feet. The scale-
divisions, seen by reflection in the mirrors, cross the
wire in the field of view of the telescope. The mirrors
have vertical and horizontal adjustments for bringing
initially the scale into the field of view of the telescope.
To turn the rollers d₁, d₂ proportionally to the extension
of the test bar, the clip a carries a pair of spring pieces
C1, C2, which touch the rollers d₁, d». The face of these
spring pieces is slightly roughened by a file or by
attaching a strip of the finest emery-paper, and they
turn the rollers by frictional contact. It will now be
obvious that any extension of the distance between
the vices a and b will cause a rotation of the mirror g
through an angle /r, where is the radius of the
roller. The apparatus is equivalent to a lever ap-
paratus having for small arm the radius of the roller
I,
and for long arm the double distance of the scale.
from the mirror. Suppose, for instance, as in one of
Bauschinger's instruments, the radius of the roller is
0.3214 cm., and the scale distance 160.7 cm. Then
the magnification of the extension is (1607 × 2)
1
0.3214 = 1,000. The scale is divided into fifths of
centimetres. Each division has, therefore, in measuring
extensions the value of 50 millimeter, or about
10b60 inch. As it is possible to estimate tenths of
oooo
divisions, the readings can be taken to 5 millimeter.
Since in Bauschinger's apparatus there are two
mirrors, two readings are taken, giving the extensions
on the two sides of the bar. The mean of these is
1
5000
222 TESTING OF MATERIALS OF CONSTRUCTION
taken to be the true extension, free from error due to
initial or induced curvature of the test bar.
Bauschinger used instruments similar in principle
for measuring compression of stone, the lateral con-
traction of metals, &c. For rougher measurements the
mirror and telescope are abandoned, and a light index-
finger moving over a scale is substituted.
Cat
An apparatus similar in principle to Bauschinger's
was used by Col. Flad in the tests of material for the
St. Louis Bridge. This apparatus had, however, only
one roller and mirror, which for delicate measurements
is essentially defective. According to the St. Louis
Bridge experiments, the modulus of elasticity of the steel
deduced from the measurements varies from 11,000,000
to 50,000,000 lbs. per sq. in. But it is almost cer-
tain that the modulus has only a range of about
27,000,000 to 33,000,000. Prof. Bauschinger pointed
out this to the author as an indication of the error of
taking measurements on one side only of the bar.
94. The Author's Roller and Mirror Micrometer.¹-The
author has attempted to get rid of the trouble of taking
two readings by a device similar in principle to that
used in the screw extensometer. Two clips, a and b
(Fig. 103), are attached to the test bar s by pointed set
screws on a plane passing through its axis. The lower
clip is supported by the adjusting screw d, and the two
clips are spaced apart by a distance-piece e with knife-
edge ends. A roller r, carrying a mirror m, is fixed
1 Proc. Physical Society, vol. viii. p. 178.
MEASURING INSTRUMENTS
223
FIG. 103.
in the upper clip at the same distance in front of the
distance-piece e as the set screws are behind it, so that
if the bar extends the roller approaches the lower clip
by the same amount that the set screw
a retires from it. In moving it rotates
against the finger-piece f, and turns
the mirror. By a reading-telescope and
scale the amount of rotation of the
mirror is observed. The roller being
at the middle of the clip between the
set screws gets a movement propor-
tional to the mean extension of the
two sides of the bar.

95. Strohmeyer's Roller Extenso-
meter.¹-Mr. Strohmeyer has designed
an apparatus acting similarly to Bau-
schinger's, though the principle is car-
ried out in a different way. A wire
of small diameter is used for the roller,
and a light index-finger attached to the
wire, moving over a graduated arc, gives
the extensions magnified sufficiently.
·
1886.
d
M
S
α
18
Fig. 104 shows one form of the apparatus.
clips are fixed on the bar by pointed set screws.
of these carries two flat plates of steel, about 1 inch
wide, one on each side of the test bar. The pairs of
plates on each side of the test bar are pressed together
Two
Each
1
'A Strain Indicator for use at Sea.' Trans. Inst. of Naval Architects,
224 TESTING OF MATERIALS OF CONSTRUCTION
by springs, and between them is placed the wire roller,
carrying a light index-finger. As the bar extends, the
plates slide relatively and rotate the rollers. Mr.
rotnog
Elman
mony
II
FIG. 104.

Kw
አስገባ
Md.
Lion
11000
1
Strohmeyer states that he has obtained good results
with a wire of 0.015 inch circumference. Then, the
graduated are having divisions equal to of the cir-
cumference, each division corresponds to Tooo inch
extension.
150
1
Comparing Strohmeyer's apparatus with Bauschin-
ger's, it is obvious that the most essential difference is
MEASURING INSTRUMENTS
225
the extreme smallness of the rolling pin which Mr.
Strohmeyer uses. That this is convenient may be
easily granted. It is more difficult to believe that such
very small wires can be trusted to be circular in section.
Further, the absolute measurement of the elongations
depends on the exact measurement of the diameter of
this very small wire; and this must in fact be impossible
to anything like the same proportionate degree of
accuracy as in the case of the larger rollers of Bau-
schinger.
It would seem, therefore, that Mr. Strohmeyer's
apparatus is rather better adapted to cases where relative
extensions only are required. To such cases Mr.
Strohmeyer has applied it with remarkable skill. By
its means he has determined the relative extensions of
members of bridges, and of different parts of the skin of
a ship and the shell of a boiler, under their ordinary
loads.
96. Instrument for Measuring the Compression of Short
Blocks. For measuring the compression of short blocks,
such as cubes of stone, extremely minute measurement
is necessary. The author has employed the arrange-
ment shown in Fig. 105, which combines lever and
optical magnification, and at the same time gives by a
single reading the mean compression of the two sides of
the block.
A
A rectangular frame c₂ C, with adjustments for
blocks of varying size, is clamped on the base of the
stone cube by four pointed set screws. It carries an
Q
226
TESTING OF MATERIALS OF CONSTRUCTION

FIG. 105.
FS
QUERIES
top, on which rests
the knife-edge of
an upper frame c₁,
which is clamped
on the cube by
two set screws
near the middle
and near the top.
The frames are
prolonged by the
levers 11, 12, so
that the ends a
and i move two
and a half times
as much as
as the
points of the frames
fixed in the cube.
The ends of the
levers carry silver
plates with a fine.
diamond scratch,
and these plates
are adjusted to be
near together in-
itially by the ad-
justing screws at p and a. The lever l₂ has a constant
W
LINKUTTA
S₂
IN
Tuustraia
C1
71
VUOMI UTITU
BILSTONE
P
M
We are
273
1 2
C 2
1000
O
DOMES
upright pillar p,
with a hardened-
steel
adjustable
MUUTA.
T

MEASURING INSTRUMENTS
227
position relatively to the plane through the points in the
set screws in the frame c₂. The lever 4, turning on its
knife-edge on the pillar p, rises at i two and a half times
as much as the stone compresses between the set screws
on c₁ and those on c. Further, as the instrument is
entirely carried by the stone cube, it is not affected by
any movement or elasticity of the machine. During
the test the distance between the diamond scratches on
a and i is measured by the microscope M- and micro-
meter m. Readings too and 5000 inch can be
taken with moderately powerful object glasses. The
chief difficulty is to get the diamond scratches fine
enough. The fixed cross wire of the micrometer is first
set on one diamond scratch, the movable wire on the
other. Then the reading of the micrometer head gives
the distance.
1
0
Q 2
228
TESTING OF MATERIALS OF CONSTRUCTION
CHAPTER VII.
AUTOGRAPHIC RECORDING APPARATUS.
97. ALL ordinary testing is largely concerned with the
determination of the relation of stress and strain at
different loads. In Chapter III. it has been shown that
the relation of stress and strain throughout a test can
be graphically exhibited by a stress-strain diagram. If
a testing machine could be made itself to describe a
stress-strain diagram, it would be a very interesting
record of the behaviour of the test bar.¹ Such a diagram
would show the yield point, if there was one, the
maximum load and breaking load, and the elonga-
tion at each period of the test. From sufficiently
detailed measurements during the test such a diagram
can be plotted, and many such plotted diagrams are
given in the Report of the U.S. Testing Board. But
such plotting is laborious, and it is very convenient to
have it done mechanically. Further, an autographic
diagram is free from personal bias and accidental errors.
of record.
¹ Much of the information in this chapter was given in a lecture on
"The Employment of Autographic Records in Testing,' at the Society of
Arts, February 1886.
AUTOGRAPHIC RECORDING APPARATUS
229
It has been stated that an autographic diagram taken
in the absence of an inspector of materials might be
accepted as equally satisfactory as the inspector's report.
But that is claiming too much for the autographic dia-
gram, which could be tampered with as easily as any
other record of a test. The datum line can be dis-
placed to increase the loads, and a finger on the pencil
will increase the extension record. Still, a perfectly
continuous record, showing all that has happened during
a test, is no doubt extremely useful.
98. Thurston's Autographic Testing Machine.'-This
machine is intended to test the quality of materials by
means of inferences from the torsional strength and
rigidity. Tests of that kind are convenient because
the specimens do not require to be large, and the twist-
ing moments necessary can be produced by comparatively
small forces at a moderate leverage. The deformation
before fracture is also large and easily measurable.
Inferences from torsional experiments, however, are
hardly so trustworthy as those from direct stresses,
except in the case where a material is intended to be
C
This machine has been very often figured and described. Professor
Thurston's papers will be found chiefly in the Trans. Am. Soc. of Civil
Engineers, and the following may be referred to: The Mechanical Pro-
perties of Materials of Construction,' 1874, vol. ii. p. 349; vol. iii. p. 1.
This paper contains the first account of the autographic torsion machine.
'Note on Resistance of Materials,' 1875, p. 334; 'Strength of Materials
deduced from Strain Diagrams,' vol. v. p. 9; 'Resistance of Materials as
affected by Flow,' vol. v. p. 199; 'New Method of Detecting Overstrain,'
1878, vol. vii. p. 53. It may be pointed out that the regression of the
stress-strain curve at the yield point (see § 30) appears to have been first
shown in some of the diagrams in these papers of Thurston.
230
TESTING OF MATERIALS OF CONSTRUCTION
used to resist twisting. Hence it is with some reserva-
tion that assent can be given to Professor Thurston's
claim, that 'the machine is capable of revealing charac-
teristic properties upon which to base sound practical
judgment as to the relative usefulness of materials for
the various purposes for which they may be required,
and under the different conditions of their production or
manufacture.' The test bar for this machine is a small
cylindrical bar inch to inch in diameter, with square
ends. It is placed in a pair of jaws, one connected
with a heavily weighted pendulum, the other with a
worm and wheel. By driving the screw-gearing one
end of the specimen is rotated, and the twisting moment
is balanced by the weighted pendulum, acting at the
other end and is measured by the sine of the angle
through which the pendulum is moved.
A drum covered with a sheet of specially ruled
section paper is fixed to the worm-wheel shackle, and a
pencil attached to the pendulum turns with it. Hence,
the pencil traces on the drum a circumferential line pro-
portional to the difference of motion at the two ends, or
to the twist of the specimen. The pencil has another
movement parallel to the axis of the test bar; as it
rotates with the pendulum, it is forced by a guide curve
to move a distance axially proportional to the twisting
moment (sine of angle of inclination of pendulum).
Hence, the pencil draws a stress-strain curve,
curve, the
abscissæ of which are the strains or angles of twist,
and the ordinates the twisting moments. Professor
AUTOGRAPHIC RECORDING APPARATUS
231
Thurston's machine is simple and ingenious, and its
use enabled him to detect directly that when a load is
applied, removed, and reapplied, the yield point is
found to be raised. But the machine has defects. It is
wrong in principle to take the register of the strains
from the clips which hold the specimen. The crushing
of the ends gets registered as part of the deformation.
The arrangements do not secure perfectly that there is
no longitudinal or bending stress. The friction of the
pendulum journal and the momentum of the pendulum
may both influence the results.
Professor Ewing's Experiments.-In 1880 Professor
Ewing made some experiments in Japan on the stress-
strain curve for small wires.¹ The wire was loaded by
filling a bucket with water. A pencil attached to the
wire marked a line on a sheet of paper, which at the
same time moved transversely a distance proportional
to the load. The paper was moved by a string attached
to a float. The diagrams are very similar to the earlier
diagrams of Thurston.
99. The Polmeyer Autographic Apparatus.-In 1882
the author saw at Dortmund a 50-ton tension testing
machine, designed by Professor Polmeyer expressly
for autographic testing. It is a pendulum machine, with
a very long pendulum, having a ton weight at the end.
As one end of the specimen is pulled by a hydraulic
press, the other pulls on the pendulum, and the stress is
related to the angular rise of the pendulum. It is easy
¹ Proc. Royal Society, 1880.
232 TESTING OF MATERIALS OF CONSTRUCTION
*
to see that a paper connected by one wire to the
pendulum, and a pencil connected by another wire to
the specimen, can be so arranged as to draw a true
autographic diagram.
Fairbanks' Autographic Apparatus.-In Mr. Abbott's
little treatise on Testing Machines there is described in
considerable detail a large testing machine, constructed
by Messrs. Fairbanks in America, with an autographic
apparatus attached. The machine is a 100-ton machine,
and adapted for tension, compression, bending, and
other tests. It is a compound-lever machine, in which
the final lever is a steelyard with travelling weight or
counterpoise.
Now to effect the adjustment of the counterpoise
on the steelyard to the stress on the specimen, a very
ingenious electrical arrangement is used. As the steel-
yard rises or falls against its stops it completes an
electric circuit, which starts an electro-magnetic engine,
which moves the poise. Thus, if the lever rises, showing
that the stress exceeds the load applied by the steelyard,
the electro-magnetic engine moves outwards the counter-
poise till, balance being restored, the circuit is broken.
Geared to the arrangements for moving the counterpoise
is a drum or cylinder on which the record is made, and
the rotation of this drum is therefore exactly proportional
to the movement of the counterpoise on the steelyard.
Consequently, a pencil held fixed over the drum would
trace a circumferential line the length of which is pro-
portional to the load on the specimen.
AUTOGRAPHIC RECORDING APPARATUS
233
The pencil, however, has a second motion parallel
to the axis of the cylinder, derived from a thin flexible
steel tape attached to two clips on the specimen. This
is led off over pulleys, so as to move the pencil axially
along the cylinder. The defect of the arrangement is
that the elongation is not magnified, and the tape is so
long that it is hardly possible it can give the pencil a
quite true movement free from any error due to slack
in the tape. It is stated, however, that the error does
exceed inch.
1
100
100. Mr. Wicksteed's Autographic Apparatus.-This
is an apparatus fitted to the Buckton testing machine,
shown in Fig. 55, p. 134. The motion of the pencil
which indicates the load is derived from the fluid pres-
sure in the hydraulic press, and not from the weighing
apparatus. A pipe from the hydraulic press F is led
to a small cylinder like an indicator cylinder, with a
piston of 1 sq. in. in area. This piston is controlled
by a strong spring, 15 inches long when unloaded,
5 inches long when loaded with 22 cwt., the full pres-
sure on the piston when the pull of the machine is
50 tons. During a test, as the pull and consequently
the fluid pressure, increases, the spring is compressed,
and the pencil P moves horizontally along the recording
drum D. On the test bar s are two clips J J, and a
wire attached to weights resting on the lower clip is
carried over a pulley on the upper clip, and over the
links G, finally serving to rotate the recording drum D
by an amount proportional to the elongation. Hence,
234 TESTING OF MATERIALS OF CONSTRUCTION
the pencil having an axial motion proportional to the
load, and the drum a motion of rotation proportional to
the extension, a stress-strain diagram is described.
To eliminate the influence of the friction of the
small indicator piston, it is kept in rotation by the
pulleys shown at the end of the recording apparatus.
The friction at a high speed is small, and practically
the friction of the cup-leather of the small piston
appears to be neutralised by this rotation. The object
of the link-work, G, is to eliminate the influence of
the motion of the test bar as a whole, due to the sway
of the lever or slipping in the clips. The arrangement
is perfectly correct in principle.
There is some practical convenience in taking the
load indication from the hydraulic press instead of the
weighing apparatus. But although the author believes
that practically correct diagrams of small size are
obtained by Mr. Wicksteed's apparatus, yet he has not
altered his opinion that it is faulty in principle to infer
the load from the pressure in the press cylinder, and
likely in unskilful hands to lead to errors.
The pressure in the hydraulic press is chiefly due to
the tension of the specimen, but a not unimportant part
of it is due to the unbalanced part of the counter-weight,
to the friction and inertia of the crosshead and slides,
and to the cup-leather friction of the main ram. The
diagram can only have a uniform scale so far as these
additional pressures are proportional to the load on the
specimen. Further, the cup-leather friction acts upwards
AUTOGRAPHIC RECORDING APPARATUS
235
or downwards according to the direction in which the
ram is moving, and therefore has a doubled effect on
the position of the pencil. Mr. Wicksteed determines
the scale of the diagrams by occasionally checking them
by the use of the lever. He has also found that for the
small diagrams taken, the scale is practically uniform, if
the ram is kept moving in one direction. Mr. Goodman
has added an electrical arrangement, by which a second
pencil marks the diagram as the jockey weight passes
each ton.
101. The Author's Autographic Apparatus.-In 1882,
when selecting a testing machine for Cooper's Hill Col-
lege, the author perceived that Mr. Wicksteed's type of
testing machine, with a single jockey weight, moved by
a screw, lent itself very conveniently to the application
of autographic apparatus, and of autographic apparatus
of a very simple kind, which would not interfere with
the ordinary operations of testing. About that time the
author saw the Polmeyer machine, and was convinced
that, if only a small diagram was required, say, 5 or 6
inches square, the movement of the pencil corresponding
to the elongation could be perfectly well transmitted by
a thin wire. An apparatus on a somewhat large scale was
completed at Cooper's Hill in 1883, and subsequently,
at the Central Institute, in 1885, the smaller apparatus
on the same principle which is shown in Fig. 106. The
chief merit of the apparatus is its extreme simplicity,
while at the same time it is accurate in principle.
In the Buckton type of testing machine (Plate II.)
236 TESTING OF MATERIALS OF CONSTRUCTION
O
€
B
COMPREH
d
alotim
FIG. 106.

M
Q
f
a
Autographic
Apparatus
есе
at
O
ш
S
C
KO
C
O
the stress is weighed by a steelyard, on which there is
a travelling jockey weight weighing one ton. This is
driven by a large screw; consequently, the rotations of
AUTOGRAPHIC RECORDING APPARATUS
237
the screw are exactly proportional to the movement
of the weight, and to the stress on the specimen. It
is from this screw that a vertical paper cylinder d is
driven. A small catgut belt drives a worm, acting on
a worm-wheel of 200 teeth on the paper cylinder. As
the resistance of the paper cylinder is very small, the
motion given by the belt is quite accurate, and it has
this convenience, that by means of a stepped pulley a
several scales are available for the diagram. Neces-
sarily, the specimens vary in size and strength, and it
is extremely convenient to enlarge the load scale of
the diagram for small specimens, and diminish it for
large ones. The pencil p slides on guides parallel to
the axis of the paper, and it is connected to the speci-
men by a very fine wire w, kept strained by a counter-
weight e. The wire is so fine that a counter-weight of
2 or 3 ounces is quite sufficient to keep the wire taut,
and overcome the friction of the slides.
-
On the specimen s are two clips c c, the construc-
tion of which is so arranged that they are perfectly rigid
in position on the bar, and which define exactly the
length in which the elongation is taken, and do not
become slack as the bar contracts. It is extremely con-
venient to magnify, more or less, the elongation, so as
to get a larger diagram. The author has tried several
plans. That most generally convenient is very simple.
The thin wire is attached to the top clip, taken over a
pulley on the bottom clip, again over a pulley on the
top clip, and then horizontally to the guide pulley ƒ on
238 TESTING OF MATERIALS OF CONSTRUCTION
the autographic apparatus. In this way the extension
is exactly doubled.
At first it was feared that movements of the speci-
men would affect the record of extension, and the author
adopted a plan of taking two wires from the specimen,
one neutralising any error in the motion of the other.
He has since found that, by properly placing the appa-
ratus, and leading off the wire from the specimen parallel
to the knife-edge of the testing machine, no measurable
error is introduced due to motions of the specimen.
Parallel to the knife-edge the specimen has no
motion. It has a small vertical motion, due to variation
of position of lever, slipping in clips, &c. But the
greatest possible motion of this kind would not intro-
duce an error in the diagram of inch.
102. Electric Semi-Automatic Recording Apparatus. —
All the ordinary forms of autographic apparatus fail to
register in any useful way the small strains within the
elastic limit. The strains are indicated on the dia-
grams, but on a scale too small to be measured. A
lever arrangement has been tried to magnify the exten-
sions, but with a great magnification the difficulty and
error introduced render the arrangement worthless. It
occurred to the author that a totally different method
of registration would in some cases be very convenient.
A large recording drum is connected with the screw
of the jockey weight so as to turn circumferentially
a distance accurately proportional to the load on the
specimen. A pencil moves on a slide parallel to the
1
100
AUTOGRAPHIC RECORDING APPARATUS
239
axis of the cylinder. To give motion to the pencil
there is an arrangement of electro-magnets and ratchet
wheels. With a commutator in hand the observer can
send a signal which makes the pencil move a step
forwards or backwards at any moment.
Now suppose a test proceeding, and that by the
telescope mirror and scale the extensions are being
FIG. 107.
+56
1:55
.58
.62
.61
60
59
-63
468
1.64
67
66
65
59
61
1.60
56
£55.5+
+63
62
1.64
58 58
1.57 [57 1.52
715
1.56.5
185-1·65
f.65
1.64
+68
68.5
67 67
66
59
J.61
-60
62
63
1.66
1.59
157
161
58
.60
56.5
163
62
-65
64
+66
67
68
Papago małaln
.57
.59
58
-61
LEO
56.5
·63
62
64
-60-
·67
.66
.65
.59
57
.60
L58
62
.64
68
468
.63
67
65
Tons per Sq. Inch
10
Sq buck

9
B
7
6
5
4
3
2
A
1
observed. If a signal is sent at each increase of ex-
tension of, say, Toooo inch, a stepped figure will be
obtained, from which the extension at any moment and
240
TESTING OF MATERIALS OF CONSTRUCTION
the corresponding load can easily be read off. And the
record in this way is effected with great ease and
rapidity.
1
Fig. 107 shows one of the diagrams obtained, and
contains a record of more than 150 extensions, taken in
less than half an hour. Half the readings are taken
with an increasing load, the other half while the load
was being removed. The figure is about one-fourth
the actual size of the diagram, and the steps correspond
to 5000 inch of extension. The diagram is one of the
first taken in this way by students at the Central
Institute. It is not a particularly perfect diagram, but
it illustrates the kind of record obtained by this method.
103. Professor Kennedy's Autographic Apparatus.—
An apparatus devised by Professor Kennedy and Mr.
A. G. Ashcroft is of a different kind. The following
description is taken from Professor Kennedy's paper :¹-
The apparatus cannot be said to be suitable for general
use, but for a laboratory, where it is in skilled hands,
and not subject to rough usage, Professor Kennedy
believes it to give more trustworthy diagrams than any
of the other forms yet devised. It has also the advan-
tage that it is wholly independent of either the poise or
the ram, or even any part of the framing of the testing
machine, and that its own parts are so light that the
diagram may be assumed to be free from any errors
due to inertia. The test-piece a (Fig. 108) is placed in
1
1 Proc. Inst. of Civil Engineers, vol. lxxxviii. p. 30. A detailed
drawing of the apparatus is given.
AUTOGRAPHIC RECORDING APPARATUS
241
the machine in series with a stronger bar b, called a
spring piece, and the two, which are connected directly
by simple coupling, are pulled simultaneously, the
one through the other. The spring piece is of such
a material that its limit of elasticity occurs only at a
load greater than that which will break the test piece.
It must also be of material ascertained by previous ex-
periment to be perfectly elastic, so that its extension is
strictly proportional to the pull on it, and therefore
to the pull on the test bar. By a simple arrangement
a very light pointer c is made to swing about an axis
b
FIG. 108.

d
a
P
through an angle proportional to the extension of the
spring piece, and proportional, therefore, to the pull on
the test bar. The end of this pointer touches a sheet
of smoked glass d, to which is given a travel-in its
own plane-proportional to the extension of the test
piece, and in this way the diagram is drawn. After
the experiment the glass is varnished to fix the black,
the necessary particulars are written on it with a
scribing point, and the whole is used as a negative,
and multiplied by photography.'
Some of the diagrams taken with this apparatus are
shown in Fig. 28, p. 67. It is a small and not serious
R
242 TESTING OF MATERIALS OF CONSTRUCTION
objection that the load ordinates are curved. The great
merit of the instrument is the very perfect registration
of the stress, free from errors due to any accidental
action of the machine.
Some particulars of a machine acting in a similar
way, and taking a very small diagram, which could
afterwards be magnified, were given by Herr Martens
in the correspondence which is appended to Professor
Kennedy's paper.
Elastic-strain Diagrams.-The only apparatus for
drawing purely autographic diagrams of the strains
within the elastic limit is also devised by Professor
Kennedy. It acts on the same principle as the last
FIG. 109,

U
B
III
10,000
POUNDS
5000
PER O INCH
E
1000
apparatus, but the swinging pointer is placed on the
test piece and used to record its extensions. The frame
is carried by the test piece, and is moved by the poise -
weight of the testing machine.
Fig. 109 shows three elastic strain diagrams taken
by this apparatus for a piece of cast iron 0.75 inch in
AUTOGRAPHIC RECORDING APPARATUS
243
diameter and 10 inches long. The distance A B is the
set after the first loading. There is a small further set,
B C, at the third loading. Exaggeration of extension,
150 to 1.
104. Autographic Extensometers, recording Time and
Extension.-Many attempts have been made to study ex-
perimentally the action of a travelling load on a structure
such as a bridge. In such cases the train which forms
the travelling load moves with uniform speed across
the structure, each member of which passes through a
cycle of changes of stress related to the position of
the moving load. If a diagram can be drawn with the
strains (extensions or compressions) as ordinates and
the time as abscissæ, it is possible to infer the stresses
corresponding to each position of the moving load.
The first instrument of this kind was designed by Dr.
W. Frankel, and constructed by Oscar Leuner in
Dresden.¹
Fig. 110 is a diagram of the instrument. Two
clips C1, C2 are attached to the member of the structure
the strain of which is to be recorded. Between these is
the tubular link attached to the clip C₁ at b, and acting
at the other end a on the unequal-armed lever . The
lever is toothed at the edge and drives the lever l₂,
and this, in turn, gears with a small pinion on the
spindle of the drum D. The levers form a spur-wheel
train magnifying the extension 200 times, and the drum
D moves under the pencil P a distance proportional to
¹ Civilingenieur, 1881; vol. xxvii. § 250.
1
R 2
244
TESTING OF MATERIALS OF CONSTRUCTION
the strain. The clock F at the same time moves the
pencil axially at a uniform speed, driving the pinion
and rack n. Consequently, a diagram is obtained with
FIG. 110.

D
ELI
A
2
12
ITL
C₂
?
လ
F
1717
& celib bond l
7,
m-4(0-1
BEDDED
C₂
abscissæ proportional to the time and ordinates pro-
portional to the strain.
The most ingenious mechanical contrivance in Dr.
Frankel's instrument is that by which loss of time, or
backlash in the spur-wheel multiplying gear, is pre-
vented. Each toothed driver consists of two parts,
connected by a spring only, which presses one part
AUTOGRAPHIC RECORDING APPARATUS
245
forwards and the other backwards against the two
faces of contiguous teeth of the driven wheel. There is
always contact, therefore, between driving and driven
teeth for motion in both directions, and any motion in
either direction is communicated instantly and without
loss of time.
Autographic Deflectometer of Askenasy.-This is a
small apparatus for drawing the deflection curve of a
beam during the passage of a load over it. A paper
recording-drum, moved by clockwork, is clamped on
the beam or bridge. An independently supported style
traces a curve on the drum. The style is on a vertical
rod, at any point of which it can be fixed, and this can
be clamped to a wooden beam supported independently
of the deflecting beam. The curve has time abscissæ
and deflection ordinates.
246
TESTING OF MATERIALS OF CONSTRUCTION
Į
CHAPTER VIII.
ELASTIC CONSTANTS FOR METALS.
105. THE accurate determination of the coefficients of
elasticity and limits of elasticity depends on the measure-
ment of extremely small deformations. Some of the
practical difficulties of measurement have been discussed
in Chapter VI. These difficulties are not the only ones.
in the path of the experimenter. For many materials
the elastic constants change with the amount of stress.
applied and with every repetition of stress, and, to add
to the confusion, there is not complete agreement as to
the definition of the constants or the methods of deter-
mining them.
The nature of the coefficients of elasticity has been
explained in Chapter I. Let it be proposed from
observations on a bar of cast iron to determine its co-
efficient of direct elasticity. When a bar is subjected
to simple longitudinal stress, the coefficient of direct
elasticity E is the ratio of the stress p per unit of section
to the extension or compression 7 per unit of length.
That is, E=p/l. But the total extension of an inch of
bar / consists of two parts-an clastic extension e, and a
plastic extension or set s. If the bar is again strained,
ELASTIC CONSTANTS FOR METALS
247
the set s will be smaller and the modulus of elasticity
p/l will be different. What is, then, the real coefficient
of elasticity?
If a coefficient of elasticity E' =p/e is calculated,
values will be obtained which vary less with repetition
of loading than the values of E. In most cases, also, E'
will be more constant than E for different ranges of
stress. Hence it is a temptation to an observer to get
rid of the sets, and to give values of the coefficient
of elasticity which are values of E', not values of E.
Virtually this is often done; and either the sets are
determined and deducted from the extension used in
calculating the coefficient of elasticity,' or, what amounts
to the same thing, the bar is loaded once or twice nearly
up to its elastic limit before proceeding to measure the
extension used in calculating the coefficient of elas-
ticity.
The following table contains Hodgkinson's results
for the tension and compression of long bars of cast
iron. These results on long bars are chosen because,
although the methods of measurement were somewhat
crude and rough, they are free from any possible
objection arising out of complexity in the measuring
apparatus. It will be seen that both E and E' diminish
as the stress increases, but that E' varies much less than
E. The coefficients are in tons per sq. in. The next
table contains some results on bars of gun-barrel steel,
1 See Lanza's statement as to what is done at Watertown. Applied
Mechanics, p. 419.
248
TESTING OF MATERIALS OF CONSTRUCTION

HODGKINSON'S EXPERIMENTS ON CAST-IRON BARS. MEAN RESULTS ON NINE BARS, REDUCED TO 10 FEET LENGTH
AND 1 SQ. IN. AREA.
Stress, in
tons per
sq. in
p
•9404
Total
extension,
in inches
120 7
•0186
⚫0391
•0613
TENSION
Total
set, in
inches
120 s
Total
elastic
extension
120 e
•0006
•0180
·0018
⚫0373
•0037 •0576
•0793
1.881
2.821
3.762 •0859 ⚫0066
4.703 •1136 •0106
5.644 •1448 •0161
6.603
•1859 ·0241
•1030
•1287
•1618
Ordinary
coefficient
of direct
elasticity
E
Coefficient
E'
6,067
6,269
5,775
6,053
5,525
5,879
5,257
5,694
4,968 5,480
4,677 5,262
4,262 4,898
Stress, in
tons per
sq. in.
•
P
.9212
1.843
2.765
3.685
4.607
5.530
6.451
Total com-
pression,
in inches
120 /
•0188
•0388
⚫0598
•0788
·0994
•1203
•1416
PRESSURE
Total
set, in
inches
120 s
Total
elastic
compres-
sion
120 c
Ordinary
coefficient
of direct
elasticity
E
⚫0005
·0183
5,879
⚫0023
•0365
5,701
⚫0040
•0558
5,549
⚫0065
⚫0723 5,611
·0085
•0909
5,560
⚫0109 •1094
5,516
•0141 •1275
5,467
Coefficient
E'
6,039
6,059
5,947
6,116
6,080
6,066
6,071


ELASTIC CONSTANTS FOR METALS
249
•
made by the Committee on Steel, and which are chosen
for similar reasons. For wrought iron and steel the
set in the earlier part of the test is comparatively in-
significant. Yet E' is more constant than E, even in
the earlier part of the test, and is nearly constant even
for stresses considerably beyond the elastic limit. For
wrought iron and steel E diminishes almost to zero ast
the breaking weight is approached.
EXPERIMENTS OF STEEL COMMITTEE.
(Bars, 14 inch in diameter. Extensions and compressions in 10 feet.)
Stress, in
tons per
sq. in.
p
6.80
7.94
9.07
10.21
11.34
12.48
13.61
17.01
6.92
10.38
13.84
15.28
16.15
17.31
18.46
Total
extension,
in feet
120 l
•0053
*0062
•0071
·0079
*0089
*0098
•0108
•0143
⚫0047
*0078
⚫0105
•0117
•0125
⚫0138
•0172
Set, in
feet
120 s
1
·0001
·0002
•0002
·0003
•0004
·0016
·0001
⚫0003
·0006
•0007
·0011
·0035
Elastic
extension,
in feet
120 e
TENSION
*0070
•0077
⚫0087
⚫0095
•0104
0127
PRESSURE
*0047
*0077
⚫0102
·0111
•0118
0127
•0137
Ordinary
coefficient of
direct
elasticity
E
12,830
12,800
12,770
12,920
12,750
12,740
12,600
11,900
13,300
13,180
13,060
12,920
12,540
10,740
Coefficient
E'
12,830
12,800
12,960
13,260
13,030
13,140
13,090
13,400
13,480
13,570
13,770
13,690
13,620
13,480
No doubt in most cases values of E are given as the
coefficient of elasticity, and it will be understood that
it is so in what follows. But then materials like cast
iron and all the brasses and bronzes have no definite
coefficient of elasticity.
250
TESTING OF MATERIALS OF CONSTRUCTION
106. If in loading a bar the yield point is passed,
the material is altered, and generally this is shown in
an alteration of the coefficient. With a rest of a day
or more after loading the bar partially recovers, so
that the alteration of the coefficient is less. The follow-
ing table gives some results from Bauschinger's paper
on the Change of the Elastic Limit':-1
(
COEFFICIENT OF DIRECT ELASTICITY IN SUCCESSIVE LOADINGS OF THE
SAME BAR, IN TONS PER SQUARE INCH.
Weld iron.
""
""
Ingot iron
""
Copper
Bronze
""
""
Material
;"
Weld iron
""
""
""
19
""
""
""
Ingot iron
""
•
•
""
•
•
""
Bessemer steel
Copper
Bronze
•
•
Bars unloaded and reloaded after a pause varying from 3 to 80 hours.
12,920
12,590
12,680 12,720
12,860
12,970
13,040
13,080
12,600
13,270 12,790 12,720
12,800
12,780 12,760
14,240 14,270 14,240
14,530
14,400 14,390
14,500
14,180 14,150
13,330 13,200
7,150 3 7,278
12,950
7,144
7,176
5,575
First
loading
Bars unloaded and reloaded immediately.
13,080
13,080
13,960
14,460
Second
loading
7,436 3
5,372
¹ Civilingenieur, 1881.
12,470 12,360
12,640
14,170
7,702
5,575
Third
loading
·
I
•
3
7,188
5,503
7,494
5,499
14,060
13,370
7,214
5,683
Fourth
loading
12,300
11,930
13,610
12,600 2
7,042
3 Yield point not reached in first loading.
12,610
12,580
12,810
12,900 2
13,210 2
14,470
13,880 2
14,100 2
13,460
7,036
6,910
In these experiments the measurements of exten-
sions were probably as perfect as any such measure-
ments which have been made. The differences of the
2 Vibrated after each loading.
-

ELASTIC CONSTANTS FOR METALS
251
coefficients for the same bar may seem not very large,
but they are large compared with the variation of the
coefficient in different qualities of the same material, and,
indeed, in some cases exceed 10 per cent.
With iron the coefficient generally diminishes with
repetition of loading if there is no pause. It diminishes
less if there is a pause. With bronze the coefficient
increases with repetition if there is no pause, and is
practically constant if there is a pause between the
loadings. With copper the coefficient diminishes in either
case.
107. The following are some of the best values of
the modulus of elasticity which have been obtained.
Kupffer's values were obtained by bending and trans-
verse vibrations, and represent values of the coefficient
for small stresses:
COEFFICIENT OF DIRECT ELASTICITY (KUPFFER).
Iron plate, in direction of rolling
across
""
""
""
""
Rolled English band iron
bar iron
""
""
Forged Swedish
Soft cast steel.
Steel adapted for files
""
•
""
•
Density
7.676
7.678
7.643
7.641
7.832
7.842
7.819
Coefficient E,
in tons per sq. in.
11,200
12,160
12,710
12,850
13,560
13,540
13,440
The following table gives a summary of the values
of the coefficient, determined by Knut Styffe, for iron
and steel. According to these experiments the co-
efficient increases slightly by annealing.
1
Styffe also
1 Iron and Steel. Styffe. Translated by Sandberg, p. 147.
252
TESTING OF MATERIALS OF CONSTRUCTION
made experiments on the change of the coefficient with
change of temperature. He found that it decreased
about 0·03 per cent. for each degree rise of temperature
(Centigrade). After a permanent stretching of the bar
it diminished by 4 to 9 per cent.
COEFFICIENT OF DIRECT ELASTICITY OF IRON AND STEEL FROM
TENSION EXPERIMENTS.
Hammered Bessemer steel
""
,,
,,
""
"9
Lowmoor iron
Dudley
>"
Motala
""
""
Rolled cast steel
Krupp
Rolled puddled steel
""
""
""
""
,,
>"
""
Surahammar iron
""
""
""
""
""
""
Charcoal iron (Aryd)
""
•
""
•
""
""
iron
""
""
•
•
•
•
(Hallstahammar)
Probable
percentage
of carbon
1.35
1.26
1.05
0.1
0.15
1.22
0.61
0.66
0.56
0.2
0.09
0.09
0.05
0.2
0.14
0.2
0.1
0.1
0.07
0.07
Coefficient E, in tons per sq. in.
After heating to
slight redness
Initially
13,450
13,660
14,430
15,290
13,940
14,000
13,360
14,280
12,680
12,260
13,510
13,200
13,880
13,610
11,960
12,410
12,940
13,760
14,220
13,640
14,060
15,440
14,340
13,540
Reduced from tables in Civilingenieur, 1879.
13,740
13,720
13,050
13,760
108. The following table¹ gives values for steel,
obtained by Bauschinger, and the tables are interesting
as giving the coefficient for bending, tension, and
pressure. The coefficient of rigidity was also deter-
mined by experiments on torsion. From the values of
ELASTIC CONSTANTS FOR METALS
253
E and G we can deduce values of Poisson's ratio m.
(See §§ 4 and 10.)
COEFFICIENT OF ELASTICITY.
Percent-
age of
carbon
Degree
of
hardness
70543
0.19
0.46
0.54
0.57
13,720
0.66
14,480
0.78
14,980
0.80
13,660
0.87 13,880
0.96
6
Coefficient of direct elasticity, E
From
bending
tests
From
tension
tests
13,780
14,300
13,690
1
(?) 14,740
From
pressure
tests
16,540
13,020
14,730
14,640
13,090 14,220
16,140
12,900 14,480
14,290
13,080 13,840
15,940
14,350
14,480 13,460
14,440 14,730
14,100 13,590
13,820 14,640 13,080 13,970
13,450
13,090
13,370
BESSEMER STEEL FROM TERNITZ.
Coefficient of
rigidity, C
From tension
tests
13,390
13,620
Mean
14,800 13,960 14,500
13,520
13,340
13,480
13,430
13,390
15,040
14,480
14,160
13,900
SIEMENS-MARTIN STEEL FROM NEUBERG-MARIAZELL.
Coefficient of direct elasticity, E
From bending
tests
Mean
13,460
13,210
13,400
13,400
13,340
From torsion
tests
5,575
5,420
5,450
5,320
5,520
5,405
5,670
5,400
5,560
1 Bessemer steel from Teschen.
Mean
5,625
Coefficient
of rigidity,
с
5,470
5,260
5,295
m =
E
20

•32
⚫30
·33
·30
*36
•34
•25
•29
•26
0.305
0.29
m=
E
20
•25
•25
•27
5,401
•24
5,150
•30
Mean 0.262
1
1
The following values are from experiments at
Watertown Arsenal, and are, it is believed, values
obtained after deducting the permanent set. They are
values of E' therefore.
254
TESTING OF MATERIALS OF CONSTRUCTION
For 10 rolled bars, single refined
""
For 9
For 10
For 9 ""
For 10 Phoenix eye-bars
For 6 steel
""
""
Cast copper.
Cast zinc
Cast tin
Brasses
Bronzes
Lead
Gold
Wrought iron
•
•
""
""
""
•
""
""
double refined.
""
•
Platinum wire
Rolled brass
Copper, hard-drawn
annealed
""
Steel castings
Aluminium bronze
Delta metal.
Gun-metal
Phosphor bronze .
•
""
Thurston has obtained from bending experiments
the following values for the bronzes. The values given
are values of E for small stresses, the coefficient diminish-
ing with increase of stress just as in cast iron. A few
other values are added:-
•
•
•
•
E =
6,240 to 4,555
3,118
3,006
5,130 to 6,580
5,935 to 6,840
1,116
Mon
5,130
10,710
5,800
5,580
5,133
8,400 to 14,000
6,704 to 6,536
5,555 to 6,060
4,762 to 5,376
5,950
Coefficient of elasticity
Lowest
Highest
13,790
13,100
15,200
13,105
12,070
13,510
•
12,040
12,310
12,335
11,410
9,996
13,230
•
•
Thurston.
""
""
""
""
""
Wertheim.
""
Unwin.
""
Bauschinger.
Wertheim.
""
Mean
12,540
12,530
12,950
12,680
11,150
13,345
""
رد
""
109. The Elastic Limit.-The difficulty of determin-
ing definitely the elastic limit is even greater than that
of determining the coefficient of elasticity. The earlier
writers took the elastic limit to be the stress at which a
noticeable permanent set was first observed. But then
the stress which is fixed on as the elastic limit depends
ELASTIC CONSTANTS FOR METALS
255
1
on the delicacy of the measuring instruments used.
In proportion as delicacy of measurement increased, it
began to be apparent that for most materials (for all,
perhaps, except very hard steel or glass) some set occurs
with the smallest stresses. To avoid this difficulty, and
get a definite measure of relative elasticity of different
materials, Wertheim proposed the arbitrary rule of fix-
ing the elastic limit at that stress at which the total
permanent set amounted to zooooth of the length of
20000th
the bar.¹ Apart from the purely arbitrary nature of
this rule, it makes the determination of the elastic limit.
extremely difficult, and it leaves out of consideration the
fact that part of the apparent set is not really permanent,
but disappears slowly during a rest. Bauschinger has
shown that for all ordinary materials Wertheim's elastic
limit is considerably above the point at which propor-
tionality of stress and strain sensibly ceases. In the
stress and strain curve of iron and steel the curve bends
somewhat sharply for stresses near those at which marked
permanent set occurs. Thalén proposed to take for the
elastic limit the point of maximum curvature. This
makes the elastic limit depend on the scales to which
the stresses and extensions are plotted, and gives a point
even further from the limit of proportionality than
Wertheim's. Knut Styffe attempted to fix a definite
elastic limit, depending on the rate of increase of set as
dependent on the time rate of loading. This, again,
gives a point far above the limit of proportionality of
stress and strain.
'Poggendorff's Annalen, Ergänzungsband II.
256
TESTING OF MATERIALS OF CONSTRUCTION
In commercial testing of iron and steel some rough
estimate of the elastic limit is usually made. Thus, it
has been proposed to take the elastic limit at the stress
at which peeling of the skin is first visible (Styffe, p.
36), or at the stress at which the testing machine lever
drops (Kennedy), or at the stress at which a rough
measurement of the elongation by compasses is first
possible (Lanza). All these measures are extremely
rough, and what they really determine is the yield point,
not the elastic limit. In almost all tables what is given
as the elastic limit is the yield point, and this may differ
from the limit of proportionality to any extent. More-
over, for materials other than wrought iron and steel
there is no definite yield point. Where there is a yield
point it is best determined from an autographic diagram.
110. The only definition which agrees with the
theoretical conception of an elastic limit, and which is
practically available in testing, is that which makes the
elastic limit to be the stress at which proportionality
between the stresses and strains first visibly ceases when
measurements of considerable delicacy are being made.
Bauschinger has re-adopted this definition, and it is to
his observations chiefly that we must look for any know-
ledge of the elastic limit thus defined.
-
The following measurements of the extension of a
piece of iron from old Hammersmith Bridge will show
how the limit of proportionality can be determined. In
this case the limit in successive loadings, none of which
reached much beyond the elastic limit, slowly rises.
ELASTIC CONSTANTS FOR METALS
257
Link from old Hammersmith Bridge, received from
B. Baker, Esq.
3
This was planed all over to get surfaces for accurate
measurement, and its section was about 12 sq. in. Ex-
tensions for each ton, taken with mirror apparatus :
4
Load in tons
per sq. in.
1234+G
6
7
8
9
10
11
12
Set, load re-
moved
""
""
""
}
Mean
Distance of gauge points, 7·94 inches.
Extensions per ton in ths of an inch
00
First loading Second loading Third loading Fourth loading
1st loading, 1 to 7 tons
2nd
3rd
1 to 7
1 to 8
1 to 9
4th
•
55
57
58
58
58
58 E. L.
61
60
62
||
+ 13
""
""
""
•
58
56
58
57
58
57
59 E. L.
60
11888
-2
54
56
58
58
58
58
58 E. L.
0.003437
0.003449
0.003996
0.004619
89811
60
59
+2
Total extension
58
56
58
58
58
58
58
58 E. L.
60
63
75
+ 32

Mean extension
per ton
0.000573
0.000575
0.000571
0.000577
0.000574
Coefficient of elasticity, 7.94/000574-13,830.
111. So long as the limit of proportionality is not
exceeded, the value of the coefficient of elasticity in
ordinary metals is tolerably constant in successive load-
ings. The following are extensions in successive load-
ings of two pieces of Hammersmith Bridge links :-
S
258
TESTING OF MATERIALS OF CONSTRUCTION
1st loading
2nd
3rd
4th
5th
6th
7th
""
""
""
,,
""
""
""
Material
Weld iron
Ingot iron
""
""
Copper.
Bronze.
""
""
""
Bronze
""
If, however, the yield point is passed, the limit of
elasticity very sensibly alters, as is shown in the following
results deduced from Bauschinger's tables. A plotting
of some of these is given in Fig. 40, p. 102.
ELASTIC LIMIT, IN TONS PER SQ. IN., IN BARS LOADED UP TO THE
YIELD POINT.
Ingot iron
Bessemer steel
Copper.
•
•
Ingot iron
•
•
:
•
•
P
First piece
Bars loaded, unloaded, and reloaded after a pause of 2 to 80 hours
Weld iron
15.84
17.45
15.78
18.80
7.92
1
(3·91) ¹
3.61
8.98
15.78
16.91
⚫00344
⚫00345
⚫00342
⚫00338
2.45 2
3.43
8.98
10.34
10.22
10.30
15.09
11.60
Extensions for six tons
Bars loaded, unloaded, and reloaded immediately
6.41
6.66
4.01
6.57
3.92
4.13
1.14 2
2.61 2
2.50
Original state. Second loading Third loading Fourth loading
First loading
12.38
8.98
15.15
16.48
Second piece
2.58
3.59
4.06
1 No pause between loadings.
⚫00346
⚫00343
*00347
⚫00339
12.94
12.29
14.22
(6·57) ¹
5.13
19.32
3.27
3.59
4:07
Second piece,
after three days
11.93
11.93
·00341
⚫00342
⚫00340
⚫00343
Bars loaded, unloaded, subjected to vibration, and reloaded after a pause
Weld iron
11.14
14.89
12.13
8.28
5.26
5.39
17.10
17.60
5.18
19.56
⚫00342
·00344
·00343

4.62
3.82
6.90
4.12
6.77
5.11
17.45
20.35
18.94
(6.81)
6.83
6.69
5.14
6.87
2 Yield point not reached.
1
259
CHAPTER IX.
CAST IRON.
112. Down to a recent period the ferrous materials
used in construction could be divided into three groups,
marked equally by difference of manufacture, of chemical
composition, and of mechanical properties. Cast iron,
the product of the blast furnace; wrought iron, the
product of the puddling forge, and steel, produced from
wrought iron by cementation, had characteristics so
marked that it mattered little which of their differences
was taken as a basis of classification. As their content
of carbon seemed essentially connected with their pro-
perties, that was generally selected as a means of
discrimination.
As to cast iron no difficulty arises; both its method
of production, its properties, and its engineering uses
leave it in a class apart. It is otherwise with wrought
iron and steel. Since the development of the Bessemer
and Siemens-Martin processes an essentially new
material has been introduced, which is commonly and
commercially termed steel, but which differs from the
s 2
260
TESTING OF MATERIALS OF CONSTRUCTION
older material of that name. The plates and bars of
so-called steel, which are superseding in construction
the old wrought iron, contain carbon, but in a quantity
varying without break, in different cases, from a percent-
age as small as that in wrought iron to a percentage as
high as that in cementation steel. Such plates vary in
tenacity from that of wrought iron to a tenacity at least
double that of wrought iron. Lastly, by far the larger
part of this new material has not the characteristic pro-
perty of the older steels of hardening when suddenly
cooled.
There is, however, a difference between wrought
iron and the new material which is replacing it im-
portant enough to justify a difference of classification.
Wrought iron, and cementation steel as made from
wrought iron, have been in the condition in the puddler's
forge of granular or spongy masses bathed with liquid
slag. This slag is never entirely got rid of, and remains
in the forged material, not in great quantity indeed,
but so distributed as to give rise to a visible structure.
Bessemer, Siemens-Martin, and crucible steel, on the
other hand, have all been fused and more perfectly
cleared of mechanically mixed impurity. They have,
when rolled, a homogeneousness and absence of grain
which is definite and important. If the difference
between puddled and cast material is recognised it will
be found that there are two parallel series of products,
first clearly arranged by M. Greiner, of Seraing :-
CAST IRON
261
PERCENTAGE OF CARBON,
0.0 to 0.15 0.15 to 0:45 | 0:45 to 0.55 | 0:55 to 1.5
Ordinary
iron
Extra soft
steel
|
SERIES OF THE IRONS.
Granular
Puddled
steel
iron
SERIES OF THE STEELS.
Soft
steel
|
Half-soft
steel
Cemented
steel
Hard
steel
|
This classification ignores the property of tempering
as a mark of distinction between iron and steel, which
is in some respects inconvenient. Hence in Germany
it is becoming common to class one series as weld metal,
the other as ingot metal. Weld iron and ingot iron
are those materials which will not temper; weld steel
and ingot steel those which harden when suddenly
cooled.
113. Constituents of Cast Iron.-Cast iron consists.
of iron mixed or combined with carbon, silicon, man-
ganese, sulphur, and phosphorus. Popularly, and
with partial truth, the carbon is regarded as chiefly
determining its characteristics. The carbon exists in
cast iron either combined with the iron or mixed with
it in the form of graphite. The greyer irons contain
most graphitic carbon, and are weaker, more fusible, and
softer than whiter iron. The white iron contains most
combined carbon; but the other constituents have an
influence on the mechanical properties. The composition
of cast iron varies within the following limits, if extreme
qualities, unsuited for foundry use, are excluded :-
-
262 TESTING OF MATERIALS OF CONSTRUCTION
Combined carbon
Graphite.
Silicon
Sulphur.
Phosphorus
Manganese
Iron
•
•
A
•
Per cent.
0.15 to 1.25
1·85,,
3.25
•
•
•
•
•
Per cent.
2.0 to 4.5
0.15 5.0
0.0
0.5
0.0
1.3
0.0
1.5
90.0 95.0
در
""
""
""
";
Silicon tends to hinder the combination of carbon
with the iron, and to render it greyer. Manganese
appears to have a reverse effect.
1
Lately, attention has been paid to the influence of
silicon, and in some cases silicon is now added to cast
iron to improve its working properties. Ferro-silicon,
a cast iron with 10 per cent. of silicon, is used to mix
with other cast iron ¹ to render it greyer, stronger, and
more suitable for foundry purposes. The softest iron
used in the foundry has about 0.15 per cent. of com-
bined carbon. With 1 per cent. the transverse strength
is greatest; with more the crushing strength increases,
but the tenacity and transverse strength diminish. The
amount of graphitic carbon has less influence. The
silicon, when it does not exceed 3 per cent., appears
to be advantageous in securing a soft, grey, strong iron.
Manganese in small quantity appears to be advantageous,
but when it exceeds 1 per cent. the iron becomes white,
and weak except for crushing. Sulphur should not
¹ See papers by Mr. Thomas Turner: 'On the Influence of Silicon on
the Properties of Cast Iron,' Journal of Chemical Society, August, 1885;
December, 1885; and March, 1886. 'On the Influence of Remelting,'
ibid., July, 1886. 'The Constituents of Cast Iron,' Journal of the Iron
and Steel Institute. See also a paper by Ferd. Gauthier, of Paris, ‘On
Silicon in Foundry Iron,' Journal o Iron and Steel Institute, 1886.
CAST IRON
263
Graphite
Combined carbon
Silicon .
exceed 0.15 per cent. Phosphorus in small quantity
renders the iron fluid, but with much phosphorus the
metal is brittle. Remelting cast iron improves its
strength, but if the remelting is repeated too long the
tensile and transverse strength suffer, though the
crushing strength and hardness increase. This change
of properties is connected with a change of the iron
from grey to white by increase of combined carbon
and decrease of silicon. The following analyses, by
M. Gauthier, show the kind of change which occurs in
remelting :

Greatest softness
""
""
""
""
رد
•
hardness.
general strength
stiffness.
In Mr. Turner's very valuable paper (Trans. Iron
and Steel Institute,' 1885) an attempt is made, from an
examination of all existing data, to determine the best
composition of cast iron to obtain certain definite quali-
ties. From this the following table of percentages is
compiled :-
tensile strength
crushing strength
1
•
Original pig
2.73
0.66
2.42
Combined
carbon
Fourth
melting
0.15
0.50
2.54
0.80
1.88
Graphitic
carbon
3.1
2.8
|
over 10 under 2·6
Sixth
melting
2.08
1.28
1.16
Silicon
2.5
under 0.8
1.42
1.0
1.8
about 0.8
264 TESTING OF MATERIALS OF CONSTRUCTION
The density varies with the composition in the
following way :-
Material
Dark grey foundry iron
Grey
Mottled
White iron
""
""
""
""
•
•
p = 6,220 e
Density
= 5,773 c -
6.80
7.20
7.35
7.60
The specific heat is 0.140 for grey iron, and 0.127
for white iron. Cast iron melts at about 2,732° Fahr.
Weight of a
cubic foot, in lbs.
114. Mechanical Properties of Cast Iron.-The elastic
properties of cast iron have already been discussed. In
tension and compression tests there is strictly no range
of stress for which the stresses and strains are propor-
tional, and there is no fixed coefficient of elasticity or
elastic limit. It has, however, already been shown that
the extensions and compressions are nearly the same
for equal stresses (§ 26).
Mr. Hodgkinson found that the relation of stress and
strain in cast iron was given very nearly by the follow-
ing equations. Let p be the stress in tons per sq. in.,
e the extension, and c the compression per unit of length.
Then-
425
450
458
474
1,298,000 €2
233,500 c².
G
The author has found the following inverse relations
still more exact :--
3
C
1.503 p³ × 10-6 +1.685 p × 10-4
c = 966 p³× 10-8 + 1·782 p × 10-4.
CAST IRON
265
These are from experiments on very long bars. For
8-inch bars-
e = 0·39 p³ × 10-6 + 1·62 p × 10-4.
The following table gives a few measurements of
extension in short cast-iron bars. The cast iron was
the ordinary mixture of a good foundry :
EXTENSIONS OF CAST-IROn Bars.
(Extensions in 8 inches, measured by touch micrometer. Bars screwed at ends
and fixed in nuts with spherical seatings.)
Load in tons
2.5
4.5
5.5
6.5
7.5
8.5
9.5
2.5
4.5
5.5
6.5
7.5
8.5
9.5
Breaking
weight, in
tons per sq.
in.
Diam. 1.0005 1.005
Area •7862 •7862
⚫0043
⚫0073
·0093
0114
0139
•0168
·0215
·999
·7832
12.94
Extensions in 8 inches, in inches
·0036 ⚫0034
·0069
·0062
·0087
·0080
•0107
•0105
⚫0132
⚫0134
1.000
·7854
Extensions per ton in 8 inches, in inches
•00172
·00144 ·00136 ·00148
⚫00162
⚫00153 ·00138
·00153
·00169
·00158
·00162
·00175 ·00165
·00172
·00185 ·00176
·00189
·00196
⚫00226
*00145
·00162
·00178
⚫0037
•0069
·0089
·0112
0142
14.37 13.87 13.04
*999
•7832
•993
•7743
⚫0039
⚫0034
•0074
•0061
·0096 ·0083
•0116
0147
⚫0104
·0131
·00156
·00136
·00165
·00136
·00175
·00151
·00178 ·00160
·00196 ·00175
14.21 13.90
115. Ultimate Tensile Strength of Cast Iron.-Tensile
tests give much the best indication of the quality of cast
iron for structural purposes. The crushing strength is
greatest in qualities of iron quite unsuitable for foundry
use, and the transverse strength depends in part on the
crushing strength.
266 TESTING OF MATERIALS OF CONSTRUCTION
area.
In making and in comparing tensile tests the follow-
ing points must be kept in mind. A few not entirely
satisfactory experiments show that in small castings the
strength varies a good deal with the size, the smaller
castings being stronger. Hodgkinson found test bars
of 1, 2, and 3 sq. ins. section to have tenacities propor-
tional to 100, 80, and 77. The form of the test bar
has less influence. Hodgkinson found that bars of
cruciform section were about 1 per cent. stronger than
bars with circular or rectangular sections of the same
Tensile tests are most commonly made on rough
bars with the skin on, and there is a popular impression
that it weakens a bar to take off the skin. This is
almost certainly erroneous, and, as accurate measure-
ments cannot be made on a rough bar, the test bars
ought to be turned. Tensile tests should be made with
shackles having spherical seats, as cast iron is greatly
weakened by non-axiality of the stress. In very careful
tests the test bars should be cast in one with the work
for which the cast iron is used, and not separately.
They can be broken off, and turned to the required
form.
The short table on the following page gives a sum-
mary of the most trustworthy results of tensile tests.
Mr. Turner attributes the higher tenacity observed
in some recent experiments to distinct improvement of
the metal, in consequence of more careful selection and
greater knowledge of the properties of the iron. He
states that a contract has been carried out in which a
CAST IRON
267

****
Experimenter
Minard and Desormes
Hodgkinson and Fair-
bairn
Hodgkinson and Fair-
bairn
Woolwich
Wade
""
Turner 3
Rosebank Foundry
Unwin
Wade
No.
of
tests
13 0.23 to 0.5
1 to 4
3 to 41/2
81
53
6
4
23
Section of
bars in
sq. ins.
6
1.0
|
0.75
TENACITY OF CAST IRON.
Tenacity, in tons
per sq. in.
Highest Lowest Mean
9.08 5.09
7.19
9.76 6.00 -7.37
4.9
6.83
15.3 4.2
10.5
15.7
18.2
20.55
4.75
6.5
10.4
13.7 1
9.12
15.34
13.7
Probable No.
of fusion
2nd
2nd
2nd and 3rd
2nd
2nd
Condition
of test
bars
1815. Love. Résistance de
la Fonte
1837. 'Brit. Assoc. Rep.' VI.
1849. 'Report on App. Iron'
1856. Report of 1858
1856. Report on Metal for
Cannon
1856. Report on Metal for
Cannon
Rough{
Rough
Rough
?
Rough 1885. 'Journ. of Chem. Soc.'
'Industries,' April 1887
Turned
¹ Selected as good iron.
2 Selected as bad iron.
3 Special series of experimental test bars, with varying proportion of silicon.
4 Mean of ten best specimens.
5
Highest result obtained.

268 TESTING OF MATERIALS OF CONSTRUCTION
minimum tenacity of 12 tons was stipulated for, and
only Cleveland iron was used.
Some qualities of iron are greatly improved by re-
melting or by being kept long in fusion. The follow-
ing results were obtained by Major Wade :-
Fusion
Tenacity in tons per sq. in.
Pig
1st
2nd 3rd 4th 5th
5 to 6 9.32 11.06 11.96 12:45
116. Crushing Strength of Cast Iron.-Hodgkinson
used for compressive tests small cylinders and square
and triangular prisms, having heights equal to from one
to three times the transverse dimensions. He placed a
sheet of lead on the faces of the prisms. It is not clear
that this may not have diminished the strength. The
most common form of fracture is shearing at an oblique
plane making an angle of about 56° with the axis.
The crushing resistance is much increased if the
height is so decreased that the plane of least resistance
to shear cuts the faces at which the pressure is applied.
The following results were obtained by Hodgkinson on
cylinders inch in diameter :-
938 1280
11 2
4
Height of cylinder, in ins.
3312
Crushing strength, in
69.3 63.5 60.0 55.0 53.3 53.3 49.6 344
tons per sq. in.
34
The strength is pretty uniform if the height is between
one and three diameters.
117. Transverse Strength of Cast Iron.-Tests by
cross-breaking are so easily made that this kind of test
has been very generally adopted as the commercial test
CAST IRON
269
Authority
Hodgkinson
""
Woolwich
Wade
Turner
Fairbairn
{
Form of test
piece
Cylinders
and prisms
Cylinders
Cylinders
Cylinders
Transverse
dimensions,
in inches
to 23/
1 to
4
Cal+
0.6
0.75
CRUSHING RESISTANCE OF CAST IRON.
|
Height No. of
Width
tests
1 to 3
1 to 2
2
3
81
273
11
|
Crushing strength in
tons per sq. in.
Highest Lowest
64.9
53.8
62.5
74.5
92.5
95.9 2
36.5
24.7
44·6
Mean
34.11
48.0
19.8 40.6
38.5
'Brit. Assoc. Rep.' v. VI. 1837
'Com. on App. of Iron,' 1849
Report, 1858
Thurston.' Materials of Construc-
tion
'Journ. of Chem. Soc.' 1885
1 Series of special test bars, with varying percentage of silicon.
2 Highest result after repeated remeltings.


270 TESTING OF MATERIALS OF CONSTRUCTION
for cast iron. Square bars of 1″ × 1″ cross section, or
more commonly of 2" x 1" cross section, are cast, and
these are placed on supports and loaded at the centre.
The distance between supports is most commonly 3 feet.
The ordinary formula for cross-breaking, which,
however, is an empirical expression when thus used, is
M = ƒZ,
where M is the bending moment, Z the modulus of the
section, and ƒ the coefficient of bending strength. For
a bar of rectangular section, loaded at the centre, this
becomes
W
alm
f
b d 2
/
"
where W is the centre breaking weight in tons of a
bar of breadth b, depth d, and length 7 in inches; ƒ is
f
the coefficient of bending strength, which varies with the
quality of the iron and with the form of the section.
Even when the section is rectangular the propor-
tions of the section affect the coefficient, and for bars of
the same proportions the coefficient is lower as the sec-
tion is larger. The values of the coefficient, as given
in the table on next page, have been calculated from
comparable series of experiments.
It will be seen that, generally, a wide bar gives a
higher, and a deep bar a lower, coefficient. Comparing
Clark's results 1, 4, and 7, and again Millar's 1 and 2,
the coefficient decreases as the section is larger. The cir-
cular section has a higher coefficient than the rectangular.
CAST IRON
271
Authority
COEFFICIENT Or Bending StrENGTH, f, FOR RECTANGULAR Bars.
Centre
breaking f, in
weight, tons per
in tons
sq. in.
W
Clark, E.
""
""
""
""
""
""
""
Millar
""
Segundo
and
Robinson 2
6
Dimensions of bars,
in inches
d
b
123HDONIQSIQ
11∞∞∞∞∞ II
2
3
1
2
131∞∞∞∞HI
2
2
し
​0.252
20.41
0.429
15:45
1.376
18.58
0.475
14-43
1.800 16.20
2 54 2.410 16.27
1.436 12.92
162
36 1.67 22.6
0.358 19.6
36
36
0.785 21.3
54
216
27
162
108
0.9
2.93 20
2.93 0.9 20
3 2 ins. diam. 20
1
4.82
1.50
3.35
18.75
19.05
24.28
D. K. Clark,
Rules,' &c., p.
562
Proc. I. C. E.'
lviii. p. 222
'Proc. I. C. E.'
lxxxvi. p. 248
in.
The actual tenacity of the iron of Mr. Millar's bars,
determined from 66 tests, was 9.45 tons per sq.
That of Messrs. Robinson and Segundo's bars was
11.06 tons per sq. in. It is obvious, therefore, that the
coefficient of bending strength for such bars differs widely
from the tenacity, as has indeed long been known.
In Mr. Millar's experiments the ultimate deflection
was in (1) 0·4 inch; in (2) 0.58 inch; in (3) 0·84 inch.
Results which agree with the formula
3
8 = 8 W 1³/b d³.
The values of the coefficent in some other experi-
ments may now be given.
According to Mr. Millar, tapping a bar with a
hammer during test reduces considerably its strength.
Mr. Millar found no difference of strength in planed
1 Single experiment.
2 These bars were planed or turned.
272
TESTING OF MATERIALS OF CONSTRUCTION
bars and rough bars with the skin on. Messrs. Segundo
and Robinson found the rough bars to be somewhat
stronger than the planed bars. Mr. Millar found that
bars run with hot metal were a very little weaker and
deflected a little more than bars run with dull metal.
COEFFICIENT OF BENDING STRENGTH FOR CAST-IRON BARS.
Coefficient, f,
in tons per sq. in.
Highest Lowest Mean

""
Authority
Fairbairn and Hodgkinson
Woolwich.
Millar
Stephenson, 1847
Turner, 1886
·
•
Dimensions of
bars, in inches No. of
tests
b d l
X
1 × 1 × 54
2 × 2 × 20
1 × 2 × 36
1 × 1 × 36
270 21.0 12.9
564 30.0 6.9
1,344
50
25.6 16.5
28.31
16.3
18.9
22.6
19.6
For the ordinary test bar, 3 feet span, 2 inches deep,
and 1 inch wide, the central breaking weight varies for
different qualities of iron from 6 to 42 cwts. Common
iron ought to carry 20 cwts., good iron 30 cwts., and
Mr. Turner states that iron carrying 40 cwts. can be
produced with tolerable regularity if necessary. The
most common tests imposed in specifications vary from
25 to 32 cwts. It is usual to take the average breaking
weight of the bars of each cast, as from flaws, cold shots,
&c., individual bars vary a good deal. The breaking
weight in cwts. of the ordinary test bar is 40/27ths of
the coefficient of bending strength.
118. Resistance of Cast Iron to Shearing.—The resist-
ance of cast iron to shearing is imperfectly known.
Mr. Stoney found a resistance of 8 to 9 tons per sq. in.
¹ Maximum of special series of test bars.
CAST IRON
273
The following results are from a paper by Messrs. Platt
and Hayward,¹ the experiments having been made at
University College. The cast iron had a tenacity of
about 11.4 tons per sq. in. The specimens were about
inch in diameter:
4
Cast iron, No. 1, turned
No. 2,
""
No. 2, skin on
99
Material
""
•
•
No. of tests
13
12
7
Shearing strength, in
tons per sq. in.
T = 0 196 ƒ d³.
f
5.29
5.08
3.92
It is extremely difficult in shearing experiments to
ensure a uniform distribution of stress on the section,
and it is possible these values are too low.
119. Resistance of Cast Iron to Torsion.-The ordi-
nary expression for resistance to torsion is T =ƒZ;
f Ꮓ
where T is the twisting moment, Z the polar modulus
of the section, and ƒ the shearing stress in the most
strained layer. For a circular section of diameter d this
becomes-
When T is the twisting moment which breaks the bar,
this expression becomes an empirical one, and ƒ then
has values greater than the real shearing stress, just as
in the case of bending. It is better to call the values
of f which correspond to the breaking twisting moment
coefficients of torsional strength.
Experiments by Messrs. Platt and Hayward on the
¹ Proc. Inst. Civil Engineers, vol. xc. p. 406.
T
274
TESTING OF MATERIALS OF CONSTRUCTION
same cast iron as that used in their experiments on
shear gave the following results. The bars were about
ğ inch in diameter. Some Woolwich results on 276
specimens of cast iron 1.8 inch in diameter are also
given, and some American results :-
""
Cast iron, No. 1, turned
skin on
""
No. 2, turned
skin on
""
""
""
""
""
""
""
Material
""
highest
lowest
mean
highest
lowest
•
•
•
•
•
Coefficient of
torsional
strength
f
Tons per sq. in. ¡ Tons per sq. in.
15.9
3,197
18.1
3,402
17.1
2,947
15.3
3,147
22.0
8.25
Coefficient of
rigidity
13.5
23.5
12.5
Authority
Platt and
Hayward
Woolwich
American
MALLEABLE CAST IRON.
120. Malleable cast iron is obtained by heating
castings to red heat in contact with hematite iron ore,
for a period varying from some hours to two or three
days. The amount of carbon in the cast iron diminishes,
and it becomes to a certain extent malleable and capable
of being bent or hammered.
The following tests were made by Professor P. C.
Ricketts, at the Rensselaer Polytechnic Institute (Van
Nostrand's Magazine, 1885). The cast iron had a
tenacity ranging from 6.5 to 13.1 tons per sq. in., the
mean tenacity being 101 tons per sq. in. The elastic
limit given appears to be the yield point. The exten-
sion was measured in series i. in a length of 5 inches ;;
CAST IRON
275
}
Form of bars
in the other experiments in a length of 7½ inches, except
in experiments 6 to 10, series iv., where it was measured
in a length of 10 inches.
TENSILE STRENGTH OF MALLEABLE CAST IRON.
Square
""
1-8
11-14
Rectangular, 1–7
Circular
1-9
1-13
1-8
""
""
·
Mean
Approxi- elastic
limit, in
mate
size
POPPYH
-10
×
X
1x
34
00/30
diam.
""
""
tons per
sq. in.
0.45
1.01
1.33
1.02
•65
Tenacity, in tons per
sq. in.
Highest Lowest Mean
19.7 16.1 17.8
14.5
15.3
16.5
14.6
19.8
16.1
18.2 12.8
Elonga- Con-
tion per traction
cent. per cent.

5.6
6.9
2.0
4.7
2.4
6.6
17.4
3.5
10.0
15.2 1.7
4.3
13.4' 0.8 3.5
1 Skin turned off.
2 Mitt. a. d. K. Techn. Versuchsanstalt zu Eerlin, 1886,
Short prisms and cylinders carried loads of from 48 to
71.5 tons per sq. in. before crushing. In bars broken
by bending the coefficient of bending strength varied
from 20 to 40 tons per sq. in. Martens 2 found the
ultimate tensile strength of malleable cast iron to be
16.4 tons per sq. in.; contraction, 8.2 per cent. ; exten-
sion in 8 inches, 2.5 per cent.; limit of elasticity, about
4.4 tons per sq. in.
p. 131.
T 2
276 TESTING OF MATERIALS OF CONSTRUCTION
CHAPTER X.
IRON AND STEEL.
121. Constituents of Weld Iron.-Broadly speaking,
wrought iron is softer, more ductile, more trustworthy,
and more valuable the purer it is. All commercial iron,
however, contains some carbon, which renders it harder
and stronger, and some other constituents or impurities.
Amongst these sulphur, while little affecting its quality
when cold, makes it red-short and difficult to roll.
Phosphorus has an effect similar to that of carbon, but
phosphoric iron is cold-short and treacherous. Other
constituents are present in quantities so small that their
effect is not well marked.
Constituents of Ingot Iron and Ingot Steel.-It is to
the homogeneousness due to the mode of manufacture
that these materials probably owe their great ductility
as compared with wrought iron. Consequently they
will bear, and as commercially manufactured do in fact
contain, a greater proportion of those hardening con-
stituents, which add to the strength at the price of some
loss of ductility. The purest of them, the low basic
steels, of a tenacity of 24 tons per sq. in., are the most
ductile. In proportion, generally, as alloying materials
D
IRON AND STEEL
277
-
increase, the strength increases and the ductility di-
minishes. Carbon, manganese, phosphorus, and silicon
are all hardening constituents, but, either in conse-
quence of inducing differences of fusibility or differences
of density, they are not equally safe constituents of
steel. Phosphorus, sulphur, and silicon are dangerous
constituents, while manganese and carbon are the most
useful and least prejudicial. Carbon may exist in steel
in proportions varying from 0·15 to 1.5 per cent., the
hardness, strength and capability of tempering increas-
ing as the proportion of carbon is greater. Manganese
appears to be necessary in the manufacture of steel. In
the fluid metal it reduces the iron oxide, and forms with
silica a fluid slag. The manganese which remains acts
like carbon in hardening the steel, but less energetically.
Perhaps, also, it diminishes the ductility less. Usually
steel contains 0.25 to 0.5 per cent. of manganese.
Chromium and tungsten have also been used in pro-
ducing hard and yet ductile steels.
In obtaining steel castings silicon is added in such
quantities that the cast metal contains 0·2 to 0·3 per
cent. of silicon. To neutralise the prejudicial action of
silicon on the stability of the iron-carbon compound,
there should be also manganese to an amount exceeding
the silicon by one-half.¹
It is beyond the purpose of the present work to give
in detail analyses of wrought iron and steel, but the
1 Chernoff. Proc. Inst. of Mech. Eng., 1880, p. 174.
278 TESTING OF MATERIALS OF CONSTRUCTION
following short summary is a guide to the ordinary
composition of these materials :-
Man-
ganese
Wrought Iron 0.02-0.25 0-0·3
Steel:
Tyres'
Rails¹
Mild Plates 2
Med.-hard do.
Carbon
•24-'63 •21-52
•35-'60 ·80-1.0
•115
•504
1·008
•33
Per cent.
Phos-
phorus
0-0·015 0-0·15 99-99.5
Silicon Sulphur
0-0.2
Iron
98 74
|
98.44
·16-3301-·09 ·04-05
04-10-07-14 03-07
·055 ·028 *037 99.35
⚫065 ⚫022 *075 98.40
122. Interpretation of Observations in a Tensile Test
of Ductile Material.-For wrought iron and steel the.
tensile test is the most trustworthy. It is desirable to
examine fully what can be deduced from observations
taken in a careful tensile test, without considering at
present what indications of quality are attended to in
ordinary commercial testing. The table on next page
gives the observations taken in testing a piece of Low-
moor plate. The direct observations are the loads
and corresponding elongations. The final elongation
is measured after the bar is broken, and at the same
time the area of the fractured section.
The maximum stress is 23.2 tons per sq. in.,
reckoned on the original area. Beyond this stress local
contraction begins, and the load has to be reduced.
All through the test the section is diminishing, and
on the principle stated in § 23 the reduced section may
' Mr. R. Routledge of the North Eastern Railway Laboratory.
2 Mr. John Rogerson. Proc. Inst. of Mech. Eng., 1881, p. 564.
IRON AND STEEL
279
•
•
PLATE OF LOWMOOR IRON, No. 142.
(Broken with stress in the direction of rolling. Section, 1 sq. in. Elongations
measured in 8 inches.)

(1)
(2)
Stress, in tons per Elongation, in ins.
sq. in.
P
7302
17
18
19
21
22
23
23.2
22.7
λ
·025
•14
•20
•28
•38
•56
•90
1.34
[1.65]
(3)
Area of section
(1)1
W₁ = w
•997
•983
•976
•966
•955
·935
·899
•857
[777]
7
1+2
9
(4)
Stress per sq. in. of re-
duced section
Pi
17.05
18.31
19.47
20.69
22.00
be calculated. If w is the section when the length is l,
the section when the length is +2, then
and wi
w l = w₁ (1 + x), and
23.54
25.59
27.08
29.20
and the corresponding real stress at the section is
P1
P₁ = p/w₁.
Columns (3) and (4) give values thus calculated. It
will be seen that the real stress increases faster than the
nominal stress.
The final measured extension 1.65 consists of an
extension 1.34 due to the load of 23.2 tons, and dis-
tributed over the 8-inch length, and a further exten-
sion, while the load was diminished, in the local contrac-
tion. By reversing the equation above, the rate of
extension at the section of fracture may be calculated.
It is easily seen to be (w-w₁) 1/w1. This gives for the
rate of elongation at the section of fracture 2.29 inches
in 8 inches, or 28 per cent., which may be called the
-
:
280 TESTING OF MATERIALS OF CONSTRUCTION
elongation at the contraction.¹ How far these deduc-
tions are useful in practically determining the quality
of the material remains to be determined. Obviously,
however, they represent the actual facts of the test more
closely than the usual mode of calculation. For com-
parison a test of Lowmoor plate crossways of the grain
is appended
p
16.0
17
18
19
19.7
Stress, in tons per
sq. in.
P
19
20
21
22
23
24
25
26
λ
26.43
25.5
•015
⚫06
•115
•20
[*32]
The area of fracture corresponds to an elongation of
0.316 inch in 8 inches, which agrees closely with the
measured elongation. This shows there was no local
contraction.
The following table gives similar calculations for a
steel plate
Elongation in
10 ins., in ins.
λ
MILD STEEL PLATE. Area, 1 sq. in.
(Elongations measured in 10 inches.)
*09
⚫33
W1
•40
⚫49
•998
•993
•986
•976
[*962]
•56
•70
.87
1.20
2.15
[2.55]
Pi
Reduced
section
W1
16.03
17.13
18.26
19.47
20.48
·991
•968
•962
•954
III
•947
•935
•920
⚫893
•823
[576]
Stress per sq. in. of re-
duced section
P₁
19.17
20.65
21.84
23.08
24.29
25.68
27.17
29.12
32.11
44.27
¹ M. Considére proposes to call the elongation up to the maximum
load the proportional elongation, and the elongation calculated from the
contracted section the elongation due to striction.
.
IRON AND STEEL
281
30
The fractured area corresponds to an elongation of
7.3 inches in 10 inches, or 73 per cent. The yield
point of this steel was 16·6 tons per sq. in.
123. Stress at which Local Contraction begins.—M.
Considére¹ has indicated that local contraction must
Tons per square inch
~
No 143 X
ot
+SET.N
DEFTON
FIG. 111.
Lowmoor Iron Plates

N:42 L
XLVI ON
JOSION
0.5
1
Extensions in 8 inches
*
2
begin when the load on the bar is a maximum. The
total load on the actual section is p₁ w₁, which is in-
creasing so long as maximum load is not reached.
Hence, the stress p, a given section will carry increases
¹ L'emploi du fer et de l'acier, p. 22.
282 TESTING OF MATERIALS OF CONSTRUCTION
faster than the section diminishes. Consequently if any
section contracts more than the rest it thereby becomes
capable of carrying a greater load. But when the
maximum load is passed this condition, analogous to
B5
B0
Load in Tons
25
20
15
10
SOV IN
N°460
N° 456
FIG. 112.
Landore Siemens Steel

45/
N 462
2
Extensions in 10 inches
stable equilibrium, no longer exists. Then p₁ wi is
diminishing, and p₁ does not increase so fast as w
diminishes. If any section contracts more than the
rest, it becomes less capable than they are of carrying
#
IRON AND STEEL
283
the load, and the deforming action gets concentrated at
that part.
124. General form of Autographic Diagrams of
Different Qualities of Weld and Ingot Iron and Steel.
Fig. 111 shows a series of autographic diagrams
from pieces of Lowmoor plate, 8 inches in length be-
40
35
Tons per square inch
30
25
@20
15
10
es
No 557
BESON
FIG. 113.
Gun Steel

ESSON
099.N
N°561
1/½°
P
Scale of Extensions
Extensions in 2″
W1/2
tween the clips, at which the extension was taken.
Half these are plates broken in the direction of rolling
(marked L), and half across the grain (marked X).
The yield point is less abruptly marked than in the
284
TESTING OF MATERIALS OF CONSTRUCTION
case of steel. The smaller plasticity of the material
Many of the plates break
across the grain is evident.
at the maximum load.
50
40
Tons per square inch
30
20
No 3G
FIG. 114.
Steel Rails

46 ON
No 38
'5"
1″
24/2
Extensions in 2¼½
1.5
Fig. 112 shows diagrams from plates of Landore
Siemens steel. The extensions are given for a 10-inch
IRON AND STEEL
285
length. The yield point is very definite, and the
plastic elongation beyond the yield point is very large.
All draw out locally, so that the final load is less than
the maximum load.
Fig. 113 shows diagrams for some specimens of a
harder steel used for guns, the elongations being taken
in 2 inches. The yield point is distinct.
Fig. 114 shows diagrams for some pieces of steel
rails. The steel here is harder, and the yield point
almost disappears. The drawing out, which seems
characteristic of very homogeneous rolled materials, is
well marked.' 1
2
125. Influence of amount of Carbon in Steel on its
Strength. The results given in table on page 286 are
from Styffe. The steel was made at Surahammar, and
the carbon determined at the School of Mines in Fahlun.
Styffe states also that for Bessemer and Uchatius
steel the strength is increased and the extension
diminished by an increase in the percentage of carbon,
until it reaches 1.2 per cent., when the strength is
61 tons per sq. in. If the amount of carbon is increased
1 The drops of the stress-strain diagram line beyond the maximum
load are easily understood if the extremely small amount of the elastic
extension on which the stress depends is remembered. These specimens
extended a great deal plastically just when the maximum load is reached,
as is shown by the flatness of the curve at maximum load. It was im-
possible then to keep the lever floating. The moment the lever came
on its stops the pump was stopped, and the weight run back till the lever
lifted again. A minute plastic extension goes on during running back,
so that the lever does not lift till the lowest point of the drop is reached.
In running out the weight again an elastic line is described till plastic
extension again suddenly begins.
2 Iron and Steel, p. 46.
286
TESTING OF MATERIALS OF CONSTRUCTION
""
Puddled steel
""
""
">
""
""
""
"
""
Material
""
Iron
""
""
""
""
>>
""
""
""
""
""
""
Mark
NP. 1
B. 1
NP. 2
>>
NH. 1
NH. 2
G. 2
P. 1
P. 2
B. 2
B. 3
G. 2
B. Iron
I
1
Percentage of
carbon
J. Cockerill
Terre Noire
Creusot, Series A (ordinary steels)
B (superior steels)
to 1.5 per cent. the strength and extension are both
diminished. The most complete experiments on the
influence of carbon on the strength of steel were made
by Bauschinger on twelve charges of steel made at the
Ternitz Steel Works. For tension, plates 24 inches long,
2.8 inches wide, and 0.48 inch thick, were used. For
compression, prisms 3.6 inches long, and 1.2 x 12
inch in section were used. The shearing test bars were
6 inches long, 2.8 inches wide, and 0.4 inch thick. The
results are given in the next table.
0.8
0.8
0.7
0.7
0.7
0.7
0.6
0.6
0.55
0.5
0.5
0.2
Various purely empirical formulæ have been pro-
posed to express the relation of the tenacity of steel to
the amount of carbon and manganese it contains. Thus
M. Marché has given the following equations for the
tensile strength T of steel, in tons per sq. in., in terms
of the percentage of carbon C:-
Breaking strength,
in tons per sq. in.
T
49.9
40.5
37.6
37.3
37.4
35.0
32.8
Mittheilungen, IV. 1874.
36.7
38.8
31.7
35.0
21.5
19.05 +44·4 C.
20.32 + 47.6 C.
13·33 + 50·8 C.
15.90 + 50·8 C.
IRON AND STEEL
287
Percentage
of carbon
•14
•19
•46
•51
•54
•55
•57
•66
.78
·80
.87
.96
Mean coefficient of
elasticity in tension
within elastic limit,
tons per sq. in.
}
14,300
13,780
14,300
14,040
13,720
14,100
13,720
14,480-
14,980
13,660
13,900
13,820
Strength at
limit of elas-
ticity in ten-
sion, tons
per
sq. in.
18.73
21.02
21.90
21.62
22.15
20.98
21.02
23.77
23.80
25.45
27.24
30.90
Breaking
tensile
strength, tons
per sq. in.
28.1
30.4
33.8
35.6
35.3
35.9
35.6
40.0
41·1
45.9
46.7
52.7
of area per
cent.
Elongation in Contraction
16 inches
per cent.
21.8
20.1
18.1
14.3
17.8
17.6
18.4
13.7
11.4
9.0
8.1
6.6
49.2
41.7
30.5
25.1
32.8
27.9
30.7
19.7
19.1
14.0
16.5
10.0
Coefficient of elas-
ticity in compres-
sion, in tons per
sq. in.
17,080
16,580
14,660
14,540
16,130
15,040
14,280
15,940
14,480
14,480
14,100
14,600
Limit of
elasticity in
compression,
in tons per
sq. in.
17.65
19.20
21.85
20.64
21.85
22.22
21.85
23.95
23.95
28.20
25.00
31.75
Ultimate
shearing re-
sistance, in
tons per sq. in.
21.7
23.6
22.8
25.5
25.0
25.4
23.1
27.2
26.3
30.6
31.7
37.0
¦
288
TESTING OF MATERIALS OF CONSTRUCTION
Bauschinger's results on Ternitz steel agree well
with the formula-
T=27·62 (1+C²).
M. Deshayes, of Terre Noire, gives the following
equations for the tenacity T and elongation in 4 inches,
per cent., in terms of the percentage of carbon, manga-
nese, and phosphorus :-
T = 19·5 + 11·4 C+ 30 C² + 11.4 Mn + 9.5Ph.
Elongation=4236 C5.5 Mn 6 Si.
-
Col. Maitland gives for steel used for guns at
Woolwich, after oil hardening-
T = 140 C + 20 Mn-10.
V p
126. Increase of Strength from Reworking.- By
repeated piling and rolling wrought iron improves in
quality; but, if experiments by Mr. Clay, of the Mersey
Steel Works, are to be trusted as giving a general law,
there is a point beyond which reworking injures the
iron. He took some puddled bar and rolled it repeatedly,
trying the elongation each time. The following are
the results-
Original State
Second Working
Third
Sixth
Ninth
Twelfth
""
""
""
""
(maximum)
•
Tenacity, in tons per sq. in.
19.6
23.5
26.6
27.5
26.0
19.6
Influence of the Amount of Reduction in Rolling on the
Strength of Iron Bars.-In the Report of the United
States Testing Board, for 1881, data are given showing
IRON AND STEEL
289
that the amount of work put on a bar considerably
affects its tenacity and elastic limit. Tests of iron for
chain cables showed differences of strength for different
diameters, and this led to a special series of experiments,
in which bars of the same iron were rolled so that the
section of the finished bar had greatly different ratios
to the area of the pile from which it was rolled. These
bars were very uniformly heated, as it was found that
underheating in rolling tended to give an increased
tenacity and higher elastic limit, and overheating a
reduced tenacity and lower elastic limit.
Size of bar
INFLUENCE ON THE TENACITY AND ELASTIC LIMIT OF THE AMOUNT
OF REDUCTION IN THE ROLLS.
IRON BARs.
4
oo on ∞ c~~N~HHHHHH
3/30
3 1/
31/1
233
23
2/1
2
ت ستر سات ساتر
1/3
1
13
XPA¡-IfIC XSARXH
1 3
1
13/
HUKKIG IKAWIH
Area of bar
in per cent.
of area of
pile
15.7
13 8
12.0
10.4
8.8
7.4
6.1
5.5
4.4
7.7
6.7
5.8
4.9
4.1
3.4
4.0
3.1
4.9
3.6
2.5
2.2
3.7
1.6
Tensile strength, tons
per sq. in.
Rough bar
21.1
21.6
21.4
22.2
22.5
22.5
22.7
23.6
23.5
22.3
23.1
22.6
22.6
23.3
23.3
24.1
25.4
Core, or bar
turned down Rough bar
20.6
20.8
21.0
21.0
21.3
20.7
21.1
22.0
21.6
22.0
21.8
21.9
23.1
21.8
22.2
22.5
22.8
22.5
22.4
22.9
23.5
24.1
26.6
Elastic limit (approximate),
tons per sq. in.
11
13.25
13.9
16.0
15.9
16.1
15.8
15.6
17.4
17.6
15.8
17.4
15.1
15.1
15.4
17.1
17.2
Turned bar
10.45
10.5
11.1
11.0
11.8
11.7
13.3
14.3
14.2
16.5
17.4
15.2
16.3
18.1
16.8
17.2
14.8
16.0
15.4
17.4
17.9
U
290
TESTING OF MATERIALS OF CONSTRUCTION
#
It is no doubt due to an analogous difference in the
amount of work done on the material in hammering and
rolling that large forgings are found to be weaker than
small bars, and the interior of large forgings weaker
than the exterior. Thus, for instance, a propeller shaft
of the U.S. despatch-boat Dolphin broke on the trial
trip, and test bars cut from the shaft gave the following
results :
From centre of shaft
From surface of shaft
Elastic limit, Tenacity,
tons per sq. in. tons per sq. in.
15.2
14.3
24.1
35.7
Elongation
per cent.
2
18
Some very interesting tests of wrought iron, cut in
different directions from forgings of large size, are given
by Mr. Mallet, in a paper on the 'Coefficients of Elas-
ticity and Rupture in Massive Forgings.' Mr. Mallet
was engaged in the construction of some 36-inch built-
up mortars, and at the same time the Mersey Company
were engaged in constructing the first large forged
wrought-iron gun. The weakest wrought iron was
some cut radially from the end of a heavy cylindrical
forging, which had been exposed during forging to
heating during about six weeks. Its elastic limit in
tension was only 31 tons, and it broke at 6½ tons per
sq. in. Mr. Mallet concluded that the iron of very
heavy shafts, forged guns, or cranks may be expected
1 Proc. Inst. of Civil Engineers, vol. xviii., Session 1858-9. This paper
is interesting from containing probably the earliest carefully plotted stress-
strain diagrams for tension and pressure.
IRON AND STEEL
291
Material
to have an elastic limit of 7 tons per sq. in., and to
break at a tension of 15 tons per sq. in.
are a few of Mr. Mallet's results :--
The following
Hammered slab (12″ × 4′)
Rolled slab (12″ × 4″)
Forged slab (48″ × 48″ × 12´´).
Mersey gun:
Original faggot bars
Longitudinal cuts
Circumferential cuts
Transverse cut
Borings from gun, reforged and
rolled into a bar
•
Tension, in tons per sq. in.
At elastic limit
15.3
10.9
8.75
12.0
9.8-10.9
6·6-5·5
3.28
5.47
At fracture
24.1
23.0
18.6
21.9
19.7 17·9
16.4-16.7
6.56
22.32
127. Effect of Quick and Slow Rates of Loading on
the Strength of Test Bars.-Before deciding on the details
of the tests of the steel for the East River Bridge, ex-
periments were made to determine whether the strength
of the specimens was affected by the rate of loading.
Nine test bars of steel, 1 inch square and 24 inches long,
were cut from the same rolled bar, and these were used
without further preparation. Three test bars were
broken in periods of 3 minutes, three in periods of
6 minutes, and three in periods of 20 minutes. No
difference in ultimate strength was found which could
be attributed to the quicker or slower rate of loading.¹
The influence of time on the elongation has been dis-
cussed in § 36. M. Barba has stated that in rapid
¹ Mr. W. Denny appears to have made experiments leading to the
same result. See Hackney, 'Forms of Test Pieces,' Proc. Inst. of Civil
Engineers, vol. lxxvi.
༦ 2
292 TESTING OF MATERIALS OF CONSTRUCTION
testing the resistance is somewhat greater and the
elongation less than in slow testing. But this conclu-
sion is certainly doubtful.
128. Form and Size of Test Pieces.-The forms gene-
rally adopted for test pieces have been described in § 77.
Unfortunately no general agreement has been come to
as to the size to be adopted. The ordinary Admiralty
test pieces of plates are of the form d, Fig. 81, p. 189,
and for all thicknesses of plates are of such a width
that the section is about 1 sq. in. The extensions are
measured in 8 inches. Other engineers adopt a length
of 10 inches for measuring the extension, and a constant
width of 2 inches for all thicknesses of plates. In the
recent German conferences it has been recommended
that the standard width for all plate specimens shall be
30 mm. (12 inch), and the extension measured in
200 mm. (7.87 inches). The French Admiralty com-
monly adopt test pieces 30 mm. wide and 200 mm.
between gauge points. Undoubtedly plate specimens
11 or 11 inch wide, with the extension measured in
2
4
S
8 inches, would be very convenient, and the results
would be comparable with the greatest number of
earlier English, German, and French results.
For many cases very much shorter test pieces are
unavoidably used. Thus in the case of tyres it is neces-
sary, and in that of rails it is convenient, to adopt much
shorter test pieces. Probably in such cases a diameter
of inch and a length for extension of 2 inches is the
most convenient size.
IRON AND STEEL
293
The criterion of ductility for practical purposes is
either the contraction of area at fracture or the exten-
sion between the gauge points. One objection to the
contraction of area is the difficulty of measuring it,
especially in the more rigid materials; another is the
probability that it is considerably affected by local
conditions of hardness and homogeneousness at the
point of fracture. The extension is less open to these
objections, but then the percentage of extension varies
with the form and proportions of the test piece. This
variation is almost entirely due to the variation of
length of the local contraction. If the extension is
taken, either (1) up to the maximum load before local
contraction begins, or (2) from the broken bar after
discarding the contraction in the neighbourhood of the
fracture, or (3) deduced from the contracted diameter
in parts not near the fracture, the variation of the per-
centage of extension with different forms and propor-
tions of test bar disappears.¹
In the discussion on Mr. Hackney's paper the
author suggested that the bar should be marked in
1-inch or -inch lengths before testing, and the exten-
sion measured, omitting the inch or two in which the
fracture occurred. In the appendix to the discussion
Prof. Styffe made the same proposal.
Professor Kennedy has made experiments on the
effect of varying the form of the ends of plate test bars
According to Barba, the extension up to maximum load is rigor-
ously independent of the proportions of the test bar.
294
TESTING OF MATERIALS OF CONSTRUCTION
on the strength and elongation.' The most important
forms tried are shown in Fig. 115. With soft basic
steel, annealed, there was no difference of strength or
extensibility distinctly traceable to the form of the ends
of the test bar. Even form
II broke fairly in the middle,
and not at the shoulder.
Some pieces of common
wrought-iron plate, however,
showed marked differences
when tested in the forms II
and VII. Hard or inferior
material seems, therefore, to
be affected by the form of the
ends.
I
I
VI
FIG. 115.



129. Variation of Quality
in Pieces cut from the same
Plate. Some experiments
seem to show a more or less considerable difference of
quality in pieces cut from the same plate. No doubt in
some of these cases the differences are due to errors in
testing. If the testing machine is not itself inaccurate,
still imperfect centring of the specimen in the machine, or
imperfect gripping of the specimen in the shackles, may
give rise to considerable apparent differences of strength.
But in other cases there appear to be real differences
in the quality of the material, and the limits of such
differences are not at present determined. Mr. Baker
1 Proc. Inst. of Civil Engineers, vol. lxxvi.
VII
IRON AND STEEL
295
RESULTS OF TESTS OF TWO STRIPS OF BASIC STEEL, UNANNEALED, AND FOUR STRIPS OF WROUGHT-IRON PLATE-ALL
SIMILAR EXCEPT IN FORM OF ENDS (KENNEDY).
(Plates about 3 inch thick and 1½ inch wide.)
Basic steel, II
""
Form
""
VII
Wrought iron, II
II
";
Means
""
Means
Wrought iron, VII
VII
""
Means
Limit of
elasticity,
in tons per
sq• in.
18.87
17.46
18.16
15.95
15.55
15.75
16.05
17.81
16.93
Breaking
stress, in
tons per
sq. in.
28.18
29.12
28.65
21.40
23.60
22.5
Extension per cent. in a length (always
including fracture) of
10 inches 8 inches | 6 inches 4 inches 2 inches
21.8
23.9
20.8 22.5
21.3
4.6 4.8
6.4 6.7
5.5
24.58
14.0
25.28 14.0
23.2
24.93 14.0
5.7
14.2
14.5
14.4
27.6
25.8
26.7
4.7
6.7
5.7
15.5
15.7
15.6
31.7
31.5
31.6
4.5
7.2
5.8
17.2
18.0
17.6
44.5
44.5
44.5
5.0
8.5
6.7
Contrac-
tion of
22.0
area,
per cent.
51.3
51.0
51.2
9.3
11.0
10.2
23.0
21.2
21.0 18.9
20.1
Square corners
Hollow corners
!
Square corners
""
""
""
Hollow corners
);


296 TESTING OF MATERIALS OF CONSTRUCTION
has stated that entire bars, 16 feet long, 10 inches wide,
and 1 inch thick, gave an average tenacity of 19 tons
per sq. in.; while ordinary test pieces, cut from the same
bars, broke at a stress 35 per cent., and even in some
cases 75 per cent., higher. An iron plate was cut up
in the workshops of the Compagnie des Chemins-de-fer
de P. L. M. into 32 test pieces. The strength length-
ways varied from 20:32 to 29.21 tons per sq. in., and
crossways from 20-32 to 23.50. The stretch varied
from 12.5 to 21.5 per cent. lengthways, and from 7.0
to 14.5 per cent. crossways.
2
HARDENING, TEMPERING, AND ANNEALING.
130. If steel containing carbon, manganese, or phos-
phorus in sufficient quantity is heated to about 1,450° or
higher, and then suddenly cooled by plunging into a
bath of cold liquid, it becomes harder, stronger, and less
plastic. The more of the hardening elements in the
steel (up to a certain limit), and the lower the tempera-
ture, and the greater the power of absorbing heat in
the cooling liquid employed, the greater the hardness
produced. Water hardens steel more actively than
oil, and pure water has a greater effect than soapy
water.
In plunging the heated steel into a cooling liquid
the exterior loses heat first, and contracts on the
1 Proc. Inst. Civil Engineers, vol. lxxvi. p. 95.
2 Lebasteur. Les Métaux, p. 194.
IRON AND STEEL
297
interior. There thus result tensions in the exterior,
which may exceed the elastic limit and cause per-
manent stretching or even fracture. Afterwards, the
interior cools and contracts. But it is now attached to
the stretched exterior, and in turn is put into tension.
Thus there may arise in hardening a condition of great
internal stress. The cracking and twisting which often
occur in hardening are indications of this condition of
stress. M. Caron has observed that the volume in-
creases in hardening. M. Considére states that if a
hardened bar is cut in two by a parting tool in the
direction of its length the pieces become curved, with
the concavity on the planed side.¹
By reheating hardened steel and allowing it to cool
slowly, the hardening previously induced is diminished.
This is termed tempering, or letting down the temper.
If the steel is raised to 1,300° or higher, the whole of
the induced hardening disappears, and the process is then
termed annealing. In annealing the temperature must
be high enough, but should not approach the fusing-
point or other changes occur. The cooling must be
slower the larger the mass to be annealed, and in the
case of large masses requires days or even weeks.
Alternate hardening and annealing alter the steel,
somewhat in the same way as mechanical forging.2
The steel, originally coarsely crystalline, and with
¹ L'emploi de l'acier, p. 10.
2 Colonel Maitland, R. A., 'On the Treatment of Gun Steel.' Proc.
Inst. Civil Engineers, 1887.
298
TESTING OF MATERIALS OF CONSTRUCTION
small elongation, changes to a condition of finer grain
and greater toughness. The hardening is most safely
effected with oil.
Sir F. Abel has studied the chemical changes which
occur in hardening and annealing. He finds that in
*Tons per sq. inch.
35
30
2.5
20
15
10
5
0
Hardened.
*****
FIG 116.

619
613 Hardened and afterwards anneuled.
Gul. Not treated.
ULÉKAMAALAJ KR
1
Manganese Steel Bars.
Extensions in 10 in.
2
CJ
3ins.
annealed steel the carbon exists almost entirely in the
form of carbide of iron of definite composition (Fe,C),
uniformly distributed through the metallic iron. In
hardening, the sudden lowering of temperature appears
IRON AND STEEL
299
to have the effect of arresting the separation of the car-
bon as a definite carbide. In tempered steel the condition
is intermediate between that of hardened and annealed
steel. There is less carbide than in annealed steel, but
what there is is of the same composition.'
The autographic diagrams (Fig. 116) show clearly
the changes in the condition of the material due to
hardening and annealing. They are diagrams from
three similar bars of manganese steel, one of which was
tested without preparation, the second hardened in
water, and the third hardened and subsequently an-
'nealed. The yield point disappears in the hardened
bar, the strength is increased, and the plastic clonga-
tion diminished. Annealing restores the steel very
nearly to its original condition, the annealed bar, how-
ever, having a raised yield point and slightly increased
elongation.
Manganese steel
Tenacity, in tons per sq. in.
Elongation in 10 inches, per cent.
Stress at yield point
Contraction of area, per cent.
Original
state
24.71
29.8
16.73
51.6
Hardened
32.69
20.1
55.3
Hardened and
annealed
25.17
30.3
18.76
62.3
alien
In the discussion on Mr. Strohmeyer's paper Mr.
Milton gave the following results of tensile tests of
plates, some of which were tested in their ordinary
state, the others after heating to red heat and quenching
in water at 80°
1 Proc. Inst. of Mech. Eng., 1885, p. 47.
300
TESTING OF MATERIALS OF CONSTRUCTION
""
Very mild steel.
Harder mild steel
steel
""
Material
Carbon, per
cent.
""
Original state
Tenacity,
Elongation
in tons per in 10 inches,
sq. in.
per cent.
Elastic
limit
20 1919
0.150 11.57 23.11 32.5
0.490 14.61 | 30·48 24.8
0.709 19.56 43.31 10.0
0.875 20.83 44.39 8.4
1.050 25.08 54.61 5.2
25
29
35
35
24
23
22 1
22
The following results are given by Lebasteur on
steel from Terre Noire, showing the increased effect of
tempering as the carbon increases :--
3
(The bars were 0.8 inch diameter and 7·9 inches between gauge points.
Stress in tons per sq. in.)
Original state
Hardened in oil
20.83 29.72 28.6
28.32 44.77 12.0
43.69 68.00 4.0
57.47 67.31 1.0
Broke in tempering
Hardened in oil
Elastic
limit
Breaking
stress
After heating and
quenching
Elongation
per cent.
Tenacity, Elongation
in tons per in 10 inches,
sq. in.
per cent.
0.521 16.70 32.90 24.5 26.48 48-58 12.0
0.060 19.81 38.80
41.28 62.87
21.4
17.4
1.305 26.16 48.58
2.008 30.29 56.20 10.5
38
43
50
43 2
Cracked in tem-
pering
A corresponding series of tests of steels containing
different proportions of manganese was also made, the
other constituents of the steel being kept constant.
Original state
10
5
0
11
Hardened in water
19.56 28.83
30.48 49 53
Broke in tempering
Elongation
per cent.
Elastic
limit
Breaking
stress
19.0
2.5
Hardened in water

Elongation
per cent.
1 In 7 inches, and after annealing. 2 Quenched in soapy water.
3 Lebasteur. Les Métaux, p. 72.
IRON AND STEEL
301
A similar series of tests was made with steel con-
taining 0.247 to 0.398 per cent. of phosphorus. The
action of phosphorus was similar to that of carbon or
manganese, but less energetic.
EXPERIMENTS ON THE TENSILE STRENGTH OF STEEL AT THE TERRE
NOIRE WORKS.¹
(Diameter of bars, 0.55 inch.)
Material
Forged steel (containing about
per cent. of manganese
and a trace of silicon)
The same, after hardening in
oil
3
Cast steel, not forged (contain-
about per cent. of man-
ganese and per cent. of
i
silicon)
1
The same, after hardening in
oil and annealing
Percent-
age of
carbon
•15
*49
709
.875
•15
•49
*709 19.69
.875
21·31
•287
*459
•750
•875
Stress, in tons per
sq. in.
Elastic
limit
•287
•459
13.70
16.32
20.43
27.79
42.86
56.38
13.08
16.51
19.00
24.42
19.69
20.87
750 22.30
28.66
.875
At
Breaking
Elonga-
tion in
22.24
34.0
30.40
24.0
42.36 15.0
9.5
46.16
66.72
66.14
4 inches,
per cent.
28.16 28.6
43.92
12.0
4.0
1.0
27.85
26.98
40.00
40.18
8.8
3.0
3.5
1.5
32.27 24.6
34.58 19.2
46.23 14.3
51.46
3.5
131. Injurious Effect when Steel is worked at a 'Blue'
Heat or Colour Heat.-It has long been known, in a
more or less vague way, that in cooling from a welding
heat steel passed through a condition in which it be-
came brittle and dangerous to work. First, it should
be noted that there is a temperature at which the steel
is brittle and little capable of being bent. In 1881 the
¹ Proc. Inst. of Mech. Engineers, 1880, p. 182.
302
TESTING OF MATERIALS OF CONSTRUCTION
Board of Trade, in a Memorandum on Steel, published
the result of experiments made at the works of the Steel
Company of Scotland. Forty-eight plates were taken,
and strips cut from each. Half the strips were bent
cold to an angle of 180° round a bar of a diameter
equal to twice their thickness. The whole of the strips
stood the test. Corresponding strips were heated in
boiling tallow and bent at that temperature. Every
one of the strips cracked before the bending reached
180°. Second, a plate heated and allowed to cool is
no worse for the operation; but this very curious
action appears to occur. If, while in cooling the steel
is at blue heat or colour heat, mechanical work by
hammering or bending is done on the then brittle plate,
it will be found when cold to be seriously injured in
quality.
Prominent attention was first directed to the in-
jurious effect of working steel at a blue heat in a paper
by Mr. Strohmeyer.¹ The most interesting results were
obtained by the bending test. The test strips were
bent alternately in opposite directions till they broke,
and the number of bendings was taken to be an index
of the ductility of the material. The test strip was
clamped between a steam-hammer and its anvil, and
the projecting end was bent down by hammering (over
a mould with rounded angle) through an angle of 45°.
The test strip was then turned over and bent in the
opposite direction. Mr. Strohmeyer takes 'blue heat'
* Proc. Inst. Civil Engineers, 1886.
IRON AND STEEL
303
as a convenient expression for any tenperature between
470° and 600°. Broadly, it was found that while a test
strip bent cold would stand twenty to twenty-six bend-
ings before cracking, if it was once bent while at blue
heat and allowed to cool, it broke afterwards with very
few bendings. The following table gives a summary of
the results :
Conditions to which the strip had been
brought
•
Unprepared or annealed
Bendings while at blue heat
Bent at blue heat once and
cooled
Bent at blue heat twice and
cooled
Bent once cold
twice
""
four times cold
eight
""
19
"
25
""
Average No. of bendings before cracking
Medium-
hard steel,
inch
Mild
steel,
inch
Very mild Lowmoor
steel,
iron,
3 inch
inch
16
21
21
CO
3
113
20
193
124
1/1
2/
- ∞
1913
-2-2
26
2
11
6851
33
19
coro
13
20
00
3
12
10
13
11
2
The first two lines show that both steel and wrought
iron suffer much fewer bendings at blue heat than cold.
That is in accordance with the Board of Trade results
quoted above. Next, if a strip is bent once at blue heat
and allowed to cool, it is afterwards a quite different
material, much more brittle, and capable of suffering
very little bending. The last series of results show
that simple cold bending reduces the ductility much
more slowly, though iron reaches its limit of endurance
sooner than steel.
304 TESTING OF MATERIALS OF CONSTRUCTION
(
All these results,' says Mr. Strohmeyer, 'point
unmistakably to the great danger which is incurred
if iron or steel is worked at a blue heat. The differ-
ence between good iron and mild steel seems to be that
iron breaks more easily than steel while being bent,
when either hot or cold; that iron suffers more injury
than steel by cold working; but, if it has withstood
successfully bending when hot, there is little proba-
bility of its flying to pieces when cold, as is almost sure
to be the case with mild steel.' Mr. Strohmeyer thinks
that there is no foundation in fact for the opinion that
local heating of a plate sets up strains which may cause
fracture. But some qualities of steel are considerably
injured if made red hot or blue hot and cooled by
holding them with one edge in water. The following
table gives these results :-
Material
Unprepared or annealed
Made red hot and quenched in
boiling water
Made red hot and quenched in
cold water
Red hot. Edge quenched in
water
Blue hot. Edge quenched in
water
No. of bendings before cracking
Very
mild
steel
Medium-
hard
steel
21
24
1
3
3
Co
Mild
steel
12/1/
10
10
8
63/1
26
19
25
19
Low-
moor
iron
20
20

27
18/1/
The following experiments were suggested to the
author by Mr. Strohmeyer's paper. A plate of mild
27-ton steel was broken in the testing machine in the
IRON AND STEEL
305
ordinary way. The longer picce after this test was
heated to a temperature a little below redness, and
while at that temperature it was bent to a shallow curve
and straightened again. It was then tested in the ordi-
nary way. The results were these :—
Tenacity
Contraction
•
First test
27.0
51.0 per cent.
Second test,
after bending while hot
32.0
21.0 per cent.
These results seem to show that the
increased at the expense of the ductility.
pieces of the same mild steel were
heated to red heat, placed on a
V block, and quietly bent to an angle
of about 15° at each end out of
straight. The bending pressure was
put on just as the redness disap-
peared. The test pieces were then
straightened in the same way. Lastly,
they were tested by tension. Fig.
117 shows the result obtained. In
the place which was the middle of
the curvature in bending there is
scarcely any measurable contraction
of area, or extension. On each side
of the middle of the bar, where there
was hardly any bending, the material
is still ductile and draws down. The
tenacity is
Some test
FIG. 117.
Bent once
Thickness
1-655439 464-1578-
Bent twice
1-729-573 -570-1731
1·518 +472
*1·3062·160
-


·476−1·613
•356 • 1·306 ▾
figure shows the widths and thicknesses of the bars.
The elongations in each inch length were as follows:-
X
306
TESTING OF MATERIALS OF CONSTRUCTION
ELONGATIONS IN EACH INCH.
Bar bent and
straightened twice.
0.120
0.154
Bar bent once
and straightened.
0.048
0.152
0.138
0·080
0.020
0.010
0.156
0.064
T: 1:
Heated part.
0.000 Heated part.
0.138
0.287
0.622 Break.
0.002
0.082.
0.174
0.610 Break.
0.232
0.160
0.100
In the part heated and worked (by bending) the
steel is not weaker but it is stiffer. The bar has been
rendered unhomogeneous, and consists of portions of
quite different extensibility. It is easy to see that by
locally treating a plate in this way it may be rendered
extremely treacherous, even without assuming that the
heating and bending has created a condition of internal
stress.
The results in the following table, obtained by Mr.
Webb, at Crewe, carry the same lesson of the gain of
strength with the loss of ductility. For convenience of
comparison the results for plates bent or hammered at
blue heat, and not annealed after, are separated from the
others. All were tested cold, except those marked as
tested hot.
132. Hammer Hardening and Cold Rolling.-It is
well known that ductile materials can be rendered more
elastic and harder by hammering, planishing, or wire-
drawing cold, and this action is identical with that
which occurs in mechanical operations in many ways,
sometimes with useful, sometimes with prejudicial,
IRON AND STEEL
307

Ordinary plate, annealed
Hammered while blue hot and annealed
Bent while blue hot and annealed .
Bent red hot and cooled
Annealed plates bent cold
and annealed
Test No.
""
36
37
Condition of material
Bent three times blue hot
Hammered while blue hot
Bent once blue hot
Tested while blue hot
38
40
""
Hot end
""
46.37
45.03
46.73
Cola' end 49.84
No. of
tests
2 inches,
per cent.
3
22.0
26.0
22.0
17.6
CO CO CO CO DO W
results. Whenever a ductile material is subjected to
deformation by pressure at temperatures below those
at which the metal is plastic, the strength and elastic
limit are raised, but the elongation at fracture is dimi-
nished. The elasticity is increased, but the plasticity
is diminished. The author has noticed that, in very
long rail bars, the colder end which passes last through
the rolls has a higher yielding point and strength, but
less elongation at fracture, than the hotter end. The
following are some results from pieces cut from steel
rails rolled 150 feet long
2
1232
Tenacity,
in tons
per sq. in.
Tenacity, in Extension in Contraction
tons per
sq. in.
30.96
30.26
30.74
31.65
32.42
30.60
49.17
54.63
46.85
33.17
of area,
per cent.
Elonga-
tion in
10 ins. p.c.
38.04
4.3
10.05
35.24
31.95
7.5
38.80 11.4
23.6
23.8
22.1
22.5
12.5
23.63


Work done
per
cub. in. in inch
tons up to
max. stress
5.15
6.72
5.45
7.07
The work done was measured from an autographic
diagram.
X 2
308
TESTING OF MATERIALS OF CONSTRUCTION
Many years ago an American process of cold roll-
ing was introduced. Round bars passed through rolls
cold were straightened, polished, and rendered stronger
and stiffer. The following experiments by Sir W.
Fairbairn on a bar of good Dudley iron show how the
mechanical properties of the material were affected by
the process :
Material
Rough rolled bar, 1 inch diameter, in or-
dinary state
The same, turned down to 1 inch diameter
in lathe
Bar, cold, rolled to 1 inch in diameter
Material
The strength increased one-third, and the plastic
elongation diminished more than one-half.
The following results are given by M. Consi-
dére :—1
Very mild steel in ordinary 16-07
state
The same, compressed by
hydraulic press at 32 tons
per sq. in.
Ship steel in natural state
The same, reduced by cold
rolling from 10 to 9:45
mm. thick
Iron plate, natural state
The same, reduced by cold
rolling from 8 to 7.1 mm.
thick
Tensile strength Elongation in
tons per sq. in. 10 ins. per cent.
26.0
26.7
38.4
Elastic limit, in Tenacity, in
tons per sq. in.
tons per sq. in.
22.67
18.80
26.92
14.48
26.42
26.99
28.32
33.34
34.61
23.75
29.78
20.3
22.4
8.0
¹ L'emploi du fer et de l'acier, p. 148.
Elongation,
per cent.
26.5
17.0
18.0
11.5
15.0
7.0
-


IRON AND STEEL
309
The gain of ultimate strength is here not large,
but the rise of the elastic limit (probably the yield
point) is very marked. The diminution of plasticity,
shown by the ultimate elongation, is also marked.
Wiredrawing is a process similar to cold rolling, and
in wiredrawing the increase of strength is very con-
siderable.
The effect produced by hammer hardening or cold
rolling is entirely removed by annealing; and doubtless
it is to the removal of some effect of this kind, due to
rolling at too low a temperature, that the diminution
of strength by annealing, which sometimes occurs, is
due.
Mr. W. Parker's Experiments.-Mr. W. Parker has
recently shown that any mechanical deformation, such
as bending, has a similar effect to cold rolling or ham-
mering. In the autographic diagram the yield point
disappears, and the true elastic limit is lowered. The
following table shows very simply the analogy in the
effect of hardening by sudden cooling and hardening
by mechanical pressure in the case of very ductile
material. Similar bars of Siemens-Martin steel plate,
3 inch thick and 2 inches wide, were taken. No. 1 was
tested in its ordinary state. No. 2 was bent cold to
a radius of 8 inches, and straightened. No. 3 was
treated similarly at blue heat. No. 4 was heated, and
quenched in cold water. No. 5 was treated like No. 2,
and then annealed. It gave a diagram almost exactly
like No. 1.
4
310 TESTING OF MATERIALS OF CONSTRUCTION
No. Tenacity, in
of
tons per
Test
sq. in.
1
2
27.2
27.75
31.2
32.7
27.1
Yield point, tons
per sq. in.
14.9
No yield point
""
""
15.3
Elongation Contraction
in 10 ins.,
per cent.
27.8
25.7
20-7
17.6
29.2
of area,
per cent.
53.6
52.6
50.5
32.0
53.5
Ordinary state
Bent cold
Bent hot
Quenched
Annealed
133. Local Hardening.-If a plate is sheared or
punched a very considerable lateral pressure is exerted
on the metal near the cut edge. The action diminishes
rapidly from the cut edge towards the interior of the
mass, like the stress in a thick cylinder subjected to in-
ternal pressure. For about inch from the cut edge
the metal is hardened, and its power of extension greatly
diminished. M. Barba cut from a punched plate the
ring of metal surrounding a punched hole, and found
it to be extremely brittle and incapable of bending.
M. Considére has shown that a permanent condition of
compressive stress is induced in the ring immediately
round the hole.
That the diminution of strength of a punched plate
is due to the hardening of the metal round the hole is
now established. M. Barba showed that rimering out
a ring inch thick round the punched hole, or anneal-
ing the plate, entirely removed the prejudicial effect of
punching. The punching is more injurious the thicker
the plate, and this is obviously due to the increase of
lateral pressure in punching thick plates. It is less in-
jurious if the die-block hole is larger than the punch, for
that diminishes the lateral pressure. Sheared strips of
IRON AND STEEL
311
ductile material are known to be brittle when bent.
Mr. Baker has mentioned a case of a steel plate which
had been sheared which cracked in several places while
being straightened cold.
Some experiments of M. Barba showed that the
diminution of strength in a bar in which a hole had
been punched (reckoned on the net section) was greater
the wider the bar.
Thus, some steel test bars 0.28 inch thick were
punched with a hole 068 inch in diameter. The
normal tenacity of the steel was 327 tons per sq. in.
The punched bars of different widths gave the following
results:
""
Width of bars, in inches
Tenacity-cylindrical holes 27.1
conical holes
1.28 2.0 2.72 3.44 4.16 4.88
25.9 25.3 22.7 24.3 23.1
31.7 28.3 26.3 22.4 22.9 23.7
•
Further experiments have been made by M. Con-
sidére on a plate of Siemens-Martin steel, containing
0.34 per cent. of manganese and 0.22 per cent. of car-
bon, and a plate of Bessemer steel, containing 0.38 per
cent. of manganese and 0.33 per cent. of carbon. The
normal tenacity of these plates was 32.7 and 38:1 tons
per sq. in.
M. Considére first verified M. Barba's result, and
determined that the increase of strength in the narrow
plates was not due to the lateral expansion of the
narrow bar under the action of the punch. He then
tried bars with a punched semi-hole on each side, leaving
312 TESTING OF MATERIALS OF CONSTRUCTION
a strip of metal between them. The following were the
results :

Material
Martin steel
Bessemer steel
•
•
Normal
tenacity
32.7
38.1
Tenacity of bar when distance between the
holes was, in inches,
+2
•24
42.6 41.5
•32
•56
1.2
2.0
40.6 33.3 28.6 27.2
46.8 39.6 33.6 30.6
Here a new result appears. When the distance
between the holes is less than inch, the punched bar
is stronger than the unpunched bar. For wider bars
the reverse is the case. Part of the excess of strength
in the narrow bars is no doubt due to the suppression
of drawing-out, explained in § 33. By tests on plates
with drilled holes, M. Considére found that 5 tons
increase of strength in the 0.2 inch bar was due to this
cause. There remains another 5 tons increase, due
directly to the punching. In this very narrow bar the
whole of the metal between the holes was hardened by
the action of punching, and the increase of strength is
that due to cold working. As the bar is made wider it
comes to consist of hard metal near the holes, and softer
metal, unaffected by punching, between. The hetero-
geneousness of the material involves unequal distribu-
tion of stress. The bar tears at the rigid material, and
the tear doubly weakens the bar, partly by loss of
section, partly by the unsymmetry which results.
Suppose Fig. 118 represents at Of the normal
stress-strain diagram of the material, and at Oe the
stress-strain diagram for the material hardened by
IRON AND STEEL
313
punching. If the bar stretches an amount O a, the
stress near the hole will be a d, and that of the un-
injured material a c. The bar must tear at the edge of
the hole when the strain reaches the value O b.
FIG. 118.
The application of these considerations is far wider
and more important than the question of the deteriora-
tion of plates by punching. It
has been seen that in many
ways the plasticity of the
material may be altered, so
that the yield point disappears
and the extensibility is greatly
diminished-by rolling at too
low a temperature, by sudden
cooling, by bending, hammer-
ing, cold rolling, or by shearing
or punching. So long as such
an action is general, the only effect is that a more
rigid material is made out of a ductile one.
But if, as
must often happen, the action is local, then the effect
on the strength, like that of the thin ring of hard metal
round a punched hole, is far more serious. To know
the danger, however, is sufficient. Either local harden-
ing can be avoided, or, if unavoidably produced, it can
be destroyed by annealing.
134. Influence of Temperature on the Strength and
Ductility of Iron and Steel.-The results of experiments
on the influence of temperature on the strength and
ductility of iron and steel are somewhat discordant. A

d
ང་
e
1
0 a b
314 TESTING OF MATERIALS OF CONSTRUCTION
paper by Sir W. Fairbairn in 1856¹ gave experiments
on wrought-iron plate and rivet iron for a considerable
range of temperature. With plate iron there was no
well-marked effect of temperature till dull red was
approached, and then the tenacity rapidly diminished.
With rivet iron the strength was slightly greater at
- 30° Fahr. than at 60°. With rise of temperature the
strength increased from 28 tons per sq. in. at 60° to
38.4 tons at 435°. At red heat the strength fell to
16 tons. Knut Styffe made similar experiments in a
more perfect way. He found the strength and extensi-
bility of iron and steel were not diminished by cold. At
temperatures between 212° and 392° the strength of
steel is the same as at ordinary temperature, but the
strength of iron is greater than at ordinary temperature.
The results in the following table show no loss of
strength at very low temperatures. At about 300°
there is an increase of strength, greatest for the iron
with least carbon. In steel there is no great difference
in strength or extensibility in the range of temperature
in these experiments.
Mr. Webster 2 made experiments on the tenacity of
iron, steel, and malleable cast iron at temperatures of
5° and 60°. He found almost exactly the same strength,
and nearly the same elongation, at these temperatures.
M. Papkoff made experiments on soft steel and iron
3
1 Report of the Brit. Assoc. 1857, p. 405.
2 Proc. Inst. of Civil Engineers, vol. lx. p. 161.
3 Proc. Inst. of Civil Engineers, vol. lxxxiii. p. 513.
IRON AND STEEL
315
Description of material
INFLUENCE OF TEMPERATURE ON THE STRENGTH OF IRON AND STEEL.
(STYFFE'S EXPERIMENTS.)
(Temperatures in Fahr. degrees. Bars of 01 to 0.13 sq. in. area.)
Bessemer steel
""
""
""
,,
""
Uchatius
""
,,
""
""
""
iron
""
""
Cast steel (Krupp)
""
""
""
steel
""
""
,,
""
Lowmoor iron
Puddled steel" (Surahammar)
""
""
""
""
""
•
""
•
•
""
""
•
""
•
Percentage
of carbon
1·14
0.68
0.33
0.33
0.42
1.78
0.69
0.62
0.62
0.8
0.7
0.55
0.21
0.21
0.21
0.21
0.21
Tenacity, in tons per sq. in.

At -40°
40° |
to - 13°
56.27
34.37¹
63.28
41.81
42.63
54.98
42.73
27.35
28.61
At 50° to 60°
62.92
51.37
55.20
29.59
34.59
33.29
59.33
51.12
42.76
41.81
52.81
45.76
40.06
32.80
25.21
29.10
26.37
At about
300°
61.17
58.49
34.67
34.11
61.97
51.86
41.63
31.35
28.64
29.19
29.62
plates at temperatures of 63° and -2° Fahr. There was
an increase of strength and of elongation at the lower
temperature. Mr. C. Huston 2 made experiments on iron
and steel at ordinary temperatures, and at 572° Fahr. and
at 932° Fahr. They show generally a gain of strength
and decrease of elongation with increase of temperature.
A small hole in the test bar was filled with an amalgam
of known melting-point, and this was kept in a semi-
fluid condition by a blowpipe. According to Barba,
steel has at 400° Fahr. an increase of strength of 30 per
cent., and a decrease of elongation of 30 per cent. The
1 At 5° Fahr.
2 Proc. Inst. of Civil Engineers, vol. liii. p. 304. Journal of Franklyn
Inst. 1878, p. 90.
316 TESTING OF MATERIALS OF CONSTRUCTION
maximum strength is reached at 572°, and for higher
temperatures decreases rapidly.
Amongst the most careful of the experiments on the
effect of temperature are those by Kollmann, at Ober-
hausen. Three materials were used, the quality of
which may be judged from the following summary of
the properties when tested at ordinary temperature :—
Fibrous iron
Fine-grained iron
Bessemer steel
Material
0°
•
100
300
500
700
1,000
1,500
2,000
Temperature. Fibrous
Fahr.
wrought iron
100
100
97
92.5
81.5
Tenacity, in tons
per sq. in.
26
10
These experiments show a regular decrease of
strength with increase of temperature in all cases. The
following table, calculated by Roelker,¹ gives the strength
at different temperatures in terms of the strength at
ordinary temperatures. For comparison the results of
some experiments made by the Franklin Institute are
added:
3.5
23.5
25.4
37.8
Fine-grained
iron
100
100
100
98.5
90
36
Stress at elastic limit,
in tons per sq. in.
15.5
5
17.1
17.4
24.5
Bessemer
steel
100
100
100
Elongation,
per cent.
98.5
68
31
12
5
17.5
20.0
14.5
Wrought iron,
Franklin Institute
96
102
106
104
92.5
36
Mr. Barnaby made some experiments on iron and
steel for the Admiralty, and these experiments are
¹ Proc Inst. Civil Engineers, vol. lxvii. p. 437.
IRON AND STEEL
317
important, both as being recent and made on test bars
of reasonably large size. The bars were partly heated
in oil, partly in sand; generally, however, they were
taken out of the hot bath and broken as quickly as
possible. The temperature was judged from the colour
of the fractured surface, or in some cases by observing
whether tin or lead melted when placed in contact with
the bars.
EXPERIMENTS ON THE INFLUENCE OF TEMPERATURE ON THE STRENGTH
AND ELONGATION OF IRON AND STEEL. By Mr. BARNABY.
(Elongations in 8 inches.)

BB Boiler iron
lengthways
The same
across
fibre
Bowling iron
Tempe- Tenacity,
rature.
Fahr.
60°
450
490
60
500
530
60
450
490
490
500
550
850 to
900
tons per
sq. in.
60
420
23.93
27.08
27.4
60 21.1
24.4
23.2
27.6
19.3
21.75
24.6
22.6
24.8
30.3
Elonga-
tion, per
cent.
22.39 13.28
27.15
10.93
26.3
10.15
23.95
8.38
12.5
9.3
6.24
3.12
15.62
12.5
9.37
17.18
18.75
23.43
21.87
Bessemer
plate
Siemens-Martin
plate
Bessemer
plate
Tempe- Tenacity,
rature. tons per
Fahr.
sq. in.
60° 26.07
40.5
38.7
24.02
450
520
880
60
29.10
430 33.45
490
610
630
34.5
28.0
30.83
Elonga-
tion, per
cent.
60
430
550
580 18.56
27.34
14.06
17.18
26.56

25.78
14.06
18.75
18.7
18.74
28.49
38.4
33.08 17.18
25.0
21.87
18.75
COLLECTED TABLES OF TESTS OF IRON AND STEEL.
135. In giving tables of the results of tests of iron
and steel, the object has been to select some of the most
318 TESTING OF MATERIALS OF CONSTRUCTION
trustworthy results, on very various qualities of material,
and to give them fully enough to permit some judgment
to be formed of the range of quality in materials nomi-
nally the same. A very large and valuable collection of
tests of iron and steel will be found in a treatise referred
to below.¹
An abstract of these tables, giving merely
mean values of very variable materials, would be of
little use.
Knut Styffe's Researches.-The following summary is
useful, as showing the general relation of the quantities
observed in ordinary testing in various qualities of iron
and steel. Knut Styffe's investigation is a very con-
scientious piece of scientific work. His measuring in-
struments were excellent, and the test bars were long,
so that the proportionate error is probably small.
On the other hand, he had perhaps the worst testing
machine ever used for so important an investigation.
Probably this in no way affected the accuracy of his
results, as care was taken to prevent any error, but it
increased very much the trouble of the inquiry. Then,
and this is a more serious defect, his bars were small in
section, varying from 0·2 to 0·3 sq. in. in sectional area.
In the following table Styffe's numbers for bars of
the same kind have been averaged. Where two values
are given for the amount of carbon, the earlier is the
estimate of the manufacturer, the second the result of a
special analysis.
J
-
¹ Die Eigenschaften von Eisen und Stahl. Supplementband, Organ für
die Fortschritte des Eisenbahnwesens. Wiesbaden, 1880.
IRON AND STEEL
319
Description of material
""
""
""
Tilted Bessemer steel. 1.2-1.35
34.6
1·0-1·14
36.6
0·9-1·05
30.2
0·6-0·68 30.8
0·3-0·33
21.6
1.85
26.6
2.16
28.7
0.99
29.4
1.29
30.7
'40-'42 15.3
0.32
15.9
37.2
32.3
28.5
23.6
16.9
14.5
14.1
15.6
13.8
12.5
18.3
26.74
12.2
22.67
12.2 20.92
TABLE I. TENSILE STRENGTH OF STEEL AND IRON (STYFFE).
Limit of
elasticity,
in tons per
Breaking Contrac-
stress, in
tons per
tion of
area, per
cent.
8q. in
sq. in.
""
""
""
""
""
""
""
""
Rolled Bessemer steel
""
99
""
""
""
""
۱۱
iron
""
""
Swedish iron
""
Rolled Uchatius steel.
""
33
""
""
""
Tilted Krupp steel
Lowmoor iron
Cleveland iron
Dudley iron
Lowmoor engine tyre
Rail from Wales.
Motala puddled iron
Rolled charcoal iron
""
•
Percent-
age of
carbon
1.57
1.19
0.69
0.62
0.21
0.07
0.09
47.39
56.50
0.2
0·07-0·18
0.07
0.07
45.97
46.40
31.33
42.29
41.20
47.99
61.57
31.07
29.17
53.10
63.01
49.59
37.49
24.73
26.81
22.30
23.86
21.43
21.62
15
41
56
36
62
244
24
53
59
12
33
53
53
42
20
34
11
47
16
65
70
Elonga-
tion, per
cent. in
5 feet
2.4
2.9
CONN
3.4
4.2
7.3
1.4
3.4
3.8
4.8
16.0
17.2
2.2
4.5
11.1
6.0
19.6
17.3
8.5
12.1
6.6
14.1
7.2
18.4
21.1
136. Report of the Steel Committee, 1868-70.-The
Committee made a series of experiments of a very in-
teresting kind. They were experiments on bars of
iron and steel of 10 feet length between the measuring
points, a very exceptional length for test bars. The
experiments were made in a chain testing machine at
Woolwich Dockyard. The specimens were placed in a
trough 11 feet in length, with cross diaphragms at 12
inches apart, having a level planed V groove to support
the specimen. A V cap was fitted above and pressed
down tightly by screws. Sliding verniers were placed
on both sides of the bar, reading to Too foot. It
1
10
•
320 TESTING OF MATERIALS OF CONSTRUCTION
is probable that, from the great length in which the
elongations and compressions were measured, and from
the use of two symmetrical verniers, eliminating to a
great extent the effect of initial bending, the measure-
ments in these experiments were very trustworthy.
One important result of this mode of experimenting
was the observation, in a clearer way than previously,
of the remarkable behaviour of ductile bars at the
yielding point or breaking-down point.
The Committee arrived at the following important
conclusion from these experiments:-
'It would appear from these experiments that
within the yielding point of steel the amount of length -
ening from tension, or shortening from compression,
produced by equal forces per unit of area, is nearly the
same, and also that the amount is rather less with steel
than with wrought iron.'
The experiments show also that the stress at which
the material yields or breaks down is nearly the same
for tension and compression.
There are two other points very worthy of notice.
The first is the great uniformity of mechanical pro-
perties within the elastic limit for all the bars, however
diverse their mode of manufacture. The other is the
much greater uniformity of the results of different tests
of the same material than in the more ordinary tests of
very short bars.
The compression and extension per ton per inch given
in the tables are the mean values before yielding began.
IRON AND STEEL
321
Mark
Y
SC
с
SC
NB
NB
NB
46
но
KA
A A
K
K
K
31
кв
H
H
H
K SLW
SLW
""
Crucible cast steel
""
""
>"
""
Cast steel
""
>"
""
"}
""
""
Crucible steel
>>
>>
""
TABLE II. TENSION AND COMPRESSION OF STEEL BARS (STEEL COMMITTEE).
(1½ inch diameter. Measurements of extension and compression made on a length of 10 feet.)
Make
""
""
""
""
""
99
""
""
Bessemer steel
""
""
19
>>
""
Cast steel
Crucible cast steel
Bessemer steel
33
""
>>
""
""
""
??
""
""
>>
""
""
Intended use
tyres
piston rods
gun barrels
"}
piston rods
rolled
tyres and axles
,"
""
Mean exten-
sion per ton
per inch
*000075
·000075
*000075
•000076
•000075
*000076
•000076
•000076
•000077
•000079
*000078
•000077
⚫000077
•000075
⚫000077
•000076
•000077
•000076
•000077
•000075
·000075
⚫000074
*000077
*000078
*000076
·000078
*000079
Tension
Yielding
Ultimate
stress, in tons stress, in tons
per sq. in.
per sq. in.
26.50
26.50
25.00
26.00
24.50
26.00
26.00
27.00
20.50
17.00
17.00
16.50
25.00
20.00
19.50
19.50
19.50
26.75
20.50
19.50
19.50
21.00
18.00
17.00
17·50
16.00
16.00
53.74
53.33
51.21
52.30
46.00
54.74
43.48
41.85
40.54
38.14
39.61
37.79
37.05
35.47
35.61
35.26
3534
33.65
34.44
34·09
34.16
34·33
34.30
33.07
33.27
34.05
33.66
Contrac-
tion of
area, per
cent.
5.7
20.0
5.2
0.0
4·1
4.3
Ultimate
elongation
per cent.
in 120
inches
5.29
41.2
7·29
4.74
1.12
4.13
7.95
13.54
9.63
1.5
48.7
44.2
11.13.
1.3
0.89
2.9
2.02
45.6 11.90
19-2 11.48
13.61.
Compression
Mean com-
pression per
ton per inch
*000073
·000073
·000073
·000074
•000076
·000075
·000071
·000071
·000076
·000077
·000076
·000076
·000071
·000071
·000073
·000071
·000073
·000073
-000074
*000076
·000076
•000076
·000076
•000074
·000076
·000076
•000077
¦
Yielding
stress, in tous
per sq. in.
26.50
26.00
26.50
26.50
27.00
25.00
25.50
26.00
18.00
16.50
16.00
16.00
24.00
19.50
17.00
18.50
18.50
27.00
24.00
22.00
20.50
21.00
17.00
15.00
16.00
15.50
16.00

322
TESTING OF MATERIALS OF CONSTRUCTION
· Mark
LS
LS
LS
L
L
L
K C
кс
K C
FRS. C.
FR
FR
Lowmoor
""
""
""
""
>>
Yorkshire
""
""
""
Make
""
TABLE III.
TENSION AND COMPRESSION OF IRON BARS (STEEL COMMITTEE).
(1½ inch in diameter. Extensions and compressions measured on a 10-foot length of bar.)
Tension
Use
││││
| │
1
1
Mean exten-
sion per ton
per inch
•000076
•000076
•000077
⚫000078
•000078
*000078
*000078
•000078
⚫000080
⚫000083
•000081
•000078
Yielding Ultimate
stress, in tons stress, in tons
per sq. in.
per sq. in.
14.00
14.00
14.00
11.00
12.50
12.00
13.00
13.00
13.50
11.50
11.50
12.50
27.80
29.53
29.33
24.60
25.72
24.07
23.62
24.16
23.29
22.48
22.48
22.92
Contrac-
tion of
area per
cent.
5.9
>48.8
51.4
47.7
Elonga-
tion in
120 inches,
per cent.
7·01
12.65
17.87
17.50
Compression
Mean com-
Yielding
pression per stress, in tons
ton per inch
per sq. in.
•000074
•000075
•000075
•000077
⚫000077
*000079
*000076
*000076
*000077
•000079
•000080
⚫000082
13.50
13.50
13.00
12.50
10.50
11.50
13.00
13.00
11.50
11.50
12.00
IRON AND STEEL
323
1
137. Board of Trade Experiments on Iron and Steel.'
-The plates were furnished by the Steel Company of
Scotland, as material suitable for ships and boilers.
The following table gives the mean results of tensile
tests of plates of different thicknesses. The elastic limit
recorded is properly the yielding stress. The plates
were tested lengthways and across the direction of
rolling, but in mild steel no sensible difference is found
in the strength, and only a small difference in elonga-
tion and contraction. The large contraction of area of
the steel plates indicates great ductility, and in this re-
spect steel compares favourably with iron. With regard
to the iron plates, the boiler plates are more uniform
than the ship plates, and contract and extend more be-
fore fracture.
¹ Memorandum issued by the Board of Trade upon the Use of Mild
Steel, 1881.
Y 2
324 TESTING OF MATERIALS OF CONSTRUCTION
TABLE IV. TENSILE STRENGTH OF IRON AND MILD-STEEL PLATES
('BOARD OF TRADE REPORT,' 1881).
Thickness
of plates, in
inches
I HAWA|WNHNHALA
1
1
Means
Means
A/WIHAT
Means
HaHamNETA
1
Means
Means
Direction of
stress
= + = + = + = +
+ =
11
11
= + = + = +
+=
Stress at yield
point, in tons
per sq. in.
Tenacity,
in tons per
sq. in.
STEEL PLATES
19.0
19.1
15.8
15.7
15.8
15.6
14.9
14.8
31.0
31.4
28.9
28.6
29.5
29.1
28.0
28.0
16.3
16.3
IRON SHIP PLATES
24.00
22.62
19.42
29.3
29.2
22.01
IRON BOILER PLATES
21.20
19.03
21.40
18.67
20.86
17.74
21.15
18.48
Elongation
in 10 inches, Contraction,
per cent.
per cent.

23.5
21.2
29.8
28.9
29.2
26.6
30.6
25.6
28.2
25.5
7·0
6.7
3.6
5.7
9.0
2.7
10.1
3.8
9.8
3.1
9.6
3.2
46.0
39.9
53.2
40.9
46.8
38.3
50.4
42.4
49.1
40.3
6.8
4.7
4.8
5.4

12.91
4.28
13.30
5.08
13.00
3.87
13.07
4.41
Tests of Iron Plates by Dr. Böhme.'-Table V. con-
tains a very complete series of tests of material, chiefly
for boilers, made on similar test pieces. They are chosen
partly because the measurements were made with great
care.
1 Mitth. aus den K. Techn. Versuchs-Anstalten zu Berlin. 1884.
IRON AND STEEL
325
123+
1 Boiler plate
4
5
7∞∞OLLRCULEBR2
8
9
10
11
12
13
14
15
16
17
18
19
3
16
© bv=b¥~b {So{&6
16
TABLE V. TESTS OF IRON BOILER PLATES (BÖHME).
(The test bars were 24 inches wide, and
to inch thick.)
16
""
40
41
42
43
44
""
""
""
"
|
""
""
""
""
""
""
""
""
""
20
21
7 Ship plate
76
""
""
""
""
""
""
""
""
""
""
""
""
29 Harkort
30
31 Wohlert
32
33
""
34 Boiler plate
35
36
37
38
39
""
""
""
""
""
""
""
""
""
""
""
·
•
•
►
·
•
.
Thickness,
in inches
•563
*559
•520
•508
•516
Stress, in tons per
sq. in.,
·516
•543
*539
•520
•386
*406
*398
•461
•461
⚫445
*449
•455
•465
•465
•425
•465
•315
•315
*472
•472
•472
*394
•295
•532
•521
•516
*557
·569
•500
413
·394
•413
•398
•433
·421
·413
·449
*480
•476
at yield
point
Tests in direction of rolling
14.10
24.03
15.62
26.42
14.08
16.15
17.14
17.00
13.64
14.21
13.70
14.27
13.70
13.83
14.52
13.90
14.08
16.68
15.72
16.00
at maxi-
mum load
15.66
17.82
15.82
Elongation, per Contrac-
cent.,
tion of
area, per
cent.
in 8 in 4
inches inches
20.8
20.8
21.60 15.7
25.35 19.0
27.54 21.5
25.11
17.3
23.54 29.3 33.6
23.97
29.6 33.9
23.35
24.3 26.9
21.95
22.83 25.7
29.4
22.65
22.5 25.6
24.10
21.4 23.6
22.84
15.4
22.57
17.7 19.2
26.04
21.0
24.05
24.2
23.38
15.2
24.18
25.1
27.35
23.3
23.75
24.2
21.45 5.6
6.4
24.93 11.4 12.6
21.75 7.2 7.5
21.75 5.7 6.4
9.6 8.8
11.95
13.20
15.22
15.60
15.40 23.60
15.66 24.23
15.40
22.95
22.90
18.14
17.70
22.83 21.3
13.76
26.95 21.3
16.18
25.25 18.7
16.36
26.40 18.7
16.06
24.74
14.50
23.00 11.0
5.7 6.2
6.9 7.3
13.7
17·44 25.80 19.3 22.6
15.75
25.35 16.1 17.8
14.78
24.35
25.5
15.60 25.05
17.70
25.57
14.46 25.57
18.20
16.50
28.4
22.3
24.7
29.7
31.4
23.8
35.4
33.2
28.0
29.5
21.0
22.2
25.7
26.7
15.0
33.1
17.0
6.4
6.6
I
4.0
5.3
19.3 25.0
27.9
27.8
23.4
24.2 22.9
40.2
45.1
33.4
29.0
14.9
19.6
17.7
27.6
25.1 30.2
25.3
28.2
25.70 24.3 28.6
24.55
27.0 33.4
16.18 24.48 25.4 28.2
24.9
32.9
29.1
34.0
30.6
326
TESTING OF MATERIALS OF CONSTRUCTION
47
48
49
50
51
45 Boiler plate
46
19-199
16
7
16
16
1 Boiler plate
(Nos. 7-9 above)
Plate
Axle
Plate.
''
2
3
4 Boiler plate
(Nos. 10-11 above) J
""
5
6
7 Boiler plate
(Nos. 13-15 above)
8
9
""
""
""
•
""
""
""
""
•
""
""
""
""
Means
""
Iron plate
""
Description
ور
""
""
TESTS OF IRON BOILER PLATES-continued.
Stress, in tons per
sq. in.,

""
Billet from
axle
Plate.
•
}
·
Thickness,
in inches
•464
•472
*457
·464
*469
•469
*469
Section of
ingot
at yield
point
•524
•524
*527
⚫394
⚫394
⚫394
*464
⚫464
*409
•315
•315
•472
·394
12" x 12"
15" x 15"
12" x 12"
15" x 15"
15" x 15"
19" x 19"
19″ × 19″
19" x 19"
27″ × 12″
19″ × 19″
Tested across the direction of rolling
13.00 20.36
10.2
13.06
8.8
21.75 12.8 15.9
19.46
12.94
13.45 20.16 8.4 9.4
14.08
19.84
7.8
8.2
14.46
21.82
13.76
21.05 7.2
8.4
13.35
20.18 7.4
7.6
15.02
21.25 15.2 17.0
14.33
21.95 7.4 7.6
15.34
23.27
15.34 20.42
14.70 22.82
at maxi-
mum load
TABLE VI. TENSILE STRENGTH OF BASIC STEEL (GILLOT, PROC. INST.
C. E.,' LXXVII. p. 304).
17.56
25.40
24.2 29.1
30.9
14.46
24.23 23.5
15.15
25.05 22.7 27.6
15.40
25.45 23.9
29.8
16.00
25.55 23.9
28.8
14.84
25.50 23.4 28.2
15.53 25.25 22.1 26.5
Section of
test piece, in
inches
Elongation, per
cent.,
X
2.015 × 46
1" diam.
2.03 × 37
1·99 × 755
2.035 × 59
1·52 × ·68
1" diam.
1·765 × 69
1·52 × 705
| 2·0 × 565
in 8 in 4
inches inches
Tena-
city, in
tons per
sq. in.
in 10
inches
Contrac-
tion of
area, per
cent.
எம்.
in 8
inches
29.2
31.5
27.6
30.8
31.7
30.8
27.8
6.8 7.7 10.2
4.4
5.0
7.5
7.1
25.0
27.5
31.3 34.1
35.0 37.5
30.0 31.3
16.8
15.1
9.6
10.2
14.9
Elongation, per cent., Con-
in 2
traction
inches per cent.
53.1
53.1
1.7
6.1




55.8
25.89
22.29
62.9
62.7
24.96
23.00
63.5
24.16
56.5
27.5 30.5
28.1 34.2
23.92
59.4 58.3
25.98
24.4 26.6 40.6 50.0
26.68 23.8 25.0 43.8 46.6
26.68 26.3 28.5 53.1 49.8
24.07 28.8 31.3 50.0 48.9
24.76
28.0 30.6 53.1 55.5
62.5
62.5
IRON AND STEEL
327
TABLE VII. KENNEDY'S TESTS OF LANDORE SIEMENS STEEL.
inch plates, suitable for furnaces
(along fibre)
3 inch similar plates (along fibre)
(across fibre)
Description of plates
""
Rivet steel
3
16
""
""
""
Description of plates
•
""
inch plate, hard steel, unannealed .
annealed
inch plate, mild steel, unannealed .
annealed
inch plate, mild steel, unannealed .
annealed
""
""
""
Limit of elas-
ticity, in tons
per sq. in.
TABLE VIII. TESTS OF STEEL PLATES, ANNEALED AND UNANNEALED.
Tenacity, in tons
per sq. in.
Elongation in 8
inches, per cent.
""
""
""
inch steel boiler plate, unannealed .
annealed
•
17.6
14.92
14.84
20.65
Tenacity,
in tons per
sq. in.
29.33
27.27
26.93
29.12
32.97
28.52
26.60
24.05
28.55
26.95
28.25
25.75
Elongation
in 10 inches,
per cent.
23.2
27.2
22.3
21.4
16.65
24.12
24.32
29.87
25.05
26.90
21.25 1
28.75 1
1
The results on inch and inch plates are given by
Mr. W. Denny; that on the thick plate by Mr. Traill.
138. The Testing of Rails.-The testing of rails is of
very great importance, from the extent of the manufac-
ture, and the serious consequences which may follow the
use of unsuitable material. The ordinary tensile test.
so trustworthy for ordinary materials of construction,
is comparatively useless, sometimes even misleading, as
a guide to the quality of rails. For rails two require-
ments have to be attended to, which are to a great
extent antagonistic. The rail must be strong and
tough, for it has to carry great weights, and suffers
1 Elongation in 10 inches.
328 TESTING OF MATERIALS OF CONSTRUCTION
severe shocks. But it also must be hard enough to
resist abrasion or lamination on the surface. The
earlier tests adopted aimed chiefly at securing tough-
ness, and led to the introduction of rails too soft to
stand the wear of traffic.
Tests of Rails.-The following table contains tests
of 30 steel rails, after use on the Furness Railway for
eight years ('Proc. I. C. E.' vol. xlii. p. 74), and of 36
mean values of tests taken weekly during the years
1869-70 (Proc. I. C. E.' vol. xxx.) :—
TABLE IX. TENSILE STRENGTH OF STEEL FOR RAILS.
Tenacity, in tons
per sq. in.
Furness rails
(Smith)
Means given by
Berkley
Maximum
Minimum
Mean
Maximum
Minimum
Mean
50.4
30.1
35.4
45.5
33.8
40.5
Elongation in 2
inches, per cent.
37.5
3.0
29.5
No convenient direct test of hardness suitable for
rails has as yet been found. Indirectly, the bending
test gives indications of the hardness of the rail. A
rail which will carry a heavy load with a high elastic
limit in bending is likely to be a hard rail. But if the
rail is too hard it is brittle. To control the bending
test a falling-weight test has been used. A monkey, or
ball, weighing 300, 600, or 1,000 lbs., and falling 6, 12,
or more feet on the rail, bends it more or less; the
number of blows the rail will stand before twisting or
breaking, or the deflection with one blow, is taken as
an index of its toughness.
IRON AND STEEL
329
Without attempting any complete account of rail
testing, the following suggestions, taken from Mr.
Sandberg's paper,¹ may
paper,¹ may be made. Mr. Sandberg
advises (1) that the bending test should be severe, but
that no maximum of deflection should be stipulated for
-the rail should be required to carry a certain load
without sensible permanent deflection; (2) the falling-
weight tests should be regulated according to the
weight of the rail. The table below, prepared by Mr.
Sandberg, gives the tests he proposes, and the ordinary
deflections observed.
TABLE X. PROPOSED TESTS FOR RAILS.
(Distance of bearings, 3 feet for all tests. Deflection and set measured on a 6-foot
length of rail. In the bending test, the load A applied at the centre should produce no
permanent set. Deflection means temporary deflection.)
Weight
of rail,
lbs. per
yard
33
35
40
45
50
56
JASTU
60
A
Load,
in tons
0000249
6
8
5 0.125
10
12
14
16
18
70 20
75
22
80
23
85
24
90
26
95
28
100
30
Usual
deflec-
tion, in
inches
""
""
""
""
""
""
""
""
""
;)
""
""
Bending tests
""
>>
B
Load,
in tons
11
13
18
22
25
26
32
35
41
43
45
48
50
51
ར
52
Usual
deflec-
Usual
tion, in set, in
inches
inches
00000100100
tolocks Alcotch no!— 00f29,
COCHINTA
--
4
-2
3
13
")
""
""
""
3
ور
""
""
ت منظر موت
400-100-1000/000
2400TCH HA-
1
CO/ES CO/ES NO{-00300/0
}
""
99
""
""
""
""
>"
دت سه ستا سرام
Weight Height
of ball, of fall,
cwts.
feet
10
""
""
20
:
""
""
""
>"
"1
"1
""
3
Impact tests

""
6789679ERDE
11
13
15
17
19
21
23
25
Usual
deflec-
Con-
stant, tion, in
с
inches
2.0
ور
3 3
""
""
2.5
3.0
3.3
3.7
4.0
4.2
4.4
4.5
4.8
5.0
¹ Proc. Inst. of Civil Engineers, vol. lxxxiv., p. 387.
2-4
""
""
""
""
""
""
")
""
""
""
""
""
""
""
330
TESTING OF MATERIALS OF CONSTRUCTION
The constant C is weight of ball multiplied by
height of fall, and divided by weight of rail per yard.
Tetmajer¹ has made a considerable number of tests
of rails, with a view of determining the connection
between the bending test and the hardness of the rails.
The pieces were 4.6 feet long, and were supported on
bearings 3.28 feet apart. The supporting knife-edges
and that of load-shackle were rounded to a diameter of
1 inch. The quantities determined were the elastic
limit in bending (or limit at which there was no mea-
surable set), the deflection with 35 tons load, the ulti-
mate, or breaking, load; diagrams were constructed
from which the work of deformation was calculated.
The rails varied from 67 to 75 lbs. per yard. The
moment of inertia of the sections varied from 21.5 to
to 25·1 (inch units). The table below gives the re-
sults on some of the rails from the Swiss Central Line,
weighing 74 lbs. per yard, and 511 inches high.
Moment of inertia, 24.8.
TABLE XI. EXPERIMENTS ON RAILS (TETMAJER).



Elastic limit in bending, tons
Breaking load, tons
Deflection at limit, inches
Deflection at 35 tons, inches
Deflection at breaking, ins.
Work of deformation up to
limit, inch tons
Work of deformation up to
35 tons, inch tons.
•
67
52
51
60
54
56
23-0 27.5 26.0 28.5 33.5 35.5
41.0 39.8 39.7 47.7 45.0 51.2
0.165 0.208 0.177 0·201 0·209 0.244
0.216 1.300 1.24 0.84 0.59 0.224
5.63 5.16 4.64 4.72 4.37 5.12
1.92 2.88 2.32 2.84 3.48 4.32
61.68 37.32 38.76 23.96 16.52 3.96
¹ Stahl und Eisen, 1886, p. 408. Proc. Inst. of Civil Engineers,
vol. lxxxvii., p. 480.
IRON AND STEEL
331
The variation of the deflection is much greater
than the variation of the tenacity in tensile tests, and is
therefore likely to be of service in determining hard-
ness.
EXPERIMENTS ON SHEARING AND TORSION.
IV
JIL
139. Let Fig. 119 represent a portion of iron or steel
plate, the large arrow indicating the direction of rolling.
FIG. 119.
امرات
VI
T
π
V
-

Then there are six directions in which the plate can be
sheared, differently placed with reference to the struc-
ture developed by rolling. In the course of an inquiry
into the causes of a boiler explosion at Hapburg,
Bauschinger experimented on the shearing resistance of
wrought iron in all these directions. The test bar was
a rectangular block, fixed in the machine between two
cutting edges, and sheared in single shear. The shear-
ing was sometimes sudden, with a loud crack, sometimes
more gradual. In directions I and II the sheared sur-
faces were laminated, or scaly; for the directions III
332
TESTING OF MATERIALS OF CONSTRUCTION
and IV, fibrous; in the directions V and VI, irregu-
The following are the mean values ob-
larly torn.
tained :
TABLE XII. SHEARING RESISTANCE OF IRON AND STEEL (BAUSCHINGER).
Shearing resistance, in tons per sq. in., in the
directions
Description of plates
Iron:
Plates from exploded}
boiler at
Puddled plate (Leon
Magis & Co.)
Puddled plate (Leon
Magis & Co.) an-
nealed
Charcoal plate
German Lowmoor plate .
Rolled iron bar
Rolled iron bar, annealed
Plates from exploded
boiler at Wurtzburg,
from uninjured plate
Plates from exploded
boiler at Wurtzburg,
from injured plate
New locomotive plate
Cast steel:
Bessemer plate
""
""
I
II
III
IV
18.36 17.84 19.68 19.68
17.78 17.30 20.16 20:00
18.64 17.60 22:05 21.95
22.15 17.16 22.55 19.00
21 20 19 68 23-23 20-25
15.42 15.06 17.62 17.68
V
16.50 16.64 18.91 19.80
8.46
8.44
17.18 16.25 20 20 19 10 10:30 10:33
VI
14.40 14.38 17.26 16.28
5.20
16.00 16.38 19.10 19.90 10.01
1
8.89 9.20
9.20 8.06
10.05 9.17
11.70 10.15
10 60 13-27
6.95
7.23
4.76
9.58
24.12 23.42 26.45 27 35 22.90 21.45
26.30 26.40 29.20 29-20 25 05 25.70
The resistance of steel in different directions is
much more uniform than that of iron.
The following are mean values of torsional tests,
made by Messrs. Platt and Hayward at the engineering
laboratory of University College. For comparison,
values of the tenacity and shearing strength from direct
experiments on tension and shearing of the same mate-
rials are also given :
1 Proc. Inst. Civil Engineers, vol. xc. p. 382.
IRON AND STEEL
333
Material
TABLE XIII. TORSIONAL STRENGTH OF IRON AND STEEL (PLATT AND
HAYWARD).
Limit of elasticity,
in tons per sq. in.
Calculated shear-
ing stress at
fracture, in tons
per sq. in.
Final twist in
revolutions in 9-
inch length
Coefficient of
rigidity, in
tons per sq. in.
Tenacity, in tons
per sq. in.
Ultimate shearing
stress, from shear-
ing tests, in tons
per sq. in.
18.76
8.99 25.2 8.90
20.28 44.64 3.84
19.36 42.30 4.36
5,714 21.60
5,750 52.20
6,098 52.16
35.21
33.30
Wrought iron,
Crown best
Bessemer steel
Crucible steel.
Landore rivet steel,
0.18 carbon, 0·6
manganese
Crown rivet iron
Steel cut from cast-
10.40
ing
Siemens-Martin steel 10.16
10.20 29.85
7.85
5,834 28.40
23.00
10.36
28.87
6.90
6,116 25.01
21.21
34.7 4.15 5,822 38.04 27.60
28.13 9.92 5,981 25.75 20.94
10.22 29.5 7.45 6,213 24.56 20.75
Wrought iron, S. C. }
The apparently high shearing stress in the torsion
experiments is no doubt due to the false assumptions
involved in the formula for torsional resistance when
applied to stresses at rupture.
STEEL CASTINGS.
140. Steel castings are now largely used, sometimes
in place of cast iron, and sometimes instead of forgings.
Roughly, they are usually assumed to have nearly
double the strength of cast iron. Tests, however, show
wide divergence in the quality of different specimens,
both as to strength and ductility. The steel melts at
about 3,500° Fahr., a temperature much higher than that
of cast iron. Consequently, the contraction of the cast-
ings is nearly double that of cast iron. To obviate danger
334
TESTING OF MATERIALS OF CONSTRUCTION
from this contraction annealing is necessary, and in
some cases the casting is removed from the mould as
soon as set, and placed in an annealing furnace, kept at a
temperature of 1,700° Fahr., for not less than 24 hours.
Hardening in oil and annealing afterwards improves
the strength, and still more the ductility, of the casting,
the effect being similar to that of forging. Unannealed
castings may have a strength of 24 tons, with 1 to 5 per
cent. of elongation. Annealed, a strength of 27 to 30
tons, with 3 to 8 per cent. of elongation. Hardened
and again annealed, a strength of 27 tons, with 20 per
cent. of elongation, or 36 tons, with 12 per cent.
elongation.¹
The amount of carbon varies from 0.25 to 1 per
cent.; a small amount of phosphorus makes the casting
sounder. The manganese varies from 0.3 to 0.7 per
cent. Silicon, added just before casting, in quantity
depending on the amount of carbon, prevents ebullition
of gas during solidification.2
The following table, from Mr. Hill's paper, shows
the effect of annealing
TABLE XIV. INFLUENCE OF ANNEALING ON STEEL CASTINGS.
Tenacity, in tons per sq. in. Extension in 5 in., per cent. Contraction of area, per cent.
Not annealed Annealed Not annealed
Not annealed Annealed
Annealed
33.79
32.10
24.01
32.80
36.60
32.30
28.40
30.08
12.00
4.16
1.00
22.00
14.60
15.00
13.00
21.90
¹ Considére. L'emploi du Fer.
2 Hill.
8.16
2.90
2.80
Proc. Inst. Civil Engineers, vol. xc., p. 359.
38.70
28.11
38.70
15.90
23.05
1
IRON AND STEEL
335
The following results were given by Mr. W. Parker
as to four specimens of a steel casting made at Terre
Noire :--1
First specimen, unprepared
Second specimen, annealed
Third specimen, annealed and tempered
in oil
No. of test
Fourth specimen, annealed and twice
tempered in oil
1234 LO
6
17
Condition of material
10
11
Valuable experiments on the strength of steel cast-
ings have been made by Mr. H. Foster, of Newburn
Steel Works :—2
231
TABLE XV. PROPERTIES OF STEEL CASTINGS AS DEPENDENT ON
COMPOSITION (FOSTER).
14
•
•
0.30
0.30
0.30
0.35
0.35
0.50
0.50
0.50
0.77
0.77
0.77
0.96
0.96
0.96
Composition, per cent.
Carbon Silicon Manga-
nese
0.22
0.22
0.22
0.23
0.23
0.40
0.40
0.40
0.46
0.46
0.46
0.62
0.62
0.62
0.63
0.63
0.63
Tenacity in tons Elongation in 5
per sq. in.
inches per cent.
0.61
0.61
0.66
0.66
0.66
0.67
0.67
0.67
0.64
0.64
0.64
32.07
33.70
38.60
41.10
31.0
30.4
Tenacity, in Elongation, Contraction
tons per
per cent. in of area, per
sq. in.
1.75 inch
cent.
33.4
33.0
36.0
44.0
45.2
42.2
39.8
39.0
33.6
31.0
38.0
35.6
16
17
17
15
1 Journal of the Iron and Steel Institute.
Castings.'
2 Proc. Inst. of Civil Engineers, vol. xc., p. 365.
24.0
24.0
24.0
22.2
21.5
12.0
5.0
9.0
1.0
1.9
1.5
2.0
1.0
1.0
43.8
43.8
41.0
41.0
37.1
16.8
6.3
12.3
1.4
3.3
1.8
2.2
0.8
1.8
'On the Use of Steel
336 TESTING OF MATERIALS OF CONSTRUCTION
Some very complete experiments on steel castings,
obtained from the manufacturers in America, were
made by Mr. A. V. Abbott.¹ The tests were made
on the test bars as taken from the sand without re-
moving the skin. The dimensions of the test bars were
as follows
For tension, 1 inch diameter, 10 inches between
gauge points. For
For pressure, 2 inches square and 24 feet
long. For bending, 2 inches square, 2 feet long; loaded
at the centre. The average tensile elastic limit was 13.1
tons per sq. in., and the elongation in 10 inches 9
per
cent. The mean coefficient of elasticity was 10,900 tons
per sq. in.
No. of sample
1223
7
9
9A
9A
10
Elastic limit in
tension, tons per
sq. in.
12.9
11.4
11.4
10.3
9.5
13.9
16.0
15.8
17.0
17.0
7.8
TABLE XVI. STEEL CASTINGS.
Breaking stress
in tension, tons
per sq. in.
19.5
16.5
18.9
19.7
17.1
20.6
25.3
23.3
28.2
28.0
15.4
1

Elongation, per
cent., in 10 ins.
6.0
0.4
0.8
6.0
10.0
2.0
10.0
9.0
29.9
20.5
8.0
Elastic limit in
compression,
tons per sq. in.
15.6
14.0
limit
transverse
stress, lbs.
Elastic
for
9.1
6,000
2,500
2,600
10.9
3,000
11.9 3,950
13.2 4,000
breaking load,
Transverse
in lbs.
8,000
.72
3,870
•45
3,950 *52
4,181
.88
5,720
•15
6,259
•60
•20
16.1 4,000
5,480
12.0 4,000 6,810
•21
in
4,010
Deflection,
inches
•35
Some experiments by the author on steel castings,
turned to ordinary test bars about 1 inch in diameter,
gave less favourable results, as shown in table XVII.
¹ Proc. Inst. of Civil Engineers, vol. lxxxiii., p. 512.
IRON AND STEEL
337
below.
of these bars.
24
per square inch
#:164
Tons
15
Test No.
Fig. 120 gives autographic diagrams for some
162
163
164
165
166
167
Diameter,
in inches
SOLLA
•997
•997
•620
•615
•619
•621
"
FIG. 120.
Cast Steel

Extensions in 8 inches
TABLE XVII. TESTS OF STEEL CASTINGS.
Tenacity,
tons per sq.
in.
16.26
13.05
15.07
19.86
997 AL
20.53
14.52
Extension, per cent.,
in 10 ins. in 8 ins.
0.61
0.30
0.68
LarÒN
0.37
0.75
0.25
1.4
Contraction
of area, per
cent.
0.76
0.38
0.60
Coefficient of
elasticity,
tons per sq.
in.
10,930
14,050
9,138
9,972
10,220
8,384
There were flaws in the fractured sections of 163, 164, and 166.
2

Mitis Castings.-These are castings of wrought iron
to which about 0.05 to 0.1 per cent. of aluminium has
Ꮓ
338 TESTING OF MATERIALS OF CONSTRUCTION
been added. The aluminium lowers the fusing point
of the iron 300° or 400°. The furnace used is a petro-
leum furnace, and the iron is melted in crucibles of
plumbago or of fireclay. The tenacity is said to be
20 per cent. greater than that of wrought iron, and the
ductility about equal to that of wrought iron.
D
339
CHAPTER XI.
COPPER, COPPER ALLOYS, AND MISCELLANEOUS TESTS
OF METALS.
1
141. Copper. This is a deep red metal of great duc-
tility, and, relatively to most metals except iron, of great
tenacity. Its density is 86 to 8.9 when cast, 88 to
8.9 when rollel. It weighs on the average 546 to
552 lbs. per cubic foot. Its fusing point is about 2000°.
Its tenacity when cast is about 8 to 12 tons per sq.
in.
Hammering or rolling increases its strength at the ex-
pense of its ductility, but the ductility is restored by a
process of annealing. Phosphorus is added to facilitate
casting, and the strength is greater the larger the per-
centage of phosphorus used. The phosphorus reduces
the oxides formed in melting the alloy.
-
The table on next page gives some of the most
trustworthy results on the strength of copper.
The coefficient of elasticity of cast copper is given
as 4,460 to 6,700 (Thurston); that of hard drawn
wire as 7,650, and of annealed wire 6,680 to 7,650
tons per sq. in. (Wertheim).
The coefficient of bending strength is 8.9 to 17.8
•
z 2
340
TESTING OF MATERIALS OF CONSTRUCTION
Cast copper
Forged copper
""
""
""
""
Description of material
Ingot copper
Cast copper
Rolled copper¹
Tons her są inch
•
20
15
Rolled copper,inch thick
Hard copper wire
Annealed
""
❤
0.015 phosphorus
⚫02
⚫03
·04
•
""
""
№ 631
N 632
""
№:633
•
·
•
•
J"
·
•
·
FIG. 121.
Copper Plates
Tenacity, in
tons per sq.
in.
8.5 to 11.2
15.2
17.0
20.1
21.4
22.3
11.6 to 13.3
6.5 to 9.2
12.9 to 14.3
13.3 to 14.2
26.0
20.0
tons per sq. in. for cast copper, and reaches 26.7 for
rolled copper (Thurston).
Authority
Fig. 121 gives autographic diagrams for copper.
The highest diagram is a normal diagram for rolled
Anderson
"
Extension in 41/2
""
""
""
""
Thurston
""
Bauschinger
Unwin
Wertheim
""

copper.
The other diagrams are for the same copper,
heated, and allowed to cool.
1 Contraction of area, 30 to 45 per cent.
2 Extension in 8 inches, 20 to 43 per cent.; mean, 37 per cent.
COPPER, COPPER ALLOYS, ETC.
341
I
Tin is chiefly valuable in engineering for alloying
with copper to form bronze. Its density is 7.3 to 7·4
(weight, about 456 lbs. per c. ft.). Thurston gives its
tenacity as ranging from 0.89 to 2.68 tons per sq. in.,
and its coefficient of elasticity as ranging up to 3,125
tons per sq. in.
142. Zinc, known also as spelter, is used for alloy-
ing with copper to form brass. It is malleable within
narrow limits of temperature, and can be rolled into
sheets for roofing. It fuses at 750° to 930°. Clean
iron immersed in melted zinc gets a protective coating,
the
process being termed galvanising. The zinc being
electro-positive protects the iron from oxidation, and its
own oxide is insoluble in water. If, however, sulphuric
acid is present, a sulphate is formed, and the zinc coating
perishes. The tenacity of cast bars is 2.0 to 2.9 tons
per sq. in. (Thurston). The author found a tenacity
of 1∙1 to 1.5 tons per sq. in. Cast zinc breaks without
sensible elongation or contraction. Trautwine gives
for sheet zinc a tenacity of 7-14 tons per sq. in., and for
wire 9.8 tons per sq. in. Wertheim gives the coefficient
of elasticity as 5,360.
Lead is a very valuable metal for certain purposes
from its great ductility. Its density is 114 (711 lbs.
per c. ft.). It fuses at 620° Fahr. In testing it con-
tracts in section very much. Its tenacity is about
1.1 ton per sq. in., reckoned on the original area of the
bar.
143. Alloys.-The most complete and extensive
342 TESTING OF MATERIALS OF CONSTRUCTION
1
investigation of the properties of alloys is that made by
Professor Thurston, for the United States Testing Board.'
Only a very brief account of the most useful alloys can
be given here. As to the general properties of an alloy
Professor Thurston says, 'The physical properties of an
alloy are often quite different from those of its con-
stituent metals. In most cases, however, the hardness,
tenacity, and fusibility will be greater than the mean of
the same properties in the constituents, and sometimes
greater than in either; while the ductility is usually less,
and the density sometimes greater, sometimes less. The
colour is not always dependent upon the colours of the
constituent metals, as is shown by the brilliant white of
speculum metal, which contains 67 per cent. of copper.'
BRONZES.
144. Bronzes are alloys of copper and tin. With a
moderate amount of tin the alloy is tough and strong.
With more than 20 per cent. of tin it becomes weak and
brittle. Up to 17 per cent. of tin the elastic limit,
according to Thurston, lies between 0.5 and 0.6 of the
breaking strength. With 25 per cent. it rises up to the
breaking weight. With more than 40 per cent. it falls
again till it reaches about 0-3 of the breaking strength
in pure tin.
Gun-metal for bearings may contain 88 to 95 per
cent. of copper.
Gun-metal for guns contains usually
Report of the United States Testing Board, vol. i., 1878. Also Mate-
rials of Engineering. Thurston. Part III.
COPPER, COPPER ALLOYS, ETC.
343
90 per cent. Bell-metal contains 72 to 82 per cent., and
speculum metal 67 to 75 per cent. The following table
gives values of the tenacity with different proportions
of tin:
Composition
Copper
92.0
91.7
91.0
90.0
84.3
82.8
81.1
79.0
76.3
73.0
Tin
8.0
8.3
9-0
10.0
15.7
17.2
18.9
21.0
Copper
96.27
92.8
92.5
90.0
87.5
86.57
82.5
80.0
23.7
27.0
Composition 1
Tin
Description
3.73
7.2
7.5
10.0
12.5
13.43
17.5
20.0
Gun-metal
"}
?"
"",
Bell-metal
Density
""
""
,,
""
""
Tenacity,
tons per
sq. in.
tons per
sq. in.
12.95
13.84
14.73
16.96
16.1
15.2
8.65
8.69
8.68
8.67
8.65
8.68
8.79 30.32
8.74 25.32
17.7
13.6
9.7
4.9
Authority
14.83
6,132
19.52
6,368
17.26 6,063
22.05 6,255
26.96 5,568
Anderson
The following table gives a reduction of those of
Thurston's results which relate to the more useful
bronzes:
6,762
5,938
tons per
sq. in.
14.29
12.74
12.46
""
11.99
13.88
:>
Mallet
Coefficient
Coefficient
of bending of elasti-
of elasti-Tenacity, Elongation
strength, ticity, tons
per sq. in.
13.14
16.16
14.72
""
""
;"
11
""
in 5 inches
per cent.
14.29
5.53
7.43
3.66
3.56
3.33
0.71
0.40
The bars for bending were 1 inch square and 22
inches between supports. The test bars for tension were
about 2 inch in diameter.
1 From original mixing, not analysis.
344 TESTING OF MATERIALS OF CONSTRUCTION
BRASSES.
145. Brass is an alloy of copper and zinc, sometimes
with a little lead added. Ordinary brass contains from
66 per cent. copper and 34 per cent. zinc, to 70 per cent.
copper and 30 per cent. zinc. Muntz metal, which can
be rolled hot, contains 60 per cent. copper and 40 per
cent. zinc, or sometimes 66 per cent. copper, 33 per
cent. zinc, and 1 per cent. lead.
Mallet obtained the following values for the tenacity
of brass:
Copper
90.7
87.7
85.4
83.0
50.0
Zinc
9.3
12.3
14.6
17.0
50.0
Tenacity, in tons per sq. in.
12.05
13.37
14.28
13.83
8.93
The author obtained for ordinary brass used for
machinery a tenacity of 10:43 to 11:62 tons per sq.
in., an extension of 13 to 22 per cent. in 8 inches,
and a contraction of area of 16 to 27 per cent. The
coefficient of elasticity is about 5,080 for rolled brass.
The table on next page gives a selection of Thur-
ston's results for brasses. The test bars were similar to
those for the bronzes already described.
The great change in the character of the alloy when
the zinc exceeds 45 per cent. is best marked in the
tension results. The coefficient of bending strength is
calculated from the load which deflected the bar 31
inches, or which broke it within that limit.
COPPER, COPPER ALLOYS, ETC.
345

ench
4Q.
squgre
Copper
Tons no
Composition
82.5
80
75
70
65
60
55
50
45
Tin
17.5
20
25
30
35
40
45
50
55
Density
8.63
8.60
8.53
8.44
8.37
8.41
8.28
8.29
1
Coefficient Coefficient
offic
of bending of elasti-
strength, ticity, tons
per sq. in.
No 432
plo
tons per
sq. in.
FIG. 122.
10.35
9.46
9.97
10.92
12.70
17.40
18.95
4,258
14.94
5,167
21.63 6,261 10.78
Fig. 122 gives an autographic diagram for brass.
146. Ternary Alloys of Copper, Zinc, and Tin.-
Thurston has made experiments on ternary alloys, with
No 159 Brass Bar
Nº 432 Aluminuum Bror Bar
1
Extensions. No 159 in Broches
No 438
-
6,440
5,567
5,985
6,265
10
-
2
6,175
5,461
Tenacity, Elongation
tons per in 5 inches
sq. in.
per cent.
14.55
14.59
13.62
13.62
16.88
18.33
19.77
13.84
26.7
31.4
35.8
29.2
37.7
20.7
15.3
5.0
0.8

35
a view to determining the strongest of the bronzes.
But these results are less completely given, and the
tenacities for most appear to be estimated from torsional
experiments. Thurston terms the bronzes of composi-
tion lying between copper 58 to 54, zinc 44 to 40, and
346
TESTING OF MATERIALS OF CONSTRUCTION
tinto 2
maximum bronzes. Some of these have
tenacities of 31 tons per sq. in., and elongations of 47 to
51 per cent. The alloys appear, however, to be subject
to great variation of quality as ordinarily made.
Delta Metal-Mr. Dick has discovered a method of
obtaining copper-zinc alloys, combined with a definite
percentage of iron, which have remarkable strength and
ductility. Iron is dissolved in melted zinc till the zinc
is saturated. This iron-zinc alloy is then used in proper
proportions in making brass. To prevent oxidation in
remelting, and the resulting variation of quality, a
small amount of phosphorus is added, in combination
with copper. The density of delta metal is 84; its
melting point 1800°. It can be worked hot and cold.
It can be brazed. Cast in sand it has a tenacity of
about 21 tons per sq. in. Forged at a dark red heat
the tenacity is 33 or 35 tons per sq. in. Hammered
cold its tenacity is 40 tons per sq. in.
TESTS OF DELTA METAL, SUPPLIED BY MR. DICK (UNWIN).
""
Material
Cast bar
""
Hexagon tilted bar
Rolled bar.
Ring cast while rotat-
ing
Ring cast while rotat-
ing, hammered cold
Elastic Tenacity,
limit, tons tons per
per sq. in. sq. in.
8.89 23.79
7.38 16.73
7.47 17.05
10.65 29.22
22.91
33.26
23.47
39.75
Elonga-
tion, per
cent. in
8 inches
Contrac-
tion of
area,
per cent.
Coefficient
of elas-
ticity,
tons per
sq. in.
7.74 11.93 5,052
9.80 15.42 5,503
8.10 5.90 7,021
12.15 18.44 6,423
11.10 50.40 5,945
25.8 21.1
COPPER, COPPER ALLOYS, ETC.
347
Aluminium Alloys produced in the Electric Furnace.~
Messrs. Cowles have been engaged for some time in
perfecting an electric furnace, in which a temperature is
reached at which most of the more difficult metals are
reduced. A mixture of coarsely pulverised gas carbon
mixed with the ores to be reduced is introduced into a
fireclay retort, and subjected to the current from a very
powerful dynamo. The products at present obtained
are-aluminium and silicium bronzes, aluminium silver,
and alloys of aluminium with other metals. The 10-
per-cent. aluminium-copper alloy has a tenacity of
48.65 tons. per sq. in. The 5-per-cent. alloy 3035
tons per sq. in. Copper with 2 to 3 per cent. aluminium
is stronger than brass. Boron in small quantity affects
copper much in the same way as carbon does iron. The
alloy has a tenacity of 22 to 27 tons per sq. in. without
loss of conductivity. A copper-nickel-aluminium alloy,
termed Hercules metal, broke without sensible elonga-
tion at 44.6 tons per sq. in. Another alloy of the same
kind broke at 49 tons per sq. in. with 33 per cent.
elongation.¹
The following results on alloys made at the Cowles
Company's works were obtained by Mr. E. D. Self
at the South Boston Iron Works. The test bars were
6 inches long between the shoulders :
1 The above data are taken from a paper in Am. Journal of Science,
1885. Also Proc. Inst. C.E., vol. lxxxiii. p. 510.
348 TESTING OF MATERIALS OF CONSTRUCTION

Alloy
10 p. c. aluminium bronze
10
10
9
9
8/3/
7호
​8
29
""
""
""
""
"?
""
""
""
""
Temperature.
Fahr.
""
122
302
545
""
""
"1
""
??
Tenacity
Elongation in 10 inches
Contraction.
Elastic limit.
Tenacity,
Elastic limit,
tons per sq. in. tons per sq. in.
40.8
41.3
43.0
Tenacity,
tons per sq. in.
14.73
13.84
11.16
34.4
32.0
32.1
27.1
32.0
25.8
A bar of aluminium bronze of a more ductile
character was scnt to the author by the London branch
of the Cowles Company. This bar, about inch in
diameter, gave the following results:-
26.7
38.0
23.1
19.6
20.3
Elongation in
6 ins., per cent.
In Fig. 122 the autographic diagram for this bar is
given, showing the great toughness of the material.
147. Effect of Temperature on the Strength of the
Alloys.-Old experiments by a Committee of the
Franklin Institute show that the tenacity of copper
diminishes with increase of temperature. The following
are some of the results :-
1.5
2.5
1.0
9.0
9.0
28.5
6.0
8.25 1
Temperature.
Fahr.
801
1016
2032
12.5 1
36.78 tons per sq. in.
33.26 per cent.
39.87 ""
17.74 tons per sq. in.
2
Tenacity,
tons per sq.
8.48
4.95
0.0
in.
1 These two tests were made at Watertown, and the elongations were
measured in 4 inches.
COPPER, COPPER ALLOYS, ETC.
349
In 1877 experiments were made, under the direction
of the Admiralty, at Portsmouth Dockyard, on the effect
of temperature on bronzes. The test bars were heated
in an oil bath, and then quickly removed to the testing
machine and broken, the operation lasting only about
a minute. This is not quite so satisfactory as breaking
specimens in an oil bath. All varieties of gun-metal
in these experiments show a slow decrease of tenacity
up to a certain temperature, at which the tenacity
suddenly falls to about half its previous value and the
ductility is almost lost. The temperature at which the
change occurred was about 370° in series I. and 250° in
series II. Phosphor-bronze was less affected. Rolled
Muntz metal and copper did not suffer serious loss of
strength below 500°.
148. Influence of Mechanical Action on the Strength of
Bronze.¹-The specimens of bronze were 3 inches in
length and 0.077 sq. in. section. They were subjected
to the following preparation
I. Metal as cast.
II. Metal subjected to a continued tensile stress of
49 cwts., which produced an elongation of 16.7 per
cent.
III. Metal subjected to a compressive stress of
15.87 tons per sq. in. for ten minutes before testing.
IV. Metal elongated 20 per cent. by rolling.
Experiment II. shows, in Major-General Uchatius's
opinion, that homogeneous bronze is susceptible of
¹ Uchatius. Proc. Inst. of Civil Engineers, vol. xlix. 284.
350
TESTING OF MATERIALS OF CONSTRUCTION
Atmo-
spheric
100°
150°
200°
250°
300°
350°
400°
450°
500°
TENACITY OF METALS AT DIFFERENT TEMPERATURES.
T =
=
Loads in lbs. on testing machine lever. D Ductility. Constant of testing machine, 50 25.
The actual tensile strength of the samples is found by multiplying the figures in columns T by 50-25.
2
2nd set.
Temperature Copper 87-75 Copper 87.75
Fahr. Tin 975 Tin 9.75
Zinc 2.5
Zinc 2.5
T
1
D
T
535
505 10
525 11
485 10
505 10
500 10
450
245
265 Nil
250 Nil
8.25 295
0.75
10
D
5
Gun-metal rods, 1 inch diam.
Copper 91
Tin 7
Zinc 2
T
CO
260
275
D
4
Copper 85
Tin 5
Zinc
10
Nil
T
D
T
525 21
480
26
12.5 575 8.75 525 16
525 15.5 550 18
525 14 530 19.5
19.5
535 8.75 460 9 523 19
385
450
450
25.5
255
3
515
16
460 26 25 440
440 26 360
18.25 435 23 255
495 17 435 25
295 0·66 265
Nil
531
Nil
260 2
435 25
250 2
152 1.2
Nil 230 2
152
Nil
10
Copper 83
Tin
2
Zinc 15
:
5
D
6
Copper 92.5
Tin
5
2.5
Zinc
485 26
1
T
D
Phosphor-
bronze rods,
1 in. diam.
562 20
Copper 92.5
Tin 7
Phos. 0.5
T
D
10
++
Muntz
metal rods,
74 in. diam.
10
Copper 62
Zinc 38
T
609 17.5 700 2.5 460
614 17
680 2.5 465
610 18
720 3.9 445
11
605 18
685 3.9 440
580 15
670
5 430
6
0.66 575 12
650 2.5 430
470
7
650 2.25 430
424
600 2.25 420
380 4
615 3.75 415
420
620 5
390
D
Copper rods,
72 in. diam.
T
D
2.5
2.5
4
10
7
6
6
6
6
6
COPPER, COPPER ALLOYS, ETC.
351
having its elasticity greatly increased by mere stretching
without compression. A bronze with an elastic limit
of 15.75 tons and a ductility such that it elongates 37
per cent. was previously unknown.
Bar
I.
II.
III.
IV.
Breaking
stress in tons
per sq. in.
19.4
21.1
24.8
32.2
Elastic limit
in tons per
sq. in.
2.54
15.75
3.17
10.79
Elongation per cent.
Ultimate
50.0
37.3
29-5
2.1
At elastic
limit
·040
.478
·058
∙170
Density
8.863
8.856
8.957
8.975
149. Strength of Screw Bolts.-The metal in an ordi-
nary bolt with screw thread and nut is weakened by the
removal of metal in cutting the thread. At the same
time the apparent tenacity is diminished from the
cause discussed in § 34. The following experiments
by Major W. R. King are interesting as giving the
results of experiments on actual screw bolts of wrought
iron. Major King is of opinion that ordinary screw
threads are too coarse in pitch, and therefore he tried
both the standard pitch of six threads to the inch and
finer pitches.
The iron of the bolts in series I. had a tenacity
of 26·1 tons per sq. in. of original section. In the
case of the bolt with eighteen threads, the diameter
diminished with the stress so as to allow the bolt to
draw out without stripping the threads. The tenacity
of the bolts has been calculated on the assumption that
the threads were of standard Whitworth section.
352
TESTING OF MATERIALS OF CONSTRUCTION
Series
1
2
Diameter of
bolt, in inches
1
""
""
""
""
No. of
threads
to inch
B BaBa
12
6
12
5. English Bessemer
6. Swedish Bessemer
7. Swedish charcoal
18
Description of wire
Breaking load,
in tons
1. BB puddled iron
2. BB piled iron, puddled
3 Extra BB, puddled and Eng-
lish charcoal
•
29.62
35.00
34.21
41.50
42.07
150. Strength of Wire.-Wire is stronger than the
material out of which it is made, in consequence of
the greater amount of mechanical work expended on it.
When in the condition in which it leaves the draw-plate
it is virtually 'cold rolled.' Annealing reduces this
excess of strength. Mr. Preece gives the following
table of the strength of various specimens of wire, when
annealed for telegraphic purposes :-
4. Extra special BB, puddled and
English charcoal
•
Fo
Diameter
""
1
abt.0.171in
""
Tenacity,
reckoned on
section at
bottom of
thread, in tons
per sq. in.
""
""
""
22.77
22.98
26.30
27.26
26.21
Elongation in
7ins. per cent.
Elongation,
per cent.
14.6
14.5
15.0
14.9
15.2
16.1
12.5
2.0
4.3
2.5
6.0
8.0
Breaking
weight, lbs.
1,379
1,266
1,461
1,449
1,946
1,386
1,218
The tenacity is about 22 tons per sq. in. for iron
and 30 tons per sq. in. for steel.
Mr. Preece gives the table on next page for copper
and silicium bronze wire.
1 Proc. Inst. of Civil Engineers, vol. lxxv.
COPPER, COPPER ALLOYS, ETC.
353
Diameter,
in inches
Silicium bronze :
·080
·059
·044
·036
·081
Copper:
·081
*082
⚫0847
·081
Elongation,
per cent.
15:10)
12·0:20
nil
nil
nil
15:10
1.5 1.0
nil
1.5: 2.5
0.5 1.0
0.5
Mean tenacity, tons per sq. in.
Elongation, per cent.
Bendings at right angles before
breaking
Bigny
charcoal
iron wire
46
0.30
18
M. Albert Bonnaud gives the following results
of tests of three qualities of wire-I. Iron wire;
II. Martin steel wire; III. Crucible steel wire. The
tensile tests were made on pieces 14 W.G. (087 inch
diameter) and 16 inches long:
No. I.
Iron
آد:
0.37
Tenacity,
in tons per sq. in.
19
27.61
29.37
47.41
50.07
29.02
27.47
30.32
29.16
30.31
28.42
Firminy wire
No. II.
Martin
steel

86
0.91
20
No. III.
Crucible
steel
102
0.75
28
The bendings were over the jaw of a vice of 0·4 inch
radius. Lest the high strength here shown should be
attributed merely to hard drawing, tests were made on
four pieces in each of the following conditions:-(a) Rod
from rolling mill ready for drawing; (b) unfinished
wire, drawn down as far as it could be before annealing,
A A
354 TESTING OF MATERIALS OF CONSTRUCTION
and then annealed in the case of iron, and specially tem-
pered in the case of steel; (c) finished wire, drawn down
to 087 inch diameter; (d) finished wire, annealed.
Firminy wire
Samples about 16 inches long,
087 inch in diameter
Tenacity, in tons per sq. in.
""
>>
Elongation, per cent.
))
""
""
""
""
""
""
1
""
""
Bendings at right angles
""
Lowest
Highest
Mean
""
""
""
""
>>
""
Unannealed.
About 0.6 in. diameter
α
b
Tenacity,
in tons per sq. in.
с
d
43.6
71.2
56.3
a
b
с
d
a
b
с
d
No. I.
Iron
27.0
28.5
39.3
31.1
7.5 to 16.8
22.0
0.31 to 0.74
20.6
8 to 11
20 to 22
21 to 29
31
The iron wire retains an increased strength, due to
drawing down, even after annealing. The steel wire, on
the contrary, is weaker after annealing than the original
bar. To utilise the value of the steel fully it must be
tempered in such a way that a sufficient flexibility is
retained.
Mr. D. K. Clark gives the following values for
phosphor-bronze wire ¹:-
1
No. II.
Steel
Tenacity,
in tons per sq. in.
63.4
88.6
101.6
54.9
22.6
28.8
24.4
6.2 to 7·0
3.0 to 5.7
1.2 to 1.8
6.8 to 8.0
1 Rules and Tables, p. 629.
2 to 4
4 to 10
16 to 37
12 to 13

Annealed.
About 0-11 inch diameter
Extension,
per cent.
88888
33
47
39
COPPER, COPPER ALLOYS, ETC.
355
The following table gives a few miscellaneous tests
of the strength of wire made by the author :-
No. of
specimen
112
113
124
125
127
128
Description
Brass wire.
Black cast-steel rod
""
Gilding metal (no tin)
""
""
Soft German silver
""
""
109 Black shear-steel rod .
110
103
102
106
107
""
Black soft-steel wire
""
""
""
Bright hard-steel rod.
•
""
Diameter
•191
•191
•249
•249
•267
•267
•194
•192
•196
•196
Sq. in.
area
•197
•198
Tenacity, Extension
in 8 ins.,
per cent.
•1929 ·0290
25.23
⚫0286
62.04
·0286
62.44
·0487
20.17
*0487
20.62
·0560
29.89
·0560
29.10
·0296
50.90
·0289
52.52
·0302
39.17
·0302 38.07
·0305 51.96
⚫0308 51.45
tons per
sq. in.
25.5
4.12
5.76
6.25
8.7
47.0
47.7
7.0
6.25
11.25
15.6
7.5
6.5
Steel pianoforte wire has been produced with a
tenacity of 150 tons per sq. inch.
A A 2
356 TESTING OF MATERIALS OF CONSTRUCTION
CHAPTER XII
EXPERIMENTS ON REPETITION OF STRESS.
ENDURANCE TESTS.
151. In 1871 was published a Report by Herr A.
Wöhler on the endurance of bars subjected to repetitions of
stress.¹ It occurred to Herr Wöhler that most structures,
especially such machine parts as railway axles, springs,
and piston-rods, are subjected to a continual variation of
stress, and that direct experiment in conditions imitating
those which occur in practice might afford useful infor-
mation as to the limits of stress permissible in such
cases. Herr Wöhler carried out a series of experiments,
extending over a period of twelve years, and undoubt-
edly the results are of great importance.
It may be mentioned that Herr Wöhler's machines
were handed over to the Royal Institute for testing
materials in Berlin. Further experiments have been
made with them by Spangenberg, some of the results of
which have been published. Since Prof. Spangenberg's
-
1 Uber die Festigkeitsversuche mit Eisen und Stahl. Angestellt von
A. Wöhler, Ober-Maschinenmeister an der Königl. Nieder-Schlesisch-
Märkischen Eisenbahn. Berlin. A good account of Wöhler's results is
given in Engineering, vol. ii. No other tolerably complete account has
appeared in English.
EXPERIMENTS ON REPETITION OF STRESS 357
death they have been used by Herr Martens, but the
later results obtained have not been published.
Wohler's Machine for Repetitions of Torsional Stress
(Fig. 123).— The test bar was a simple cylindrical bar
with enlarged ends. An oscillating lever c, driven by a
connecting-rod, is attached by a links to the lever l'
on the back end of the test bar. The stroke of the
lever c can be adjusted by moving the connecting-rod
pin in a slot in the lever. At the upper end of the link
h
N
h'
Prop
f
PHWW
FIG. 123.

9
رود
f
C
s there are nuts, which come in contact with knife-edges
on the lever h', and which give a further means of
adjusting the stroke of the lever h'. To ensure the bar
from being strained beyond the exact stress intended,
the opposite or front end of the test bar is fixed in the
double-lever h. This lever presses on the short ends of
the levers g, g', the other ends of which rest on the
bearing screws k, k, and which are held down by the
long springs f,f. If the torsion given by the lever h' is
in excess of a fixed amount, the lever h lifts either the
358
TESTING OF MATERIALS OF CONSTRUCTION
lever g or g' against the spring. By adjusting the
springs, the exact stress at which the levers g or g' lift
can be arranged. If the test bar is to be twisted in one
direction, only one of the levers g or g is required. If
the stroke of the lever l' is large enough it twists the
bar alternately in opposite directions, and then both
levers, g and g', are used to limit the stresses. When
working in adjustment, the stroke of his sufficient to
just lift one or both the levers g or gat each stroke.
Wöhler's Machine for Repeated Tensions (Fig. 124).
-This consists of a wrought-iron bed-plate, at the left-
FIG. 124.
A
b
JO
0.
h

ป
O
10
L
O
O
m
O
O
O
K
KALIM
f
hand end of which is a cast-iron standard, supporting the
knife-edge of the principal lever h. The test bar A is
held in a shackle attached to the lever; the other shackle
is attached to an adjusting-screw b. The long arm of
the lever is connected by a link to the equal-armed
beam m. The centre of this beam is pulled down by a
lever worked by a connecting-rod, a bent spring g being
interposed to prevent shock. The other end of m rests
EXPERIMENTS ON REPETITION OF STRESS
359
on the short arm of the lever k, which has a bearing-
screw and long spring f, as in the torsion machine. If
the pull on m exceeds a certain value the lever k lifts,
and by adjusting the spring f the tension can be regu-
lated as desired. To facilitate the adjustment the rod d,
which the pull is applied to the beam m, is in two
parts, connected by a long coupling nut with right and
left hand screws. The rod d is continued down through
a bracket, and a nut under this bracket serves to limit
the extent to which the test bar is relieved of stress.
-
In adjusting the machine to give a range of tension
between a fixed lower and fixed upper limit, the spring
fis first adjusted to the minimum stress. The nut on
the end of d can then be adjusted, so that when d rises
it just keeps the lever lifted. Then the spring ƒ is
k
adjusted for the maximum stress, and the machine is
ready for use. As made by Wöhler the machine had
four sets of levers, so that four bars could be tested
simultaneously.
Wöhler's Machine for Repetition of Bending Stresses.
-For applying repeated bending stresses to bars, the
stress ranging between a fixed lower and upper limit,
Wöhler employed the machine shown in Fig. 125. The
test bar A rests on knife-edges carried by pairs of links.
At a the links are suspended from a fixed bracket. At
b they hang from the short arm of the lever d. This
lever has a bearing-screw at its longer end, and it is
held down by a spring f. The bar is bent by the rod.
I 7, furnished with an adjusting coupling, and moved up
360 TESTING OF MATERIALS OF CONSTRUCTION
and down by a lever and connecting-rod. When the
bar is not to be entirely released from stress, but to
be strained between a fixed upper and lower limit of
stress, the screw m is used. As the bar unbends it
comes in contact with m at some fixed amount of de-
flection. To adjust the screw m, the spring f is set to
the desired minimum tension, and the screw m is then
α
魚
​Grain
FIG. 125.
in

9
A
b
d
f
Ümumi
adjusted till it just lifts the lever d. Then the spring
f is set to the maximum tension, and the machine is
ready for use.
Wöhler's Machine for Repeated Bending in Opposite
Directions. For repeated bendings in opposite direc-
tions Wöhler used the very simple machine shown in
Fig. 126. It consists of a wooden frame carrying in
bearings the axle a, which is rotated by a belt. In the
ends of a are conical recesses, into which can be fixed by
driving two test bars. After being fixed, the test bars
are turned in the lathe so as to run truly. At the ends
EXPERIMENTS ON REPETITION OF STRESS 361
of the test bars are fixed spring balances, which can be
adjusted to any required stress. As the bar rotates
b.
S
α
"
FIG. 126.


S
b
wwww.
wwww
every fibre is subjected to bending alternately in oppo-
site directions, precisely as is the case with journals of
railway axles.
152. Results of Wöhler's Endurance Tests.-The fol-
lowing tables contain all Wöhler's more important
results. Table I. gives some ordinary statical tests of
the materials used in the subsequent endurance tests.
The elongation was probably measured in 8 inches, but
the length is not given.
b
362 TESTING OF MATERIALS OF CONSTRUCTION
No. of
bar
1934 LON∞
6
7
8
9
10
11
23LE
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
2872**
29
30
31
TABLE I. STATICAL TENSILE STRENGTH OF THE MATERIALS
EXPERIMENTED ON BY WÖHLER.

32
33
34
WROUGHT IRON :
Phoenix Co.'s axle.
""
""
Bar iron from Königshütte
Rivet'iron (Berlin, Borsig)
""
Boiler stay iron (Borsig).
12 Krupp, steel axles
""
HOMOGENEOUS IRON :
Pearson, Coleman, & Co.
""
""
Material
""
""
CAST-STEEL AXLES AND BARS:
""
""
""
""
""
""
""
""
>>
""
""
Borsig, steel axles
""
""
Bochum Company, steel axles
""
""
Borsig
""
""
Vickers, Sons, & Co., steel axles
Werner, hardened-steel axle
""
Krupp, cast-steel rails
CAST-STEEL PLATES:
Krupp,
•
·
""
""
Firth & Sons, tool steel.
""
""
""
""
""
same axle annealed
•
direction of rolling.
""
""
|| direction of rolling.
""
·
""
•
•
•
❤
•
•
•
Tenacity,
in tons per
sq. in.
21.1
21.5
29.2
24.4
33.0
34.0
29.6
24.4
27.5
27.7
29.2
49.0
49.7
49.7
41.8
41.8
42.0
42.5
39.4
37.3
29.2
26.3
52.3
60.2
48.7
47.8
48.7
55.0
33.9
36.3
32.0
36.3
37.7
33.0
Elongation,
per cent.
17.8
21.8
7.0
20.8
22.0
23.6
17.0
19.0
24.6
16.2
21.7
12.1
18.6
11.7
23.7
17.4
18.3
19.0
21.7
22.3
19.5
15.8
1.1
2.2
2.7
15.8
15.4
9.1
12.2
10.8
10.2
9.5
22.0
22.3
Only a few endurance tests with the torsion machine
are given. These consist of some experiments with
EXPERIMENTS ON REPETITION OF STRESS 363
Krupp's axle steel, twisted in one direction only and in
opposite directions alternately.
No. of
bar
1234+ B
TABLE II. WÖHLER'S EXPERIMENTS ON BARS SUBJECTED TO
REPEATED TWISTINGS.
6789
Material
Krupp's
axle steel
Stress applied (at surface
of bar), in tons per sq. in.
Maximum Minimum
Krupp's
axle steel
I. Torsion in one direction only
0
22.9
21.5
20.1
19.1
18.1
Range of
stress, in tons
per sq. in.
+13·4
+ 12.4
+11·5
+10.5
22.9
21.5
20.1
II. Equal alternate torsions in opposite directions
- 13.4
26.8
- 12.4
24.8
- 11.5
23.0
- 10.5
21.0
19.1
18.1
No. of repeti-
tions before
fracture
1
198,600 ¹
373,800
334,750
879,700
[23,850,000]
187,500 3
1,007,550
859,700
19,100,000]
For any given stress a certain number of repeti-
tions of load produce fracture, the smaller the greater
the intensity of the stress. But below a certain limit
of stress a practically unlimited number of repeti-
tions of load is required to cause fracture. Roughly
speaking, the stress for which an unlimited number of
repetitions is required to cause fracture is only half as
great when the bar is alternately strained in opposite
directions as when it is strained in one direction.
A bar strained in one direction will stand 24 million
repetitions of a stress of 18 tons per sq. in., a much
larger stress than would ordinarily be considered safe.
1 Had previously suffered 286,000 repetitions of stress of 21.5 tons
per sq. in.
2 Not broken.
3 Had previously suffered 1,070,000 repetitions of a stress of from 9 5
to 12.4 tons per sq. in.
364 TESTING OF MATERIALS OF CONSTRUCTION
Table III. gives Wöhler's results on the endurance
of bars subjected to repetitions of tensile stress, the
stress in some cases varying from zero to a maximum
limit, in others from a minimum to a maximum value.
Two forms of bars were tried. The bars marked A
had well-rounded corners at the point where the small
middle part joined the enlarged end. Those marked
B had square corners. It may be noted at once that
for any given stress the bars B broke with far fewer
repetitions of stress than the bars A. Thus, bar 5 of
form A stood 480,000 repetitions of a stress of 17.19
tons per sq. in., while bar 9 of form B stood only 37,000
repetitions of a stress of 17·10 tons per sq. in. Bar 16
of form A was not broken with 13,000,000 repetitions
of a stress of 22 tons per sq. in., while bar 21 of form
B broke with 35,000 repetitions of this stress.
The next most important point in Table III. is that
the amount of variation of stress, not the absolute amount
of the stress, determines the number of repetitions before
fracture. Thus, bars 7 and 8 endured nearly as many
repetitions as bar 6, though in the former case the
maximum stress was 21 tons and in the latter 15. But
then the load was not entirely taken off bars 7 and 8, and
the range of stress was only 9 and 11 tons. Again,
bar 18 is not broken with 12,000,000 repetitions of a
stress of 38 tons per sq. in., the minimum load being
19 tons per sq. in. ; but bar 10 broke with 19,000 re-
petitions of a stress of 38 tons, the minimum stress
being zero.
EXPERIMENTS ON REPETITION OF STRESS 365
TABLE III. WÖHLER'S EXPERIMENTS ON BARS SUBJECTED TO REPEATED
TENSIONS BETWEEN DEFINITE LIMITS.

No. Form
of of Material
bar bar
123
3
8
9
10
11
12
13
14
15
16
17
18
19
OD 228
BB
20
21
22
23
24
25
26
AA
A
A
322333
AAAAB
AAAAAAAAAA
B
B
B
27
28
29
30
31
32
33
34
35
36 A
A
AAAAAAA
Iron axle, Phoenix
Company
Krupp's axle steel
Krupp's axle
steel
Cast iron from loco-
motive cylinder
Stress applied, in tons
per sq. in.
Maximum Minimum
22.92
21.01
19.10
17.19
17.19
15.28
+ 21.01
+ 21.01
17.10
38.20
33.40
28.65
26.14
23.87
22.92
21.95
+38·20
38.20
38.20
23.89
21.97
20.08
19.10
17.18
15.29
14.34
7.62
6.69
6.22
5.73
5.26
5.03
5.03
4.78
4.78
4.78
0
+ 9.55
+ 11·46
0
0
+ 23.87
19.10
16.70
0
1 Not broken.
Number of
Range of
stress, in tons repetitions before
fracture
per sq. in.
22.92
21.01
19.10
17.19
17.19
15.28
11:46
9.55
17.10
38.20
33.40
28.65
26.14
23.87
22.92
21.95
14.33
19.10
21.50
23.89
21.97
20.08
19.10
17.18
15.29
14.34
7.62
6.69
6.22
5.73
5.26
5.03
5.03
4.78
4.78
4.78
800
106,910
340,853
409,481
480,852
10,141,645
2,373,424
[4,000,000]¹
37,828
18,741
46,286
170,170
123,770
473,766
[13,600,000]¹
[13,200,000]¹
[1,801,000
[12,100,000]¹
[12,000,000]

23,546
35,486
65,658
75,343
208,883
274,970
[1,100,000]¹
3,140
4,000
10,342
45,028
78,682
27,885
35,599
208,439
[7,200,000]
[7,600,000]¹
1
366 TESTING OF MATERIALS OF CONSTRUCTION
This table contains some results on cast iron which
are interesting. Although this material is somewhat
more irregular in quality than wrought iron or steel, it
evidently behaves in the same general way.
In Table IV. are given the results of the experi-
ments on the endurance of bars subjected to bending.
These exactly confirm those obtained with torsion and
simple tension. Further, as bending tests are made
more easily than other tests, and the deflections are
large and easily determined, these experiments are
numerous and very regular. The stress given in the
tables is that of the extreme fibres, calculated from the
load, by the usual formula ƒ = M/Z; and of course this
f
stress, for all cases in which the elastic limit is exceeded,
is greater than the real stress due to the load. It has
several times been alleged that this discrepancy destroys
the value of any deductions from these experiments by
bending. This view is put forward by those who hesi
tate to accept the conclusion that the breaking stress
with repetition of loading is so much smaller than the
statical breaking strength. It seems to have been over-
looked that whatever error there is in the calculated
stress given in Wöhler's tables is in the opposite direc-
tion, and that the bars broke, in fact, with smaller stresses
than those calculated and recorded in the tables. Bend-
ing experiments are not less trustworthy than tension
experiments, and for stresses considerably less than the
statical breaking weight probably the error in the calcu-
lated stress is not a large one.
*g
EXPERIMENTS ON REPETITION OF STRESS 367
TABLE IV.--WÖHLER'S EXPERIMENTS ON BARS SUBJECTED TO REPETITIONS
OF TRANSVERSE STRESS (REPEATED BendingS) BETWEEN DEFINITE LIMITS.

No. of
bar
123+
67
8
9
10
ERRED 0022
11
12
13
14
15
16
17
18
19
21
2****~
22
23
24
25
26
27
*2*7***3
28
29
30
31
33
34
35
36
37
Bars
marked
H were
hard-
ened
= = = = = = = I I I
H
H
H
H
H
H
H
H
H
1 Not broken.
Material
Iron for axles,
Company
made by Phoenix
-ошон
geneous
iron
Krupp's
cast-steel
axles
Bochum
Company's
steel axles
Krupp's steel
plates
Stresses applied, in
tons per sq. in.
Krupp's spring steel
Maximum Minimum
26.25
23.87
21.50
19.10
17.18
15.28
14.33
38.20
33.41
19.10
26.25
25.07
24.83
23.87
23.87
33.41
28.65
26.25
23.87
23.87
21.50
25.07
23.15
23.87
22.93
28.65
26.10
0
19.10
14.31
0.
0
0
0
0
0
52.50
47.75
42.95
38.20
35.85
35.85
33.40
33.40
33.40
28.65
2 Across direction of rolling.
0
Range of
stress, in tong
per sq. in.
26.25
23.87
21.50
19.10
17.18
15.28
14.33
19.10
19.10
19.10
26.25
25.07
24.83
23.87
23.87
33.41
28.65
26.25
23.87
23.87
21.50
25.07
23.15
23.87
22.93
28.65
26.10
No. of repetitions
of load before
fracture
169,750
420,000
481,950
1,320,000
4,035,400
[3,420,000]
[48,200,000] ¹
1
475,500
1,234,600
[34,500,000]
1,762,300
1,031,200
1,477,400
5,234,200
[40,600,000] ¹
104,300
317,275
612,500
729,400
1
1,499,600
[43,000,000]¹
175,300 2
387,700 2
[4,100,000]¹
271,800 2
420,100
3
[3,600,000]13
52.50
47.75
42.95
38.20
35.85
35.85
389,200
33.40
293,300
33.40
455,700
33.40
28.65
268,900
[36,500,000]
3 In direction of rolling.
54,600
76,300
200,100
339,150
330,750
1
368
TESTING OF MATERIALS OF CONSTRUCTION
No. of
bar
88&=***
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
བྱསྐྱབ
78
79
Bars
marked
I were Material
hard-
ened
H
H
H
H
H
H
H
H
====
H
H
H
Η
Krupp's spring
steel
Krupp's spring
steel
Krupp's spring steel
Bochum
Company's
spring steel
TABLE IV.-continued.
Stresses applied, in
tons per sq. in.
Maximum Minimum
47.75
42.95
38.20
38.20
33.40
28.65
23.87
21.50
57.30
""
,,
""
""
""
""
,,
47.75
""
""
""
42.95
""
""
""
""
"
38.20
""
""
""
""
""
""
33.41
""
""
""
52.50
47.75
42.95
38.20
0
14:33
19.10
23.87
28.65
33.42
33.42
38.20
42.95
7.92
15.92
23.87
27.83
31.52
9.55
14·33
19.10
23.87
23.87
28.65
4.77
9.55
14.33
14.33
19.10
19.10
26.75
4.77
9.55
11.94
14.33
1 Not broken.
Range of
stress, in tons
per sq. in.
47.75
42.95
38.20
38.20
33.40
28.65
23.87
21.50
42.97
38.20
33.43
28.65
23.88
23.88
19.10
14.35
39.83
31.83
23.88
19.92
16.23
33.40
28.62
23.85
19.08
19.08
14.30
33.43
28.65
23.87
23.87
19.10
19.10
11.45
28.64
23.86
21.47
19.08
52.50
47.75
42.95
38.20
No. of repetitions
of load before
fracture
39,950
72,450
132,650
117,000
197,400
468,200
[40,600,000] ¹
[32,942,000]
1
22,900
35,600
86,000
191,100
50,100
251,400
[35,600,000]
33,478,700
62,000
149,800
400,050
376,700
[19,673,300]¹
81,200
156,200
225,300
1,238,900
300,900
[33,600,000] ¹
99,700
176,300
619,600
2,135,670
[35,800,000]
[38,000,000]
[36,000,000]
1
286,100
701,800
[36,600,000]
[31,150,000]
45,850
108,850
93,800
148,400
1
1
1
1
EXPERIMENTS ON REPETITION OF STRESS 369
Bars
No. of marked
H were
bar
80
81
82
83
84
85
86
87
88
88888
89
90
91
92
93
94
95
hard-
ened
H
= = = =
H
H
H
H
II
Material
Mayr's
spring steel
Seebohm's
spring steel
Seebohm's
spring steel
TABLE IV.-continued.
Stresses applied, in
tons per sq. in.
Maximum Minimum
47.75
33.42
31.04
28.65
23.87
62.10
57.30
52.50
47.75
45.35
42.95
38.30
33.42
28.65
26.25
23.87
Range of
stress, in tons.
per sq. in.
47.75
33.42
31.04
28.65
23.87
62.10
57.30
52.50
47.75
45.35
42.95
38.30
33.42
28.65
26.25
23.87
No. of repetitions
of load before
fracture
39,860
212,700
360,100
[30,500,000]
[26,260,000]
28,350
45,500
46,550
141,750
190,050
80,850
154,000
210,000
471,800
538,850
1,165,500
1
Lastly, Table V. gives the results of experiments
on rotating bars subjected to bending. As the bar
turns round while bent in a fixed direction by the spring,
every fibre is alternately in compression and tension,
and these are the only experiments of Wöhler in which
alternate opposite stresses of tension and compression
were obtained. The torsional experiments agree with
the bending experiments as to the effect of stresses in
opposite directions.
Wöhler tried three forms of bars in this research.
Two of these had square corners at the enlarged end.
These two forms were relatively much weaker than the
bars of the third form with rounded corners, and only
1 Not broken.
BB
370 TESTING OF MATERIALS OF CONSTRUCTION
the results of these latter are given in the following
table :
TABLE V. WÖHLER'S EXPERIMENTS ON BARS SUBJECTED TO REPETITIONS
OF TRANSVERSE STRESS (ROTATING BARS) BETWEEN EQUAL AND
OPPOSITE LIMITS OF STRESS.

No. of
bar
123HON∞~
4
6
7
9
24
25
26
27
28
29
30
31
32
1281985 /**
33
34
35
36
37
38
39
40
46
47
48
49
50
51
52
53
Material
Iron for axles,
Phoenix Company
Homogeneous iron
Krupp's cast-steel
axles
Cast-steel axles,
Bochum & Co.
Stress applied, in tons
per sq. in.
Maximum
+15.3
14.3
13.4
12.4
11.5
10.5
9.6
8.6
7.6
+ 23·9
22.9
21.9
18.2
16.3
14.3
13.4
12.4
11.5
+ 20·1
17.2
16.3
15.3
15.3
15.3
14.3
14.3
+17·2
16.3
15.3
15.3
14.3
14.3
13.4
12.4
Minimum
-15.3
14.3
13.4
12.4
11.5
10.5
9.6
8.6
7.6
- 23.9
22.9
21.9
18.2
16.3
14.3
13.4
12.4
11.5
- 20.1
17.2
16:3
15.3
15.3
15.3
14.3
14.3
- 17·2
16.3
15.3
15.3
14.3
14.3
13.4
12.4
1 Not broken.
Range of
stress, in tons
per sq. in.
30.6
28.6
26.8
24.8
23.0
21.0
19.2
17.2
15.2
47.8
45.8
43.8
36.4
32.6
28.6
26.8
24.8
23.0
40.2
34.4
32.6
30.6
30.6
30.6
28.6
28.6
34.4
32.6
30.6
30.6
28.6
28.6
26.8
24.8
No. of repetitions
before fracture
56,430
99,000
183,145
479,490
909,840
3,632,588
4,917,992
19,186,791
[132,250,000]'
2,375
4,986
11,636
31,586
94,311
161,262
464,786
636,500
3,930,150
55,100
127,775
797,525
642,675
1,665,580
3,114,160
4,163,375
45,050,640
127,775
342,850
627,000
20,467,780
2,845,250
[57,360,000]
3,558,700
[14,176,171]
1
EXPERIMENTS ON REPETITION OF STRESS
371
No. of
bar
54
55
56
57
58
C168500 RENK
63
64
66
67
69
70
71
72
73
74
75
76
77
78
79
80
Material
steel axles
Borsig's cast
Vickers & Sons'
cast steel axles
Firth &
Sons' tool
steel
Copper
""
""
""
>>
1
""
TABLE V.--continued.
Stress applied, in tons
per sq. in.

Maximum
+18·2
17.2
16.3
15.3
14.3
+16·3
15.3
14.3
13.4
12.4
11.5
10.5
+17·2
16.3
15.3
14.3
+7·64
7.64
6.69
6.21
5.97
5.73
4.78
Minimum
-18.2
17.2
16.3
15.3
14.3
-163
15.3
14.3
13.4
12.4
11.5
10.5
- 17.2
16.3
15.3
14.3
7.64
7.64
6.69
6.21
5.97
5.73
4.78
Range of
stress, in tons
per sq. in.
36.4
34.4
32.6
30.6
28.6
32.6
30.6
28.6
26.8
24.8
23.0
21.0
34.4
32.6
30.6
28.6
15.28
15.28
13.38
12.42
11.94
11.46
9.56
No. of repetitions
before fracture
157,700
239,875
553,850
1,373,225
1,023,625
51,240
72,940
205,800
278,740
564,900
3,275,860
[8,660,000]¹
370,975
694,450
233,700
1,528,550
30,875
67,725
480,700
663,100
798,000
2,834,325
19,327,460
153. Wöhler's Conclusions.-In certain structures the
whole load is a permanent, or dead, load. With such
cases Wöhler's investigation is not concerned. But in
most cases a part or the whole of the load is occasional,
or varying. In those cases the engineer has to allow
for a practically unlimited number of repetitions of load.
Railway axles, for instance, may make 300 million
revolutions, involving reversal of stress, before being
put out of service. Now, with such varying conditions
1 Not broken.
B B 2
372 TESTING OF MATERIALS OF CONSTRUCTION
of straining action, safety depends, according to Wöhler,
not at all on the maximum stress, but only on the range
of variation of stress.
The following table gives the stresses and ranges of
stress which Wöhler considers to be the limiting values
which, in the materials he experimented on, would only
produce fracture after an indefinitely large number of
repetitions :-
TABLE VI. LIMITS OF STRESS FOR UNLIMITED REPETITION OF Load
(WÖHLER).
""
Wrought iron
""
"5
""
Cast-steel axles
Material
""
""
""
A. Bars subjected to simple tension, compression, or bending
""
""
,,
Untempered cast-steel springs
""
,,
Cast-steel axles
""
""
""
+38·20
+23·90
+33·50
+38.30
+ 43·00
B. Bars subjected to shearing or torsion
10.50
18.20
""
""
Maximum Minimum
stress, tons per stress, tons per
sq. in.
sq. in.
""
""
+ 7·65
+15·80
+ 21.00
+ 13:38
+ 23:00
7.65
0
+ 11.50
- 13.38
J
0
+16·70
0
+ 11.50
+ 19·10
+ 28.70
-10.50
0
Range of
stress
15.30
15.80
9.50
26.76
23.00
21.50
23.90
22.00
19.20
14.30
21.00
18.20
154. Experiments by Spangenberg with Wöhler's
machines entirely support Wöhler's conclusions. If
the stresses are plotted as abscissæ, and the number
of repetitions causing fracture as ordinates, curves are
obtained such as those in Fig. 127. These curves cut
the axis of abscissæ at the statical breaking stress, and
they are asymptotic to a vertical, the abscissa of which
EXPERIMENTS ON REPETITION OF STRESS 373
is the stress which the bar will carry if repeated an un-
limited number of times.
155. Endurance Tests made by Mr. B. Baker.'-Mr. B.
Baker has given the results of a series of experiments
Repetitions
uril 1000
4 500
4.000
3.500-
3.000
2.500
8.000
1.500F
1.000
800
1
-
Axle Iron (Bending)
10
Stress tons per sq. in.
FIG. 127.

15
Estphalia
O
Westphalia Iron (Bending)
20
❤
(Bending) Krupp Steel
Krupp
25
Steel
on iron and steel made with a machine like that shown
in Fig. 126. The rotating bars were 1 inch in diameter
1 Notes on the Working Stress of Iron and Steel.' Am. Soc. of
Mech. Engineers. 1886.
374 TESTING OF MATERIALS OF CONSTRUCTION
and the weight was hung at 10 inches from the fixed
end. The bars rotated 50 to 60 times a minute. The
soft steel was fine rivet steel, with a tenacity of 26.8
to 28.6 tons per sq. in., and an elongation of 28 per
cent. in 8 inches. The hard steel was fine drift steel,
having a tensile strength of 54 tons per sq. in., and
an elongation of 14 per cent. in 8 inches. The iron was
best rivet iron, with a tenacity of 25.9 to 27.3 tons per
sq. in., and an elongation of 20 per cent. in 8 inches.
Some further experiments by Mr. Baker on simple
bending are also given :-
TABLE VII.
No.
123 LO
6
78
PREDRER
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
EXPERIMENTS ON THE ENDURANCE OF ROTATING Bars
SUBJECTED TO BENDING (B. BAKER).

Material
Soft steel
""
""
""
""
""
""
""
""
Hard steel + 29·9
29.1
23.9
23.9
20.8
22.8
18.1
15.2
""
95
55
""
""
""
Maximum
stress, tons
per sq. in.
Best
bar
iron
+16.1
16.1
15.2
15.2
15.2
15.2
15.2
11.6
+ 15.2
15.6
15.2
14.3
13.5
14.3
13.8
Minimum
stress, tons
per sq. in.
- 16.1
16.1
15.2
15.2
15.2
15.2
15.2
11.6
- 29.9
29.1
23.9
23.9
20.8
22.8
18.1
15.2
- 15.2
15.6
15.2
14.3
13.5
14.3
13.8
Range of
stress, tons
per sq. in.
32.2
32.2
30.4
30.4
30.4
30.4
30.4
23.2
59.8
58.2
47.8
47.8
41.6
45.6
36.2
30.4
30.4
31.2
30.4
28.6
27.0
28.6
27.6
Number of repeti-
tions to cause
fracture
40,510
60,200
68,400
92,070
107,415
128,650
155,295
14,876,432
5,760
7,560
14,600
16,300
26,100
32,445
157,815
472,500
108,160
110,000
141,750
389,050
408,000
421,170
480,810
..
EXPERIMENTS ON REPETITION OF STRESS 375
The following table gives results of experiments
on flat bars, some bent alternately in opposite directions,
the others bent one way only. The soft steel had a
tensile strength of 31.3 tons per sq. in., and an elonga-
tion of 20 per cent. in 8 inches. The iron was best
bar iron. The bars were 32 inches long, 1 inch wide,
and inch thick.
TABLE VIII. ENDURANCE TESTS. BARS SUBJECTED TO BENDING
(B. BAKER).
Stress applied, in tons per
sq. in.

No.
K
24
25
26
27
28
29
30
31
32
33
22885
34
35
36
Material
Soft steel
""
""
""
""
""
""
""
""
""
Best
bar
iron
Maximum
+ 19.7
19.7
19.7
18.8
18.8
16.1
15.4
15.2
12.3
15.4
+15.2
15.2
15.2
Minimum
- 19.7
19.7
19.7
18.8
18.8
16.1
15.4
15.2
12.3
0
-15.2
15.2
0
Range of
stress, in tons
per sq. in.
39.4
39.4
39.4
37.6
37.6
32.2
30.8
30.4
24.6
15.4
Number of repeti-
tions before
fracture
12,240
12,325
12,410
18,100
18,140
72,420
147,390
262,680
1,183,200
[3,145,020]
30.4
184,875
250,513
15.2 [3,145,020]
30.4
The bars 33 and 36 were not actually broken, but
when taken out of the machine were found to have
deep flaws.
156. Bauschinger's Experiments on Repeated Tensions.
-Table IX. contains a summary of all Bauschinger's
experiments on the endurance of a bar subject to re-
peated stresses. He constructed a machine of the same
kind as Wöhler's, in which a bar could be subjected
to stresses ranging from 0 to an upper fixed limit in
376 TESTING OF MATERIALS OF CONSTRUCTION
I
tension. He ascertained both the initial elastic limit and
the elastic limit acquired under repeated repetition of
stress; the initial breaking strength and the strength
after the bar had been broken in the Wöhler machine.
TABLE IX. ENDURANCE TESTS. BARS SUBJECTED TO TENSION
(BAUSCHINGER).
Stresses in tension varying from 0 to an upper limit.)
Endurance test
Material
Wrought-
iron
plate
Mild-steel
plate
Bar iron
1
Elastic limit, in tons
per sq. in.
Original
6.84
6.84
6.84
6.84
15.6
15.6
15.6
15.6
15.6
15.6
15.6
15.6
15.6
15.6
15.6
15.6
15.6
15.6
15.6
15.6
11.8
11.8
11.8
11.8
11.8
14.8
14.8
14.8
Acquired Load
during applied,
repetition tons per
of loads
sq. in.
12.3
13.2
14.4
16.4
19.4
18.0
20.0
16.4
19.1
19.0
19.0
19.9
16.4
15.3
20.0
16.9
17.9
12.3
11.5
21.4
10.7
10.8
10.6
10.9
16.3
18.6
11.9
7.1
9.85
13.1
16.4
16.0
16.0
16.0
16.0
19.7
19.7
23.0
23.0
23.0
23.0
23.0
26.2
26.2
26.2
26.2
26.2
13.2
16.4
19.7
19.7
19.7
13.8
17.2
19.7
No. of
repetitions
before
fracture,
in millions
5.17
5.19
5.18
2.28
6.68
3.55
[11.03]
7.35
0.67
1.01
0.32
0.76
0.16
0.44
0.62
0.34
0.49
0.07
0.11
0.04
9.11
7.40
0.64
0.24
0.84
16.48
9.31
0.67
Tensile strength, in
tons per sq. in.
Original
25.2
25.2
25.2
25.2
28.5
28.5
28.5
28.5
28.5
28.5
28.5
28.5
28.5
28.5
28.5
28.5
28.5
28.5
28.5
28.5
26.6
26.6
26.6
26.6
26.6
26.7
26.7
26.7
After
breaking
by repeti-
tion of
loads
23.6
24.3
24.5
1
1
28.2
2
11
27.1
26.6
Not yet broken in endurance test.
2 Elastic limit rose to 167, and then fell near the end of the en-
durance test.
EXPERIMENTS ON REPETITION OF STRESS 377
Material
Thomas
steel axle
Thomas
steel rail
Mild-steel
boiler plate
Elastic limit, in tons
per sq. in.
Original
17.6
17.6
17.6
17.6
17.6
19.0
19.0
19.0
19.0
TABLE IX.-continued.
17.6
17.6
17.6
17.6
17.6
17.6
17.6
17.6
Acquired
during
repetition
of loads
20.4
20.8
24.0
17.6
18.0
18.4
18.0
16.0
Endurance test
Load
applied
16.3
26.2
19.7
26.2
26.2
16.4
19.7
26.2
26.2
18.4
21.0
21.0
21.0
16.4
18.7
16.4
18.7
No. of
repetitions
before
fracture,
in millions
[9.58]
0.62
9.04
0.22
0.06
10.19
7.91
0.57
0.56
Tensile strength, in
tons per sq. in.
Original
40.1
40.1
40.1
40.1
40.1
39.0
39.0
39.0
39.0
4.85
0.40
0.49
26.6
0.88
26.6
6.34
26.6
0.40
26.6
[6.54]
26.6
[4.87] 26.6
26.6
26.6
After
breaking
by repeti-
tion of
loads
41.0
39.4
37.7
All the published experiments on endurance have
now been brought together and reduced to common
measures, because the subject of safe limits of stress,
especially in bridges, must before long be reconsidered,
and because, while experiments of this kind take a long
time to make, it is the number and consistency of the
results which are most impressive. A few results of bars
breaking with comparatively small stresses might be
put aside as possibly accidental or abnormal. But here
are four completely independent series of researches, by
different observers, with stresses of different kinds, on
Not yet broken.
378
TESTING OF MATERIALS OF CONSTRUCTION
very various materials; and the whole of the results
are very singularly consistent.
In all cases the number of repetitions of loading
the bar will bear diminishes with increased range of
variation of stress. Further, it is very striking how
regularly progressive the diminution of the number of
repetitions is as the range is increased. It is impossible
not to conclude that, whatever the cause of decreased
life of the bar may be, it is a cause which acts con-
tinuously, altering in some way the structure or the
properties of the bar.
Gal
Undoubtedly it would appear likely that any gradu-
ally progressive alteration or fatigue of the bar would
be manifested in some way in alteration of the strength,
the elastic limit, or the elongation of the bar when tested
in the ordinary way. But this, so far, appears not to
be the case. A bar subjected to so many repetitions of
loading that it is known to be on the point of breaking,
or a piece of a bar already broken in an endurance test,
gives in the testing machine no indications that the
strength or ductility has been altered. Both Mr. Baker's
and Professor Bauschinger's results agree in this, and it
is in accordance with experiments on pieces of structures
long subjected to loading. Professor Kennedy has
given a series of tests of old rails, tyres, and other long
used material,¹ and no one would guess from the results
that these test pieces were in any way different from
new material. But this in no way gets over the fact
¹ Prof. Papers of Royal Engineers, 1884.
EXPERIMENTS ON REPETITION OF STRESS
379
that material subjected to repeated loading is different
from new material. The material, after a certain num
ber of repetitions with a given range of stress, does
break with fewer subsequent repetitions. For some
reason the ordinary testing machine observations are
too coarse to detect the difference.
Whatever the alteration produced by repetition may
be, it certainly does not appear to be a loss of strength
(statical resistance). If it is a loss of ductility or
power of elongation, then it must be a loss confined to
very short portions, or planes of weakness, in the bar,
for if not it would be shown in ordinary testing.
In
certain cases flaws or fissures have been found to be
present in bars subjected to so many repetitions of load
that they were on the point of breaking. It is at least
conceivable that repetition of stress picks out sections.
of weakness in the bar, and that the deterioration is
almost confined to such planes; the deterioration
may be primarily a loss of power of yielding in the
particles near the plane of weakness, and not a loss of
tenacity. Such a loss of ductility at a section might
well show itself finally in a rapidly-spreading fissure or
crack. This explanation is purely hypothetical, but it
is at least in accordance with a very curious fact ob-
served in the fracture of bars in Wöhler machines.
Such bars after fracture usually show no trace of draw-
ing out, however ductile the material may be, when
tested statically. The bars break as if the material
was perfectly brittle. This peculiar fracture, without
380 TESTING OF MATERIALS OF CONSTRUCTION
indication of any plastic drawing out, is not uncommon
in fractures of tyres, axles, and other structures in
ordinary experience.
On what principle, then, is the limit of working stress
in different cases to be decided? As to structures
subjected to a purely resting load there is not much
practical doubt. There is no evidence that the deforma-
tions due to ordinary dead loads on ordinary materials
increase with time, however indefinitely prolonged. Se-
cular experiments, such as Sir W. Thomson is making
at Glasgow, will probably show that a structure may be
loaded with a considerable fraction of its breaking weight
and will carry it for a practically unlimited time without
sensible increase of deformation. What is exactly the
safe limit of stress in this case is not known, but pro-
bably there is a limit of stress, such that smaller loads
are safe and greater loads unsafe.
157. Account of the Adoption of Fixed Limits of
Working Stress independent of the Conditions of Loading.-
Nothing has hindered so much the recognition of the
importance of Wöhler's researches as the existence of
officially sanctioned rules for the limits of working
stress, and the prevalence of opinions having no better
origin than the habit of working to such rules. It will,
therefore, not be out of place to indicate how such rules
originated. It will appear that they are rather the acci-
dental product of momentary exigencies than the result
of any scientific induction. No doubt the ordinary
practice of engineers is to divide the statical breaking
D
EXPERIMENTS ON REPETITION OF STRESS
381
strength of a material by an assumed 'factor of safety
to find the proper limit of working stress; and it has,
or had, come to be tacitly accepted that the ratio of the
working stress to the statical breaking strength measures.
in all cases the margin of safety.
The so-called factor of safety has been supposed to
be required to allow for the following possible causes of
weakness :--
1. Variation in the quality of the material.
2. Imperfections of workmanship, causing either
scant dimensions or unequal distribution of stress.
3. Corrosion, wear, and other deterioration arising
gradually with lapse of time.
4. Errors of calculation, or straining actions
neglected.
5. Vibration, shock, and other dynamical actions.
A margin of safety between the working and break-
ing stresses is undoubtedly required to allow for the
contingencies thus enumerated. But it would be im-
possible, with these contingencies alone in view, to
explain the varying factors of safety which are adopted
in practice; and, if Wöhler's results are true, it is
absolutely false to reckon as the margin of security the
difference between the calculated working stress and the
statical breaking stress.
Previous to 18492 no defined rule, recognised
" 1
1 Or, to use an American phrase, 'factor of ignorance.'
2 See a very complete account of the Board of Trade rules, in a paper
on the Design of Girder Bridges,' by W. Shelford and A. H. Shield.
Brit. Assoc. Report, 1886.
382 TESTING OF MATERIALS OF CONSTRUCTION
officially, appears to have existed, limiting the discretion
of the engineer in the design of bridges and other struc-
tures. In 1847 a Royal Commission was appointed to
inquire into the conditions which should be observed
in the application of iron to structures. The Commis-
sion reported against fettering engineers by legislative
enactments. But they made some recommendations
with respect to cast-iron bridges which were adopted
as rules by the Board of Trade. According to these
recommendations, the breaking weight of a cast-iron
bridge was to be six times the live load added to three
times the dead load. They also recommended that an
allowance should be made for dynamic action in bridges
of less than 40 feet span. A discussion arose shortly
afterwards as to the safety of the Torksey Bridge, and
then, for the first time, a proposal was made to limit the
stress in all wrought-iron bridges to 5 tons per sq. in.
The Torksey Bridge appears to have been finally passed
in a condition in which the working stress probably
reached 6 tons per sq. in. In 1858 a further dispute
arose as to the safety of the bridge over the Spey,¹ built
by Sir W. Fairbairn. An attempt was made to get the
Board of Trade to allow for wrought-iron bridges, as
for cast iron, a different factor of safety for the stresses
due to the dead and live loads. But the Board of
Trade then formally adopted the rule that the stress in
wrought iron should not exceed 5 tons per sq. in., and
1 It was in connection with the discussion about the Spey Bridge that
Sir W. Fairbairn made the experiment on the action of repetition of stress
on a wrought-iron girder.
EXPERIMENTS ON REPETITION OF STRESS 383
that without reference to the quality of the iron or the
character of the loading. Later, for steel bridges, a
limiting stress of 6 tons has been allowed, under certain
restrictions as to the testing of the material.
2
It will be seen that as early as 1847 the Railway
Commission recognised a difference between the action
of a dead and a live load. Unfortunately, they were
disposed to ascribe this difference entirely to the dyna-
mical action of the live load causing increased deflection,
and therefore increased stress. Since the publication
of Wöhler's results a quite different view of the differ-
ence between the action of a fixed, or deal, and a vary-
ing or live, load has been recognised by the more
thoughtful engineers. Although the official rules in
this country have remained unaltered, practice no longer
strictly conforms to those rules; and in other countries
varying limits of working stress, depending on the range
of variation of stress, have been boldly adopted.
-
Mr. Baker states that the short spans of the Elevated
Railway in New York were designed for a stress of
3.6 tons per sq. in. on the flanges, 34 tons on the web
bracing, and 2-0 tons for members subjected to alternate
tension and compression; that a recent German bridge
over the Danube was designed for limits of stress vary-
ing with the range of stress from 31 tons to 5'8 tons
per sq. in.; and that a Hungarian bridge over the same
river was designed for stresses varying from 3.9 to 5
tons per sq. in. On the other hand, Mr. Baker estimates
that on the Conway Bridge, which carries the heavy
384
TESTING OF MATERIALS OF CONSTRUCTION
traffic of the London and North Western, and in which
the ratio of dead to live load is large, the stresses reach
the value of nearly 6 tons per sq. in.'
1
158. Bauschinger's Later Researches on the Variation
of the Elastic Limit.—It has been an obstacle to the adop-
tion of rules based on Wöhler's experiments that they
stand apart as empirical results unexplained on any
theory of the resistance of materials.
The old view of the condition which fixes the limit
of safe stress was that, up to some definite stress, the
material was perfectly elastic. Any load producing
a less stress might be imposed and removed without
in any degree altering the material. The molecules
strained by the load returned on its removal absolutely
to their original condition. But a load exceeding the
elastic limit altered the material-the molecules after
straining assumed new positions. If it could be shown
that Wöhler's ranges of stress were ranges within which
the material was perfectly elastic, and that when those
ranges were exceeded a plastic or permanent deforma-
tion occurred, then an explanation of Wöhler's results
would be found. For deformations, however small,
accumulating with repetition of the load, would ulti-
mately cause fracture. But here two obvious and con-
siderable difficulties have to be met:-
G
1. A bar subjected to alternate pressure and ten-
sion breaks after a sufficient number of repetitions with
a stress less than its primitive elastic limit.
-
1 'Notes on the Working Stress of Iron and Steel.' By B. Baker.
American Society of Mechanical Engineers. 1886.
EXPERIMENTS ON REPETITION OF STRESS 385
2. It has long been known that the application of a
stress exceeding the elastic limit raised the elastic limit.
In certain cases it appeared that the elastic limit could
be raised by strain nearly to the breaking stress. This
appeared inconsistent with the view that the safe limit
of stress could depend on the elastic limit.
A very important memoir by Prof. Bauschinger
throws some light on the difficulties thus raised.¹
Prof. Bauschinger's conclusions rest on extremely
delicate measurements of the behaviour of bars in ordi-
nary testing, and are not likely to be generally accepted
without further and independent investigation. But
this may be said, that the memoirs of Prof. Bau-
schinger represent an amount of scientific work in testing
materials to which there is no parallel in this country,
either in the extent and completeness of the researches
or the accuracy of the measurements. Prof. Bau-
schinger believes that his measurements are minute
enough to determine definitely the true elastic limit
of a material, the limit at which proportionality of
the stress and strain first sensibly ceases. Let it be
assumed for the moment that such a limit can be defi-
nitely ascertained. Then, take this very simple point.
It is known that applying a tension to a bar greater
than its elastic limit in tension raises its clastic limit
in tension. No one has cared to inquire whether such
M
1 Ueber die Veränderung der Elasticitätsgrenze und die Festigkeit des
Eisens und Stahls. Mittheilungen aus dem Mech. Techn. Laboratorium in
München. 1886.
CC
386 TESTING OF MATERIALS OF CONSTRUCTION
raising of the elastic limit in tension affected the limit in
compression. Suppose that initially the elastic limits in
tension and compression were 10 tons per sq. in., and
that by a load of 15 tons the elastic limit in tension has
been raised to 15 tons-it has been universally assumed
that the bar would then be perfectly elastic from 10 tons
compression to 15 tons tension.¹ But this is exactly
what Bauschinger's experiments appear to conclusively
disprove. The elastic limit in tension cannot be raised
without lowering the limit in compression, and vice versa.
Even a moderate raising of the tension limit may lower
the compression limit to zero.
This furnishes a complete solution of one of the
difficulties in accepting Wöhler's laws. When a bar is
subjected to alternating compression and extension the
elastic limit cannot be raised. Any attempt to raise it
in one direction lowers it in the other. The law that
the elastic limit can be raised by stress does not apply
to a bar subjected to alternate stresses of opposite sign.
Why the elastic limit in this case is even lower than
the primitive elastic limit in most cases will be dis-
cussed presently. At present, it is enough that under
alternating stresses we cannot expect that the elastic
limit will rise, and therefore cannot expect a bar to be
safe under a range of stress greater than that between
its primitive elastic limits.
¹ One single exception should be noted. Prof. James Thompson, in
1877, stated that the common assumption that the elastic limit could be
extended both for compression and tension was unproved, and that the
determination of the point was a matter of importance in the theory of
elasticity. Encyclopædia Britannica, Elasticity.'
EXPERIMENTS ON REPETITION OF STRESS 387
Next consider the case of a stress of one kind only.
Bauschinger's experiments, like earlier experiments,
show that under stresses of one kind only, the elastic
limit of a bar can be raised by strain nearly to the
breaking stress. But they show, at the same time, that
these artificially produced elastic limits are extremely
unstable. The following table illustrates these points.
TABLE X. BAUSCHINGER'S EXPERIMENTS ON THE CHANGE OF POSITION
OF THE ELASTIC LIMIT.
(Bar subjected to tension only. Tons per sq. in.)
Treatment
Bar of Bessemer steel, No. 939c:
1. Original condition.
2. One day after
3. Immediately after (2)
4. Immediately after (3)
5. One day after (4) .
Broke with 34 tons
Bar 9396. Same steel:
1. Original condition
2. 69 hours after (1) .
3. Half an hour after (2)
straightened in the lathe
4. 68 hours after (3) .
5. 3 years after (4)
6. 2 days after, and after being
vibrated by hammering on
end
•
7. After 2 years, and after heat-
ing to cherry-red and cool-
ing in water
Broke at 35 8 tons
Elastic limit
11.6
8.05
12.0
20.0
4.05
6.9
33.0
12.5
0
Yielding
Greatest
stress
stress or
breaking- imposed on
down point
bar
17.4
24.8
27.0
28.3
32.4
18.6
24.0
25.6
33.0
33.0
32.0
24.6
22.6
26.8
28.3
29.6
34.0
21.3
26.6
32.3
33.0
33.0
32.0
25.2
It will be seen, in the case of the first bar, that
loading again immediately after stretching to the yield-
ing point, the elastic limit is lowered from 11.6 to 8.05
tons. In the case of the second bar, similarly strained
C
cc 2
388 TESTING OF MATERIALS OF CONSTRUCTION
but with a period of rest of 69 hours allowed, the elastic
limit is raised from 12 to 20 tons. But on reloading
immediately the elastic limit is lowered to 4.05 tons.
With a three years' period of rest it is raised to 33 tons,
just the load with which it had previously been strained.
But this artificially produced elastic limit is so unstable
that on hammering the bar on the end and reloading it
has fallen to 12.5 tons.
Now, to return to the case of a bar subjected to
alternate compressions and tensions. It was seen that
one of the difficulties of Wöhler's laws was, that the
limit of safe stress for alternate tensions and compres-
sions is a stress less than the primitive tensile elastic
limit. Bauschinger explains this by advancing the
view that the primitive elastic limit of many materials
is an artificially raised elastic limit. The material has
been subjected to mechanical operations in manufacture
which are equivalent to straining actions. Now, Bau-
schinger found that alternate compression and extension
had the effect of raising an artificially lowered, or lower-
ing an artificially raised, elastic limit. By subjecting a
bar to a few alternations of equal stresses, which are
equal to or somewhat exceed the elastic limits, they
tend towards fixed positions which Bauschinger calls
the natural elastic limits. The range of stress for which
a bar is perfectly elastic after a few repetitions of such
alternating stresses appears to agree very closely with
Wöhler's range of stress for unlimited repetitions of
alternating stresses.
EXPERIMENTS ON REPETITION OF STRESS 389
TABLE XI. BAUSCHINGER'S EXPERIMENTS ON ALTERNATING TENSION
AND COMPRESSION.
(Tons per square inch.)
Time between the loadings
Wrought-iron bar :
1. Original condition
2. 6 days.
3. 1 hour
4. 5 minutes
5. 20 hours
6. 1 hour
7. 46 minutes
8. 30½ hours
9. 15 hours
10. 2 hours
11. 9 minutes
12. 27 hours
13. 30 minutes
14. 3 days.
15. 2 days.
16. 2 days.
17. 5 hours
18. Next day
19. 2 days.
20. 24 hours
21. 4 hours
22. 1 day
23. 9 hours
•
•
•
3. 5 hours
4. 4 days.
5. 2 days.
6. 5 hours
7. 21 hours
8. 2 days.
9. 4 hours
10. 2 hours
11. 16 hours
12. 23 hours
·
Bessemer steel bar :
1. Original condition
2. 23 hours
Elastic limit
Tension
13.7
4.8
6.35
7·15
8.75
17.7
1.6
5.55
8.85
10.5
9.65
Compression
|
4.8
9.65
12.9
12.7
4.8
7.15
1 1
7.95
7.95
3.24
4.85
8.85
| |
9.65
9.65
Load imposed

Tension
13.7
14.5
14.5
│1
6.45
7.25
7.25
17.5
6.35
7·15
7.95
8.75
I
24.0
24.0
8.5
9.7
11.3
11.3
Compression
| 1
14.5
14.5
14.5
14.5
6.45
17.3
17.5
6.35
7.15
7.15
8.75
9.55
24.3
|
8.5
9.7
9.7
11.3
11.3
The preceding table illustrates Bauschinger's attempt
to find the natural elastic limits by alternating stresses
in tension and compression. It will be seen that after a
390 TESTING OF MATERIALS OF CONSTRUCTION
succession of loads in tension which lower the limit in
compression, and of loads in compression which lower
the limit in tension, the elastic limit settles down-as
the loads are diminished towards an amount not greatly
exceeding the elastic limit-to a value not greatly dif
ferent in tension and compression, and below the initial
elastic limit. Further, the limits thus obtained-about
8 tons for wrought iron and 9tons for mild steel-
differ very little from the stresses which Wöhler found
to be the greatest which a bar would bear indefinitely
when subjected to equal alternating stresses.
The tables given are only a sample of the numerous
tables in Professor Bauschinger's memoir. But these
may serve to show that the elastic limits of a material
are variable limits, restricted only by this, that the range
of perfect elasticity seems to be a fixed range. In this
a point of agreement is found with Wöhler's results.
Elastic Limit in Bauschinger's Endurance Tests.—In
the endurance tests given in Table IX. the initial
elastic limit, which was determined from measurements
on a 5-inch length of bar, and the elastic limit ac-
quired during repetition of stress, are given. It will
be seen that the elastic limit usually rises with repeti-
tion of stress to a point above the load applied. When
that is the case, the bar suffers a large number of
repetitions of load before fracture. If the elastic limit
is very near to, or below, the load applied, the bar
breaks with comparatively few repetitions of load. As
far as the statical strength of the bar is concerned, it
EXPERIMENTS ON REPETITION OF STRESS 391
does not appear to be diminished by any number of
repetitions of load. There is a small diminution in
wrought iron, and an increase in other cases.
159. Gerber's Parabola.-Suppose the ranges of
stress for unlimited repetition known for any material.
Then it has been shown that, if the ranges of stress
are plotted as ordinates, and the minimum stress as
abscissæ, the points fall on a parabolic curve.
Let fmax, fmin be the limits of stress, and A=fmax
fmin be the range of stress. The upper sign is to be
taken if the stresses are of the same kind, and the
lower if they are of different kinds. Let f be the sta-
tical breaking strength. Then Gerber's equation is-
2
( ƒmin + ½ ▲ )² + k ▲ = ƒ ² ;
where k is a constant for any material. If the statical
strength ƒ is known, and the value of fmin and fmax
for any one range of stress at which the bar stands
a practically unlimited number of repetitions before
breaking, then k can be determined, and the limits of
stress for all conditions of loading can be calculated.
The values of k have been calculated for all
Wöhler's and Bauschinger's experiments in which the
bars stood over 5 million repetitions of load, and from
the equations the parabolas in Fig. 128 have been
drawn. It will be seen that these quite independent
experiments give fairly consistent values for the ranges
of stress under all conditions of loading. Bauschinger's
results are specially valuable in connection with
392
CONSTRUCTION
TESTING
MATERIALS OF
OF

ug
30
bs ad sugg
Stress in
20
Range of
10
15
-10
+
Bur Iron
0
WOHLER'S
FIG. 128.
Wrought Iron Plate.
AND
ENDURANCE TESTS.
**I*X
BAUSCHINGER'S
܀
Steel Axle.
Steel Rail
Wrought Iron
Mild Steel Boiler Plate.
Bessemer Steel Plate.
Bar Iron
10
20
30
Minimum Stress in tons per square inch.
WOHLER'S RESULTS IN FULL LINES
BAUSCHINGER'S
DOTTED LINES.
Untempered Spring Steel.
Krupp's Axle Steel.
40
50
1
60
EXPERIMENTS ON REPETITION OF STRESS 393
Wöhler's, because in two of the materials used by
Wöhler the statical strength was exceptionally high.
The following tables give the values of fmax and
fmin for the most useful cases, recalculated from the same
equations. The last column is of course the experi-
mentally determined breaking strength of the material
used:
TABLE XII.
BAUSCHINGER'S ENDURANCE TESTS.
(Stresses requiring 5 to 10 million repetitions to cause fracture. Tons per sq. in.)

Material
Wrought-iron
plate
Bar iron
Bar iron
Bessemer mild
steel plate.
Steel axle
Steel rail.
Mild steel
boiler plate
•
Material
Opposite stresses One stress zero Similar stresses
Wrought iron
Krupp's axle
steel
Untempered
spring steel
Least Greatest Least Greatest Least Greatest
7.15 + 7·15 0
7.85 + 7·85
8.65 + 8.65
0
0
0
0
6
8.55 + 8.55
- 10.5
+10.5
9.7
+ 9.7
8.65 + 8.65
Opposite stresses
13.10
14.4
15.75
15.70
19.70
18.4
8.6
+ 86 0
- 14.05 +14.05 0
- 13.38 +13:38 0
15.8
11.4 19.2
13.3 22.02
13.2 21.92
14.3 23.8
20.0 32.1
19.5 30.85
13.3 22.55
TABLE XIII.
LIMITS OF STRESS, FROM WÖHLER'S ENDURANCE TESTS.
(Stresses, in tons per sq. in., for which fracture occurs only after an indefinitely
large number of repetitions.)
One stress zero Similar stresses
Least Greatest Least Greatest Least Greatest
Range
zero.
Ultimate
statical
strength
15.25 12.0 20.5
26.5
17.5 37.75
25.5
12.5
22.8
26.6
26.4
28.6
40·0
39.0
26.6

Range
zero.
Ultimate
statical
strength
22.8
52.0
34.75 57.5
394
TESTING OF MATERIALS OF CONSTRUCTION
CHAPTER XIII.
TIMBER.
160. Unlike the materials hitherto examined, timber
has, in consequence of its organic origin, a remarkable
and definite structure, so that its mechanical properties
cannot be understood without reference to its mode of
growth. Nor is this all. The quality of timber is
largely influenced by the soil and climate, the age of
the tree and season of felling, and the duration of the
seasoning process. Hence, experiments on timber, to
be valuable, should be made on logs the history of
which is known, and should be directed so as to deter-
mine the relative influence of all the circumstances
which affect its mechanical properties.
Timber is composed of vegetable cells, and, chiefly,
very elongated cells, termed wood-fibres, arranged
A stress
nearly parallel to the axis of the stem.
applied to a transverse section must break the fibres
across, while a stress applied to a longitudinal section
separates them from each other. The strength along
the grain depends on the strength of the fibres; that
across the grain on their adhesion. Hence, in pine wood
the lateral strength is only one-tenth to one-twentieth
;
TIMBER
395
of the longitudinal; in leaf wood, one-sixth to one-
fourth. All the timber commonly used in construc-
tion is derived from exogenous trees. In the section
of an exogenous stem there may be recognised the
pith, the woody tissue forming the greater part of the
section, and the bark. The growth of the stem occurs
by the addition, annually, of a ring of new fibres be-
tween the bark and the already formed timber. Hence
most exogenous stems indicate, by distinct annual
rings, the age of the tree. The timber is sometimes
broadly marked, so as to be distinguishable into two
portions-the heart-wood, and sap-wood; and usually,
but not invariably, the sap-wood is weaker and less
sound than the heart-wood. In some trees, plates of
cellular tissue extend radially from the pith towards
the bark. These are termed medullary rays, and are
planes of weakness in the timber.
From the joiner's point of view, timber is broadly
distinguished into soft wood and hard wood. The dis-
tinction roughly agrees with a distinction between
timber derived from the needle-leaved trees (coniferous
trees), and timber derived from broad-leaved trees. By
far the largest part of the timber used in construction
is the soft wood derived from needle-leaved coniferous
trees. In Europe the most important timber tree is
the northern pine (Pinus sylvestris), yielding timber
known as red or yellow fir, Memel, Dantzig, or Riga
fir, or yellow deal. Next to this, the spruce fir (Abies
excelsa) yields the valuable timber known as white
396
TESTING OF MATERIALS OF CONSTRUCTION
deal. Similar timber, coming from America, the pro-
duce of allied species, is commonly known as pine.
The yellow pine of the pattern maker, and the pitch
pine of the joiner are examples. All timber, after
felling, requires to be seasoned, and in ordinary season-
ing timber loses one-fifth to one-seventh of its weight.
When perfectly dried it may lose one-third of its
weight. During this seasoning it shrinks, and much
more in a transverse direction, and especially along the
annual rings, than longitudinally. A plank of oak may
shrink in width one-twelfth, and one of pine or fir one-
thirtieth to one-fortieth. This shrinkage, which con-
tinues a long time, is one of the determining conditions
in the arrangement of timber in construction. It is
during seasoning that the shrinkage causes the heart
shakes (radial), or cup shakes (along the rings) which
often detract so much from the value of timber.
W
Till recently, nearly all tests of timber have been
made on comparatively small specimens. Such test
specimens are virtually selected, not average, specimens.
They are more homogeneous and better seasoned than
larger pieces, and are free from knots, shakes, and other
serious defects. Hence they give values for the strength
of the timber very much in excess of the strength of
large pieces. To furnish useful data for construction,
tests must of necessity be made on large pieces. Hence
very few of the mass of tests hitherto made need here
be quoted. The following short table gives the general
relation of the strengths for a few of the more important
timbers:
TIMBER
397
PROPERTIES OF TIMBER, FROM SMALL TEST SPECIMENS.

Coefficient
of elasti-
Length of
Kind of timber seasoning, tension,
city for
years
Yellow pine.
Spruce
Red pine.
British oak
Teak, Indian
Mahogany
White oak
•
""
•
""
Spruce
Yellow pine
Lignum vitæ
Pitch pine
White pine
Ironbark.
Blue gum
Jarrah
•
•
•
•
4
1-2
13-18
1
1-6
434
tons per
sq. in.
714
750
656
1,071
871
910
317
Tenacity
along
fibre, tons
per sq. in.
5.54
5.80
6.70
6.70
5.51
8.70
8.93
5.44
6.87
7.14
5.09
5.10
7.12
8.97
1.31
Crushing Coefficient Shearing
strength of bending resistance
along strength, along
fibre, tons tons per fibres, tons
sq. in.
per sq. in.
per sq. in.
2.41
2.59
4:46
5.36
3:30
2.81
2.88
2.66
3.60
4:40
3.99
2.24
4.54
3:45
3.20
4.91
3.71
5.27
6.92
4:46
4.46
4.69
2.68
4.51
7.18
3.03
8.15
5.86
4.13
0.27
0.29
1·03
161. Bauschinger's Investigation of the Elasticity and
Strength of Pine Wood. - By far the most thorough
and valuable investigation of the properties of timber
is contained in two papers in the 'Mittheilungen,' of
the Munich Laboratory. 1
In Bauschinger's earlier
investigation the object was to determine the condi-
tions which should be observed in testing timber, the
relative value of different modes of testing, the in-
fluence of conditions of growth, time of felling, and
seasoning on the strength of timber, and the rela-
tions between the physical constants of the material.
Bauschinger immediately found that the amount of
moisture in the timber had a very great influence on
¹ Mittheilungen aus dem Mech. Techn. Laboratorium in München.
1883 and 1887.
398 TESTING OF MATERIALS OF CONSTRUCTION
its density and strength, so that comparative values
could only be obtained by reducing experimental re-
sults to a uniform standard dryness. He determined
the dryness for every test piece. At first this was done
by taking a few grams of sawdust, raspings, or chips
from the timber, drying them at 101° C. in a current
of dried air for about eight hours, and then reweighing
to determine the loss. The percentage of moisture was
calculated on the original weight of the specimen. In
later trials the whole test specimen was dried in an
oven kept at 101° to 105° till it ceased to lose weight
The drying usually lasted two to four days. To deter-
mine at all accurately the strength or density at a
standard dryness, it is necessary to experiment on
three test specimens in three stages of dryness. If the
results are plotted, a curve can be drawn giving the
relation of strength or density to dryness, and from this
the required value at standard dryness can be deter-
mined. Bauschinger takes 15 per cent. of moisture
as the most convenient standard dryness, that being
the condition most often reached by simple exposure
to air.
The bending tests were made on beams about 20
inches square and 9 feet long. These were broken
with a clear span of 98.4 inches. The tension tests
were made on small test bars of the form m shown
in Fig. 81, and with the shackles shown in Fig. 74.
These tests presented difficulty from the tendency of
the wood to draw out of the part in the shackles by
TIMBER
399
shearing along the fibres. The bar had to be well
bedded against its shoulders by driving the wedges at
the back, and the side screws had to be strongly tight-
ened during the test. The elastic limit in tension almost
coincides with the breaking point. The coefficient of
elasticity was determined from the extension with a
load of about one-third the breaking load. Pressure
tests were made with specimens of the form shown in
Fig. 85, and afterwards with simple square prisms,
about 3 to 4 inches length of side, and about 6 inches
long. Shearing tests were also made on radial planes
in the timber.
-
The tension results show very great differences, due
partly to the small section of the test pieces, which
allowed the greatest influence to original differences of
quality in the timber. The tenacity is very great, ex-
traordinarily so if the large amount of vacant space is
allowed for which is observable in microscopic sections.
Pieces cut near the heart of the tree are much weaker
than pieces cut nearer the periphery; and this is con-
nected generally, but not always, with less density in
the wood near the heart. The strength does not directly
depend on the width of the annual rings. But it ap-
pears to be more directly connected with the propor-
tionate width of the summer zone of the annual rings
as compared with the spring zone. In tension experi-
ments the influence of time of felling is not recognisable
a short time after felling. The coefficient of elasticity
varies very significantly with the strength, increasing
C
400 TESTING OF MATERIALS OF CONSTRUCTION
and decreasing with it. The bending tests on beams of
the full useful section of the log showed generally that
the strength and coefficient of elasticity varied directly
with the density. The results were, however, influenced
by the presence of knots and other defects. The pressure
tests gave, on the whole, the most uniform results, the
section of the test pieces being fairly large, and a uniform
distribution of stress being fairly well obtained. But
the elastic limit and coefficient of elasticity are difficult
to ascertain accurately in pressure tests.
The strength
increases with the density, but the heart pieces are
weak. In timber tested within three months of felling,
the winter-felled timber was 25 per cent. stronger than
summer felled. But later researches showed that this
difference disappeared after a longer time of seasoning.
The strength increases in seasoning, but the increase
probably ceases after about one year.
Bauschinger concludes that when the question is
the average quality of a timber, as in inquiries with
reference to the influence of time of felling or seasoning,
or the influence of the soil or locality of growth, then
the pressure tests are the easiest and most trustworthy.
Discs about 6 inches thick should be sawn from each end
and the middle of the log, and these then divided into
four sectors. From each of these a square prism should
be cut, the height being 1 times the length of side.
The compressive strength should then be ascertained
for as nearly as possible the standard dryness (15 per
cent. of moisture). The test pieces should be measured,
1
TIMBER
401
The co-
and weighed to determine the density.
efficient of elasticity is best determined from bending
tests of a beam of the whole useful section of the log.
As this depends on the quality of the whole section,
and is determined for stresses within the elastic limit,
it is probably a very valuable indication of the structural
value of the timber. By plotting his results, Bauschinger
shows that there is a definite relation between the co-
efficient of elasticity and the bending and crushing
strength, and that this can probably be expressed by a
linear equation. There is also a definite relation in
pine wood between the density and the strength, ex-
pressed by the following equation :-
Red pine
Spruce
>"
where ẞ is the crushing strength in tons per sq. in., and
the density at a standard dryness of 15 per cent.
The following are some of the results in the earlier
research, the timber being tested about three months
after felling
""
Timber
B = 6·35 0.635,
d d −
TENSION EXPERIMENTS.
(Test pieces, 1·6 × 0·4 inch section. Mean values as tested.)
Locality
Lichtenhoff
Frankenhofen
Regenhütte
Schliersee
Summer felled.
Tenacity,
tons per sq. in.
Cir-
Mean
cum- Heart of
ference
Winter felled.
Tenacity,
tons per sq.
in.
Cir-
cum-
log ference
6.67 1.46 5:01 4.76
6.16 1.97 4.76 7.87
6·542·60 | 5·24 6·10
6.44 184 359 | 3-68
Mean
Heart of
log
1.84 3.78
2.19 5.97
1·90 4.70
1.62 2.99
D D
402
TESTING OF MATERIALS OF CONSTRUCTION
PRESSURE EXPERIMENTS.
(Test pieces, about 34 × 3} inches, and 6 inches long. Mean strength, as tested, and
also reduced to a standard dryness-10 per cent. of moisture.)

""
Red pine
Spruce
""
Timber
""
Spruce
""
Timber
""
""
""
""
·
Red pine Lichtenhoff
Locality
Lichtenhoff
Frankenhofen
Regenhütte
Schliersee
BENDING EXPERIMENTS.
(Beams, about 7 × 7 inches, and 98 inches span. Mean values. The upper value for
each timber is for a summer, and the lower for a winter, felled tree.)
Locality
2.03 [26]
1.78[19]
1.56 [20
1.49 [27]
1.03 [20]
1.99 17
1.78/20
1.43 [19]
The figures in brackets give the moisture per cent.
""
686
654
""
Frankenhofen 698
737
730
698
Regenhütte
Schliersee
Summer felled.
Compressive
strength, in tons
per sq.
in.
As tested
Coeffi-
cient of
elasticity,
tons per
sq. in.
464
438
Standard
dryness
Elastic
limit,
tons per
sq. in.
1.28
1.40
1.45
1.66
1.37
1.44
0.93
0.84
Winter felled.
Compressive
strength, in tons
per sq. in.

2.37
2.13
2.41
1.41
As tested
Coefficient
of bending
strength, Density
tons per
sq. in.
Standard
dryness
3:00
0.50
2.86
0.55
2.66
0.45
2.86
0.45
2.64
0.46
2.83
0.43
1.87 0.355
1.63 0.375
3.20
2.50
2.43
1.89

Content
of mois-
ture, per
cent.
23
33
29
27
34
31
23.5
25
I
These results are directly comparable with Lanza's
results, given below. These latter were also on pretty
large beams.
The influence of a longer time of seasoning is
shown in the following table :-
TIMBER
403
AVERAGE CRUSHING STRENGTH OF WHOLE SECTION OF Loc.
(Ten per cent. moisture. Tons per sq. in.)
Lichtenhoff
Frankenhofen
Regenshütte
Time of felling
Summer
felled
Winter
felled
Ꭺ
2.34
3.03
B
A
B
A
B
3.21
2.15
2.86 2.37 2.81
2.83 2.51 2.95 2.39 2.83
A. Tested 3 months after felling.
B. Tested 5 years after felling.
Schliersee
A
B
1:40
2.04
1.89 2.13
162. American Tests of Timber, with Large-sized Test
Pieces. It has already been stated that tests of large
test pieces give values of the strength of timber con-
siderably smaller than those obtained from small test
pieces. Of tests with large test pieces the most im
portant are those made in the United States, chiefly
under the direction of Prof. Lanza, of the Massachusetts
Institute of Technology.¹
Prof. Lanza appears to have failed to make satisfac-
tory tension experiments on large specimens. He con-
cludes that tie bars used in construction will always
give way in some other manner than by direct tearing-
for instance, by pulling out the fastenings, and shearing
and splitting the timber. Tests of crushing strength
are much less difficult. The following table gives a
summary of a series of tests of wooden posts, generally
7 to 10 inches in diameter, made for an insurance com-
pany under Prof. Lanza's direction. In all these tests
1 Applied Mechanics. Lanza, p. 497. Also, 'Report on Strength of
Wooden Columns,' Lanza; and Executive Document 12, Forty-seventh
Congress, First Session.
DD 2
404 TESTING OF MATERIALS OF CONSTRUCTION
the strength was simply proportional to the area of cross
section, the deflection laterally being insignificant.
TESTS OF WOODEN POSTS AND BLOCKS, USUALLY WITH FLAT ENDS (LANZA).
Crushing strength, in tons per
sq. in.
Form
Round
""
""
Rectang.
""
Round
Round
99
Round
""
""
""
Approximate size
Length,
feet
22~2~
12
12
12
|
12
12
12
13
133
Section,
sq. ins.
32-63
47-93
30-65
45-61
48-86
100
81-103
45-48 2.18
Max.
24
25
79-87
60-65
YELLOW PINE
2.10
2.05
2.10
|
Min.
1.63
1.82
1.93
1.61
WHITE OAK
1.69
1.99
1.34
1.40
Mean
1.97
1.94
2.01
2.331
2.41
1.90
1.56
1.57
OLD AND SEASONED WHITE OAK
2.69
2.05
1.89
131
2.08
1.73
2.18
1.53
2.28
1.55 2
1.92
1.82
Coefficient of
elasticity,
tons per sq. in.
728-984
949
734-1091
545-781
493-582

823-955
646-916
Another series of tests on large rectangular posts of
white and yellow pine timber was made with the Water-
town machine. The lengths varied up to 30 feet. The
results are too numerous to give here, but they have
been plotted by Mr. E. F. Ely, of the Massachusetts
Institute of Technology, and from the plotting the fol-
lowing rule is derived. The posts had flat ends, and the
load was evenly distributed.
Let I be the length, and r the least sectional dimen-
sion. Then, the crushing stress ƒ per sq. in. of section
in tons is as follows:-
-
22
1 One end flat, one with rectang. pintle. * Maple cap and oak base.
TIMBER
405
し
​ř
0-10
10-35
35-45
45-60
White pine
~
W
=
ƒ
1
4
1.116
·893
*669
•446
ƒ
b h²
2
ι
163. Bending Tests.-The American bending tests
are not on so large a scale as those on crushing, but,
with the exception of those of Bauschinger already given,
they afford the most trustworthy data as to the strength
of timber beams. They were made under Prof. Lanza's
direction. The beams were 2 to 6 inches wide, and 2 to
12 inches deep. The span varied from 4 to 20 feet.
Usually, in bending tests, the beam is supported at
the ends and loaded at the centre. Let W be the load
at the centre; b and h the breadth and depth of the
beam; the span of the beam; the dimensions being
in inches, and the load in tons. Let f be the greatest
direct stress on the fibres furthest from the neutral axis ;
f the shearing stress at the neutral axis, in tons per
in.; & the deflection at the centre, in inches. Then, so
long as the elastic limit for bending is not exceeded,
sq.
W 18
E b h 3
; f = 3
;
ƒ₁ = 3/13
fs
E
0-15
15-30
30-40
40-45
45-50
50-60
W
b h
INF
T
1
4
Yellow pine
W l
bh2
f
W 73
dbh s
1.785
1.562
1.339
1.116
893
*669
·
(1).
(2).
(3).
406 TESTING OF MATERIALS OF CONSTRUCTION
Equation (1) may be used to determine the dimen-
sions for a given limit of stress; and equation (2) to
determine the coefficient of elasticity of the timber,
from observations within the elastic limit. When,
however, W is the load which breaks the beam, the
value of ƒ obtained from equation (1) is no longer the
f
real stress in the beam. Since, however, it is a con-
venient measure of the strength of the timber for
practical purposes, it may be called the coefficient of
bending strength. The coefficient of bending strength
is always greater than the real breaking stress.
stress. From
the great weakness of timber along the grain, beams
give way about as often by shearing along the neutral
surface as by tearing the extreme fibres. Then the
shearing stress f, calculated by equation (3), bears a
similar relation to the real shearing stress that f bears
to the real tenacity of the timber.
The following summary gives the most important
results of Professor Lanza's bending tests :-
Spruce beams.
""
""
""
Yellow pine beams. Max.
Min. .
Mean
""
""
""
""
""
در
""
""
""
Oak beams. Max.
Min.
Mean
""
""
""
""
White pine. Max.
Min.
""
Mean
Max.
Min.
Mean
""
i
Coefficient of
bending strength,
tons per sq. in.
3.910
1.337
2.180
5.071
1.769
3.255
3.419
2.225
2.712
3.237
1.535
2.146
Coefficient of
elasticity,
tons per sq. in.
709
401
594
1,063
519
779
789
381
577
572
413
484
TIMBER
407
Beams which gave way by Shearing.-In Lanza's tests
six spruce beams and five yellow pine beams gave way by
longitudinal shearing near the neutral axis. The intensity
of the shearing stress varied from 117 to 248 lbs.
per
sq. in. in the spruce beams, and from 153 to 397 lbs. per
sq. in. in the yellow pine beams. The mean values were—
Spruce beams
Yellow pine beans
•
Ash.
Yellow birch
White maple
Red oak
White oak.
White pine
Yellow pine
Spruce
Whitewood
•
Shearing strength,
lbs. per sq. in.
191
248
•
On the beams which did not fail by shearing the
mean intensity of shearing stress was about the same.
Hence it may be concluded that, for soft wood timber,
beams give way by shearing at the neutral axis or by
tearing at the convex surface almost indifferently.
164. Direct Experiments on Shearing along the Grain.
-Direct experiments on the shearing resistance along
the grain were made at the Watertown Arsenal, and gave
somewhat higher values of the shearing strength. This
is probably due to the fact that, in shearing experi-
ments, the timber is forced to shear at a selected section,
while in the beam experiments the shearing occurred
along the weakest of the planes near the neutral axis of
the beam. The specimens were also comparatively small.
SHEARING TESTS (WATERTOWN ARSENAL).
Shearing strength,
lbs. per sq. in.
458 to 700
563 815
367 647
726 999
752,, 966
267 366
286 415
""
""
رو
""
""
tons per sq. in.
0·0853
0.1107
253 374
382 406
>>
>>
408 TESTING OF MATERIALS OF CONSTRUCTION
The greater shearing strength of the leaf woods is
noticeable.
1
165. Influence of Time on Bending Strength and Elas-
ticity.-Experiments by Herman Haupt, and more
recent experiments by Thurston and Kidder," show:
(1) That the deflection of a beam of pine under a¸
statical load increases with time, or the modulus of
elasticity is less for a prolonged than for an immediate
loading; (2) that the beam breaks in course of time
with a statical load a good deal less than that required
to break it immediately. In Thurston's experiments a
plank of yellow pine was selected. Bars 1 to 3 inches
square, and 40 to 54 inches long, gave a density of
0.75 to 1·0, a coefficient of bending strength of 4·91 to
5.36 tons per sq. in., and a coefficient of elasticity of
1,005 tons per sq. in. Kiln dried, the coefficient of
bending strength increased one-fifth, and that of elas-
ticity one-ninth. For a bar 1 inch square on supports
40 inches apart the centre breaking load was 375 lbs.
Nine bars of this size were prepared, three being loaded
with 350 lbs., three with 300 lbs., and three with
250 lbs. at the centre. All the first three broke in less
than 43 hours; all the second three in from 80 to 719
hours; and all the third set, loaded with only 60 per
cent. of the immediate breaking weight, broke in from
6,000 to 11,000 hours. These experiments seem to
¹ Proc. Am. Assoc. for Advancement of Science, 1881. Proc. Inst.
C.E. lxxi. p. 428.
* Journal of Franklyn Institute, 1882. Proc. Inst. C. E. lxxi. p. 431.
TIMBER
409
show that a statical load of 60 per cent. of the imme-
diate breaking weight is not safe. When broken imme-
diately, the ultimate deflection was about 18 inch;
with 350 lbs. it was 2.3 inches; with 300 lbs. 3.0
inches, and with 250 lbs. 2.5 inches. Hence the de-
flection is greater with a prolonged load. In Mr.
Kidder's experiments on dry spruce beams 12 inch
square, the deflection increased with time, even when as
small as th of the immediate breaking weight. He
concluded that one-half the immediate breaking weight
could not be permanently supported.
1
Single leather.
LEATHER BELTING.
The following few results may find place here :-
STRENGTH OF LEATHER BELTS AND FASTENINGS.
""
""
""
""
""
""
""
""
""
""
""
""
Double belt, copper sewn.
Single belt, ordinary laced joint
""
""
""
""
""
""
""
""
Max.
Min.
Mean
Max.
Min.
Mean
•
butt laced
joint scarfed and
glued.
grip fastener
•
Crowley's fastener.
hose riveted, 12,
rivets in two rows.
3
Tenacity,
Dimensions, in in lbs. per
inches
inch of
width
2·0 × 0·2
2.5 × 206
2·5 × 314
2.5 × 203
3·0 × 21
3·0 × 21
2·5 × 22
3·0 × 21
7·0 x 22
1,600
700
1,280
1,272
616
964
1,110
473
265
544
242
635
394
Authority
Riehle Bros.
••
Unwin'
F
*?
**
:
11
>
>>
>>
ܕ
Watertown
410
TESTING OF MATERIALS OF CONSTRUCTION
CHAPTER XIV.
STONE AND BRICK.
166. Building stone is derived from rocks of widely
different origin and very various age. The rocks may
be distinguished into volcanic or plutonic rocks con-
solidated from igneous fusion, and stratified rocks
deposited under water. The former are crystalline in
the granites, less obviously crystalline in the traps, and
glassy in other cases. The stratified rocks, which show
more or less distinctly lamination or bedding, are some-
times aggregates of detritus derived from denudation
of land surfaces, cemented by subsequent infiltration.
Sometimes they are precipitates from solution in water.
Sometimes they are of organic origin, and consist
largely of siliceous or calcareous skeletons. In some
originally stratified rocks a slaty cleavage has been
developed by pressure, which is more conspicuous than
the original bedding.
The value of stone for building depends on its
strength, its durability, and the facility with which it
can be worked. The durability depends partly on its
hardness and chemical composition, but also largely on
its power of resisting the absorption of water.
The most abundant constituents of the rocks are
STONE AND BRICK
411
silica, alumina, oxide of iron, lime, and magnesia.
Silica occurs nearly pure as quartz, flint, and sand, and
is almost universally present in combination with other
earthy bases. Alumina, combined with silica, occurs in
clay, and in mica and felspar. Magnesia occurs com-
bined with silica in soapstone, augite, and hornblende,
and as a carbonate in some limestones. Lime occurs as
a carbonate, nearly pure, in some limestones.
The most important building stones may be classed
as granite, clayslate, sandstone, or limestone.
Granite consists normally of quartz, colourless and
transparent; felspar, opaque, red, yellow, or grey,
giving the prevailing tint to the rock; and mica.
Hornblende and tale are sometimes associated with or
replace the mica. Granite is an extremely valuable
building stone. It is heavy, strong, non-absorbent, and
capable of taking a fine polish. On the other hand, it
stands fire badly, and is difficult to work. The horn-
blendic varieties have great resistance to abrasion.
Inferior granites sometimes decay, either by decomposi-
tion of the felspar, or by surface disintegration by frost.
Trap, Greenstone and Basalt have some of the
qualities of granite. They are compact crystalline
rocks, composed of felspar, hornblende, and augite.
They are strong, but difficult to dress.
Clayslate, composed of quartz and mica, is some-
times a very compact rock, yielding a fine-grained and
strong building stone. Sometimes the slaty cleavage is
so developed that it yields slabs and roofing slates.
412 TESTING OF MATERIALS OF CONSTRUCTION
Sandstones are stratified rocks, composed largely of
quartz grains, with a siliceous, clayey, or calcareous
cement. The fineness of grain varies greatly. In some
sandstones the cement is nearly pure silica, and these
are strong, durable, and non-absorbent. The best
sandstones for building, in England, are obtained from
the millstone grit and coal measures, and from the new
and old red sandstone formations.
Limestones are of very various texture and quality.
Marble is a nearly pure carbonate of lime, hard enough
to take a polish. Granular and oolitic limestones con-
sist of grains of carbonate of lime cemented by a
calcareous or siliceous matrix. Some of these yield
excellent, durable, and easily-worked building stone.
Generally, however, limestones are softer, more ab-
sorbent, and less durable than sandstones. Shelly
limestones consist of shells embedded in a more or less
crystalline matrix, and some of these are useful as
building stone.
Magnesian Limestones, or dolomites, consist of car-
bonates of lime and magnesia. When properly crystal-
line in structure they yield a good, easily-dressed, and
durable stone. Steatite, or silicate of magnesia, is
valuable from its power of resisting fire.
167. Strength of Stone.-In most cases stone is used
in compression. A block of stone at the base of a pier
or in an arch ring is subject to a thrust due to the
weight of the structure, and, as far as the condition can
be secured, the thrust is normal to the faces of the block.
p
STONE AND BRICK
413
Generally the pressure does not reach 10 tons per sq. ft.,
though in some lofty structures it reaches 20 to 30 tons,
and possibly in some arch rings 40 or 50 tons, per sq.
ft.
Now, the crushing resistance of stone, tested in small
cubes, is seldom less than 250 tons, and often reaches
1,000 tons or more per sq. ft. Hence it has been
argued that the strength of stone is of little consequence,
its lowest strength being in excess of what is required.
It must be remembered, however, that small cubes of
stones are selected specimens, more homogeneous and
free from defect than large blocks. The cubical form
is a stronger one than that of the blocks used in
building, and single blocks are stronger than aggre-
gates of blocks. Further, it is quite impossible in any
actual structure to secure a simple condition of crushing
stress. Settlement, imperfect bedding, unequal compres-
sibility of different blocks, and other causes, introduce
unforeseen and incalculable straining actions. Hence,
the real factor of safety is not nearly as great as the
nominal one.
168. Mode of Crushing in Rigid Materials.—In duc-
tile materials like wrought iron the mode of yielding to
pressure is nearly the inverse of the mode of yielding to
tension, and the two resistances are not widely different.
But in cast iron and stone and other rigid materials, the
tenacity of which is small compared with the resistance
to crushing, the mode of yielding is quite different. It
has been shown in § 9 that the stress on any oblique
plane in a prism subjected to a pressure p in the direction
414 TESTING OF MATERIALS OF CONSTRUCTION
of its axis may be resolved into a tangential component
p sin cos 6, and a normal component p cos² 6. On
a plane making 45° with the axis the intensity of the
shearing stress is greatest, and equal top. Now
small cylinders of cast iron frequently give way exactly
as shown in Fig. 4, and Coulomb inferred that the
action was then a simple shearing. But that this is not
an exact view of the matter is shown, partly because
the inclination of the plane of yielding to the axis often
differs a good deal from 45°, partly because the intensity
of the stress on the plane of yielding is usually con-
siderably greater than the shearing strength of the
material when not in compression. Obviously, the
normal component p cos² is not without influence on
the angle and intensity of stress at which the prism
breaks. It produces a frictional resistance to sliding
which balances part of the tangential stress. But this,
also, is probably an incomplete account of the mode of
resistance of rigid materials. The axial pressure and
longitudinal compression correspond to a lateral dilata-
tion and transverse tension (§ 4). In some cases stone
breaks up into nearly vertical prisms, splitting up at a
number of almost vertical planes. In these cases it
appears to yield to the lateral tension. Any cause
which increases the lateral tension readily produces this
kind of fracture, as will be seen presently.
•
In a square prism there are four symmetrical planes
similarly situated with respect to the axis. Hence such
prisms frequently yield simultaneously at these four
STONE AND BRICK
415
FIG. 129.
planes. Thus, a cube breaks into six similar and equal
pyramids (Fig. 129; see also Fig. 132). With a rect-
angular base a prism breaks
similarly, but the upper and
lower pyramids are termi-
nated by an edge instead
of a point. A cylindrical
prism shows, after fracture,
two cones with the sides split
off all round. In an even-

-
17:
grained material like sandstone these forms are often
very regularly developed.
FIG. 130.

Fig. 130 shows a cube of cement concrete after frac-
ture. Here the pyramidal form of fracture is pretty
obvious, in spite of the irregularity of the material. The
416 TESTING OF MATERIALS OF CONSTRUCTION
middle part, near the apex of the pyramids, is really
loose and fissured. Fig. 131 exhibits a cylinder of cement
mortar showing very distinctly the conical fracture.
When the height of the prisms is greater than their
length of side, the two pyramids which stand on the
surfaces at which the
pressure is applied are
often of unequal height.
re-
169. Preparation of
Specimens for Crushing.
-The specimens
quired for crushing may
be obtained by sawing,
or by dressing with ham-
mer and chisel. It is
of the greatest import-
ance that the surfaces at
FIG. 131.

which the crushing pressure acts should be plane and
parallel, a requirement sometimes too little attended to.
To obtain plane parallel surfaces a planing machine may
be used, with a black diamond for a cutting tool; or the
surfaces may be ground smooth with emery on a plate
of stone or metal. As these processes are troublesome,
especially when dealing with bricks, concrete blocks,
and other rough material, the author has adopted a plan.
which is simpler and appears to be quite as satisfactory.
When the surfaces are approximately right, they are
covered with a thin layer of Parian cement or plaster of
Paris, which can be easily strickled so as to be plane.
STONE AND BRICK
417
This thin layer does not crush under even the heavy
pressures required, and it does not yield or flow. It is,
for all practical purposes, a part of the block.
1
To avoid the trouble of getting parallel plane sur-
faces, it has been common to make crushing experiments
with a layer of pinewood, or lead, or other weak material
interposed between the block to be crushed and the
cast-iron crossheads of the testing machine. The idea
has been that the wood or lead distributed the pressure
over the surface, and virtually annulled the inequalities
of surface. This, however, can be shown to be erro-
neous. Any weak material may very greatly alter the
crushing pressure, and falsify the result of the experi-
ment. It is important that the block to be crushed
should be placed directly between the parallel metal
surfaces by which the pressure is applied. The only
thing the author uses between is a sheet of hard mill-
board. This is nearly as incompressible as iron, and is
not indented by the crushing pressure. It does no
harm, and it is doubtful if it does any good. To neu-
tralise, as far as possible, the effect of any want of
parallelism of the surfaces of the block and machine, a
spherical joint, like that shown in Fig. 105, p. 226,
should invariably be used.
-
170. Diminution of the Crushing Resistance of Stone
when bedded on Lead.-Twenty years ago it was common,
in experiments on crushing, to bed the test specimens of
rigid materials like stone on lead plates, with an idea of
¹ In some cases leather has been used, and in some a layer of sand.
E F
418 TESTING OF MATERIALS OF CONSTRUCTION
securing uniform distribution of pressure on the faces
at which the crushing pressure is applied. The author
has long had the opinion that to support blocks for
crushing on a plastic support is wrong in principle.
Hence, in experiments on the crushing of stone and of
Portland cement and concrete, he has adopted the plan
of preparing the faces on which the crushing pressure
acts with a thin layer of plaster. This can easily be
worked to smooth and parallel surfaces, which receive
the iron plates of the crushing shackles directly, if
necessary; but sometimes a sheet of millboard is
interposed, which is a very hard and only slightly
compressible material. It seemed desirable to try what
was the difference of the crushing strength of blocks
supported in these two ways. Two series of 4-inch
cubes of Portland stone and Yorkshire grit were obtained
of very uniform quality. The results of the tests are
given below. The great reduction of strength when a
thin plate of plastic material like lead is used on the faces
to which the crushing pressure is applied is interesting
both practically and scientifically. It will be seen
that the crushing pressure of blocks between lead plates
is in one case only three-fifths, and in another only
three-sevenths of that of blocks prepared with plaster
and crushed between millboard. One block was cemented
carefully between two rigid iron plates with parallel
surfaces, and this carried a little more, but only a little
more, load than the block prepared with plaster and
crushed between loose millboards. An examination of
STONE AND BRICK
419
Description of
stone
the mode of fracture of the blocks shows why the lead
has so dangerous an effect on the strength. The blocks
crushed between millboards sheared approximately at
45°, forming regular pyramids; but the blocks crushed
between lead broke up into a number of vertical prisms.
The lead, flowing under the crushing pressure, pro-
duced by friction a tension in the block at right angles
to the crushing pressure, and this, added to the tension
due to lateral expansion, tore the block in pieces, com-
pletely altering the angle of fracture.
The pressure
of fluidity of lead is from 1 to 3 tons per sq. in.,
and these pressures were exceeded in the crushing
experiments.
CRUSHING OF STONE BLOCKS, 4-INCH CUBES (APPROXIMATELY).
Crushing load,
in tons
Portland:
535
536
538
537
Yorkshire grit:
539
542
540
541
57·665
52.600
45.65
33.50
79.72
80.05
56.20
35.90
Stress, in tons
per sq. ft.
516.38
469.87
408.8
299.95
712.08
716.86
504-43
322.27
Remarks
Between
two mill-
boards on each face
One plate of lead on
each face
1
One plate of lead on
each face, inch
smaller than face all
round
Three plates of lead
on each face
The lead plates were 0.085 inch thick.
Between two mill-
boards on each face
Cemented between
two strong iron
plates with plaster
of Paris
One lead plate on each
face
Three plates of lead
on each face
EE 2
420 TESTING OF MATERIALS OF CONSTRUCTION

FIG. 132
541
540
539
The result seems im-
portant, because it is still
a common practice to use
lead, or deal, or some other
plastic or compressible
material in crushing ex-
periments, and it is not
generally known that this
has the effect of diminishing
the crushing resistance.
Fig. 132 shows three of
the blocks of the Yorkshire
grit series after crushing.
Block 539, crushed between
millboards, has crushed in
the normal way, a central
wedge being formed, and
the sides shearing on the
four faces of the wedge.
But in the two other blocks,
supported on lead, the
shearing angle is completely
altered by the horizontal
tension induced by the
flow of the lead. The blocks
are broken into a series
S
of prisms or wedges, the di-
viding planes being nearly
vertical.
STONE AND BRICK
421
6
In a note in the Trans. Am. Soc. of Civil Engi-
neers,' 1872, p. 192, it is mentioned that the Commis-
sion of 1851 on the Selection of Stone for the Capitol
at Washington discovered the remarkable fact that the
crushing stress of stone was reduced to about one-half
if pieces of lead were interposed between the stone and
the steel faces of the shackles.
171. Influence of the Form of the Test Piece on the
Crushing Strength.—Building stone is most commonly
tested in cubes, and cubes of 4 inches length of side are
convenient. For some of the stronger stones, it may
be necessary to use cubes of 2 to 3 inches side in many
testing machines. Portland cement is often tested in
cubes of 4 inches length of side. For cement mortar
the author has used cylinders of 7 inches diameter and
10 inches height. Irregular artificial material like
cement concrete is best tested in the largest practicable
blocks. Cubes of 7 to 10 inches length of side are
convenient.
It will be obvious, from the account given of the
way in which materials of this kind crush, that know-
ledge of the crushing strength of different forms and
sizes of specimen is purely experimental. The first
attempts to examine precisely the laws of crushing
strength of such materials were made by Rondelet,¹
Vicat,² and Hodgkinson. More recently, Bauschinger
has made a very much more complete investigation. A
3
1 L'Art de Bâtir, t. iv. 2 Annales des Ponts et Chaussées. 1833
3 Mitth. aus dem Mech. Tech. Laboratorium. 1876.
-
422 TESTING OF MATERIALS OF CONSTRUCTION
brief account of the results will here be given-partly
because test specimens are sometimes unavoidably of
exceptional form, and it is necessary to reduce the
results to those on a standard form; partly because a
knowledge of these results is useful in applying the
results of testing in practice.
For test blocks of geometrically similar form, all
experiments show that the crushing strength varies as
the area of the surface on which the crushing pressure.
acts. Thus, Rondelet experimented on cubes of 12,
1.6, 2.0, and 2.4 inches length of side, of three different
kinds of stone. The crushing pressures per unit of
area were, in tons per sq. ft. :
First series
Second series
Third series.
246
107
50
243
104
50
243
114
50
248
112
51
More generally this law may be stated thus: The
strength of geometrically similar test pieces varies as
the square of homologous sides.
The variation of the crushing strength of prisms
with the form of the cross section is less obvious.
Hodgkinson concluded that the form of the cross sec-
tion had little influence. But Rondelet found, with
prisms of circular, square, and triangular bases of
equal area, that the strengths were proportional to
1:0·93: 0·86; and for prisms on a square base and
rectangular base, with sides as 1: 2, of equal area, the
strengths were as 1: 0.95. These numbers are nearly
STONE AND BRICK
423
7
in the reciprocal ratio of the square roots of the circum-
ferences.
When cubes are used, placed on each other, the
strength diminishes with the number of cubes. Thus, for
columns of one, two, and three cubes of 2 inches length
of side, Rondelet found the strengths in two series of
experiments to be 1: 0·61: 0·54, and 1 0 80: 0·75.
:
The strength in prisms of similar base but different
heights diminishes as the height is greater, and that
for heights within the limit at which any bending
occurs. Vicat concluded that for prisms of less height
than the cube the strength could be expressed by the
equation-
f = a + b.
h
·
(1),
where f is the strength per unit of area, and a and b
constants for each material.
Lastly, a single block is always stronger than a
compound block of the same form made of separate
blocks without cement. Thus, a cube made up of four
blocks of gypsum had a strength only 0.78 of that of
a single block of the same size. A block of eight small
cubes had a strength of 0.84 of that of a single cube of
the same size.
ƒ= (YA) + (~+~A).
f
入​十
​C
h
4
Bauschinger has found that all these results can be
expressed by the relation-
(2),
424
TESTING OF MATERIALS OF CONSTRUCTION
where A is the area of section of prism, C its circumfer-
ence, h height of prism, f strength per unit of section,
and λ and are constants for each material.
It gives at once the law that prisms and cylinders
of geometrically similar form have the same strength.
Also, that in prisms of the same height and sectional
area the strength varies inversely as the square root
of the circumference. Thus, prisms of circular, square,
and triangular base, of the same height, should have
strengths varying as 1 0.94 0.88. For square prisms
of different heights the equation becomes-
•
:
cs
S
f=λ + v
h
1
(3),.
where s is the side of the square. According to Bau-
schinger, this equation is valid up to values of h = 4 s
or 5 s. This agrees with Vicat's formula. A series of
experiments on square and rectangular prisms of dif
ferent heights, varying from 06 to 12 inches, of fine
Swiss sandstone, gave the following values of the con-
stant (f, in tons per sq. in.)-
λ = 239.5
V =
292.5,
when the axis of the prism was parallel to the layers.
In another series of experiments on prisms of the same
sandstone, crushed perpendicular to the layers, the
height, however, not exceeding that of the cube,
บ 316.
λ= 283.5
A third series of tests on rectangular and square
STONE AND BRICK
425
prisms of Perlmooser Portland cement, hardened ninety
days, gave-
P
λ = 139
น 98.6.
Tests were made on rectangular and cylindrical
prisms, of about 4 inches diameter or length of side and
very different heights, cut out of fine-grained Bunter
sandstone, and crushed parallel to the layers. These
gave-
For prisms.
cylinders
99
Mean.
λ=317
337
327
""
""
v=111
105
,, 107.5.
22
A series of tests with square and rectangular prisms
of different heights, having sides with the ratios 1: 2,
3 4, and 1 1, also of a fine-grained sandstone, gave-
λ = 356·5
•
v = 97.
Bauschinger shows that the agreement of the equa-
tion with the results is throughout satisfactory.
Bauschinger made a further research on the crush-
ing strength of cubes when on one
surface the crushing load was con-
fined to a portion of the area. Sup-
pose Fig. 133 is the plan of a cube, d
and that either by bevelling the edges,
or by using a small steel pressure-
plate, the load is confined to the
area of the small rectangle. If o is the centre of the
rectangle, and
ob = e₁; o d = С2 ; o α =
FIG. 133.
b
ία
= c2 ; o α = & ; o c = e'',
5

426
TESTING OF MATERIALS OF CONSTRUCTION
f = crushing pressure per unit of area when pressure
is uniform on whole face of cube ; fi
crushing pres-
sure per unit of area of pressure-plate.
Then,
3
2
f₁ = ƒ √ / 98
fi
f
If A and a are the areas of the surface of the cube and
pressure-plate, then, when the pressure-plate is central—
f₁ = ƒ √ √ A
a
2
If two equal pressure-plates on both faces of the cube
are used, then the strength becomes that of the prism
of material between the pressure-plates, and is nearly
independent of the amount of material surrounding this
prism. It is easy to see, therefore, how much a block
of stone may be weakened by imperfect bedding.¹
172. Determination of the Porosity of Stone.-Speci-
mens for this purpose should be cubes, and should be
well dried. The stone should be brushed, weighed,
and then gradually immersed in water. The stone is
allowed to remain under water till saturated. It will
become nearly saturated in twenty-four hours, but it
may,
for certainty, be left for five days. It is then taken
out, care fully dried on the surface, and weighed. The
gain of weight is estimated in per cent. of gross weight.
Sometimes the process is hastened by removing the air
pressure by an air-pump and allowing it to return.²
1 A similar research by M. Flamant is given in Ann. des Ponts et
Chausseés, vol. xiv., and Proc. I. C. E. vol. xci.
D
2 Hatfield. Trans. Am. Soc. of Civil Engineers, 1872, p. 145..
STONE AND BRICK
427
Granites (various)
Syenite
Porphyry
Granites
For strictly comparable results the specimens should be
of the same volume and surface.
•
Trachyte
Slate
Roofing slate
Old red sandstone
New red sandstone
Lias sandstones.
Craigleith
Kenton
Mansfield.
""
Sandstones (various) .
Coal-measure sandstones
·
•
Limestones (various).
Portland
Ancaster
•
•
•
•
Box ground (Bath)
Ketton
Chilmark
Roche Abbey
Oolitic limestones
Shelly limestones (Purbeck)
Kent rag
•
POROSITY OF STONES.
Dolomite
Magnesian limestone.
•
Per cent. of
water absorbed
0·42-1·2
0.50
0.4-2.8
0·2-3·0
2.0-4.5
•54-70
0.5
0·7-8·2
1·0-7·0
1.6-3.8
6·0-10·0
3·0-8·0
8.0
9.9
10.4
2.6-4.8
0·31-6·4
13.5
16.6
17.0
15.1
8.6
17.2
4·0-12·0
4·0-2·0
0.5
1.5
3.5
No. of
hours
immersion
125
125
125
24
125
125
24
125
24
24
24
24
24
24
24
24
125
24
24
24
24
24
24
24
24
24
125
24
Authority
Böhme
ر,
""
Wray
Böhme
""
Wray
Böhme
Wray
""
""
""
Royal Com.
""
""
Wray
Böhme
Royal Com.
99
""
""
""
Wray
""
""
Böhme
Wray
The table on next page gives the density and absorp-
tion of water of a series of 3-inch cubes of English stone.
The blocks were weighed dry and then immersed in water
for from seven to fifteen days. The weighings were
carefully made for the author by Mr. H. M. Martin.
428
TESTING OF MATERIALS OF CONSTRUCTION
Aberdeen granite, red
grey
Clayslate
""
SANDSTONES:
Red Grinsell
""
Red Mansfield
White
Red
""
""
White Grinsell
Scotgate Head (coal measure)
Corse Hill (new red).
Robin Hood (coal measure)
Hollington
Attleborough
Hansworth
Flag-rock Grinsell
Red Alton (new red)
Derbyshire grit
Billstone
Howley Park
Sydanope.
Kenilworth
Duston (ironstone)
Ispatria
LIMESTONES :
•
•
•
White Portland
Portland
Brown Portland
•
Ancaster
Ketton
Stoke ground
Corsham Down
Westwood ground
Caen
Box ground
Church Anson
Doulting.
Material
•
•
•
•
•
·
·
•
•
·
•
•
•
•
Density
2.62
2.68
2.76
2.76
2.16
2.15
2.39
2.29
2.32
2.19
2.35
2.30
2.37
2.21
2.16
2.18
2.21
2.33
2.02
2.32
2.12
2.17
2.16
2.06
2.31
2.31
2.27
2.15
2.21
2.17
2.19
2.01
1.96
1.88
2.39
2.19
Per cent.
of water
absorbed
0.70
0.81
0.31
0.23
5.49
6.89
3:43
5.05
5.41
6.42
4.44
5.55
4.67
5.08
7.43
6.06
6.03
4.28
9.52
3.84
10.10
8.07
6.06
9.11
8.64
5.23
6.22
8.52
9.00
8.90
9.49
12.75
12.56
10.10
6.29
7.99
Resistance to Frost.-The power of resisting frost
can be inferred to some extent from the porosity. It
is better, however, to saturate a stone with water and
then freeze it, repeating the operation ten or more
STONE AND BRICK
429
times. The percentage loss of weight is the measure of
the injury done by frost. Brard's test is to immerse
the stone for half an hour in a boiling saturated solu-
tion of sulphate of soda, and then hang it up for the
absorbed salt to crystallize. The process is repeated
daily for a week. It is a test of doubtful value.
Resistance to Wear.-The only method of satisfac-
factorily testing the resistance of stone to wear is one
devised by Bauschinger. A block of the stone, with a
face 4 × 4 inches, is placed on a horizontally-revolving
cast-iron plate at a radius of 18 inches.
The con-
ditions are found to be most constant when the block
is loaded with 66 to 68 lbs. Emery is regularly
supplied between the block and plate and cleaned off.
The best rate of supply is twenty grams for each ten
turns.
173. Coefficient of Elasticity for Stone.-The measure-
ment of the compressions and extensions of stone is
very difficult, partly from the limitation of size of
specimen, partly from the smallness of the deformations,
partly from the difficulty of securing uniform distribu-
tion of stress. Professor Bauschinger appears to have
overcome these difficulties' by the use of a modification
of his mirror apparatus. Plottings to a very large
scale of the stresses and deformations show that stone
has no elastic limit. It takes permanent sets with
very small loads, and the deformation does not increase
GO
1 'Uber den Elasticitäts-Modul Baustein.' Mitth. aus dem Mec. Tech.
Laboratorium in München. 1875.
430 TESTING OF MATERIALS OF CONSTRUCTION
at first proportionally to the loads and afterwards de-
viate from proportionality. For very hard and dense
stone the compressions and extensions are indeed
initially nearly proportional to the loads, but this
remains so up to the breaking stress.
For all others,
especially for the weaker stones, the greatest departure
from proportionality is for the smaller stresses. The
greater the loads the more do the deformations approach
to proportionality. For sandstone and the less hard
granites, the compressions increase first more quickly
than the loads and afterwards less rapidly. Hence, the
stress-strain curve is at first convex and afterwards
concave to the axis of loads. With repetition of load-
ing the reversal of curvature gradually disappears.
In the later research on Bavarian stone in 1884,
Bauschinger had an opportunity of re-examining the
elastic properties of stone with somewhat more perfect
test specimens. He found for the hardest stone, and
especially limestone, that the coefficient of elasticity was
nearly constant, equal for tension and compression, and
very large. For most other stone the coefficient of elas-
ticity for tension diminishes with increasing loads. For
pressure it sometimes increases with increasing loads,
but for the weaker kinds it diminishes at first and then
increases.
The stress-strain curves for tension and pressure
pass into each other at the origin of co-ordinates with-
out forming a cusp. But three cases are distinguish-
able (1) If the coefficient of elasticity is nearly
-
STONE AND BRICK
431
constant, the two curves for tension and pressure are
nearly straight lines and inclined at nearly the same
angle to the axis. (2) If the coefficient of elasticity
diminishes with increasing loads in tension, the curve is
concave to the axis of deformations. Then, (a) if the
coefficient of elasticity for pressure increases from the
beginning, or is nearly constant, the two curves form a
regular line always concave in the same direction. But
if (b) the coefficient of elasticity for pressure diminishes
first and then increases, there is a point of contrary
flexure at the origin of co-ordinates. Bauschinger is
inclined to attribute this appearance to a disintegration
of the test block in dressing it by hammer and chisel.
The author has obtained measurements of compression
of stone similar to Bauschinger's. It seems possible
Granite (Metten)
""
""
COEFFICIENT OF ELASTICITY FOR STONE (BAUSCHINGER).
(Stresses and coefficients, in tons per sq. ft.)
""
""
(Passau)
""
""
""
Nummulite limestone
Bunter sandstone (Phalz).
•
""
""
104,000 41
40,000 73
Jura limestone (Kelheim). 315,000 1.5
58,500 27
685,000
""
•
""
•
(Würtzburg)
>
Molasse sandstone (Kemp-
ten)
Molasse sandstone (Kemp-
ten)
Bending
Coefficient
E
At a
stress
of
Tension
Coefficient
E
At a
stress
of
Pressure
Coefficient
E
At a
Istress
of
192,000 2.2 216,000 2.6 264,000 27
125,000 86 54,000 35 244,000 460
202,000 0.6 113,000 14
28,000 33 199,000 410
175,000 13 310,000 1.8
| | |
71,500 12.5 185,000 172
475,000
26,600 0.6
27,400 1.1
17,000 28 11,900 6
562,000
60,200 0.9
172,000 207
137,000 0.9
93,000 13 113,000 0-6
35,600 57 35,600 19
165,000 340
173,000 1.1 116,000 2.2 153,000 1.4
43,000 56
29,200 31 240,000 530
432
TESTING OF MATERIALS OF CONSTRUCTION
that, in a granular substance like stone, the action of the
pressure may be to bring the particles to a bearing, and
that this may explain the decrease of the coefficient with
increase of pressure.
174. Bauschinger's First Research on the Strength of
Stone (Mitth. aus dem Mech. Techn. Laboratorium, in
München.' 1874).-A few results will be selected from
this paper as giving very conveniently the relative resist-
ance to different kinds of straining action. The pres-
sure tests were made on cubes with accurately ground
surfaces, on which the cast-iron pressure-plates acted
directly. For the shearing strength, three directions of
shearing may be distinguished. The shearing plane
may be normal to the lamina, or beds, of the stone, and
is then distinguished by the symbol ; or it may be
in the plane of the beds, and is then indicated by the
symbol . Bauschinger experimented in some cases in
||
a third direction also; but these results are omitted.
The same symbols apply to the bending experiments,
and indicate the position of the plane of fracture.
1
Bauschinger's Second Research on the Strength of
Bavarian Building Stones.'-In this series of tests paral-
lelopipeds about 44 inches long and 10 inches x 8 inches
square were used for bending tests, with a span of
40 inches. From one of the broken pieces a prism was
cut for pressure parallel to the lamina. From the other,
a test piece for tension parallel to the lamina, and also
afterwards for shearing. Cubes were also obtained for
1 Mitth. aus dem Mech. Tech. Laboratorium in München. 1884.
STONE AND BRICK
433

F F
GRANITE:
Coarse-grained grey (Selb, in Oberfranken)
""
Fine-grained yellow
""
""
Black and white of mean coarseness (Hauzenberg)
Hard coarse-grained (St. Gotthard)
""
""
""
Dolomite
""
""
""
Yellow, rather fine-grained (Passau)
""
""
Limestone (Pappenheim)
"}
""
""
""
""
LIMESTONE AND DOLOMITE
White marble (Schlanders, in Tyrol)
Muschelkalk (Wurtzburg)
(Kronach)
""
""
""
""
SANDSTONE:
Bunter sandstone (Kronach)
""
39
"
""
(Konigstein)
""
""
""
""
""
""
""
""
""
""
Strength of BUILDING STONES (BAUSCHINGER).
""
""
""
""
Keuper sandstone, red and fine-grained (Wurtemburg)
""
""
""
""
**
red and fine-grained (Wertheim)
•
""
""
""
""
Molasse sandstone, blue, fine-grained (Allgau)
""
""
""
""
white, fine-grained (Coburg).
""
""
""
·
""
1
·
Pressure
Crushing
stress,
tons per
sq. ft.
725
750
930¹
940¹
820
720
810
850
850
820
400
1,460
740
1,000
695
1,190
1,080
500
Bending
Direc-
Coefficient of
Shearing Direc-
tion of stress, tons] tion of
bending
pressure per sq. ft. shearing strength, tons
per sq. ft.
300
174
720
760
580
420
290
240
465
4=4
1
||
1
+
t =
1
+4=4
1
1
||
1
=
1
1
11
1
↓
11
1
34
46
100
72
55
52
Shear
83
61
53
54
43
61
40
64
47
2131
20
61
68
47
14
12
39
29
Cubes not crushed with this stress.
1
!!
1
1
11
||
1
11
1
÷ 4 = 4
1
1
1 44
+
=4
=
192
136
84
1
.84
89
63
| | | |
165
73
105
27
22
Direction
of plane
of fracture
||
1
||
1
L
| 1
L
141
Tension
Tenacity,
tons per
sq. ft.
1981 GE
40
30
25
20
17
。 | № ! | | | No
9
| |
14
4
Direc
tion of
pull
11
+
=
1
!!
1
-
434 TESTING OF MATERIALS OF CONSTRUCTION
pressure tests parallel and perpendicular to the laminæ.
Some cubes were kept in water, and as opportunity
served taken out and exposed to frost. After being
frozen about twenty-five times, they were dried, and
crushed in a direction parallel to the layers.
Granite (Metten)
(Passau)
STRENGTH OF BAVARIAN BUILDING STONE (BAUSCHINGER).
(Stresses in tons, per sq. ft.)

""
w
""
(Kempten)
Nummulite limestone
(Rosenheim)
•
Diabase (Ochsenkopf)
Lyenite (Wölsau)
Coefficient of bending
strength, to bed
Tenacity, || to bed
Jura limestone (Kelheim)
Bunter sandstone (Pfalz)
(Wurtzburg)
""
Green sandstone (Kel-}
10
6
177
277
heim)
Molasse sandstone}
(Kempten)
ne
38 21 545 930
Molasse sandstone
ne 62 33 930 1,120
Crushing strength of
prism, 1 : 1 : 21
40
87
830
77 44 850
3013-7 226
Mortar
1 cement, 3 sand
1
6
Crushing strength
of cubes
30 7 334
63
40
710
•
Il to
bed
""
""
1 cement, 7 lime, 16 sand
1 lime, 2 sand
1,210
1,290
560
1,380 1,230 88 9
1,310 | 1,230 93 55
213
210
460
32 19
435
435
23
525 37
780 835 63 35
302 22
870 43 24
1,850 64 49
115 58 1,220 1,320 1,200 1,240 95 73
2,500
2,340
1,700
1,740
286
455
970
to bed
after
freezing
I to
bed
260
•
Shearing
strength

The following tests were made by Dr. Böhme¹ of
cubes about 10 × 10 × 10 inches of rubble limestone
masonry, set in different mortars.
The cubes were
three months old :-
I to to
bed bed
123.4
69.6
64.3
46.5
1 ¹ Mitt. aus der k. techn. Versuchsanstalt zu Berlin. 1884, p. 86.
21
Mean crushing strength,
in tons, per sq. ft.
STONE AND BRICK
435
GRANITES:
Mount Sorrel
Description
Aberdeen grey (2-inch cube)
(cylinder, 21/1
inches diameter, 34 inches
high)
""
Aberdeen red (2-inch cube)
""
""
inches diameter, 34 inches
high)
Quartz
BASALTS:
""
""
Penmaenmawr (2-inch cube)
Hornblendic greenstone
Felspathic
CRUSHING STRENGTH OF STONE.
Tons per sq. ft.
LIMESTONES :
""
Slate.
Valencia (Irish) (1-inch cubes)
Killaloe
""
""
(cylinder, 21/1
SLATES:
Compact Welsh clayslate (3-733-1,052
SANDSTONES :
Bramleyfall
Craigleith (2-inch cube)
Darley Dale
Giffneuk
""
""
""
""
""
Kenton
Morley Moor
Park Spring
Stanley
Runcorn (sixteen 4-inch cubes)
six 3-inch cubes)
(six 4 inch cubes)
York grit (3-inch cube)
""
Red Mansfield
""
""
""
""
""
White Italian marble
White statuary
Portland
99
White
Red Alton (3-inch cubes)
Sydanape
""
""
•
""
""
(2-inch cubes)
་
(4-inch cube)
(2-inch cube)
•
•
19
Purbeck (13-inch cube)
D
832
1,412
1,162
1,614
1,357
1,270
•
1,086
1,580
1,106
1,205
720
1,974
389
504
455
310
318
318
487
383
267-443
295-416
427-514
712
609
327
337
309
490
1,400
206-389
239-292
516
250
587
Authority
Fairbairn
Unwin
""
",
""
Mallet
Fairbairn
Wilkinson
Unwin
Mallet
Wilkinson
99
Rennie
Roy. Com.
""
""
""
""
"1
""
Unwin
""
""
""
""
">
""
Unwin
".
Rennie
99
""
Unwin
""
">
Roy. Com.
""
""
,,
""
""
Roy. Com,
Rennie
FF 2
436
TESTING OF MATERIALS OF CONSTRUCTION
CRUSHING STRENGTH OF STONE-continued.
Description
Tons per sq. ft.
Ancaster (2-inch cube)
150
Barnac
114
Ketton
164
312
577
95
484
380
295
104
409
259
278
278
250
""
""
(3-inch cube)
Bolsover (2-inch cube)
Bramham Moor
Brodsworth
Cadeby
Chilmark
Hamhill
Huddlestone
Park Nook
Roche Abbey
Tottenhoe
""
Ketton rag (2-inch cube)
Bath, Box ground (2-inch cube)
""
""
""
""
""
""
""
""
""
Caen (3-inch cube)
•
•
I
•
·
•
124
198
Authority
Roy. Com.
""
""
Unwin
Roy. Com.
""
""
13
""
""
""
""
"')
""
""
""
Unwin
""
""
""
""
""
""
""
""
""
,,
99
""
BRICKS.
175. Bricks are made from clays, loams, or marls
containing silicate of alumina, mixed with sand, oxide of
iron, and carbonates of lime and magnesia. The plastic,
strong, or pure clays contract very much in burning,
and do not vitrify, so that the bricks are not durable.
Sand diminishes contraction, and permits partial vitri-
fication in burning. Iron acts as a flux, facilitating
fusion of the silica, and, in many cases, determines the
colour of the bricks. Lime diminishes contraction,
and acts as a flux; but lumps of lime become quick-
lime in burning, and slaking afterwards cause the
brick to crack. The following short summary gives
the composition of some clays: 1
1 Notes on Building Construction. Part. iii. p. 88.
STONE AND BRICK
437
Material
6
Silica and alumina
Oxide of iron.
Carbonate of lime
Carbonate of magnesia
Burham London
clay
brick clay
63.3
5.0
18.9
0.1
83.8
7.7
1.4
5.1
Loam
93-7
13
0.5
Marl
43·0
3.0
46.5
3.5
Malm is clay mixed with chalk in a wash mill.
Bricks are either hand-moulded or machine-moulded.
In the latter case the clay may be wet and plastic, or
dry or semi-dry. Hand-made bricks have usually a
cavity, or frog, on one side, which is supposed to afford
a key for the mortar. Wire-cut machine-made bricks
have necessarily no cavity or frog. Some pressed
bricks have frogs on both sides. Bricks are either
clamp burned' or 'kiln burned.' The weight of
bricks varies a good deal. London stocks weigh about
6.8 lbs. Pressed bricks and blue bricks may weigh
10 lbs. Ordinary red bricks weigh about 7 lbs., while
some of the lightest weigh only 5 to 6 lbs. The
absorption of water by bricks also varies. Staffordshire
blue bricks absorb 2 to 6 per cent. of their weight;
ordinary stocks and red bricks, 7 to 10 per cent.; and
the softer and more porous bricks 20 per cent.
The following table gives the crushing strength of
a sufficient variety of bricks. It may be added, how-
ever, that Mr. Ward gives some tests of bricks of
exceptional strength. In these tests, Staffordshire blue
bricks carried 650 to 1,064 tons per sq. ft., and bricks
made of slate débris 1,056 tons per sq. ft.
1
¹ Proc. Inst. of Civil Engineers, lxxxvi. p. 24.
438
TESTING OF MATERIALS OF CONSTRUCTION
CRUSHING STRENGTH OF BRICKS (UNWIN).
(Single bricks. Faces made smooth and parallel by plaster of Paris. Crushed between
two millboards, or the iron pressure-plates of the testing machine.)
""
London stock .
""
""
Description
""
""
>>
,,
99
""
Aylesford, common. 8.9
""
""
8.9
pressed 9.1 × 43
Rugby, common
9.5 x 4.2
Lodge Colliery, Notts
""
Digby Colliery, Notts
""
""
Ruabon, pressed
Grantham, wire cut
Leicester, wire cut.
Candy, pressed
Gault, wire cut
""
""
""
U
""
""
""
""
Cranleigh, pressed.
""
""
•
•
""
•
Terracotta block
""
""
Staffordshire blue,
common
Staffordshire blue,
""
•
common
Staffordshire blue,
""
•
common
Staffordshire blue,
pressed
Glazed brick
Red rubbers, three
in column, bedded
in putty
•
•
•
•
·
Dimensions, in
inches
4.6
× 4.1
× 2.4
2·4
4.6 x 40
× 2:45
9.2 × 4·1 × 2.8
8.9 × 4.2 × 2·3
8.9
× 4.25 × 2.5
× 44 × 2.7
× 44 × 2.7
× 2.7
× 2·9
9.0 × 4.2 × 30
9.0
x42
x34
9.0 × 4.2 × 3.25
93
x 41
4.6
× 4.2
8.8
× 43
9.2
× 4.4
44
x4·1
×2·6
4.3 × 4.1
× 2.6
9·06 × 4·2 × 2·8
4.7 × 4.6 × 2.5
4.6 × 4.6 × 2.5
8.8
× 43 × 2·8
8.7 x 4.1 × 3·0
44 × 4.2 × 2.5
8.7 x 4.1 × 2.9
2·9
4.5 × 43 × 3·0
4.3 × 4.2 × 3·0
8.9 × 43 × 3·1
9.0 × 43 × 3·1
88 × 44 × 3.3
8.9 × 44 × 2.9
9.0 × 4.5 × 8.0
6 sq. ins.
15
15
6
""
,,
x 3.25
× 3.2
× 2.7
× 3.2
""
99
""
·
Cracked, at
tons per sq. ft.
128
133
48
111
71
158
251
109
115
149
120
127
159
55
122
248 [353]
414
414
361 [361]
165
80
111
119
ft.
Crushed, at
tons per sq.
216
69
166
103
183
228
141
190
237
381
173
145
169
464
152
386
240 [353]
275
166
174
177 Yellow Half-brick
181
129
113
Colour
25
168
139
267
104
""
Pink
99
""
""
Red
""
""
"g
>>
""
""
""
""
""
""
""
83
337 Pale red Half-brick
""
308
229
181
""
""
""
White
""
""
""
2
""
Blue
""
""
""
Remarks
Deep frog
Between
pine boards
""
Not crush'd
Half-brick
Not crush'd
""
""
Half-brick,
frog
Half-brick,
frog
Half-brick
17
Half-brick
""
Not crush'd
Frog
STONE AND BRICK
439
176. Strength of Brickwork.-Comparatively few
accurate tests have been made of the strength of brick-
work masses. The following results of tests of brick
cubes, with different mortars, were made at Berlin by
Dr. Böhme. The brick cubes were approximately
10×10 × 9.5 inches, and were three months old. Two
kinds of brick were used :-
05 ti
Beneckendorfer brick :
1. 1 lime, 2 sand
2. 7 lime, 1 cement, 16 sand
3. 1 cement, 6 sand
,,
""
33
5. 1 cement, 3 sand
6.
Mortar
""
""
>>
Hertzfelder brick :
7. 1 lime, 2 sand
8. 7 lime, 1 cement, 16 sand
9. 1 cement, 6 sand
10.
""
""
""
11. 1 cement, 3 sand
12.
>>
•
""
•
""
•
""
""
•
For mortar of 1 lime, 2 sand
>>
>"
•
""
Mean
crushing
Condition strength,
in tons
per sq. ft.
Dry
Dry
Dry
Wet
Dry
Wet
Dry
Dry
Dry
Wet
116.2
130.4
139.4
141.9
158.8
169.8
70.0
73.3
93.2
87.4
Dry 100.7
Wet 104.6
7 lime, 1 cement, 16 sand.
1 cement, 6 sand
1 cement, 3 sand
Crushing Crushing
strength strength of
of single mortar in
brick, tons cubes, tons!
per sq. ft. per sq. ft.
263·2
15
>
""
"}
""
160.9
""
"
This gives for the ratios of strength of brickwork to
strength of single bricks :-
??
">
11.4
42.0
112.4
0.44
0.48
0.55
0.63
192.9
""
11.4
42.0
112.4
""
192-9
A
";
The following experiments on bricks and brickwork
pillars were made by Curioni.' The bricks were placed
flat. All the bricks were of the same clay. The mortar
¹ Proc. Inst. of Civil Engineers, lxxiii. p. 385.
440 TESTING OF MATERIALS OF CONSTRUCTION
consisted of equal parts of Casale Monferrato cement
and fine sand, and was allowed fifty days to set:-
Single bricks, between lead
Single bricks, with faces made even with
Description
""
mortar
Pillars of 2 bricks, mortar faces
4
""
""
""
""
""
•
""
99.
""
Crushing stress, in tons per sq. ft.
Machine-made bricks
Hand-
made
bricks
119.8
237.8
142.6
86.9
""
Second
First
pattern pattern
214.9 142.7
282.6 211.2
150.0 142.6
The reduction of strength by using lead is obvious.
If we take the length of a brick to be twice the width
and 4 times the thickness, Bauschinger's formula for
pillars of this kind takes the form
b
f=a+b
12
127·1
114.3
where f is the strength per sq. ft., n the number of
bricks in height, and a and b are constants.
The formula agrees pretty well with the results, if
the following values are taken :—
Hand-made bricks.
225
f=13+
N
225
Machine-made bricks (1st) f= 58 +
22
136
22
(2nd) ƒ= 75 +
which at least seems to show that the diminution of
strength is due to form, and not to influence of the
mortar joints.
441
CHAPTER XV.
LIMES AND CEMENTS.
177. Limes and cements are of the greatest impor-
tance to the engineer, and, being artificially manufactured
products, they vary in quality according to the care
exercised in the selection of the materials of which
they are made, and the skill and attention with which
the processes of manufacture are carried on.
To secure
a uniform and trustworthy cement, the engineer has
been driven to test regularly the cement supplied. To
Mr. Grant is largely due the credit of establishing sys-
tematic tests of cement, with the result that, from the
pressure brought to bear on manufacturers, and the
knowledge gained of the conditions on which the
strength of a cement depends, there has been achieved
a very considerable and general improvement of
quality. In large works, like the Metropolitan Main
Drainage, it was perceived that a considerable sum
might economically be spent on systematic and regular
tests of the quality of the cement supplied. A com-
paratively large sum spent in testing formed but a
small percentage on the value of the cement, and as the
quality of cement may vary through very wide limits,
1
442 TESTING OF MATERIALS OF CONSTRUCTION
from qualities absolutely trustworthy to qualities abso-
lutely dangerous, the cost of testing was fully repaid
by the greater value of the cement obtained, and the
thorough confidence with which after testing it could
be used.
The cementing materials ordinarily used are classi-
fied thus:-
1. Rich or fat limes.
2. Poor limes.
3. Hydraulic limes.
4. Hydraulic cements.
The rich or fat limes are produced by the calcination
of nearly pure limestones, and they consist of lime
nearly free from other ingredients. Such lime, when
mixed with water, slakes violently, and afterwards sets
or hardens extremely slowly, if at all, by the absorption
of carbonic acid from the air. Such lime makes very
weak mortar. Poor limes contain 10 to 40 per cent. of
sand or other inert matter. They slake much less
violently, or even imperfectly, and also make a very
weak and very slowly setting mortar.
Hydraulic limes and cements are those which contain
ingredients capable of combining and hardening apart
from any absorption of carbonic acid from the air.
They will, therefore, set under water.
The hydraulic limes contain a large amount of pure
lime, so that they slake. But they contain also clay,
silica, or other ingredients in a condition capable of pro-
ducing chemical action in the presence of water.
LIMES AND CEMENTS
443
This action results in the setting of the lime, which
hardens and becomes insoluble. Feebly hydraulic lime
makes mortar which hardens enough to resist a finger-
nail in a month. The Lias and Mountain limestones
yield limes more actively hydraulic.
Artificial hydraulic limes or cements are mixtures
of lime and clay in proportions which produce eminent
hydraulic or setting properties. The mixture is calcined
to clinker at a suitable temperature, and then ground
to a fine powder. Such a cement hardly slakes at all,
but sets with great rapidity, becoming in course of
time extremely hard. The name Portland cement,
given to the first successful artificial cement of this
kind, has become a general name for all artificial cements
formed by calcining mixtures of chalk or limestone
and clay.
178. Portland Cement.-About the year 1850 there
was first produced a new cement, which from its resem-
blance to Portland stone when set was called Portland
cement. It has the properties of setting rapidly and
setting under water, and it slowly hardens to a condition
in which it is nearly as strong as natural stone. In
hardening, it has the very important quality of altering
extremely little in volume. It rapidly established its
superiority as a constructive material to Roman cement,
and it bids fair, in spite of its greater cost, to largely
supplant hydraulic lime. It can be kept with little
deterioration and shipped to distant countries. Its use
has extended till its manufacture has become one of the
444
TESTING OF MATERIALS OF CONSTRUCTION
most important industries in this country, in Germany,
in France, and in the United States.
Success in its manufacture depends on careful judg-
ment and the rigid observance of essential conditions.
It may be produced from a great variety of natural
rocks, but, broadly speaking, it consists of 72-79 per
cent. of chalk and 28-21 per cent. of clay.
Experience shows the exact proportion of the natural
materials used which is most suitable. These materials
must be so mixed that the cement is absolutely homo-
geneous and invariable in composition. At first, the
chalk and clay were ground together with a large
volume of water into a liquid slip. Now, it is found
that grinding with only 35 per cent. of water is
not only economical, but prevents the segregation of
materials which took place in fluid slip. With some
materials no water is used in grinding. The mixed
materials are then calcined to a clinker at a temperature
just short of that which produces fusion or vitrification.
Underburned clinker is weak, and overburnt clinker is
an almost inert cement. Lastly, the clinker must be
broken up and ground to a powder, so fine that the
cement particles expose a maximum surface at which
chemical actions may occur, and are not too large to
fill the smallest interspaces in the sand with which the
cement is mixed in use.
According to Michaelis, the hydraulicity of a cement
is due to the silica, alumina, and oxide of iron. In a
good cement the sum of these should be about one-
LIMES AND CEMENTS
445
1
third of the total weight, the rest being chiefly lime.
The calcination removes carbonic acid and water, and
leads to the formation of calcium silicate, calcium alu-
minate, and calcium ferrate. In the setting and harden-
ing of a paste formed of the cement, there is probably
a hydration of the silicates, and perhaps the formation of
double hydrated silicates.
Silica
Alumina
Oxide of iron
Lime
Magnesia
The composition of a Portland cement varies more
or less, but generally lies between the limits given in
the following table :-
Agata
•
Per cent.
20-26
5-10
2-6
67-58
ww
0.5-3
179. Ordinary Cement Tests for Strength.-The ordi-
nary test is a tensile test of a small briquette of neat
cement, made in a brass or gun-metal mould, left twenty-
four hours to harden in air, and then placed in water.
The cement is tested in seven days, and, if possible,
at later dates also. At least five briquettes should be
tested at each date, and the mean result taken.
The form of the briquettes has a considerable in-
fluence on the strength. Fig. 134 shows some of the
forms which have been used. Form a, used in all the
earlier tests, is a very bad form, the square corners
producing unequal distribution of stress with a rigid
material. The most common form now is e, known
In the French rules a cement in which the ratio of silica and
alumina combined to lime is less than 0:44 is regarded as doubtful.
446 TESTING OF MATERIALS OF CONSTRUCTION
sometimes as Grant's, and this is universally used in
Germany. A few engineers use forms like ƒ and g. A
small metal plate is placed in the holes at the ends, and
a knife-edge of the shackle passes through each hole.
In some of Mr. Grant's tests, briquettes of the same
cement gave strengths ranging from 280 lbs. per sq. in.
for form a, to 460 lbs per sq. in. for form e, at seven days
after gauging. For some time briquettes with a sec-
FIG. 134.
b
с
ISXX
XX!
е

tion of 24 sq. ins. were used, but it is far more usual
now to make the section 1 sq. in. The smaller bri-
quettes are more easily moulded, and give more uniform
results.
The briquettes are broken in small lever testing
machines, of which there are now many in the market.
It is very important that the load should be applied at
a regular rate and without shock. Adie's machine is
a single-lever machine with a rolling weight. Reid
& Bailey's machine is a single-lever machine, with a
LIMES AND CEMENTS
447
A
cistern at the end which fills with water to apply
the stress. In Michele's machine, a bent or pendulum
lever is used. Mr. Faija has designed a neat single-
lever machine with a spring balance at the end.
worm and sector, acting on the spring balance, regu-
larly increase the load. The ordinary German ma-
chine is a double-lever machine, and is loaded with
shot.
Precautions in Gauging Briquettes.-A sample of the
cement should be taken from every twenty-five or fifty
barrels or sacks; the samples should be mixed, anl
a portion taken for gauging. To obtain the best re-
sults, the gauging must be done with the smallest
amount of water which will make a smooth stiff paste.
Preliminary tests must be made, to ascertain exactly the
quantity of water necessary. A small quantity of the
mortar, dropped from the trowel at a height of 20
inches, should leave the trowel clean, and retain form
without cracking. It should be capable of being
moulded into a ball by hand which can be dropped
20 inches without cracking. Having ascertained how
much water is necessary (18 to 25 per cent. of the
weight of the cement usually), the cement and water
for gauging should be accurately weighed.
The cement is generally gauged on a slate or marble
slab with a light trowel, and the more rapidly this is
done and the moulds filled the stronger are the bri-
quettes. Usually mortar to fill five or six moulds is
gauged, six ounces of cement being necessary for each
448 TESTING OF MATERIALS OF CONSTRUCTION
mould. The mixing with the trowel should take five
minutes, and then the moulds, placed on a glass or slate
slab, are filled and rammed and shaken. It is important.
that the operation should be finished before setting
begins.
Mr. Faija has introduced a very convenient cement-
gauger, which gauges the cement in less time and more
uniformly than it can be done by hand.
The briquettes are removed from the moulds when
set, and in twenty-four hours they are placed in water.
The temperature during all the operations should, if
possible, be 15° to 18° C.
In testing the briquettes, the load should be applied
at the rate of 100 lbs. in fifteen seconds.
Briquettes of Sand and Cement.—Briquettes of sand
and cement give far more trustworthy indications of
the value of a cement than neat cement tests.
The ce-
ment is always used in construction mixed with other
materials, and the cement which is strongest neat is not
always strongest tested with sand. The gauging of the
briquettes also is easier, and the results are less affected
by small variations of procedure. On the other hand,
the briquettes must harden twenty-eight days before
being tested, and this is in many cases a longer time
than can be allowed.
The greatest difficulty of the sand test is securing
an identical quality of sand for all tests which are to be
compared. A sharp pit sand is best, which should be
carefully washed and sifted. The sand used should be
LIMES AND CEMENTS
449
the portion which passes through a 20-mesh, and
remains on a 30-mesh, sieve. In Germany, a special
sand has been selected, and washed and sifted portions
of this normal or standard sand are sold by the Go-
vernment laboratories. In France, a standard sand is
obtained by crushing quartzite, and sifting through
sieves of practically the same sized mesh as is given
above.
In the ordinary sand test, the mortar is gauged
with one part by weight of cement and three of dried
sand. The water required is about 12 per cent. of the
weight of cement and sand. The sand and cement are
mixed dry, the water added, and the mortar is gauged
for five minutes. The briquettes are placed in water
twenty-four hours after gauging.
M
180. Increase of Strength in Hardening. Initial
Strength, and Rate of Gain of Strength.-The construc-
tional value of a building cement depends on two quite
distinct elements-on its power of setting into a rigid
form soon after it is gauged, and on its power of at-
taining in course of time a considerable strength. In
the actual process of building, especially building under
water, it is important that the cement should set
rapidly, and gain strength enough to keep its form.
But, generally, it is only after the lapse of months, or
even of years, that the structure is called on to exert its
full strength. Hence any strength acquired by harden-
ing during that time is advantageous.
Consequently, in judging of a cement from tests of
G G
450 TESTING OF MATERIALS OF CONSTRUCTION
its strength, both the initial strength acquired in a
short time and the rate of gain of strength with age
require to be considered.
Now, suppose experiments have been made, say,
at seven days, four weeks, and twelve weeks. One
would still like to be able to predict the strength at
a greater age, and even in judging of the data in
hand some difficulty arises from the discrepancies and
anomalies incident to such experiments, and due to the
difficulty of making the experiments numerous enough
to get true average values. If anything were known.
of the law of increase of strength with age, if we could
put our results in a formula, their meaning would be
much clearer.
Now beyond the first week, and up to a period at
which the full strength of the cement is reached, the
rate of hardening follows very approximately a simple
law. For ordinary tension briquettes, for instance, the
gain of strength is nearly proportional to the cube root
of the time of hardening, and that both for neat cement
and cement mortar. It is possible, therefore, to repre-
sent the results of a series of tests in a simple formula,
the constants of which indicate the character of the
cement with very great clearness.
Let Y be the strength of a cement, or cement mortar,
in lbs. per sq. in., at an age of a weeks after mixing.
From some preliminary tentatives the author found for
the relation between x and the expression-
Y
y = a + bx”
M
(1),
LIMES AND CEMENTS
451
In this
where a, b, and n are empirical constants.
form the equation would not be very convenient to use,
for it would require at least three sets of experiments
at three different ages of the test pieces to determine
the three constants; and a still greater number would
be required for satisfactory results in consequence of
the discrepancies which occur in cement testing.
It appeared, however, that for any given kind of
cement, and any given kind of straining action, n had
a constant value. Further, by a modification of the
formula, a might always be the strength of the cement
at seven days' age. Consequently there would remain
only one constant to determine. The formula then is
y = a + b (x−1)"
(2),
where y is the strength of a cement or mortar, at a
weeks after mixing, the initial strength of which at
seven days is a lbs. per sq. in. The constant n has
values which can be assigned beforehand, and only the
constant b remains to be determined by experiments
on test pieces more than one week old. It will be seen
hereafter that, though b varies, its variation is not
within very
wide limits, so that when the characters of
cements are better known it may be possible to assign
for it a probable value, even if experiments are wanting
in any given case.
Now since in this equation a is the initial strength
of the cement, and b a constant, varying with the
rate of increase of strength with time, the two con-
G G 2
452
TESTING OF MATERIALS OF CONSTRUCTION
stants exhibit very clearly the character of a cement.
If their values are determined for any given cement,
and inserted in the equation, a numerical equation is
obtained which may be termed the characteristic equa-
tion for the cement.
181. Application of the Characteristic Equation to
Tension Tests. To examine the applicability of the for-
mula, let the constants be determined for the series of
tests of Portland cement briquettes extending over seven
years given in Mr. Grant's first paper.¹ Mr. Grant's table
gives in each case the mean strength of ten briquettes,
21 sq. ins. in section. In one series the cement was
gauged neat ; in another series the cement was mixed
with an equal weight of clean Thames sand.
Grant's numbers, reduced to lbs. per sq. in., are as
Mr.
follow :-
7 days
1 month
3 months
6
9
12
""
""
""
2 years
3
""
•
•
•
Age
•
·
•
•
•
Strength per square inch
Neat cement
363
415
470
525
542
547
590
585
1 cement + 1 sand
157
202
244
285
307
320
351
350
1
Now, for Portland cement in tension, n =
; the
constant a has the values 363 and 157 for the two series,
¹ Minutes of Proceedings Inst. C.E. vol. xxv. p. 89; also vol. xxxii.
p. 280.
LIMES AND CEMENTS
453
1
and it only remains to determine the most probable
value of b in the equation-
y = a + b 3 x −1.
Age
X
This is best done by calculating b for each of the
experiments, except that at seven days, and taking the
mean of the values so found. Thus-
1
4
13
26
39
52
104
156
Age
a
يع
1
4
13
26
39
52
104
156
208
260
Strength
У
363
415
470
525
542
547
590
585
Mean
Strength
Y
157
202
244
285
307
320
351
350
363
365
Neat cement.
Cement mortar
NEAT CEMENT.
y-a
52
107
162
J
179
184
227
1 CEMENT + 1 SAND.
y-a
45
87
128
150
163
194
193
Mean
•
b =
У
By
3
Y
Ꮖ
Y
b=
y-a
36
47
56
53
49
48
48
t
31
38
44
45
44
41
36
40
a
=
Hence the characteristic equations for this cement
and cement mortar are-
=
1
Strength
Y
by formula
363
431
471
503
525
541
588
Strength
У
by formula
157
214
249
274
292
305
345
372
363 + 48 3/x
157 + 40 3/x
-
1
454 TESTING OF MATERIALS OF CONSTRUCTION
Hence, the sand reduces the initial strength of the
cement by rather more than one-half (from 363 to
157 lbs. per sq. in.), and the gain of strength at any
age is less for the mortar than for the neat cement in
the proportion of 40 to 48. By comparing the calculated
and observed values of y, it will be seen that the formula
FIG. 135.

LBS. 650
600
500
400
300
200
100
O 10 20
40
1
1
1
60
1
1
I
1
}
NEAT CEMENT
I CEMENT + 3 SA
80
100
120
140
WEEKS
agrees closely enough with experiment for practical
purposes. Mr. Grant's figures show that the neat
cement reached its maximum strength in one hundred
and four weeks, and the cement and sand in one hun-
dred and fifty-six weeks. Hence values of b are cal-
culated from data up to those dates only.
In Fig. 135 the experimental values are shown by
LIMES AND CEMENTS
455
small circles, connected by a broken dotted line, and
the calculated values lie on the curves.
In the case of cement mortar the briquettes gain in
LBS
850
800
700
600
500
400
300
200
100
0
6-
10
20
FIG. 136.

30
40
1
"
1
1
P
50 WEEKS
strength up to any period to which experiments are
usually extended. But with neat cement briquettes
a maximum strength appears to be reached, often in
456
TESTING OF MATERIALS OF CONSTRUCTION
about three months, after which the strength remains
constant or slightly falls off. For example, in the ex-
periments given by Mr. Grant on the relative strength
of briquettes made on an impervious slab, and on a
porous (gypsum) slab,¹ the strength slightly diminishes
after thirteen weeks. Hence, for such results the value
of b must be deduced from experiments before the maxi-
mum is reached, and the formula ceases to apply beyond
the maximum. The following characteristic equations
were deduced for these experiments from the results for
four, eight and a half, and thirteen weeks.
Impervious slab
Gypsum slab
x
Weeks
1.0
4.0
8.5
13.0
26.0
39.0
52.0
•
Impervious base
Y
Observed
449
687
765
808
NEAT CEMENT.
731
746
718
Y
Calculated
449
681
765
819
x = 449 + 161 3x-1;
x = 257 + 164 3x-1.
Gypsum slab
Y
Observed
257
454
634
626
620
655
608
Calculated
257
493
577
631
These results are plotted in Fig. 136.
182. Values of Constants for different Cements.-First
some data have been selected from the Table XLVII.,
p. 169, of Mr. Grant's paper. The only principle of
selection adopted was to take those cements for which
the completest series of data are given. The following
1 Minutes of Proceedings Inst. C.E. vol. lxii. p. 142.
LIMES AND CEMENTS
457
table gives the characteristic equations obtained for neat
cement briquettes, the constants being in all cases de-
duced from the strengths given at one, four, and thir-
teen weeks. In none of these cements did the strength
increase beyond that period.
No.
1
12
13
""
""
15
""
19
CHARACTERISTIC EQUATIONS FOor Mr. Grant's CEMENTS.
(Units, lbs. per sq. in., and wecks. Gauged neat.)
Water Setting
used, time, in Characteristic equation
per cent. minutes
18.5 Slow
22.5 15
20.0 600
21.2
22.5
20.0 480
""
22.5
22.5
""
6
رد
""
y=558+ 963½ – 1
422 + 118
""
""
""
""
""
""
""
614+ 91
610 + 91
520 + 112
626+ 56
576 + 140
422 +188
""
""
""
""
>>
""
""
Initial
strength
558
422
614
610
520
626
576
422
Strength at
13 weeks
Observ. Calc.
815
778
744 692
846
824
840
820
783
780
824
755
833
896
793 852
Strength
at
52 weeks
825
694
813
779
772
718
785
747
The tests of cement which form the most complete
series are, however, to be found in the publications of
the Engineering Laboratories of Munich and Berlin.
In the Mitt, aus den Mech. Techn. Laboratorium in
München,' for 1879, there is a remarkable series of ex-
periments on the tensile strength of cements, by Pro-
fessor Bauschinger. In Table II. are given no less
than three hundred and sixty results, each the mean of
ten separate experiments. Ten different cements were
used, and these were made into test pieces of 72 sq.
cms. (11 sq. ins.) section. From these results the
author obtained the following equations, those for
neat cements being deduced from results on test pieces
one week to sixteen weeks old, and those for cement and
1
458
TESTING OF MATERIALS OF CONSTRUCTION
sand from results on test pieces one week to one hundred
and nine weeks old.
The extreme regularity of the constants for a great
variety of cements and their limited variation in value
is remarkable. The comparatively low initial strength
may be partly due to the cement being fresh, partly to
the size of the test pieces.
CHARACTERISTIC EQUATIONS FOR TENSILE STRENGTH OF BAUSCHINGER'S
CEMENTS.
(Units, lbs. per sq. in., and weeks.)
Cement Setting time,
mark minutes
ABCDEFGIRE
с
Ꮐ
H
Ꭱ
T
80
49
195
136
13
416
9 to 17
14,, 26
344
146
Neat cement
y ==
199 +403x-1
121 +49
199 + 95
199 +53
185 +42
256 + 37
227 + 64
227 + 36
299 + 61
227 + 61
Mean 54
1 cement + 3 sand
y =
81+293/x-1
46 +36
108 +40
53 +61
85 + 40
112 +41
91 + 40
80+ 46
136 +37
114 + 28
Mean 40
1 cement + 5 sand
y =
43 +313/x-1
26 + 30
78+37
37 +47
60 + 28
67 +38
67 + 33
50+ 36
105 + 31
71+24
Mean 33.5
The French official standard of strength for neat
cement briquettes is a minimum of 284 lbs. per sq. in.
at 7 days, 498 lbs. at 28 days, and 640 lbs. at 84 days
after gauging. This agrees nearly with the equation-
y=284+ 155x-1.
The strength is taken to be the mean of the three
highest of each set of six tests.
183. Values of the Constants in Shearing Tests.-Parts
of the briquettes used in Bauschinger's tension tests
LIMES AND CEMENTS
459
Cement
mark
given above were subjected to shearing. The following
are equations for a few of them :—
ARRE
B
T
Neat cement
y =
270 +433/x- − 1
142 +67
412 + 57
242 × 92
1 cement + 3 sand
y =
112 + 493% −1
46 +53
185 + 55
131 +43
1 cement + 5 sand
=
Y
60+523/- 1
31 + 57
131 + 61
105 + 44
184. Characteristic Equation for Tests of other Cement-
ing Materials.-Some experiments by Dr. Böhme on
These are
hydraulic lime have also been examined.
not very extensive, and they were carried to an age of
thirteen weeks only. However, they agree well with a
formula of the same general form with n = 1. The
equation is therefore-
y = a + b (x−1).
The following were deduced from the data :-
Tension; 1 lime + 1 sand,
y = 20 + 11 (x-1).
Tension; 1 lime + 3 sand,
y= 31 + 17 (x-1).
Compression; 1 lime + 1 sand,
y = 97 +44 (x−1).
Compression; 1 lime + 3 sand,
122 + 22 (x-1.)
Y
185. Fineness of Grinding.-The greater part of the
improvement in the quality of cement which has been
effected in the last ten years has been due to the dis-
460 TESTING OF MATERIALS OF CONSTRUCTION
covery of the importance of grinding the clinker to ex-
treme fineness. The amount of surface the particles of
cement expose increases inversely as the diameter of
the particles. A cubic inch of cement would have 150
sq. ins. of surface if the particles were spherical and
inch in diameter, and 600 sq. ins. if they were To
inch in diameter; so that the area on which chemical
action occurs increases as the cement is ground more
finely. But probably this is only part of the explana-
tion of the greater value of very finely ground cement.
255
1
100
If cement is taken and sifted through a sieve of fifty
meshes to the inch, the residue on the sieve of particles
larger than the holes in the sieve will not adhere to-
gether sufficiently to form a briquette. They are almost
absolutely without cementitious value. But if these
same particles are reground, they are converted into
valuable cement.
The extremely small value of these larger particles
in the cement was not for some time perceived. For a
long time all tests of the strength of cement, or nearly
all, were made with neat cement, the reason being that
tests of this kind can be made more rapidly than any
others. Now, a good cement will bear the addition of
a certain amount of inert matter without any sensible
reduction of strength; indeed, with a certain gain.
Hence it happens that in neat cement tests a somewhat
coarsely ground cement gives results higher than a
finely ground one. But cement is never, in fact, used
neat; it is used mixed with three to seven or more
LIMES AND CEMENTS
461
times its weight of the cheaper material, sand or gravel.
In the German laboratories, therefore, it was thought
desirable not to test the cement neat, but to test it in
the condition in which it is used in practice, mixed with
sand; and directly this was done, it was found that the
cements which were strongest tested neat were by no
means always strongest tested as mortar mixed with
sand. There may be more reasons for this than one,
but the principal reason is that the more finely ground
cement will bear a considerable addition of sand with
less loss of strength than the coarsely ground cement.
The coarse cement has, in fact, a proportion of matter
as inert as sand already mixed with it.
Suppose a cement has 10 per cent. of inert matter;
then, when mixed with sand in the proportion of 2: 1,
the true ratio of cement to inert matter is 1 to 2:33;
but if the cement initially contains 40 per cent. of inert
matter, then, when mixed with double its weight of
sand, the true ratio of cement to inert matter is 1:4.
It
may also be noted that the cement and sand test is
to some extent a test of adhesion, the neat cement test
being a test of tenacity only.
The fineness of grinding is determined by careful
sifting through copper or brass wire sieves with square
meshes, and these should be carefully and accurately
made. Obviously, in specifying the sieves to be used,
it is necessary to state not only the number of meshes
to the inch but the size of wire used. The following
are the sieves most commonly used in cement-testing:--
462
TESTING OF MATERIALS OF CONSTRUCTION
For cement
3S. 750
700
600
500
400
For sand.
300
200
100
50
""
""
""
""
""
ور
UNSIFTED
SIFTED
NEAT CEMENT
10
20
•
•
•
LBS 450
30 WEEKS
400
300
200
100
50
0
No. of meshes
to in.
929995
50
74
100
120
180
20
28
145
625
2,500
5,476
10,000
14,400
32,400
400
774
FIG. 137.
SIFTED
UNSIFTED
/CEMENT J SAND
No. of meshes
to sq. in.
10 20
LBS 300
30 WEEKS
200
100
Diameter of
wire
50
inches
.01.2
·005
⚫0044
·0031
⚫0146
⚫01.23



SIFTED
/CEMENT
INSIFTED
SAND
0 10 20 30 WEEKS
The best German cements are ground so fine that
they leave a residue of only 3 to 10 per cent on a
76-mesh sieve.¹ English cements are more commonly
1 The German standard for fineness is that not more than 10 per
cent. remains on a 76-mesh sieve, the wire of which has a thickness equal
to half the width of mesh; lb. of cement is used for this test.
LIMES AND CEMENTS
463
specified to pass entirely through a 25-mesh sieve,
and to leave not more than 10 per cent. on a 50-mesh
sieve.
Fig. 137 shows the results of a series of tests by
Messrs. Dyckerhoff, given in Mr. Grant's paper. The
same cement was used in all the tests; but in one
series the cement was used as manufactured, in the
other after sifting through a fine sieve. The former
left 10 per cent. on a 50-mesh sieve; the latter all
passed through a 180-mesh sieve.
Neat cement.
The equations corresponding to the curves in the
diagrams are as follows:-
Neat unsifted cement-
y = 353 + 122x-1
Neat sifted cement-
Y 346 + 36x-1
1 cement + 3 sand.
Cement unsifted-
t
3
y = 75+ 69x-1
Cement sifted—
y = 252 + 53x-1
1 cement + 5 sand.
Cement unsifted—
Cement sifted—
3
y = 31 +46 V-1
3
y = 136 + 47 Va-1.
A series of experiments, given in Mr. Elliot Clarke's
very interesting 'Report on the Boston Main Drainage
464 TESTING OF MATERIALS OF CONSTRUCTION
Works,' shows the effect of fineness of grinding still
more strikingly. An English Portland cement was
taken and divided into portions, which passed through
a 50, 70, 100, and 120 sieve. Briquettes made with
these and with different proportions of sand were tested
at different periods, from one week to fifty-two weeks.
The following equations give the results:
EFFECT OF FINENESS OF GRINDING (BOSTON).
Percentage which
would not pass
through a 100 sieve
55
33
28
18
8
0
1 cement + 3 sand
y = 39+283x − 1
92 + 42
97 +45
117 +44
123 + 50
154 + 44
M
1 cement+ 5 sand
y = 19+ 193/x-
43 + 32
47 +35
65 + 35
73 +36
86 + 35
1
186. Heaviness of Cement. It was early discovered
that heavy, well-burnt clinker produced better cement
than the lighter under-burnt clinker. Hence for a long
time it was prescribed in all specifications that the
cement should have a certain weight per bushel.
measure.
To get uniform results the cement is sifted through
a very coarse sieve, and allowed to fall through a
funnel 18 inches to 3 feet high into the standard
The cement is strickled off, and the measure
weighed without shaking. The size of the measure
must be defined, as the cement packs closer in a large
than in a small measure. Bauschinger found 13 per
cent. difference between the weight of cement in a 50-
litre and a 1-litre vessel. But another influence affects
LIMES AND CEMENTS
465
the result. A cement ground coarsely will give a
heavier weight than the same cement ground finely, so
that the weight test is a premium on coarse grinding.
Since this has been understood, the weight test has been
generally abandoned.
1
The weight per cubic foot of the same cement of
different degrees of fineness was determined at Boston,
with the following results :-
Per cent. retained
on 120 sieve
PER CENT
LEFT ON
120 SIEVE
40
30
20
10
0
10
20
30
40
0
•
LBS. 75
FIG. 138.
•
80
90
85
WEIGHT PER CUBIC FOOT
Weight per
cubic foot
95
75
79
82
86
90

100
Fig. 138 shows these results plotted in a curve.
It
is still, however, convenient to know the weight per
1 'Boston Main Drainage.' By Elliot C. Clarke. p. 115.
H H
466 TESTING OF MATERIALS OF CONSTRUCTION
cubic foot, and if the fineness is taken into account it
affords some indication of the quality.
The French official weight test is free from the
objections to the ordinary weight test. The cement is
sifted through a sieve of 180 meshes to the inch, and
only the sifted cement is used for weighing. This is
filled into a litre measure. The weight of 1 litre
must be within 100 grams of that of a litre of cement
of similar fineness ground from specially selected heavy
clinker produced at the same factory.
187. Influence of the kind of Sand used in making
Cement Mortars.-The sand used with cement in making
mortar is commonly directed to be clean, sharp, siliceous
sand. It is usually specially directed that the sand
should be free from clay. Experiment seems to show
that a percentage of clay does not really harm the
But leaving this question aside, and suppos-
ing we have got a clean siliceous sand, tests will give
very different results, according to the quality of the
sand. For instance, experiments given by Mr. Grant
with Berlin standard sand and a coarser sand give the
following equations :--
cement.
Standard Berlin sand. Briquettes pressed-
y = 73 + 31x-1
Standard sand. Briquettes not pressed
89+ 19x-1
Y
Coarser sand-
Y
=
172 + 28 x - 1
3
--
P
Ma
LIMES AND CEMENTS
467
-
These experiments extended over a year. The ex-
periments are plotted in Fig. 139.
Fig. 140 shows some experiments on a Portland and
American (Rosendale) cement,¹ made with a sand un-
sifted (marked mixed on the diagram), and on portions
of the same sand of different degrees of fineness obtained
by sifting. It will be seen that the coarser sands give
lbs
300
200
WH
13
13
8/2 26 39 52 1 8/2 26 39
52 1
WEEKS
WEEKS
100
FIG. 139.
1
300

200
100
13
0
82 26 39 52
WEEKS
briquettes of greater strength; but the unsifted sand is
nearly as strong as the coarsest. For use on works the
mixed sand would be good, but for comparative experi-
ments sand of a definite size is preferable.
¤ и 2
By coarseness of the sand we mean, primarily, size
of grain. Large-sized sand is good for exactly the
Boston Main Drainage.' Clarke. p. 123.
468
TESTING OF MATERIALS OF CONSTRUCTION
inverse reason that fine cement is good. Fine cement
coats a large surface, and fits well into the interspaces
of the sand. Large-grained sand has less surface to
coat, and its spaces are more easily filled with cement.
Now, uniform size of grain may be obtained by sifting.
Standard Berlin sand is passed through a 20- and is re-
tained by a 28-mesh sieve. But sands of uniform size
lbs
400
300
200
100
0
Very Fine.
PIC 25
R
P.
R.
IC
Fine
IC.
IC
R IC.
FIG. 140.

13 S
2 S
13 S
12 S
9 MONTHS
MONTHS
2 WEEKS
4 WEEKS
I WEEK
Medum
w
Very Coarse
Mixed
of grain do not make equally good mortar. Two sands
sifted through and retained on the same sieves give
different tests. There is something in the form of the
grains and the kind of space between them-possibly
even something in the chemical condition of the sand-
which affects the initial strength and rate of hardening
of the briquette. These different qualities are shown
very clearly in the following characteristic equations,
B
LIMES AND CEMENTS
469
deduced from experiments by Mr.
Harbour Works at Wilhemshaven.
cement to 3 sand, the same cement used throughout
Arnold, at the
The tests are 1
Wilhemshaven blue sand, fine-grained and sharp—
y = 101 + 22x-1
Dangast normal sand, sifted in the same way as
Berlin normal sand, not very sharp-
= 124 + 23x-1
Y
Dangast common building sand-
y = 165 + 13-1
Wangeroog, coarser, clean and sharp-
3
193 + 41 x − 1
Y
Berlin normal, clean sharp quartz sand—
y = 250 +44 V-1
3
188. Influence of Proportion of Sand on the Strength
of the Mortar.-Cement mortars are weaker than neat
cement, probably because the adhesion of the cement
to the sand is less than the tenacity of the cement.
The larger the proportion of the sand, the weaker the
mortar. It appears that, even with a proportion of
1 cement to 3 sand, the whole of the interstices of
the sand cannot be filled with cement, and as the pro-
portion of sand increases the proportion of unfilled
space must increase, and therefore there must be a less
section to break.
From a series of tests, by Mr. Elliot Clarke, of
about 500 briquettes, all made with the same cement
470
TESTING OF MATERIALS OF CONSTRUCTION
1
(the tests extending over two years), the following very
uniform series of equations are obtained :--
PORTLAND CEMENT MORTAR, WITH DIFFERENT PROPORTIONS
OF SAND (BOSTON).
Neat cement
1 cement + 1 sand
1
1
""
""
55
100A
Mixture
+2
+3
+ +
90A + 10B
90A + 100
90A + 10D
90A + 10E
90A + 10F
50A +50F
235
+ 5
>>
11
""
y = 303 + 613x
160 + 57
126 +44
95 + 36
55 +26
Neat
15
y=583+ 883/x-1
498 + 93
526+ 69
469 + 77
452 + 107
514+ 71
262 + 88
>>
Below are given the results of experiments by Dr.
Böhme on the influence of the addition of various sub-
stances to cement. Some of these, such as gypsum,
have been added at times with an idea that they im-
proved the cement; others have been added occasionally
as adulterations. Slacked lime has sometimes been
used with cement in very cold weather. It will be seen
that, with the exception of sifted cement, every one of
these additions reduces the strength of the cement :-
"
PORTLAND CEMENT WITH VARIOUS ADDITIONS (BÖHME).
(A, Cement; B, Sifted cement; C, Fine sand; D, Slag; E, Brick-dust ;
F, Slack-lime.)
""
M
1
1 cement to 3 sand
y 199 +483/x-1
213 + 45
128 +65
128 +59
137 +58
155 +48
82 +44
189. Determination of the Setting Time.-The roughest
means of determining the time in which a cement sets
is to observe when a flat pat can no longer be indented
by the finger-nail. A more accurate method is to use a
LIMES AND CEMENTS
471
2
loaded needle or wire. Perhaps the French standard
test is as definite as any. The cement paste, as soon
as possible after gauging, is filled into a metal box
1½ inch deep and 3 inches diameter. Over this is
suspended, by a pulley and balance weight, a needle of
101 oz. weight, with a square section of 1 sq. mm. (side
of square, 0·04 inch). The cement is said to have taken
initial set when the needle fails to penetrate the whole
depth if lowered gently on it, and final set when its sur-
face just supports the needle. A cement commencing
to set in less than 30 minutes, or setting finally in less
than three hours from commencement of gauging, is re-
jected. For certain purposes quicker cements are useful.
In America a needle inch in diameter, loaded with
-1
12
1 lb., and a needle 24 inch in diameter, loaded with 1 lb.,
are used to determine setting time.
4
Effect of Time of Setting on the Qualities of a Cement.-
There is a prevalent opinion that quick-setting cements
do not continue long to gain in strength, but reach a
maximum, and then fall off, or diminish in strength.
This curious diminution in strength, often shown in
experiments, may be due to minute and imperceptible
cracks, but perhaps it is rather an error of testing
than a real loss of strength. The cement, no doubt,
gets more brittle, and that has the effect of making the
test more difficult, and increasing the chance of break-
ing the briquette with a load rather less than the real
tenacity.
Mr. Grant has given a table of tests of quick and
472
TESTING OF MATERIALS OF CONSTRUCTION
slow cements, which give the following characteristic
equations. Mr. Grant does not say, but I believe these
are 28-day tests of mortar gauged 1 to 3 of sand :—
Set, in
minutes
2289
10
20
30
45
Quick cements
y= 7+ 953/x-1
34 + 113
83+ 86
23+ 90
Set, in
hours
Gauged neat
1 cement to 3 sand
5
7
10
11
2
Quick cements
These results show that the slower cements have
very much greater initial strength than the quick
cements, but the quick cements in this table are some-
what exceptional. The means of four series of tests on
quick cements and four on slow cements, from Bau-
schinger's tables, give the following equations.
y = 183 + 483/x − 1
y= 76 +363/x 1
-
Slow cements
y = 166 +803/x-1
101 + 94
143 + 70
140 + 67
Slow cements
y = 220 + 55.3/x 1
y = 88+473/x-1
Here the slow cements have greater initial strength
and greater rate of gain with age than the quick cements,
but the difference is not so great as in Grant's table.
At any rate, the opinion is general that the slower
cements are more trustworthy. The German manufac-
turers propose different standard tests for quick and
slow cements, the standard being higher for the slow
cements.
190. Influence of Quantity of Water on the Strength of
Neat Cement and Cement Mortar.—A certain quantity of
LIMES AND CEMENTS
473
LBS.
500
water must be used in gauging cement or cement mortar,
which varies with the character of the cement. The
finest ground and quickest cements require most water.
Now, unfortunately, every drop of water added beyond
what is necessary weakens the cement, and this is the
chief source of the discrepancies which occur in cement-
testing. In purely commercial testing it is naturally
400
300
200
100
0
15
SLIGHTLY DAMP
20
DAMP
I YEAR
6 MONTHS
I WEEK
STIFF PASTE
25
FIG. 141.
/ MONTH/
SOFT
30
NEAT PORTLAND
GROUT
35
THIN CROIT
40
PER CENT
and not unfairly desired to get the best result possible
out of the cement. In this country the briquettes are
moulded on an impervious slab of slate or marble or
glass. The cement is gauged neat with the least amount
of water which will permit moulding, and the very stiff
paste into which the cement is formed is pressed into
the moulds as rapidly as possible. To get uniform
results the water used must be very accurately measured.
}

¡
I
1
|
i
i
{
1
474 TESTING OF MATERIALS OF CONSTRUCTION
¦
It varies from 18 to 25 per cent. of the weight of
cement.
In Fig. 141 are shown the results of some experi-
ments at Boston, on the same cement, mixed with
different proportions of water. The greatest strength
is obtained with between 20 and 25 per cent. of water.
The proportionate difference of strength as the time of
hardening increases is less; so that it is for short, one-
week tests that the quantity of water makes the greatest
difference.
191. Test for Soundness.-One of the most dangerous
qualities of a cement is a tendency to blow or crack
after setting, in consequence of expansion due to the
chemical actions which are going on. Expansion of
this kind, producing cracks, is commonly due to the
presence of unslacked lime in the cement; gypsum
added as an adulteration is open to the same objection.
These substances are the more dangerous that they
rather add to than detract from the strength of the
cement, and hence escape detection by the ordinary test.
That Portland cement does expand in hardening
may be shown easily by filling lamp glass chimneys
with the cement, and placing them for hardening in
water. With both neat cement and cement and sand the
chimneys invariably crack about the third day, and in
the course of ten days the glass is cracked all over.
1
The ordinary test for soundness is to make a pat or
cake, 2 or 3 inches in diameter and inch thick, with
thin edges, and place it in water. If the cake, in
LIMES AND CEMENTS
475
hardening, shows any tendency to crack or contort,
the cement is dangerous.
It is often extremely important to determine the
soundness of a cement in a shorter time than this pro-
cess requires. Now, heat accelerates greatly the harden-
ing process, and hence sometimes the pats of cement
are placed on an iron plate heated by a gas jet. Then
any tendency to crack shows itself in a short time.
This may be called the baking process. Tetmajer re-
commends that a pat 4 inches diameter and 3 inch thick
should be baked in a drying chamber at 120° C. for
three or four hours.
A still better process is to heat the pats in a steam
bath. Mr. Faija makes a convenient apparatus, consist-
ing of a double bath with regulated gas jet. The water
in the outer bath is kept at 110°, and the pats are placed
at first on a slip of glass in the steam, in the inner bath,
in vapour at about 100°. After five or six hours the
pat is hard enough to be placed in the water, and may
be kept cooking for twenty hours. If at the end of that
time the pat is still adherent to the glass, and without
cracks, the cement is perfectly sound.
German Standard Test.-The minimum tensile
strength of briquettes of 1 cement to 3 sand by weight,
after hardening 1 day in air and 27 days in water, is
2274 lbs. per sq. in. The crushing strength is 2,275 lbs.
per sq. in.
192. Measurement of Expansion of Cement.-Bau-
schinger took cubes of cement of 4.8 inches length of side.
476 TESTING OF MATERIALS OF CONSTRUCTION
I
10
Twenty-four hours after mixing, a small brass plate,
about inch diameter, was fixed into two opposite
sides of the cube, by cementing. After forty-eight
hours' hardening, the accurate measurements between
the brass plates were commenced. The cube was placed
in a measuring instrument, having a spring touch-lever
on one side and a micrometer screw on the other. The
touch-lever ensured the constancy of pressure between
the measuring points and the block to be measured.
The pitch of the screw was very accurately determined ;
and as a perfectly constant temperature cannot be insured
in experiments lasting a long time, a correction for the
expansion of the cement blocks by heat was determined.
Neat cement briquettes hardened in air sometimes
showed a small expansion at first, but all ultimately
shrank in volume. Neat cement briquettes hardened
in water all showed a very small expansion, generally
less than 05 m. in 120 mm. length in sixteen weeks.
With briquettes mixed with sand the changes of volume
were of the same kind, but smaller.
Quickness of Loading.-I believe Mr. Faija first
pointed out that the rate of loading a briquette affected
the breaking weight. The quicker a briquette is loaded,
the greater the load which can be got on before it
gives way. In some definite experiments, Mr. Faija
found a difference of 23 per cent. in the breaking
weight of exactly similar briquettes, broken quickly
and broken slowly. It is now generally recommended
that the weight should be added at the rate of 100 lbs.
LIMES AND CEMENTS
477
in fifteen seconds.¹ Mr. Adie has devised an ingenious
arrangement for regulating the speed of loading. Mr.
Deacon, I believe, puts half the probable breaking weight
on the briquette, and leaves it twelve hours, and then
completes the test.
193. Tests by Pressure.-Almost all that has been
said thus far relates to the ordinary mode of testing
cements and cement mortars by tensile stress. That mode
of testing was adopted for mere reasons of convenience.
The cement has only about one-tenth the strength in
tension which it has in compression. Hence, for tension
tests a small, cheap, easily managed testing machine can
be used. For compression tests, the testing machines.
must be much larger and more costly. But as a matter
of fact cement is but little used in positions in which its
resistance to tension is in play. The most important
works in which cement is used are expressly designed
to avoid tension in any part. If, indeed, in some
positions structures are exposed to the possibility of
tensile strains, due to failure of foundations or backing,
still the tensile stresses so developed are small com-
pared with the normal crushing stresses for which the
structure is designed.
Tension tests having been adopted, and being con-
venient no doubt, find defenders. Broadly speaking,
a cement with high tenacity will be strong to resist
crushing; but the correspondence in the resistance to
1 The German rate of loading is lb. per second, the briquettes being
0.775 sq. ins. section.
478
TESTING OF MATERIALS OF CONSTRUCTION
the two kinds of stress is far from exact. Bauschinger
has found that the ratio of resistance to crushing to re-
sistance to tension varies from eleven to one to seven to
one; and that the order of merit for cements tried for
tension is not the same as the order for crushing. It
has even been said that crushing tests are useless and
inaccurate. If they have proved so, it is only because
the proper conditions of accurate testing have been neg-
lected. In Bauschinger's tests of 5-inch cubes, the
results are considerably more uniform than the tests of
the same cements in small briquettes by tension.
In proper crushing experiments two conditions
must be fulfilled, which have hitherto been too much
neglected in crushing experiments. (1) The faces of
the block on which the crushing pressure acts must be
plane parallel surfaces. (2) The crushing pressure
must be uniformly distributed on those surfaces.
In moulded blocks of cement or cement concrete
the surfaces are hardly ever as parallel as is desirable.
The surfaces are generally more or less rough, and more
or less warped. By striking over the faces a thin layer
of gypsum or Parian cement, which sets immediately,
perfectly plane and parallel faces can be obtained, with-
out in any way altering the strength of the block.
Weak as these cements are, thin layers stand the crush-
ing pressure perfectly. To ensure the equal distribution
of the crushing pressure on the faces it is only necessary,
in a properly constructed testing machine, to interpose
a spherical joint between the block and the face of the
machine.
LIMES AND CEMENTS
479
It may be useful to examine if the rate of hardening
in pressure tests can be expressed as simply as that in
tension tests. In Bauschinger's paper already referred
to there are a series of pressure tests of the same series
of cements as that used in the tension tests.
fore-
1
The test pieces were cubes of 144 sq. cms. (22.3
sq. ins., or 4.75 inches length of side). Either from
the large size of the cubes, or the nature of the stress,
or some other cause, it is necessary to take n in the
general equation, instead of its value for tension. With
this change, the equation fits the compression results
satisfactorily. The equation for compression is there-
y = c + d √ x−1,
where y is the compressive strength in lbs. per sq. in.
at x weeks after mixing.
Cement
mark
ABCDEFGHRE
K
The equations obtained from Bauschinger's results
are as follow, the equations being all applicable to an
age of two years at least :-
с
Ꭱ
T
Neat cement
y =
1,877 +206/x − 1
953 +227
1,991 + 490
1,770 + 327
1,592 + 341
2,404 +299
1,582 + 270
1,436 + 334
2,631 +441
1,920 + 455
Mean 339
1 cement + 3 sand
y=
953+299/x- -1
313+248
1,038 +313
427 + 412
668 + 320
825 + 334
782 + 270
711 + 270
1,507 + 341
1,024 + 313
Mean 312
1 cement + 5 sand
y =
469 +299/x-1
199 +199
740 + 305
284 + 313
356 +263
540 + 284
483 + 249
341 + 256
995 + 341
626 +227
Mean 274
1
480
TESTING OF MATERIALS OF CONSTRUCTION
TESTS OF NINE-INCH CUBES OF PORTLAND CEMENT CONCRETE.
(When the block did not crush the greatest load is given in brackets. The dates in the second column are taken from Mr. Deacon's letter.)
No. of
block
Nov.
Dec.
Jan.
9
11 Mar.
3 May
June
June
Sept.
78a
CO TH LO co
4
5
6
2*# **2
12
13
14
18
19
20
Date of
moulding
21
22
23
24
25
Dec.
Mar.
June
Date of testing
1883 Dec. 2, 1885
1884 Nov. 27, 1885
1884 Dec. 2, 1885
1882 Nov. 30, 1885
1882 Dec. 3, 1885 |
1883 Dec. 1, 1885
9.02 × 8.93
8.95 × 8.96
8'96 × 9.02
1883 Nov. 28, 1885 8.93 x 8.99
1883 Nov. 12, 1885
1883 Nov. 12, 1885
1883 Nov. 13, 1885
1883 Nov. 13, 1885
9.02 × 8.95
9.05 x 9.05
8.82 × 9.02
8.98 × 9.00
June
Sep.
1885 Nov. 28, 1885
1885|Nov. 28, 1885
Sep. 22, 1885 Dec. 8, 1885
Sep. 29, 1885 Dec. 8, 1885
Oct. 14, 1885 Dec.
9, 1885
9, 1885
9, 1885
9, 1885
Mean horizontal Mean
dimensions
section
Oct. 27, 1885 Dec.
Nov. 4, 1885 Dec.
Nov. 11, 1885 Dec.
Inches
9.05 × 9·05
9.00 × 9.04
9.06 × 9.02
9.02 × 9.02
9.03 × 9.03
9.02 × 9.02
9.02 × 9.02
9.01 × 9.02
9.04 × 9.03
9.02 × 9.02
9.02 × 9.02
Sq. ft.
Load at
which
first Crushing
crack load
was ob.
served
Tons
90.3
•559
•557
.561
•558
•563 82.23 91.12
•569 41.80 81.08
•552 89.30 [100-10]
.561 29.35 62.69
72.95
Tons
94.86
54.00
•569
•565
•568 99.50
Time
between
moulding
and
testing
103.6
36
[104.52] 35
[104.16] 31
100.6
32
29/1/20
28/1/
99.51
92.4
106.33
Months
51.27 69.73
*565
•566
40.44
51.30
*565
50.10
63.32
•565
32.30
47.61 70
•564
44.50
53.52 56
64.68 43
•567 61.97
•565 60.50
•565 61.75
60.51 35
80.21 28
28/1/
25/
33223
20
17
10 2
5
77 days
""
35
""
""
*
""
Crushing
pressure
Tons per
sq. ft.
185.4
[187·6]
[185·7]
180.3
161.8
142.5
[181-3]
111.7
174.9
163.6
187.2
122.4
90.6
112.10
84.23
94.90
114.10
107.10
141.99
Crushed
between
Millboards
"
""
""
""
""
""
""
""
""
""
*
""
*
""
""
ง
""
,,
""
15
""
Remarks
[not crushed
Parian cement on top face;
Ditto, not crushed
Badly cracked, not crushed
Parian cement on top face
""
"
"",
""
""
""
""

LIMES AND CEMENTS
481
Here the first constant, which can be obtained by
tests lasting one week only, varies a good deal; but the
second constant has no very great range of variation
about its mean values. If the initial strength of the
cement is known therefore, the strength at any age up
to two years can be inferred with a certain degree of
approximation.
Strength of Concrete.-The table on opposite page,
from the Report of Mr. G. F. Deacon on the Vyrnwy
Masonry Dam, gives the strength of a series of nearly
cubical blocks of Portland cement concrete, made at
various dates during the progress of the work.
The following summary gives a general view of the
average strength at different ages :-
Age of block,
in months
32-36
28-29/1/
17-251/
2-5
1-2
Main strength.
in tons per sq. ft.
over
180
162
159
102
114
The blocks prepared with Parian cement to ensure
a plane face give rather higher crushing pressures than
the others. Some blocks cut out of the work itself
gave
crushing pressures somewhat greater still.
Detection of Adulteration.—The means of detecting
adulteration of cement have been examined by Drs. R.
and W. Fresenius. Adulteration by lime is shown by too
low a specific gravity, great loss by ignition, high alka-
linity of aqueous solution, and too great absorption of
I I
482 TESTING OF MATERIALS OF CONSTRUCTION
"
carbonic anhydride. An adulteration by slag is shown
by slightly lowered specific gravity, lowered alkalinity,
and by the large amount of chamaeleon solution which
may be added. The details of the methods of testing
are given in a paper abstracted recently for the Institute
of Civil Engineers.
Ay
3
INDEX.
ABB
ABBOTT, experiments on steel
castings, 336
Abel, Sir F., on hardening and
annealing, 298
Adamson, testing machine, 139
Admiralty experiments on effect of
temperature on strength, 349
Adulteration of cement, 481
Alloys, 341
Aluminium alloys, 347
Annealing, 296; tests of plates,
327; tests of steel castings, 334
Askenasy, deflectometer, 245
Autographic diagrams, time curves,
87; effect of removing load, 99;
elastic diagrams, 239, 242; time
extension curves, 243; of iron
and steel, 281; of hardened and
annealed steel, 298; of steel
castings, 337; of copper, 340;
of brass and bronze, 345
Autographic recording apparatus,
228, 243
BAILEY, testing machine, 152
Baker, B., on perforated and
nicked plates, 83; variation of
strength in pieces cut from one
plate, 294; endurance tests, 373;
on limits of working stress, 383
Barba's law, 75; on effect of
punching, 310
Barnaby, influence of temperature
on strength of iron and steel, 317
BOH
Basic steel, tests of, 326
Bauschinger, on yield point, 65;
raising of elastic limit, 98; in-
fluence of rest after loading, 101 ;
shackle for wood, 183; mirror
extensometer, 220; change of
elastic limit in successive load-
ings, 250; ín bars loaded beyond
yield point, 258; strength of
steel, 286; shearing tests of iron
and steel, 331; experiments on
repeated tensions, 375; variation
of elastic limit, 384; alternate
tensions and pressures, 389 ;
endurance tests, 393; strength
of timber, 397; influence of form
on crushing strength, 421; elastic
constants for stone, 429; strength
of stone, 432; of cement, 457;
expansion of cement, 475; crush-
ing strength of cement, 479
Bell-metal, 342
Belting, leather, strength of, 409
Bending and temper test, 163
Bending strength, of cast iron, 268;
of rails, 329; of copper, 339; of
brass and bronze, 343, 345; of
timber, 402, 405; of stone, 433
Bending stress, 35
Blue heat, influence on strength of
steel, 301
Onl
Board of Trade, tests of iron and
steel, 323; experiments
punched plates, 77
Böhme, tests of iron plates, 324;
of limes, 459; on addition of
484
TESTING OF MATERIALS OF CONSTRUCTION
BOH
various substances to cement,
470; on strength of masonry,
434; strength of brickwork, 439
Bottomley, hardening effect of
long-continued stress, 90
Bramah testing machine, 109, 125
Brasses, 344
Breaking stresses, 7
Brick, 410, 436
Brickwork, strength of, 439
Bronzes, 342
Buckton & Co., testing machine, 132
CAL
YALIBRATION of testing ma-
chine, 167
Carbon, in iron and steel, 259;
in cast iron, 261; influence on
steel, 285, 300, 319; in steel cast-
ings, 335
Cast iron, extension and compres-
sion of, 248; definition of, 259;
composition of, 261; properties
of, 264; tensile strength, 265;
crushing strength, 268; trans-
verse strength, 268; shearing
strength, 272; resistance to tor-
sion, 273
Cathetometer, 210; differential,
218
Cement, 441; tests for strength,
445; form of briquettes, 445;
gauging briquettes, 447; sand
and cement briquettes, 448; rate
of hardening, 449; characteristic
equation of, 450; shearing tests,
459; fineness of grinding, 459;
heaviness, 464; influence of kind
of sand used, 466; proportion of
sand, 469; setting time, 470;
quantity of water in gauging,
472; soundness, 474; expansion,
475; pressure tests, 477; adul-
teration, 481
Clarke, Elliot, on cements, 463, 469
DUP
Clay, on the effect of, in reworking
iron, 288
Coefficient of bending strength,
270; for cast iron, 271; for
bronzes, 343; for brasses, 345; for
timber, 402, 406; for stone, 433
of elasticity, 20, 246; for
different materials, 251; for
iron and steel, 252, 287; for
bronzes, 254, 343; for steel
castings, 337; for brasses, 345;
for delta metal, 346; for timber,
402, 406; for stone, 429
of volume, 29
of rigidity, 28, 253; determina-
tion by torsion, 35; for cast iron,
274; for iron and steel, 333
Cold rolling, effect of, 306
Compression of lead, copper, and
iron, 94
Concrete, tests of, 480
Considére, stresses in hardened
bars, 297; effect of cold working,
308; experiments on punching, 311
Contraction, local, 281; relation to
elongation, 84, 278
Copper, 339
Cowper, extensometer, 214
Creusot testing machine, 127
Cross-breaking, machines for, 162;
shackles for, 186
Crushing strength of cast iron, 268;
of stone, 435; of brick, 438; of
cement, 479
Curioni, strength of brickwork, 439
EFLECTION of a beam, 40
Deflectometer, 245
DE
Delta metal, 346.
Drawing out, 68; distribution along
bar, 72; suppression of, 77; in
bars broken by repetition of
stress, 379
Ductility, 18, 293, 302
Dupuy, extensometer, 217
INDEX
485
ELA
LASTIC constants, 246
ELASTIC
Elasticity, limits of, 6; raised
by stress, 98; influence of rest
after loading, 101; change in suc-
cessive loadings, 250; mode of de-
termining, 254; variation of, 384
Emery testing machine,
152;
shackles, 179
Endurance tests, 361
Ewing, time curves, 87; auto-
graphic arrangement, 231
Expansion of cement, 475
Extensions and compressions of
cast iron, 58; of steel, 60; of
indiarubber, 61; in bars of dif-
ferent lengths, 75; of stone, 429
Extensometer, 205, 206, 208
FAIJA, cement testing machine,
477; gauging machine for
cement, 448; test for soundness
of cement, 475
Fairbairn, testing machine, 126;
on cold rolling, 308
Fairbanks, testing machine, 120;
autographic apparatus, 232
Fineness of cement, 459
Flow of solids, 47, 96
Foster, tests of steel castings, 335
Frankel, extensometer, 243
Friction grips, 174
Friction of cup-leathers, 108
Frost, resistance of stone to, 428
GA
AUGING briquettes, 447
Gerber's parabola, 391
Grafenstaden testing machine, 122
Granite, 410
Grant on cement testing, 441, 446,
452, 456, 466
Greenwood & Batley, testing ma-
chine, 123
Gun-metal, 342
LOA
HAMMER hardening, 306
M
Hardness, determination of,
187
Hardening of cement, 449
of steel, 296
Heaviness of cement, 464
Henning & Marshall, extensometer,
206
Hercules metal, 347
Hill, strength of steel castings, 334
Hodgkinson, experiments on cast
iron, 58, 247; relation of stress
and strain in cast iron, 264;
crushing strength of cast iron,
268
Hydraulic limes, 442
INDIARUBBER,
curve of, 61
Ingot metal, 260, 276
Isotropy, 24
stress-strain
ENNEDY, on yield point, 65
stress-strain curves, 67; tor-
sion shackle, 185; lever extenso-
meter, 216; mirror extenso-
meter, 220; autographic appara-
tus, 240, 242; on form of test
bars, 294; tests of steel, 327
Kortum, rope shackle, 183
Lead, 341
LANZA, experiments on strength
of timber, 403
Lebasteur on tempering iron and
steel, 300
Limes, 441
Loading, influence of rate of, in
testing, 291, 476
486
TESTING OF MATERIALS OF CONSTRUCTION
MAI
MAILLARD, testing machine,
123, shackles, 180
Maitland, Col., influence of time in
testing, 89; on oil hardening, 297
Malleable cast iron, 274
Mallet, tests of heavy forgings, 290
Manganese in steel, 277, 286, 300
Martens, testing machine, 120
Masonry, strength of, 434
Measuring instruments, 192; for
strains, 199
Millar, strength of cast iron, 270
Milton, effect of quenching on
steel, 299
Mitis castings, 337
Modulus of section, 42
Moment of inertia, 42
Monge balance, 163
Morin and Tresca on bending, 37
OLSEN,
LSEN, testing machine, 142
PAR
ARKER, W., effect of bending
on strength of steel, 309; on
steel castings, 335
Phosphor bronze, 354
Phosphorus in steel, 277, 301; in
copper, 339
Pin grips, 172
Pipes, testing of, 165
Plasticity, 17, 45, 53, 96
Platt and Hayward, on strength of
cast iron, 273; on iron and steel,
332
Poisson's ratio, 20
Polmeyer, autographic apparatus,
231
Porosity of stone, 426
Preece, strength of wire, 352
Pressure of fluidity, 46, 52
Pressure tests of cement, 477
Proportionality, limit of, 256
Punching, 47, 78, 310
STE
AILS, tests of, 327
Repetitions of load, 356
RAIL
Ꭱ
Richard, measuring machine, 199
Richard's experiments on perforated
plates, 80
Ricketts on malleable cast iron, 274
Riehle, testing machine, 122;
wedges, 177
ST.
T. CHAMOND testing machine,
127
Sand, standard, for cement-testing,
449
Sandberg on rail tests, 329
Screw bolts, strength of, 351
Screw micrometer, 194; extenso-
meter, 205
Self on aluminium bronze, 347
Sensitiveness of testing machine,
111, 169
Shackles for tension, 171; for
crushing, 184; for torsion, 185;
for shearing, 186; for cross-
breaking, 186; for indenting, 187
Shearing stress, 25; tests of iron
and steel, 331; of cement, 458
Sieves for cement and sand, 449
Silicon in cast iron, 262
Spangenberg, endurance tests, 372
Steel, extension and compression
of, 249; composition of, 277;
castings, 277; influence of car-
bon, 285; hardening, tempering,
and annealing, 296; influence of
carbon, manganese, and phos-
phorus on properties, 300 ; in-
jurious effect of blue heat, 301;
influence of temperature on
strength, 313; Styffe's experi-
ments, 319; Steel Committee's
experiments, 319; Board of
Trade experiments, 323; shear-
ing strength, 332; torsional
strength, 333
INDEX
487
STE
Steel castings, 333
Steel Committee's experiments, 319
Stone, 410; influence of bedding
on crushing strength, 416;
strength of stone, 412; porosity,
426; Bauschinger's experiments,
433; crushing strength, 435
Straightedge, 192
Streinitz, differential cathetometer,
218
Stress-strain curve, correction of, 91
Stress-strain diagrams, 56; for
brittle material, 58; for elastic
material, 60; for ductile material,
63, 94. See also Autographic
diagrams
Strohmeyer, experiments on per-
forated plates, 79 ; roller extenso-
meter, 223; on influence of blue
heat, 302
Styffe, definition of elastic limit,
255; on properties of iron and
steel, 285; influence of tempera-
ture on strength, 314; experi-
ments on iron and steel, 318
Superposition of stresses, 23
Sweet, Professor, micrometer, 196
TANGYE, testing machine, 162
Tempering steel, 296
Temper test, 163
Temperature, effect on strength of
iron and steel, 313; on alloys, 348
Test bars, 188, 292, 446
Testing machines, 106; types of,
119; Woolwich machine, 125;
single-lever machines, 128; com-
pound-lever machines, 139;
Union Bridge Co.'s machine,
143; manometer machines, 148;
emery machines, 152; special
machines, 161; cement-testing
machines, 446
Tests of cement, 440; of pipes, 165
UNW
Tetmajer, tests of rails, 350
Thalen on elastic limit, 255
Thomasset, testing machine, 121,
148
Thurston, extensometer, 205; tor-
sion machine, 229; on copper,
339; on bronzes, 342 ; on brasses,
344; on other alloys, 345
Timber, 394; strength of small
specimens, 397; elasticity of,
397; tensile strength of, 401;
crushing strength of, 402; bend-
ing strength of, 402; American
tests, 403; strength of posts,
404; of beams, 405; shearing
strength, 407; influence of time
on strength, 408
Time, influence in testing, 291, 476;
on strength of timber, 408
Tin, 341
Torsion, 31; machine, 161; shackle,
185; of cast iron, 273; of iron
and steel, 331
Touch micrometer, 212
Tresca on plasticity, 46
Turner on cast iron, 262
UCHATIUS,
[CHATIUS, strength of bronze,
349
Union Bridge Company's testing
machine, 143
Unwin, extensometer, 208; touch
micrometer, 212; mirror extenso-
meter, 222; instrument for
measuring compressions, 225;
autographic apparatus, 235; elec-
tric semi-autographic apparatus,
238; change of ductility in steel
when worked hot, 304; experi-
ments on steel castings, 337; on
delta metal, 346; on aluminium
bronze, 348; on wire, 355; on
strength of stone, 417; on porosity
of stone, 428
488
TESTING OF MATERIALS OF CONSTRUCTION
I
VER
VE
ERNIER calipers, 193
Vicat on strength of stone
blocks, 424
Viscosity of solids, 100
WADE, testing machine, 127;
strength of cast iron, 268
Watertown testing machine, 152
Wear, resistance of stone to, 429
Webb on working steel at colour
heat, 306
Wedge gauge, 204
Weld iron, 261, 276
Werder, testing machine, 123, 128
Wertheim on elastic limit, 255
Whitworth measuring machine, 198
Wicksteed, testing machine, 120;
apparatus, 233;
autographic
shackles, 175
Wire, strength of, 352
Wöhler's experiments on repetition
of stress, 356
Woolwich testing machine, 125
Work done in tension and compres-
sion, 21; in plastic deformation,
54; measured from stress-strain
diagram, 104
Working stress, 9; history of limits
adopted, 380
ZIN
Wrought iron, composition of, 276;
tenacity, 278; effect of reworking,
288; effect of cold rolling, 308;
effect of temperature, 314; tensile
strength, 318; tests of, 324;
shearing strength, 332; torsional
strength, 333
YIELD point, 10, 64
Young's modulus, 20; deter-
mination by bending, 44
Z
INC, 341
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SPOTTISWOODE AND CO., NEW-STREET SQUARE
LONDON
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DANTE.—La Commedia di Dante.
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LIONEL W. LYDE,
W. LYDE, M.A.
With 3
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bility-Both or Neither. By the
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MACAULAY (Lord).—WORks of.
Complete Works of Lord Ma-
caulay :
Library Edition, 8 vols. 8vo. £5 5s.
Cabinet Edition, 16 vols. Post 8vo. £4 16s.
}
History of England from the
Accession of James the
Second:
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Critical and Historical Essays,
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3s. 6d. gilt edges.
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Essays which may be had separately
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Ranke and Gladstone.
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Lord Bacon.
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Lord Byron, and The Comic Dramatists of
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[Continued on next page.
14
*
善
​A CATALOGUE OF BOOKS IN GENERAL LITERATURE.
MACAULAY (Lord).—WORKs of.-
continued.
Miscellaneous Writings and
Speeches:
QUE
Popular Edition, I vol. Crown Svo. 2s. 6d.
Student's Edition, in 1 vol. Crown Svo. 6s.
Cabinet Edition, including Indian Penal
Code, Lays of Ancient Rome, and Mis-
cellaneous Poems, 4 vols. Post 8vo. 24s.
Selections from the Writings
of Lord Macaulay. Edited,
with Occasional Notes, by the Right Hon.
Sir G. O. TREVELYAN, Bart. Cr. 8vo. 6s.
The Life and Letters of Lord
Macaulay. By the Right Hon.
Sir G. O. TREVELYAN, Bart.:
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Cabinet Edition, 2 vols. Post 8vo. 12s.
Library Edition, 2 vols. 8vo. 36s.
MACDONALD (Geo.).—WORKS BY.
Unspoken Sermons. Three
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The Miracles of Our Lord.
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A Book of Strife, in the Form
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Poems.
12mo. 6s.
MACFARREN (Sir G. A.).—WORKS
BY.
Lectures on Harmony. 8vo. 12s.
MACKAIL.-SelectEpigrams from
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MACLEOD (Henry D.).- WORKS BY.
The Elements of Banking.
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The Theory of Credit.
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Vol. I. 7s. 6d.; Vol. II. Part I. 4s. 6d. ;
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MºCULLOCH.-The Dictionary of
Commerce and Commercial Navi-
gation of the late J. R. MCCULLOCH.
8vo. with 11 Maps and 30 Charts, 63s.
MACVINE. Sixty-Three Years'
Angling, from the Mountain
Streamlet to the Mighty Tay. By JOHN
MACVINE. Crown 8vo. Ios. 6d.
MALMESBURY.-Memoirs of an
Ex-Minister. By the Earl of
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MANNERING. With Axe and
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NERING. With 18 Illustrations.
8vo.
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MANUALS
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Natural Theology. By BERNARD
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Political Economy. By CHARLES
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MARBOT.-The Memoirs of the
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MAUNDER'S TREASURIES.
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The Gladiators.
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MENDELSSOHN.-The Letters of
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16
!
A CATALOGUE OF BOOKS IN GENERAL LITERATURE
MERIVALE (The Very Rev. Chas.).— | MOORE.-Dante and his Early
WORKS BY.
Biographers. By EDWARD
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History of the Romans under
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Popular Edition, 8 vols. Cr. 8vo. 3s. 6d. each.
The Fall of the Roman Republic:
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General History of Rome from
B.C. 753 to A.D. 476. Cr. 8vo. 7s. 6d.
The Roman Triumvirates. With
Maps. Fcp. 8vo. 2s. 6d.
MILES. The Correspondence of
William Augustus Miles on
the French Revolution, 1789-
1817. Edited by the Rev. CHARLES
POPHAM MILES, M.A. 2 vols. 8vo. 32s.
MILL.-Analysis of the Pheno-
mena of the Human Mind.
By JAMES MILL. 2 vols. 8vo. 28s.
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Principles of Political Economy.
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Utilitarianism. 8vo. 5s.
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trated. Crown 8vo. 5s.
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The Story of a Spring Morning,
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Stories of the Saints for Chil-
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NANSEN.-The First Crossing of
Greenland. By Dr. FRIDTJOF
NANSEN. With 5 Maps, 12 Plates, and
150 Illustrations in the Text. 2 vols.
8vo. 36s. Cheaper Edition, abridged.
With numerous Illustrations and a Map.
In I vol. crown 8vo. 7s. 6d.
NAPIER.-The Life of Sir Joseph
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cellor of Ireland. By ALEX.
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NAPIER.-The Lectures, Essays,
and Letters of the Right Hon.
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NESBIT.-Leaves of Life: Verses.
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Lays and Legends. By E. NESBIT
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NEWMAN.-The Letters and Cor-
respondence of John Henry
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English Church. With a brief Autobio-
graphical Memoir. Arranged and Edited
by ANNE Mozley. With Portraits.
vols. 8vo. 30s. net.
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Apologia pro Vitâ Sua. Cabinet
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Discourses to Mixed Congrega-
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Sermons on Various Occasions.
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[Continued on next page.
PUBLISHED BY MESSRS. LONGMANS, GREEN, & CO.
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›
NEWMAN (Cardinal).— WORKS BY. | NEWMAN (Cardinal).—WORKS OF.—
continued.
Loss and Gain: a Tale.
Edition, Crown 8vo. 6s.
Crown 8vo. 35. 6d.
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Historical Sketches.
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3
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The Arians of the Fourth Cen-
tury. Cabinet Edition, Crown
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Select Treatises of St. Athan-
asius in Controversy with the
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Discussions and Arguments on
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An Essay in Aid of a Grammar
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Present Position of Catholics in
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Callista: a Tale of the Third Cen-
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Cabinet
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Essays on Biblical and on Ec-
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Tracts. 1. Dissertatiunculæ. 2. On
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A CATALOGUE of BOOKS IN GENERAL LITERATURE
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Hard Knots in Shakespeare.
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POOLE.-Cookery for the Diabetic.
By W. H. and Mrs. POOLE. With Pre-
face by Dr. PAVY. Fcp. 8vo. 2s. 6d.
PRAEGER.-Wagner as I knew
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Crown 8vo. 7s. 6d.
PRATT. To the Snows of Tibet
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PROCTOR (R. A.).— Works by.
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[Continued on next page.
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PROCTOR (R. A.).—WORKS BY.-
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RICHARDSON.-National Health.
Abridged from 'The Health of Nations'.
A Review of the Works of Sir Edwin
Chadwick, K.C.B. By Dr. B. w.
RICHARDSON, Crown, 4s. 6d.
RILEY.-Athos; or, the Mountain
of the Monks. By ATHELSTAN RILEY,
M.A., F.R.G.S. With Map and 29
Illustrations. 8vo. 21s.
RILEY-Old-Fashioned
Poems.
RILEY.
Roses:
By JAMES WHITCOMB
12mo. 55.
RIVERS.-The Miniature Fruit
Garden; or, The Culture of Pyra-
midal and Bush Fruit Trees. By THOMAS
and T. F. RIVERS. With 32 Illustrations.
Crown 8vo. 45.
RIVERS.-The Rose Amateur's
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Fcp. 8vo. 4s. 6d.
ROBERTSON. The Kidnapped
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ROCKHILL.-The Land of the
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ROGET.-A History of the 'Old
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ROMANES. Darwin, and after
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tions. Crown Svo. Ios. 6d.
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tions. Crown 8vo. 10s. 6d.
ROUND.
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ville: a Study of the Anarchy.
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Early Life of Anne Boleyn: a Critical
Essay'. 8vo. 16s,
RUSSELL.-A Life of Lord John
Russell (Earl Russell, K.G.).
By SPENCER WALPOLE. With 2 Por-
traits. 2 vols. 8vo. 36s. Cabinet Edition,
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20
A CATALOGUE of books in geNERAL LITERATURE
SEEBOHM (Frederic).— WORKS BY.
The Oxford Reformers-John
Colet, Erasmus, and Thomas
More; a History of their Fellow-
Work. Svo. 145.
The English Village Commu-
nity Examined in its Relations to
the Manorial and Tribal Systems, &c. 13
Maps and Plates. 8vo. 16s.
The Era of the Protestant
Revolution. With Map. Fcp.
8vo. 2s. 6d.
SEWELL.-Stories and Tales. By
ELIZABETH M. SEWELL. Crown Svo.
Is. 6d. each, cloth plain; 2s. 6d. each,
cloth extra, gilt edges :-
Amy Herbert.
The Earl's Daughter.
The Experience of Life.
AGlimpse of the World.
Cleve Hall.
Laneton Parsonage.
Ursula.
Gertrude.
Ivors.
Home Life.
After Life.
Katharine Ashton.
Margaret Percival.
Family Shakespeare.
Bowdler's
1 Vol.
8vo. With 36 Woodcuts, 14s. or in 6
vols. Fep. 8vo. 21s.
Outlines of the Life of Shake-
speare. By J. O. HALLİWELL-
PHILLIPPS. With numerous Illustrations
and Fac-similes. 2 vols. Royal 8vo. £I IS.
A Calendar of the Halliwell-
Phillipps' Collection of Shake-
spearean Rarities Formerly
Preserved at Hollingbury Copse, Brighton.
Enlarged by ERNEST É. BAKER, F.S.A.
8vo. 10s. 6d.
SHAKESPEARE.
Shakespeare's True Life.
By
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Imp. 8vo. 21S.
The
Shakespeare Birthday
Book. BY MARY F. Dunbar.
32mo. Is. 6d. cloth. With Photographs,
32mo. 55. Drawing-Room Edition, with
Photographs, Fcp. 8vo. 10s. 6d.
SIDGWICK.--Distinction: and the
Criticism of Belief. By ALFRED SIDG-
WICK. Crown 8vo. 6s.
SILVER LIBRARY (The).
Crown 8vo. 35. 6d. each volume.
Baker's (Sir S. W.) Eight Years in
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Baker's (Sir S. W.) Rifle and Hound in
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SILVER
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LIBRARY
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Baring-Gould's (Rev. S.) Origin and
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Brassey's (Lady) A Voyage in the 'Sun-
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3s. 6d.
Clodd's (E.) Story of Creation: a Plain
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Conybeare (Rev. W. J.) and Howson's
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St. Paul. 46 Illustrations. Crown 8vo.
3s. 6d.
Dougall's (L.) Beggars All: a Novel.
Crown 8vo. 35. 6d.
A
Doyle's (A. Conan) Micah Clarke.
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3s. 6d.
Froude's (J. A.) Short Studies on Great
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Froude's (J. A.) Cæsar: a Sketch. 3s. 6d.
Froude's (J. A.) Thomas Carlyle: a
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Froude's (J. A.) The Two Chiefs of
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Gleig's (Rev. G. R.) Life of the Duke
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Haggard's (H. R.) She: A History of
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Haggard's (H. R.) Allan Quatermain.
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Haggard's (H. R.) Colonel Quaritch,
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Haggard's (H. R.) Beatrice. 3s. 6d.
Howitt's (W.) Visits to Remarkable
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Jefferies' (R.) The Story of My Heart:
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Jefferies' (R.) Field and Hedgerow. Last
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Jefferies' (R.) Red Deer.
3s. 6d.
With 17 Illus-
trations by J. CHARLTON and H.
TUNALY. Crown 8vo. 35. 6d.
Knight's (E. F.) The Cruise of the
Alerte' the Narrative of a Search for
Treasure on the Desert Island of Trinidad.
With 2 Maps and 23 Illustrations. Crown
Svo. 3s. 6d.
Lees (J. A.) and Clutterbuck's (W. J.),
B. C. 1887, A Ramble in British
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tions.
3s. 6d.
[Continued on next page.
published BY MESSRS. LONGMAns, green, & CO.
21
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continued.
Macaulay's (Lord) Essays and Lays.
With Portrait and Illustration.
3s. 6d.
Macleod's (H. D.) The Elements of
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Marshman's (J. C.) Memoirs of Sir
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Max Müller's (F.) India, what can it
teach us? Crown 8vo. 3s. 6d.
Merivale's (Dean) History
Romans under the Empire.
3s. 6d. each.
LIBRARY
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of the
8 vols.
Mill's (J. S.) Principles of Political
Economy. 35. 6d.
Mill's (J. S.) System of Logic 3s. 6d.
Newman's (Cardinal) Historical
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Newman's (Cardinal) Apologia Pro
Vitâ Sua. 3s. Cd.
a Tale
Newman's (Cardinal) Callista :
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3s. 6d.
Newman's (Cardinal) Loss and Gain:
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Newman's (Cardinal) Essays, Critical
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Newman's (Cardinal) An Essay on the
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Newman's (Cardinal) The Present Posi-
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Newman's (Cardinal) Parochial and
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Newman's (Cardinal) Selection, adapted
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(
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Newman's (Cardinal) Difficulties felt by
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Newman's (Cardinal) Biblical and
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A
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Newman's (Cardinal) The Arians of
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continued.
Newman's (Cardinal) Lectures on the
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Newman's
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Phillipps-Wolley's (C.) Snap: a Legend
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tious. 3s. Ed.
to
Stanley's (Bishop) Familiar History of
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35. 6d.
Stevenson (R. L.) and Osbourne's (Ll.)
The Wrong Box. Crown 8vo. 3s. 6d.
Weyman's (Staniey J.) The House of
the Wolf: a Romance. Cr. 8vo. 35. 6d.
Wood's (Rev. J. G.) Petland Revisited.
With 33 Illustrations.
35. 6d.
Wood's (Rev. J. G.) Strange Dwellings:
With 60 Illustrations.
35. 6d.
Wood's (Rev. J. G.) Out of Doors.
II Illustrations. 3s. Ed.
SMITH (R. Bosworth).--Carthage
and the Carthagenians. By
Maps,
R. BOSWORTH SMITH, M.A.
Plans, &c. Crown 8vo. 6s.
STEEL (J. H.).—-WORKS BY.
A Treatise on the Diseases of
the Dog; being a Manual of
Canine Pathology.
Svo. 10s. 6d.
SS Illustrations.
A Treatise on the Diseases of
the Ox; being a Manual of
Bovine Pathology. 2 Plates and 117
Woodcuts. 8vo. 15s.
A Treatise on the Diseases of
the Sheep; being a Manual of
Ovine Pathology. With Coloured Plate
and 99 Woodcuts. 8vo. 125.
STEPHEN.-Essays in Ecclesi-
astical Biography. By the
Right Hon. Sir J. STEPHEN. Crown
8vo. 7s. 6d.
STEPHENS.-A History of the
French Revolution. By H.
MORSE STEPHENS, Balliol College,
Oxford. 3 vols. 8vo. Vols. I. and II. 18s.
each.
22
A CATALOGUE OF BOOKS IN generaL LITERATURE
STEVENSON (Robt. Louis).—WORKS | SYMES (J. E.).—WORKS BY.
BY.
A Child's Garden of Verses.
Small Fcp. 8vo. 5s.
A Child's Garland of Songs,
Gathered from A Child's Garden of
Verses'. By ROBERT LOUIS STEVEN-
SON, and set to Music by C. VILLIERS
STANFORD, Mus. Doc. 4to. 2s. sewed,
3s. 6d. cloth gilt.
The Dynamiter.
sewed; 1s. 6d. cloth.
Fcp. 8vo. Is.
Strange Case of Dr. Jekyll and
Mr. Hyde. Fcp. 8vo. is. swd.;
Is. 6d. cloth.
STOCK.-Deductive Logic. By
ST. GEORGE STOCK. Fcp. 8vo. 3s. 6d.
STEVENSON and
OSBOURNE.—
The Wrong Box. By ROBERT THOMPSON (D. Greenleuf).—WORKS
BY.
LOUIS STEVENSON
and LLOYD OS-
BOURNE. Crown 8vo. 3s. 6d.
' STONEHENGE--The Dog in
Health and Disease. By
STONEHENGE'. With 84 Wood En-
gravings. Square Crown Svo. 7s. 6d.
STRONG, LOGEMAN, and
WHEELER.—Introduction to
the Study of the History of
Language. By HERBERT A.
STRONG, M.A., LL.D.; WILLEM S.
LOGEMAN; and BENJAMIN IDE
WHEELER.
Svo. Ios. 6d.
Prelude to Modern History:
being a Brief Sketch of the World's
History from the Third to the Ninth
Century. With 5 Maps. Crown 8vo.
2s. 6d.
The Teacher's Handbook of
Psychology, on the Basis of
Outlines of Psychology'. Cr. 8vo. 5s.
Supernatural Religion; an In-
quiry into the Reality of Divine Reve-
lation. 3 vols. 8vo. 36s.
Reply (A) to Dr. Lightfoot's
Essays. By the Author of ' Super-
natural Religion'. 8vo. 6s.
A Companion to School His-
tories of England. Crown
8vo. 2s. 6d.
Political Economy. With Prob-
lems for Solution, and Hints for Sup-
plementary Reading. Crown Svo. 2s. 6d.
TAYLOR.-A Student's Manual of
the History of India. By
Colonel MEADOWS TAYLOR, C.S.I., &c.
Crown 8vo. 7s. 6d.
SWINBURNE.-Picture Logic; an
Attempt to Popularise the Science of
Reasoning. By A. J. SWINBURNE, B. A.
Post 8vo. 5s.
The Problem of Evil: an Intro-
duction to the Practical Sciences. 8vo.
IOS. 6d.
A System of Psychology. 2 vols.
8vo. 36s.
The Religious Sentiments of
the Human Mind. 8vo. 7s..6d.
Social Progress: an Essay. 8vo.
7s. 6d.
The Philosophy of Fiction in
Literature: an Essay. Cr. 8vo. 6s.
Three in Norway.
By Two of
THEM. With a Map and 59 Ilustrations.
Cr. 8vo. 2s. boards; 2s. 6d. cloth.
THOMSON.
Outlines of the
Necessary Laws of Thought:
a Treatise on Pure and Applied Logic.
By the Most Rev. WILLIAM THOMSON,
D.D., late Lord Archbishop of York.
Post 8vo. 6s,
SULLY (James).- WORKS BY.
The Human Mind: a Text-Book
of Psychology. 2 vols. 8vo. 215.
Outlines of Psychology.
With
Special Reference to the Theory of Edu- TIREBUCK.-Dorrie: a Novel. By
cation. Svo. IOS.
WILLIAM TIREBUCK. Crown 8vo. 6s.
TOYNBEE.-Lectures on the In-
dustrial Revolution of the
18th Century in England.
By ARNOLD TOYNBEE. 8vo. 10s. 6d.
TREVELYAN (Sir G. O., Bart.).—
WORKS BY.
A
The Life and Letters of Lord
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POPULAR EDITION, Crown 8vo. 2s. 6d.
STUDENT'S EDITION, Crown 8vo. 6s.
CABINET EDITION, 2 vols. Cr. 8vo. 12s.
LIBRARY EDITION, 2 vols. 8vo. 36s.
[Continued on next page,
PUBLISHED BY MESSRS. LONGMANS, GREEN, & CO.
23
TREVELYAN (Sir G. O., Burt.).—
WORKS BY.--continued.
VERNEY.-Memoirs of the Ver-
ney Family during the Civil
War. Compiled from the Letters
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don House, Bucks. By FRANCES PAR-
THENOPE VERNEY. With a Preface by
S. R. GARDINER, M.A., LL.D. With
38 Portraits, Woodcuts and Facsimile.
2 vols. Royal 8vo. 42s.
The Early History of Charles
James Fox. Library Edition,
8vo. 18s. Cabinet Edition, Cr. 8vo. 6s.
TROLLOPE(Anthony).—NOVELS BY.
The Warden. Crown 8vo. IS.
boards; Is. 6d. cloth.
Barchester Towers. Crown 8vo. | WELLINGTON.-Life of the Duke
Is. boards; Is. 6d. cloth.
of Wellington. By the Rev. G.
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WELLS. Recent Economic
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and the Well-being of Society. By
DAVID A. WELLS. Crown 8vo. 10s. 6d.
VILLE. The Perplexed Farmer:
How is he to meet Alien Competition?
By GEORGE VILLE. Translated from the
French by WILLIAM CROOKES, F.R.S.,
V.P.C.S., &c. Crown 8vo. 5s.
_____
VIRGIL.-Publi Vergili Maronis
Bucolica, Georgica, Æneis;
The Works of VIRGIL, Latin Text, with
English Commentary and Index.
By
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The Eneid of Virgil. Translated
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TON, M.A. Crown 8vo. 6s.
WAKEMAN and HASSALL.—
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Study of English Constitu-
tional History. By Resident
Members of the University of Oxford.
Edited by HENRY OFFLEY WAKEMAN,
M.A., and ARTHUR HASSALL, M.A.
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WALKER.-The Correct Card; or
How to Play at Whist; a Whist Cate-
chism. By Major A. CAMPBELL-
WALKER, F.R.G.S. Fcp. 8vo. 2s. 6d.
WALPOLE-History of England
from the Conclusion of the
Great War in 1815 to 1858.
By SPENCER WALPOLE. Library Edition.
5 vols. 8vo. £4 IOS. Cabinet Edition.
6 vols. Crown 8vo. 6s, each.
WALFORD. The Mischief of
Monica: a Novel. By L. B.
WALFORD. Crown 8vo. 6s.
me pl
The Poems of Virgil. Translated
into English Prose. By JOHN CONING-
TON, M.A. Crown 8vo. 6s.
The Eclogues and Georgics of
Virgil.
BY.
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Latin by J. W. MACKAIL, M. A., Fellow
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Dutch Hand-made Paper. Royal 16mo.
55.
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Papers on Maritime
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By ERNEST
EMIL WENDT. Royal Svo. £I IIS. 6d.
WEST.-Half-hours with the Mil-
lionaires: Showing how much
harder it is to spend a million than to
Edited by B. B. WEST. Crown
make it.
8vo. 6s.
WEYMAN.-The House of the
Wolf: a Romance. By STANLEY
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WHATELY (E. Jane).-WORKS BY,
English Synonyms. Edited by
R. WHATELY, D.D. Fcp. 8vo. 3s.
Life and Correspondence of
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WORKS
Elements of Logic. Crown 8vo.
4s. 6d.
Elements of Rhetoric.
Crown
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Lessons on Reasoning.
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Bacon's Essays, with Annotations.
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Whist in Diagrams: a Supplement
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24
A CATALOGUE OF BOOKS IN GENERAL LITERATURE.
WILCOCKS.—The Sea Fisherman,
Comprising the Chief Methods of Hook
and Line Fishing in the British and other
Seas, and Remarks on Nets, Boats, and
Boating. By J. C. WILCOCKS. Pro-
fusely illustrated. Crown 8vo. 6s.
WILLICH.-Popular Tables for
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value of Lifehold, Leasehold, and Church
Property, the Public Funds, &c. By
CHARLES M. WILLICH. Edited by
H. BENCE JONES. Crown 8vo. 10s. 6d.
its Big Game.
WILLOUGHBY.-East Africa and
By Capt. Sir
JOHN C. WILLOUGHBY, Bart. Illus-
trated by G. D. Giles and Mrs. Gordon
Hake. Royal 8vo. 21s.
WITT (Prof.).—WORKS BY. Trans-
lated by FRANces Younghusband.
The Trojan War. Crown 8vo. 25.
Myths of Hellas; or, Greek Tales.
Crown 8vo. 35. 6d.
The Wanderings of Ulysses.
Crown 8vo. 3s. 6d.
The Retreat of the Ten Thou-
sand; being the story of Xeno-
phon's Anabasis'. With Illustrations.
Crown 8vo. 3s. 6d.
C
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Rambles in the Black Forest.
Crown 8vo. 7s. 6d.
The Watering Places of the
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The Country of the Vosges.
With a Map. 8vo. 12s.
WOOD (Rev. J. G.).-WORKS BY.
Homes Without Hands; a De-
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classed according to the Principle of Con-
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7s. net.
Insects at Home; a Popular
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ture, Habits, and Transformations. With
700 Illustrations. 8vo. 7s. net.
10,000/6/92.
Insects Abroad; a Popular Account
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Habits, and Transformations.
600 Illustrations. 8vo. 75. net.
With
WOOD (Rev. J G.).—Works by.—
continued.
Bible Animals; a Description of
every Living Creature mentioned in the
Scriptures. With 112 Illustrations. 8vo.
7s. net.
Strange Dwellings; a Description
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Out of Doors; a Selection of
Original Articles on Practical Natural
History. With 11 Illustrations. Crown
8vo. 3s. 6d.
With 33
Petland Revisited.
Illustrations. Crown 8vo. 3s. 6d.
WORDSWORTH.-Annals of My
Early Life, 1806-46. By
CHARLES WORDSWORTH, D.C.L.,
Bishop of St. Andrews. 8vo. 15s.
WYLIE.-History of England
under Henry IV. By JAMES
HAMILTON WYLIE. 2 vols. Vol. I.,
1399-1404. Crown 8vo. 10s. 6d. Vol. II.
[In the Press.
YOUATT (William).—WORKS BY.
The Horse. Revised and enlarged.
8vo. Woodcuts, 7s. 6d.
The Dog.
Revised and enlarged.
8vo. Woodcuts, 6s.
ZELLER (Dr. E.).—WORKS by.
History of Eclecticism in Greek
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The Stoics, Epicureans, and
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Plato and the Older Academy.
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Outlines of the History of Greek
Philosophy. Translated by
F.
ALLEYNE and EVELYN
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ABBOTT.
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