CONCRETE
DESIGNERS' MANUAL
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CONCRETE
DESIGNERS' MANUAL
TABLES AND DIAGRAMS FOR THE DESIGN
OF
REINFORCED CONCRETE STRUCTURES
BY
GEORGE A. HOOL, S.B.
CONSULTING ENGINEER, PROFESSOR OF STRUCTURAL, ENGINEERING,
THE UNIVERSITY OF WISCONSIN
AND
CHARLES S. WHITNEY, M.C.E.
STRUCTURAL ENGINEER MT- r A UXEE r WI8.
FIRST EDITION
McGRAW-HILL BOOK COMPANY, INC.
NEW YORK: 370 SEVENTH AVENUE
LONDON: 6 & 8 BOUVERIE ST., E. C. 4
1921
H k7
COPYRIGHT, 1921, BY THE
McGRAW-HiLL BOOK COMPANY, INC.
THE MAPL>: I'KKHS YORK PA
PREFACE
The tables and diagrams presented in this manual make possible the rapid design-
ing of reinforced concrete structures in accordance with the Joint Committee Recom-
mendations, the American Concrete Institute Recommendations, the New York
Building Code Requirements and the Chicago Building Code Requirements. Some
of these tables and diagrams will also be found of such a general nature that they
can be used when the designing requirements are different from any of those men-
tioned. No tables are presented based on the flat slab recommendations of the
Joint Committee as these recommendations are so conservative that they are not
used to any extent.
The authors have for some time been preparing and using in their practice various
tables and diagrams in order to finally obtain complete data in the most convenient
form and of the greatest value to the majority of designing engineers. The collection
given in this book is the result.
No attempt has been made to develop theory or to duplicate information not
directly relating to concrete design which can conveniently be found hi other hand-
books possessed by all designers.
G. A. H.
April, 1921. C. S. W.
47789
CONTENTS
PAGE
STANDARD NOTATION 1
FORMULAS ........ i. . 2
SECTION 1 SLABS . . . i ........ 5
SECTION 2 FLAT SLABS i ...... 31
SECTION 3 RECTANGULAR BEAMS 47
SECTION 4 DOUBLY REINFORCED BEAMS 63
SECTION 5 T-BEAMS 77
SECTION 6 SHEAR REINFORCEMENT . 83
SECTION 7 COLUMNS. 91
SECTION 8 BENDING AND DIRECT STRESS \. . . 199
SECTION 9 FOOTINGS 225
SECTION 10 MISCELLANEOUS . 237
APPENDIX RULINGS PERTAINING TO DESIGN AND WORKING STRESSES 243
Joint Committee Recommendations 243
American Concrete Institute Recommendations 255
New York Building Code Requirements 265
Chicago Building Code Requirements 270
VU
CONCRETE
DESIGNERS 1 MANUAL
FLEXURE FORMULAS USED IN PREPARING TABLES AND DIAGRAMS
The flexure formulas made standard by the Joint Committee relate to working
stresses and safe loads, and are based on the straight-line theory of stress distribution.
These formulas were used in preparing the tables and diagrams in this book.
STANDARD NOTATION
Rectangular Beams.
f s = tensile unit stress in steel.
f e = compressive unit stress in concrete.
E = modulus of elasticity of steel.
E e = modulus of elasticity of concrete.
H.
n = F c
M moment of resistance, or bending moment in general.
A s = steel area.
b = breadth of beam.
d = depth of beam to center of steel.
k = ratio of depth of neutral axis to depth d.
z = depth below top to resultant of the compressive stresses.
j = ratio of lever arm of resisting couple to depth d.
jd = d z = arm of resisting couple.
^
p = steel ratio = 7-3-
T-Beams.
b = width of flange.
b' = width of stem.
? = thickness of flange.
Beams Reinforced for Compression.
A' = area of compressive steel.
p' = steel ratio for compressive steel.
// = compressive unit stress in steel.
C = total compressive stress in concrete.
C" = total compressive stress in steel.
d' = depth to center of compressive steel.
z = depth to resultant of C and C'.
Shear, Bond and Web Reinforcement,
r = total shear.
V = total shear producing stress in reinforcement.
v = shearing unit stress.
fo 1
* TORMULAS
u = bGiid^tres^pef >unii area of : bar.
o = circumference or perimeter of bar.
So = sum of the perimeters of all bars.
T = total stress in single reinforcing member.
s = Horizontal spacing of reinforcing members.
A v = area of shear steel in section of beam considered (A. C. I. notation).
f v tensile stress in web reinforcement (A. C. I. notation).
a = spacing of shear steel measured perpendicular to its direction (A. C. I.
notation).
Columns.
A = total net area.
A s = area of longitudinal steel.
Ac = area of concrete.
P = total safe load.
FORMULAS
Rectangular Beams.
k = V2pn + (pnT* -pn = - I = -
or -, or
jr.-ar.yCW, or w-^.- or f
_ 2f s p f.k
'~
n(l - k)
T-Beams. With a T-beam it is necessary to distinguish two cases; namely, (1)
the neutral axis in the flange, and (2) the neutral axis in the web.
Case /. The Neutral Axis in the Flange. All formulas for "moment calculations"
of rectangular beams apply to this case. It should be remembered, however, that
b of the formulas denotes flange width, not web width, and p (the steel ratio) is
A, x A,
W not Vd
Case II. The Neutral Axis in the Web. The amount of compression in the web
is commonly small compared with that in the flange, and is generally neglected. The
formulas to use, assuming a straight-line variation of stress and neglecting the com-
pression in the web, are:
1
k =
i+4
nf e
2ndA s + bt z
2nA a + 2bt
= 3kd - 2t t_
2kd - t'3
jd = d - 2
2
FORMULAS
M M
J A,jd pjbd*
fe = n(l - fc)
-V
" ft
, = f,Ajd
Approximate formulas can also be obtained. The arm of the resisting couple is
never as small as d %t, and the average unit compressive stress is never as small
as K/c, except when the neutral axis is at the top of the web. Using these limiting
values as approximations for the true ones,
M c = V 2 f c bt(d - i#)
M, = AJ.(d - HO, or A t = -
The errors involved in these approximations are on the side of safety.
Formulas which take into account the compression in the stem are recommended
.where the flange is small compared to the stem. Such formulas may be found in the
report of the Joint Committee, and are as follows :
pnd
\-
A, + (6 - b')t* . fnA. + (b - b')i\ * nA, + (b - b')t
[(kd -
t(2kd - l)b + (kd - t)*b'
jd = d - z
f a =-**-
. 2Mkd
[(2kd - t)bt + (kd - t)*b']jd
Rectangular Beams Reinforced for Compression.
p' + n*(p + p'; 2 - n(p
, M M
Js
Ajd pjbd*
f f' k
n(l - fc)
>--*THi
FORMULAS
f e n(l - k)
k
M s = bd%pj
Shear, Bond and Web Reinforcement.
V
Joint Committee (Recommended V =
Vertical web reinforcement
Tjd
--
' s / \
= -vj- (a)
Bars bent up at angles between 20 and 45 deg. with the horizontal,
and web members inclined at 45 deg.
_ A s f g jd _ Tjd V^s
~ 0.75F' ~ 0.75F' 4 jd
American Concrete Institute:
A v f v jd _ V'a
o, TTT or A v
V
Columns.
Square Cored
P = Afdl + (n - l)p]
Round Cored Hooped
P = Af e [l + (n - l)p] Joint Committee
P = Af e [(l + 4np') + (n - l)p] Am. Cone. Inst.
P = Af e [l + (n - l)p] + 2/ s p'A New York Code
P = Af e (l + 2.5wp')[l + (n - Dp! Chicago Code
(In the above formulas p f = percentage of spiral. /, in the New York
formula is taken at 20,000 Ib. per sq. in.)
SECTION 1
SLABS
Diagrams 1 to 9 inclusive give the total safe loads on solid slabs of different depths
for the various combinations of working stresses, bending moment coefficients and
span lengths.
Diagrams 10 and 11 give the bending moments for different values of the total load
per square foot, the span length, and the bending moment coefficients.
Diagrams 12 to 17 inclusive may be used to find the moments of resistance and
area of steel required in solid slabs for various combinations of working stresses.
Table 1 may be employed to find the size and spacing of round or square rods for a
given sectional area of steel per foot of solid slab.
Tables 2 to 7 inclusive give the total safe load for ribbed slabs for various combinations
of working stresses.
Example of Design of Solid Slab
Given: Live load = 300 Ib. per sq. ft.; span length = 8 ft. 6 in.; M = ~; j c = 650;
/. = 16,000; n = 15.
Using Diagram 3, a slab of 8%-H. span, with a depth to steel of 4% in., is found
to have sufficient strength to carry a total load of 405 Ib. per sq. ft. Assuming a
5>9-in. rough slab with 1 in. of finish on top (not placed monolithically) and plastered
below, the loading will be as follows :
6^ in. of concrete =81
Plaster = 5
Live load =300
Total load =386 Ib. per sq. ft.
Diagram 11 shows the bending moment for this load on an 8 3^ -ft. span, when
rty/2
M = 12-, to be 27,900 in.-lb
Entering Diagram 12 at the left with this bending moment, it is found that the
area of steel required per foot width for a slab having a depth to steel of 4% in. is
0.42 sq. in., or K-in. round rods spaced 5^ in. on centers (see also Table 1).
The use of the bending moment coefficient ^2 means that the slab is continuous
over supports and that the area of steel over the supports must be the same as at the
center of the span. From Diagram 25, page 57, it will be found that one-half of the
rods can be bent up from the bottom at 22 in. from the support and these rods should be
run to the quarter point of the adjacent span.
Example of Design of Ribbed Slab
Given: Live load = 100 Ib. per sq.ft.; hottow-tile floor; span of joists 19 ft; M =
~;f c = 650; /. = 16,000; n = 15.
5
SLABS
Assuming a 2-in. topping and an 8-in. tile, Table 2 shows the total safe load to be
190 lb. per sq. ft., with a steel area per joist of 0.90 sq. in. The table also shows the
dead weight of floor to be 73 lb. per sq. ft. which makes a total load to be carried of
173 lb. per sq. ft., or less than the maximum safe load. The floor is usually plastered
below, which would make the total load 178 lb. per sq. ft. A 3)4- in. topping with 6-in.
tile would also answer.
When the size of tile and thickness of topping have been determined, it is necessary
to design the joists with reference to shear, bond, and compression in the concrete at
the haunch by treating them as individual beams.
DIAGRAM 1
SOLID
SLABS
SAFE LOAD ON SOLID CONCRETE SLABS
IT/ 2
M
8
f c =650
f s = 16,000
f s = 18,000
n=15
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SLABS
DIAGRAM 2
f s =16,000
f s = 18,000
SAFE LOAD ON SOLID CONCRETE SLABS
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h
SOLID
SLABS
DIAGRAM 10
SLABS
CO
j
j
II
r
40
30
10
XZSffSXSZZ'SSSSl'SSXSSSi'SK^SSSZS'SSSSi'StXZ
LULL
~fh
I
U-
&.
t
8?
00
\r\
Span in feel*
10
DIAGRAM 11
SOLID
SLABS
BENDING MCMENt- 'FOR SLABS :; ' :
SOLID
SLABS
DIAGRAM 12
f c =650 MOMEOT * OP kfcSlSTAWCE AttD STEEL REQUIRED
f s =16,000 FOR
n=15 SOLID CONCRETE SLABS
Area of steel in sq. in. per ft width
DIAGRAM 13
SOLID
SLABS
MOMENT OF RESIST AN CE> AiNLX ST-EET^ -RfcQtf HED f c =650
'FOR' f 8 = 18,000
SOLID CONCRETE SLABS n = 15
Area of steel in sq. m. per ft width or s ab
SOLID
SLABS
DIAGRAM 14
f c =700
f a =16,000
n=15
AND STEEL REQUIRED
' 1
SOLID CONCRETE SLABS
Area of steel in sain, per ft width of felab
DIAGRAM 15
SOLID
SLABS
MOMENT OF RESISTANCE AND 3TELT,. REQUEUED
""
SOLID CONCRETE SLABS
f s =18,000
n = 15
Area of steel in sq. in. per ft width of slab
SOLID
SLABS
DIAGRAM 16
f c = 750
f s =16,0
n=15
Or RESISTANCE AND STEEL REQUIRED
"-FOR
SOLID CONCRETE SLABS
Area of steel in sq.in.perft.widthof slab
22
DIAGRAM 17
SOLID
SLABS
MOMENT OF RESISTANCE* AWD : 8TEE ''REQUIRED f e =750
FOR f. = 18,C
SOLID CONCRETE SLABS n = 15
Area of steel in sa in, oer ft. width o
SOLID
SLABS
TABLE 1
SPACING OF RODS IN SLABS
ROUND RODS
Diam-
eter
(inches)
Sectional area of steel per foot of slab when spaced as follows:
2 in.
2Y 2 in.
3 in.
3^ in.
4 in.
4^ in.
5 in.
5H in.
6 in.
7 in.
Sin.
9 in.
10 in.
12 in.
K
Ke
H
Ke
H
Me
*A
1 X<
%
l *A*
H
We
1
1 H
i H
i
i M
0.29
0.46
0.66
0.90
0.23
0.36
0.53
0.72
0.94
0.20
0.31
0.44
0.60
0.78
0.99
0.17
0.26
0.38
0.51
0.67
0.85
0.15
0.23
0.33
0.45
0.59
0.75
0.92
0.13
0.20
0.29
0.40
0.52
0.66
0.82
0.99
0.12
0.18
0.26
0.36
0.47
0.60
0.74
0.89
0.17
0.24
0.33
0.43
0.54
0.67
0.81
0.96
0.15
0.22
0.30
0.39
0.50
0.61
0.74
0.88
0.13
0.19
0.26
0.34
0.43
0.53
0.64
0.76
0.89
0.17
0.23
0.29
0.37
0.46
0.56
0.66
0.78
0.90
0.15
0.20
0.26
0.33
0.41
0.49
0.59
0.69
0.80
0.92
0.13
0.18
0.24
0.30
0.37
0.45
0.53
0.62
0.72
0.83
0.94
0.15
0.20
0.25
0.31
0.37
0.44
0.52
0.60
0.69
0.78
0.99
1.23
1.48
,.77
1.18
1.49
1.84
1.19
1.47
1.78
1.23
1.48
1.77
1.05
1.27
1.51
1.78
2.23!
2.65
3.11
3.61
1.11
1.32
1.56
1.80
2.12
2.48
2.88
3.31
3.77
1.18
1.38
1.60
1.84
1.06
1.24
1.44
1.66
1.88
2.07
2.40
2.76
3.14
3.98
1.13
1.31
1.51
1.71
.04
.20
.38
.57
.99
2.06
2.37
2.69
3.41
1.03
1.18
1.35
1.70
4.14
4.71
2.07
2.36
2.98
3.68
1.03"
1.18
1.49
1.84
2.23
2.65
2.09
2.65
3.27
3.96
1.05
1.33
1.64
1.98
4.77
2.39
2.95
3.56
2.17
2.68
3.24
3.86
1.19
1.47
1.78
4.91
4.21
2.45
2.97
3.53
2.10
2:55
3.03
5.09
4.45
5.30
4.71
4.24
2.36
2.12
SQUARE RODS
Di-
men-
sion
(inches)
Sectional area of steel per foot of slab when spaced as follows:
2 in.
2M in.
3 in.
3H in.
4 in.
4M in.
5 in.
5H in.
6 in.
7 in.
8 in.
9 in.
10 in.
12 in.
K
-6
^
Me
K
Ke
^
*Ha
%
l 6
%
%
1
i H
i K
1 ^8
1 H
0.37
0.59
0.84
Iti6
1.50
1.90
0.30
0.47
0.67
0.92
0.25
0.39
0.56
0.77
0.21
0.33
0.48
0.66
0.86
0.19
0.29
0.42
0.57
0.75
0.95
0.17
0.26
0.37
0.51
0.67
0.84
0.15
0.23
0.34
0.46
0.60
0.76
0.13
0.21
0.31
0.42
0.55
0.69
0.12
0.19
0.28
0.38
0.50
0.63
0.17
0.24
0.33
0.43
0.54
0.15
0.21
0.29
0.37
0.47
0.13
0.19
0.25
0.33
0.42
0.17
0.23
0.30
0.38
0.14
0.19
0.25
0.32
1.20
1.52
1.00
1.27
1.08
2.34
2.84
3.37
3.96
1.87
1.56
1.99
1.34
1.62
1.93
1.17
'1.42
1.69
1.98
1.04
1.33
1.50
1.76
0.94
0.85
0.78
0.94
0.67
0.81
0.96
0.59
0.71
0.84
0.99
0.52
0.66
0.75
0.88
0.47
0.57
0.67
0.79
0.92
0.39
0.47
0.56
0.66
0.77
0.88
2.27
2.70
3.17
3.67
1.13
1.35
1.58
1.84
1.03
1.23
1.44
.1.67
1.92
2.25
2.64
3.06
3.52
1.12
1.32
1.53
1.76
2.26
2.62
3.01
3.43
4.34
5.36
6.48
1.13
1.31
1.51
1.71
4.59
5.27
6.00
2.30
2.64
3.00
3.80
2.04
2.34
2.67
3.37
1.15
1.32
1.50
1.89
l.t)2
1.17
1.33
1.69
4.22
4.80
6.08
2.11
2.40
3.04
3.75
1.05
1.20
1.52
1.87
4.00
5.06
6.25
2.18
2.76
3.41
2.00
2.53
3.12
3.78
1.00
1.27
1.56
1.89
2.17
2.68
3.24
3.86
4.69
5.67
6.75
4.17
5.04
6.00
2.34
2.84
3.37
2.08
2.52
3.00
.... ....
4.54
5.40
4.12
4.91
2.27
2.70
4.50
2.25
TABLE 2
RIBBED
SLABS
SAFE LOAD OH RIBBED SLASS : :
c = 650
f s =16,000
n=15
urn
'Si;
~
N-i
CCXXCCM-CNO
cc 05 <N i-o x ~ *
CXCOOO-<O
i--: c: re I- X * O O ?H CO S
01 01 CO CO CO * -*
X * O <
01CO-*-
OCO Ot^COC5C COC5COIXM < O COOSiCOlX^O COCSCC01XTt<rH
iQCO COCCl^t^X l^ l^ X O> OS C <-( XXOSCO iCN OS O O rH i-> 01 CO
O01X XCOCOCSC O CO * OJ OS 1C 01 X^CSO-HOO COOlXCOCt*l^
i-I^O t-XOSOO OSOtHOlOlCOrf OSi-iOl-*CCOCO OCNCOCCOI^X
iCCOO) ^-^<t>-
^-^<t>-C>C COlOl^HCSXt^ OS <-i <-i X C O CO
t^XCS^Ol -(CO>Ct^XOOI f X ~ n '* Gl ~ <
OS <-i <-i X C O CO C Ol OS t^ O ^ t^
OSi-H O5 CO CO O Tf N. O
01CO 1-1 01 01 CO CO CO *
OIOICO OIOICOCO'*
OlOlCOCO'Tt<Tj*U5 OlOlCOCO^^iO
thes
those
n
11
^:
s-s
22
S'S
II
I
So"
25
RIBBED
SLABS
TABLE 3
: : SAFE- LOAD- ON MBBED SLABS
f c 700
f. =16,000
8
CO CO I-H 1><N t~ <N X "*< X O CO CO rf CO M< *O >O CO O OS CO
OS XOrHCO-^Ol>. rHCOOXOlMCO ^t^OCOOXrH
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8
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xorHco>c eocxocoici> t^i-ncxrHTfx <N^<MOOICX
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rH I-H I-H I-H (N i-H (N (N IM CO CO ^* <N CO CO Tt< Tt< 1C 1C CO CO -* >C >C O t^
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fella
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XO COOXi-H-^l O'OOSiMOO'^ X-^O3COiCO O CO r-H X >C I-H X
rH rHrHi-<(MOl (N <N IN CO CO ^ Tf (N CO CO * 1C 1C O CO Tf >C >C O t l>
^ a
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XOM lOCOOO OrHOrHlCOiC >C(NC5t^COO5iC kCrfCO^i-H
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<*COIC (NO*-H(NCO (NOJOSOOCOO CONTt<OS COO ;
i-Hi-HrH NCOCOCO^ CO-^iCOOt^-X iCOt^-X OX
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11
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OS-^Xt-OS XOrHOOSOlM i-HOOCOi-HOOS XXt>-(MCO'!J<rH
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. . . ^I^I^^KM rH M (N (M CO CO CO <M (N CO CO TJ< Tt 1C CO CO * 1C 1C O O
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p
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centers
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I
OOCO Ot>COO5*C COOSiCNXr^O CO OS "O (M X rJH O CO C3 O <N X TH rH
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ON.!-- XOJOrHi-H OSrHC^CO^-iCO ON^^OOt^X i-HCOCOXO5O
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d
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.
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Joists o
.8 M
l- s
c 2 A
ft
c o.
8.S-
COTfiiC J>OiOC-5cO <Nrt<OO5rHCO>C OOSCOOO3IMIC OiCOSCOt^-rHiC
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^5
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s
* CO X O Ol
rH
pt.fe
* H-
26
TABLE 4
SAFE LOAD ON
f e
3
gl
5MCX~Tji
b- CO
<N rH 1- 00 "5 <N
CS X O <N O O CO
csc-ii.co TH co o eo b- oo
10 cs
co co eo rH co TJ< cs
CS CO b- rH ^ OC i-i
rH <N (N CO CO CO <<
XCOb- C5 X XO
O *O O CC b* r- 1 1C
"^ b- X X Tf rH 1C
Tf C5-* C5-*OCO
<N <N CO CO "* * C
r-ieOOb-O OS * X O
r-icoob-o ooeo
l <N (
_H^, rt ^-i<N i-l <N (N (N CO CO CO
CC OXO
eoo co b- IN
OCOb-CS
i-i o o
CO CO ***
t^ co r^ co w co co
<N GO .-i * o
d-i OSOOOOt^OO
05-H ^t^OCOCD
-H ^H ,-H C<l <N N
NOOC^t^CCO
t^CCOrt-Ci
<N CO CO * Tf <*
COt^^COCS O
CO O O i- O C! t
COC^J < ^f
rC C 00 >O
CO t^ t^ 00
2lil
eoicx coco osb->c
-^^ ^NCJdCO
S SSSfggT
rH rH rH CM(N(MCCCO
(N "3 O
ifl O O
N CO CO
CO O O Tf b- t 1C
T}* rH X >C rH 00 rjt
CO^lTti C OOb-
O >C 1C rH CO CO 1C
X O T}< C<> C5 O CO
COTjfiCOOb-X
* O5 O 00 C) CO
CO<NNOOOt^ -.
Tf( C CO t t* 00
OSt^OO OS CO * r* 1-1 T* OS -H r-( Tj< t*
i-HTj<l^ COWCCOOCO OCO^HOOIC^
iCOOO
O5O5O
* >c t~
J<tCOb.X
SiS :
COi-HN
(MOOS
cot^oo
t^OS^ COOOC<Jt
COOO t-WOCCO
i-l 1-1 N O< CO CO *
OOrPt^t^O
1-iOGCCCiC
r}< 1C C CC l>
OOCO
CO OC
>C CO
OS CO i 'OO^Ot**
i-l I-H CM COCOTj<lC>C
CS
t^
CO
00
b-OOO rJ<W^HiCTt(
OCCOt^ t>.Tj<(NO5t^
CM <*< O TjfCMCSt^
Nt^CO Tj<COi-iO
NNCO Tjii
O O
t* i-t
OOO
16.
24.
the distance center to center of joists and divid
the distance center to center of joists and divid
cs ic i-t i> O<NOOC^N.CO w w * o b- co cs
Ot^OOOO ICOCC^OOOOO COOt^OOOOCSCS
TjiTjir-iiCiCTtiTH COCOt>.Ct*i-iO
t>- O CO C 1-- CS i-( 00 I-H Tj< b OS CM ^<
O C (N t- rfi
C^iCOOOCO OCCr^-^HiCOOCN
^rt rt cN<N ^HWINCOCOCO'*
t^MOOOO^O t^HHOCOOSO
O!Nt>-COQOCOt^ CCi-HXCi-it^T)'
(Meow*-* 1C "3 CO -* ^ it} CO CO b-
CS COe
-b. ^H
C rHX^CiOXCO XiCMb-O^CO C-^rHb-CSCNCO
! TtCCO XO(NCOC CO O X O CO C 00 b-r-irjoO<NCX O}b-CMOOOC:
rHi-HrHrH rH rH rH M (M <N <N rH CS <N <N CO CO CO <N IN CO CO * TJH *
S X
r^ ^ ^
CS CS CO CO * * I
X
ing of joists multiply the values in these columns
ing of joists multiply the values in these columns
For other
For other
27
RIBBED
SLABS
TABLE 5
v.. jt < SAfcE JLQ&P, k)N RIBBED SLABS
f s = 18,
r>. O OJ T* *O OO rH i < O 00 ^ Ci "*t* O5 *O ^ *O *> Ci> 00
OOOrHCOCO^ OCO^iCb-000 CO 1C 00 CO T}I
g
5
CO * O 1C 00 CO 1C O CO OS rH CO OS b" CO GO OS b- 1C rH CO GO
OS 00 O rH CO Tt< 1C b- rH CO CO 00 OS rH CO T}< b- O CO CO 00 O
,0
S
Tf< 1C 00 OO CD ^ OS 1C O b- 1C >H t> rH rH CO rH CO CO O CO CO rH b-
OOO3O OS <-< CO ^ CO 00 OS CO CO OO rH CO 1C b- b-O-^b-OCOiC
1 5
* -S
*
CO
r^CO
^^
s5 8 j
s _, .,
CO
OOCOb-COrH b- CO b- 00 O CO 1C 00 * rH * CO rH 00 O OS CO rH CO CO 03
XOrHCOiC CO CO 00 O CO 1C b- OO CO CO OS CO 1C b- Tf< OO CO 00 CO CO OS
rQ,O
33
!i 1
S
COCOCOrHCO CO b- CO CO 00 1C CO OO CO CO CO O 1C 00 rHOCDrHrHOCO
OCO-^COCO CO OS CO 1C b- O CO CO b- rH 1C OS CO 1C OSiCOcOrHCOO
>>
TJ^a
Sslla ss
0)
OS
rH
00 b* b- 00 CO CO 00 rH OS 00 00 OS CO rH O 1C CO rH b CO 00 O rH CO O O5
rHCOlCb-O 00 rH 1C b- O CO CO lCOlCO5COb-O CO OO 1C rH CO CO CO
-
03 c3
fg ii 8
*
M
a
00
1C rHCOCOOSCO Tf* CO O rH CO CO rH CO CO O O CO 1C CO O5 CO CO O rH rH 1C
^ -HrHrnScO CO CO CO CO CO CO ^ CO CO CO ^ * 1C 1C CO * 1C 1C CD CO b-
2
2.2
Si i
1
b-
COCO t^rHb-COCO O CO ^ O5 CO CO rH CO J> 00 CO rH O5 1C CO 1C CO O5 00 1C CO
GOO ^ b- OS CO 1C CO b rH ^ 00 CO CO rH b- CO OS ^ 00 CO O 00 "^ CO O t^ CO
rH rH rH rH CO CO CO CO CO CO CO * Tf CO CO Tt* CO 1C 1C CO *# Tj< 1C CD b- b- 00
"0*0
5 "
"s-a 1 . ih
CO
OOOO COCOCOCOCO OS 00 Tj< CO ^ CO O CO 1C -^ CO O * 1C TftCDiCOCS^i
OOOCO COOSCOiCOO 1C O 1C OS CO b- CO 1C CO OS 1C rH CO rH IC-^COCOOSb-
rH rHrHCOCOCO CO CO CO CO * M* 1C CO Tt< Tj< 1C CO CO b- * 1C CO b- b- 00
_fe S3
*t 2
S M ii
1C
CO rH CD OSOCOCOiC ^ O CO b- 1C rH CO CO CO rH Tt< 1C 1C rt< COCOCOO
OJrHCO OOCOiCOOCO OS 1C O * OS T}H OS O 00 CO CO OS 1C rH rH CO CO CO
rHrH rH CO CO CO CO CO CO Tj< * TJH 1C 1C * Tt< 1C CD CO b- 00 1C CO b- 00
S
cS g 1 si
SI * -
rH
iCb-CO b-COOOOCO 00 CO CO <* 00 CO O CDiCiCOOOOb- rt*iCO
O CO 1C rHiCOSCOb- CO O CO rH CO CO 00 CO 1C Tt< CO OS CO OSrHCO ....
rHrHrH COCOCOCOCO CO ^ Tt* 1C 1C CO CO ** 1C CO b- b- 00 iCb-00
-22
ft fp
11 a 1
CO
COOOrH rHCOb-rHCO CO CO CO CD OS CO OS O <* 00 Tj* OSO3
PH S
r^
rHrHrH CO CO CO CO Tj( CO * 1C 1C CO b- b- lCCOb-00 OOO
CP CJ
8
CO
rHrHCO CO CO CO Tj< 1C Tj< 1C CO b- b- 00 CDb-00 .... 00
O a>
a
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o
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COOCOCOOO OCDCOOSiCrHb. COCOOOiCrHb-CO COOO^Ob-COOS
. TjHiCiCcOCO 1C 1C CO CO t^ 00 00 1C CO CD b- GO 00 OJ CO CO b 00 00 OS OS
>> >>
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3 3
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OSOrHCOCO rH CO * 1C CO CO b- CO r}H CD t>. GO OS O CO 1C t^ OS rH CO CO
'o'o
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OrHCOlCb- 1- 5 OS rH Tj< CD OS rH rH CD O * b- O *< b- CO OS * OS CO b-
.S S
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33
||
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fls*
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SCOCO ObCOOSiC CO OS 1C CO 00 * O CO OS 1C CO 00 "* O CO OS CO CO 00 * rH
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s ^!s
r-
CDrHCO ICrHCOrHb. b- 00 CO rH b- CO b- "* b- OS OS CO CO b- OS 1C 00 O rH OS CO
tiCiC CDbb-OOOO t^OOOSOOrHrH OO O3 O rH CO CO CO OO O rH CO Tj< rf< 1C
3 3
e s
1-1 02
c
a ft .-
".9
OOO OOOOO OOOl-lrHrHrH O O rH rH rH rH rH O rH rH rH rH rH rH
II
I Is
({I
1
COOOi OOOSrHCOb. CO CO 1C rH 00 1C CO CO -* CO 00 O CO CO CO * 1C b- 00 CO
CO-*"* COb-OSOrH O CO Tt< CO b- OS rH rf< b- CO 10 b- OS 00 CO CD OS CO 1C 00
rHrH rHrHrHrHrHrHCO rHrHCOCOCOCOCO rHC>lCOCOCOCOCO
;s;s
"0*0
M M
S "
|M
-3
COCOCO COCOCOCOM* COCOCOCO^TftiC COCOCOCO^rtiC COCOCOCO^'*1C
ft ft
tn CQ
II
O O
H
3
* ? 00 O CO
II
H
28
TABLE 6
RIBBED
SLABS
SAFE LOAD ON *IBBEJ> SLABS
f c =700
f, = 18,000
oad.
Total safe load in pounds per square foot
including weight of floor (dead and live)
on M - ~~ For M - ~. add 20% to
! g
rH TO <! 1C TO TO X
rH CO O t O rH CM
O "i OS >C O 10
-*t> CS CM * t^
rHW* CO rH 00 Tf O "5 rH t- CO t* rH CM * CM
QOOSO OS i-l CM <* O t OS CM O t> O N ^ 5O
^H rH i-l ^H ^H ^i i-> i-l ^ i-l CM CM CM CM
O>t^"5CM-i OObOTO^T}t tt^O
TJICOOOOCM * r^ O TO 00 O 00 CM
t^ ^ >O CO t* 00 OS
CM "3 *> OS ^H TO O
Tj<00-HCM<N^
t^ O * l> O TO ifl
OS t^ I-H ^ OS OS D
^H O -H iO 00 <N CO
OO t O OS CO U5
^OOCMTOOiCM
HO 00 T-( Tj<
1-H X rH OS T}< rH 1C
- - - - - .-:
CM TO TO 1C 1C
IQ * OS CO rH X CM
rH X T}< C CC i b-
TO TO rf< 1C C CC CO
OCMCOr-.t^
TOOt^OCM
i-*^Hi-iCMCM
OOSMCOOS-*
^t< t* I-H * t* I-H
CMCMTOTOTOTt*
CO^-C
TOXTO
OX rH i
O O - >O *
IO CM OS CC CM X Tt*
TO * * 1C CO CO t-
CO USOl^'tTO OXi-iOSCOTOi^
O -*t>.OSCMO CMW^TfXCMCO
rH ,-H i-H T-I CM CM CM CM M TO TO T}< *
SOXOCOi-n
t^CMXTOCi
TO Tf Tf it} it}
O'O^'CTO'tf'
OS t* C CM OS CO
TO rfi iO CO CO t^
CMOO-HTO TO-HXCMTO-^t*
COOSCMOX O O Tj< OS TO t^ 1-1
>^>-lCMCMCM CM TO TO TO Tf ^ O
CO IO O "3 i <N CM
^ i-< X Tf O CO ^-
TO ^ T* >O CO CC t*
t* CM <-> O CO
TOTOCMCt^O
& IO CO 1-- t^ X
TOIOOS
r-ICMCM
1-1 os CM c os t
XTOU3 OSOOOX CO CO rf< t* OC Oi CM OCMX
i-H^t* TOXCMt^^H t & 1-1 1^ TO OS CO ^<-<O
TOCCO N.CMt^-CMX TOrHCsr^rfirH . OSrHCM
rH 1C CS CO CM TO
COOSTO CMX^<
rHrHCM MM Tf I
CO(
Xi
1-HCM-*
^
t^ OX
CMTOTO-*CO ICCSrHrHOOSX CSbTOOSXXrJ< <*< OS rH t^ OS Tf C
rHrHrHrHrH rHCMCMCMMTOTO CMCMTOTO^^Tf TOTOrji'tiiCiCCO
COTO Ol>COOSiO OSCCMX-*O TO OS C CM X * O TO OS CO CM X * .-i
CCO cOOt-t^X t^ t* X OS OS 1-1 XXOSOO iCM OS OS O "H rH CM TO
000 00000 00-1,-lrHrHrH Q rH rH rH rH rH rH O rH rH rH rH rH rH
tXOrHTO rHTOCOX
>CMCMCMX Ol
< i-i CM CM CM TO :
I O N. T} CJ CO O
)Tt<XCMC 3STO
ICMCMTOTOTO-tf
CMCMTO CMCMTOTO-* CM CM CO TO * TJ< 1C CMCMTO-*^iC CM CM M TO * TJ< >C
16.
24.
ter of joists and divid
ter of joists and divid
ce center to
ce center to
the d
the d
mns
mns
col
er spacing of joists multiply the values in these
er spacing of joists multiply the values in these
oth
For
For
29
RIBBED
SLABS
TABLE 7
LPADPJJF RIBBED SLABS
' fc = 750 '
24."
'
co
OrH 00 CO CO OS Tt* OS IO O iO OS CN CO iO O COCOCOcOHHCOO
OSO OOOCNCOIOCOOO CNHHCOOSrHCOiO lOOOrHrfb-OCO
.
oo
OOOCOlO rH CN rH OS b- * CN OOb-^OiOOCO lO rf 00 CO "0 GO OS
b-OSOrH O CN HH IO b- OS rH CO CO OS CN Tfl b- OS b rH Tjl 00 rH HH b-
1
CD
CN
sj S -g
! s
OS CO CO O b GO CD CN t> rH Tf OS 00 b- H^ OS CO b* 00 OS rH b IO OS HH IO
COOCN^tiiO COCOO5rHTt<COOO OOcNCOOSCOCOOS COO5COGOCNb-rH
rHrHrHrH rH rH rH CN CN CN CN rH CN CN CN CO CO CO CN IN CO CO <* * IO
|5 a J
S3
II 1 2
o
OS CNlOb-OCN OS CO b- rH Tt< 00 rH b CN b- CO b- CN b- H< rH 00 IO rH 00 TJH
rH rH rH CN CN rH CN CN CO CO CO HK CN CO CO Tjf <* O IO CO Tf H^ IO CO CO b-
SdVa
2
CDO CNOSCOCOrH O >O CD CO TfH rH O O CN rH 00 CN O CO rH HH OS >O * CO CO
OOO HHCDOSCNIO cNCDOH^COcNCO OCDcNb-COOOCO OOCOCOrHCOiOCN
rH THrHrHCNCN CM CN CO CO CO Ttl Ttl CO CO HH H/ O IO CO CO Tt< >O CD CO b- 00
f S II 8
fe "S
J
a ^
OS CO CO OOOSOOOSO iO O rH CO CO OS CO Tf CO OS CN CN CN 00 rJH b- O O IN rH
b-OSrH lOOOrHTtlOO Tf OS HH CO CN CO rH CO O CD CO O5 IO O CN rH O 00 CO Tf<
rH rHrHCNCNCN CNCNCOCOHHHHIO COTf*Tj<lOlOCDb- TjflOCOCOb-00
OS 00 CN b-CNTt<osrt< ^rHCOCOOCO>O HHH^cOb-H^rHr)< COOCOOOlO
H "
rHrH rHCNCNCNCO <NCOCOHHT^1O>O COHHlO'OCCb-b- HHlOCOb-OO
1'S t ^i
02 ; co
8CN OS OOSCOiOHi O CO <N CO CN CO O CN O CO rt< O CD b- HI O5 b-
CNHH OCOb-rHiO rHb-COX-^OSiO CNrHO3b-iOCN CO"O>OCO
,-lrHTH CN CN CN CO CO COCOHlTtiiO'OCD H^iOiOCDb-CO lOCDb-OO
rHrHrH CN CN CO CO TjH CO ^ ** IO CO CO b- Tf >O CD b- GO CO b- CO
"3 fl II SH
a'l * t
s
rHQSiO CNCNOrHCN lOOO^oOOOiOOO CNCOOO CN>O----
COIOOS COrHCOrHCD OOOCOCOOb-^ -*COb-OO O'O
rHrHrH <NCOCOT}<Tt< TflrflOCDb-b-OO iQCOb-GO b-00
*"o -
.2 o fe
CO
IN
iH
O OO CN OCDrHb-CO b- CD iO <* CN rjn b- O rH
rHrHCN COCOHH^IO -flOCOb-00 COb-OS - 00
brHCD lOCNOSCOCO lOCOCOCO*'- IOO--
g
rH IO rH CN O 00 CO Tt< >O OS rH
2
COCNrH CNCNCDiOCO *
CNCOCO lOCDb-COCS b-
2 8,1
1 a-;
V
:
. COOCOCNGO O CO CN OS iO rH b- CDCNOOiOrHb-CO CNOO^Ob-COOS
. . . HHiOiOCOCO iOOCOCOb-OOCO >OCOCOb-OOOOO3 CO CD b- 00 00 OS Oi
rj
S 'o c
^ ! J
'all?
OiOHHrffCO OS OS b- rH CN rH rH O >O 00 00 CO GO O OS GO CO CO CO rfi rH
CNCO-tiiOCD CO>Ol--OSOrHCN lOb-Oli-iCO^CD "OCOrHCOiOb-OS
c
^- .rt
CNCNCN CNCNCNCN CN CN CN CN CN
O i
co -L
.2M
3 8.S
"> OH
. . H/IGOOCOb- .HOsCOOCOiOOS OSH^TiOOb-O OCNb-CNCNCOCN
CN'tt^.CSrH OCNCDOfOCOOS IO rH O rH CD O IO COOCOCOOJlOrH
oU
1 1!
j "~
OCDCO Ob-COOSiO COCSiOCNOO-^O COOsiOCNGOTj<O COO5COcNOOrt<rH
IOIOCO COCDb-b-00 b-b-OOO3CSOrH OOCOOSOOrHOJ OSOSOrHrHCNCO
1 1
S 55.3 d-~
00-*rH OOCOCNOS COCOOOb-iOrHb- O b- CN iO CO 5 CO CO iO CN 00 rH CO *
lOCOb- OOOSOSOO OS O rH CN CO * H^ O rH CO Tfi >O CO b- O CN * >O b- GO OS
^ W
C
* M
1-5 rt"*
III
rHOrH CNCOCOOSiO b-COb-OOJCOO COOSCOCOb-COb- OOOrH0'OO>O
TjHiOCO OOOSrHcN't' CN'Ob-OcN'fCO b- O rt< b- O CO CO CNCDrHiOOSCOb-
.-HrHrH rH rH rH CN CN CN CN rH CN CN CN CO CO CO CN CN CO CO CO Tt< "*
H fl "
~I
CN CN CO CN CTsTcO CO T>< CN CN CO CO*-* -<tiO CNCNCOCO^'^iO CNCNCOCO^r^iO
a^o'S^
Q -
=1
* O CO O CN
SECTION 2
FLAT SLABS
The designs of square interior flat slab panels according to the American Concrete
Institute recommendations, and the New York and Chicago Codes are given in Tables
8 to 13 inclusive. These are for panels from 16 to 26 ft. square, both with and without
drops, and for live loads from 100 to 350 Ib. per sq. ft. of floor. An allowance of 6 Ib.
per sq. ft. was made for weight of finish.
The quantities given are believed to be conservative and by careful detailing it will
usually be found possible to keep the weight of the steel slightly below that given in
the tables.
Rectangular panels and wall panels must be designed according to the special
requirements of the different codes.
Columns supporting flat slab floors must be designed to take the bending moments
produced by the cantilever action of the slab. After the bending moments in the
columns have been estimated, the stresses may be determined by the diagrams of
Section 8. The majority of columns used have round hooped cores and Diagrams 60
to 64 inclusive have been constructed for the design of such columns when subjected
to bending.
31
FLAT
SLABS
FLAT SLAB FLOORS
AMERICAN CONCRETE INSTITUTE RECOMMENDATIONS
INTERIOR SQUARE PANELS
f c =650 for positive moment
f c =750 for negative moment
f 3 = 16,000
JL
!?>
:jo '
*>! ^
!a \
I J-
T\ w;
LM-
a
*:0>
^f
i *|^0 ;0^ I
t ab. ^jv] j-.
iQ
.^J
>
+
i
i^n
-J.
\
l^;|i
;gfi
i^^
tii
-j (Vj
Aj
-s\j
a:
JSP
?
IS
S)i
* 231
SI
/"
' lltll ! Drop Construction j ' Cap Construction
h
Section A-A
Bending Moment Coefficients
Moment coefficients shown on diagram are to be multiplied by WL.
W = wL\
w = total dead and live load in pounds per square foot.
L = span center to center of columns for square panels.
Values shown above moment coefficients are percentages of numerical sum of moments in one
direction across panel.
Numerical sum of moments in one direction across panel = 0.0648 WL.
Minimum size of drop =0.3L.
Minimum diameter of capital = 0.225L.
,,. . [ 0.02L\/w + 1 (t in inches, L in feet)
Minimum t =
t = total thickness of slab.
32
TABLE 8
FLAT SLAB FLOORS
AMERICAN CONCRETE INSTITUTE RECOMMENDATIONS
INTERIOR SQUARE PANELS
DROP CONSTRUCTION
f c = 650 for positive moment
f c = 750 for negative moment
f,
n=15
FLAT
SLABS
Superimposed load = 100 Ib. per sq. ft.
Panel
size
(feet)
Capital
ttiam-
eter
Size of
drop panel
Depth
of slab
(inches)
Depth
of drop
(inches)
Concrete
in cubic
feet per
sq. ft.
Round steel rods in each band
Steel in
Ib. per
sq.ft.
Direct
Across
direct
Diagonal
16X16
3' 6"
4' 10" X 4' 10"
6
2K
0.52
14-%"
8-%
H-%
1.95
17X17
3' 9"
5' 2*X5' 2"
6j-
2J4
0.56
16-%"
9-%
13-%
2.14
18X18
4' 0"
5' 6"X5' 6"
6^i
ovz
0.58
18 %"
10-%
15 %
2.25
19X19
20X20
4' 3"
4' 6"
5' 8"X5' 8"
6' 0"X6' 0"
?i
iM
0.62
0.65
21-%"
17-Ke"
11-%
16-%
15 K *
2.38
2.53
21 X21
4' 9"
6' 4"X6' 4"
8
25^
0.69
20-Ke*
10 -K
16-K *
2.70
22X22
5' 0"
6' 8"X6' 8"
O I/
0.71
21 -He*
12-H
16-K *
2.81
23X23
24X24
5' 3"
5' 6"
7' 0"X7' 0"
7' 4"X7' 4"
9^
3M
0.76
0.78
23-Ke"
26-K6*
13-K
14- K
18-K *
21-K *
3.06
3 . 30
25X25
5' 9"
7' 6"X7' 6"
9K
3J
0.82
29-K6*
16-K
23 K *
3.44
26X26
6'0"
7' 10" X 7' 10" 9%
3^
0.84 31-Ke* 17-K
25-K *
3.55
Superimposed load = 150 Ib. per sq. ft.
Panel
size
(feet)
Capital
diam-
eter
Size of
drop panel
Depth
of slab
(inches)
Depth
of drop
(inches)
Concrete
in cubic
feet per
sq. ft.
Round steel rods in each band
Steel in
Ib. per
sq. ft.
Direct
Across
direct
Diagonal
16X16
3' 6"
4' 10" X 4' 10"
6
2% 0.52
18-%"
10-%"
15-%
2.54
17X17
3' 9"
5' 2"X5' 2"
6J^
2 3 4 0.56
20-%"
16-%
2.56
18X 18
4' 0"
5' 6"X5' 6"
gax
3K 0.59
23-%"
14-%"
19 %
2.90
19X19
4' 3"
5' 8"X5' 8"
7H
0.63
26-%"
14-%"
20-%
3.00
20X20
21X21
4' 6"
4' 9"
6' 0"X6' 0"
6' 4*X6' 4"
J*
3H
3M
0.65
0.69
22-Ke" 12-He*
24-Ke" 13-He*
17-K
20 K
3.27
3.52
22X22
5' 0"
6' 8*X6' 8"
8J<4
4
0.72
26-K6*
14-Ke"
22 K
3.62
23X23
5' 3"
7' 0"X7' 0"
8^i
4
0.76
29 -He*
16-He*
23-K
3.78
24X24
5' 6"
7' 4"X7' 4"
&
0.78
31-Ke'
18-He*
26-K
3.98
25X25
5' 9"
7' 6"X7' 6"
9M
4j|
0.83
35 Ke"
29- K
4.27
26X26
6'0"
7' 10" X 7' 10"
9*i
4% 0.85
39-Ke*
21-He*
31-K
4.45
Superimposed load = 200 Ib. per sq. ft.
Round steel rods in each band
Panel
size
(feet)
Capital
diam-
eter.
Size of
drop panel
Depth
of slab
(inches)
Depth
of drop
(inches)
Concrete
in cubic
feet per
sq. ft.
Steel in
Ib. per
sq. ft.
Direct
Across
direct
Diagonal
16X16
17X17
3' 6"
3' 9*
4' 10" X 4' 10"
5' 2"X5' 2"
i
3
0.58
0.59
20-%
24-%
11-%"
13-%"
17-%"
19-%"
2.83
3.07
18X18
4' 0*
5' 6"X5' 6"
7J4
3?i
0.63
26-%
15-%"
22-%"
3.45
19 X 19
4' 3"
5' 8"X5' 8"
7H
4
0.66
30-%
16-%"
25-%"
3.50
20X20
4' 6"
6' 0"X6' 0"
8
4
0.70
25- K *
13-Ke*
20-Ke*
3.70
21X21
22X22
4' 9"
5'0"
6' 4"X6' 4"
6' 8"X6' 8"
m
A 1 ^
0.72
0.76
27- K *
30 -H *
16-Ke*
22-Ke"
25-K 6*
3.87
4.15
23X23
5' 3"
V 0"X7' 0"
9 J4
4- ^>
0.81
33- K *
18-He*
26-K.6"
4.26
24X24
5' 6"
V 4"X7' 4"
9M
5
0.83
36-K *
20-K6*
30-Ke"
4.45
25X25
26X26
5' 9" .
6' 0"
7' 6"X7' 6*
7' 10" X 7' 10"
10
5
0.87
0.92
39 -He"
43-K6*
22-Ke*
23-Ke*
31-He*
4.59
4.92
33
FLAT
SLABS
TABLE 8
FLAT SLAB FLOORS
AMERICAN CONCRETE INSTITUTE RECOMMENDATIONS
INTERIOR SQUARE PANELS
DROP CONSTRUCTION
f c = 50 for positive moment
f c = 750 for negative moment
f s = 16,000
n=15
Superimposed load = 250 Ib. per sq. ft.
Round steel rods in each band
Panel
size
(feet)
Capital
diam-
eter
Size of
drop panel
Depth
of slab
(inches)
Depth
of drop
(inches)
Concrete
in cubic
feet per
sq. ft.
Steel in
Ib. per
sq. ft.
Direct
Across
direct
Diagonal
16X16
3' 6"
4' 10" X 4' 10"
7
3K
0.61
22-%"
12-%"
18-%
3.05
17X17
3' 9"
5' 2"X5' 2"
7M
3^
0.65
25-%"
14-%"
20 %
3.32
18X18
4'0"
5' 6"X5' 6"
4
0.68
28-%"
17-%"
23 %
3.55
19X19
4' 3"
5' 8"X5' 8"
SjJ-i"
0.72
23- KG"
20- K
3.77
20X20
4' 6"
6' 0"X6' 0"
8H
4H
0.74
27- fi 6 "
14-Kc"
22-K
4.00
21X21
22X22
4' 9"
5'0*
6' 4"X6' 4"
6' 8"X6' 8"
9
4%
0.79
0.83
30-K 6 "
33-Me"
16-Ko"
18-Kc"
23- K
26-K
4.15
4.42
23X23
5' S"
7' 0"X7' 0"
10
5
0.87
35-Kc"
20-Kc"
29 K
4.60
24X24
5' 6"
7' 4"X7' 4"
5
0.91
39-Kc"
22-Kc"
31-K
4.81
25X25
5' 9"
7' 6"X7' 6"
11
5/4
0.96
43-Kc"
23-Kc"
36-K
5.21
26X26
6'0"
7' 10" X 7' 10"
UK
5%
0.98
47-Kc"
26-K 6 "
38-K
5.39
Superimposed load = 300 Ib. per sq. ft.
Panel
size
(feet)
Capital
diam-
eter
Size of
drop panel
Depth
of slab
(inches)
Depth
of drop
(inches)
Concrete
in cubic
feet per
sq. ft.
Round steel rods in each band
Steel in
Ib. per
sq. ft.
Direct
Across
direct
Diagonal
16X16
3' 6"
4' 10" X 4' 10"
7K
3%
0.66
25-%"
14-%"
19-%"
3.35
17X17
3' 9"
5' 2"X5' 2"
7%
4 1/
0.68
29-%"
16-%"
23-%"
3.70
18X18
4' 0"
5' 6" X 5' 6"
4%
0.72
31-%"
18-%"
25-%"
3.83
19X19
4' 3"
5' 8"X5' 8"
8%
434
0.77
14-Kc"
21-Kc
4.07
20X20
4' 6"
6' 0"X6' 0"
9M
4%
0.81
29 ^KG"
16 KG"
23- KG
4.30
21X21
4' 9"
6' 4"X6' 4"
9%
5
0.85
3 1 - K G "
26- KG
4.47
22X22
5' 0"
6' 8"X6' 8"
10
0.88
35-Kc"
20-Kc"
29- K e
4.82
23X23
5' 3"
7' 0"X7 / 0"
10H
5%
0.92
3 6- KG
21-Kc"
30- KG
4.77
24X24
5' 6"
7' 4"X7' 4"
11
6M
0.96
18- M"
26- Yz"
5.25
25X25
5' 9"
7' 6"X7' 6"
i iM
6M
1.01
35-^ "
20 Yv "
29 -K"
5.52
26X26
6'0"
7' 10" X 7' 10"
12
7
1.05
39- W*
22-M"
5.77
Superimposed load = 350 Ib. per sq. ft.
Panel
size
(feet)
Capital
diam-
eter
Size of
drop panel
Depth
of slab
(inches)
Depth
of drop
(inches)
Concrete
in cubic
feet per
sq. ft.
Round steel rods in each band
Steel in
Ib. per
sq. ft.
Direct
Across
direct
Diagonal
16X16
3' 6"
4' 10" X 4' 10"
7%
4%
0.68
27-%"
14-%" 23 %"
3.79
17X17
3' 9"
5' 2"X5' 2"
8 z4
5
0.73
30 %"
16-%"
25-%"
3.91
18X18
4' 0"
5' 6"X5' 6"
8%
5M
0.77
26-Kc
20-Kc"
4.10
19X19
4' 3"
5' 8"X5' 8"
5%
0.82
27- KG
14-Kc"
22-Ke*
4.27
20X20
4' 6"
6' 0"X6' 0"
9%
6
0.86
17-K 6 "
25 KG"
4.55
21X21
4' 9"
6' 4"X6' 4"
10J4
6J4
0.90
34- KG
18-Kc"
4.81
22X22
5' 0"
6' 8"X6' 8"
10%
6%
0.95
36-K 6
30-K 6 "
4.96
23X23
5' 3"
7' 0"X7' 0"
\\YL
0.99
40- KG
23 KG"
33-K K "
5.26
24X24
5' 6"
7' 4"X7' 4"
11%
7%
1.04
34- M"
19-M" 28-^"
5.54
25X25
5' 9"
7' 6"X7' 6"
1.09
37 M"
2\-Yz" 30- K"
5.76
26X26
6'0"
7' 10" X r 10"
12%
8H
1.13
41-K"
33-M"
6.07
34
TABLE 9
FLAT SLAB FLOORS
AMERICAN CONCRETE INSTITUTE RECOMMENDATIONS
INTERIOR SQUARE PANELS
CAP CONSTRUCTION
f c = 650 for positive moment
f e = 750 for negative moment
f s = 16,000
n=15
FLAT
SLABS
Superimposed load = 100 Ib. per sq. ft.
Panel size
(feet)
Capital
diameter
Depth
of slab
(inches)
Concrete
in cubic
feet per
sq. ft.
Round steel rods in each band
Steel in
Ib. per
sq. ft.
Direct
Direct over
column, add'l
Across
Diagonal
each way
16X16
3' 6*
6M
0.542
17-%*
4-%*
Q a/ it
13-%*
2.54
17X17
3' 9*
Q^A,
. 563
20-%*
4-%*
n-%"
15-%*
2.66
18X18
4' 0*
7
0.584
23 %*
e 3 / tt
12-%*
2.84
19X19
4' 3*
7^4
0.625
25-%*
5-%*
13- %*
19-%*
3.04
20X20
21X21
4' 6*
4' 9*
8
0.667
0.688
24-Ke"
4 Ke*.
11-Ke"
16-Ke"
18-Ke"
3.24
3.45
22X22
5'0*
8%
0.730
26-Ke"
5 Ke*
14-Ke"
19-Ke"
3.62
23X23
24X24
5' 3*
5' 6*
9
0.750
0.792
29 7^e*
32-Ke"
4-Ke*
15-7^6*
17-Ke*
23-Ke*
3.78
3.96
25X25
5' 9*
9?i
0.813
35-Ke"
5 Ke*
18-Ke"
26-Ke"
4.17
26X26
6'0*
10
0.833
39-Ke*
5 Ke
21-Ke*
29-Ke" 4.36
Superimposed load = 150 Ib. per sq. ft.
Panel size
(feet)
Capital
diameter
Depth
of slab
(inches)
Concrete
in cubic
feet per
sq. ft.
Round steel rods in each band
Steel in
Ib. per
sq. ft.
Direct
Direct over
column, add'l
Across
Diagonal
each way
16X16
3' 6
7
0.583
20-%*
4-%*
n-%*
14-%*
2.83
17X17
3' 9
0.605
23-%*
4-%*
12 %*
17_i^
2.98
18X18
4'
7%
0.646
26-%*
4%*
14-%*
19 %*
3.14
19X19
4' 3
8M
0.688
21 Ke
4-Ke"
12-Ke"
15-Ke*
3.27
20X20
21X21
22X22
4' 6
4' 9
5'
I/
9
Ql/
0.709
0.750
0.792
mi
29- K e
4-Ke"
6-Ke"
5-Ke"
13-Ke"
15-Ke"
16-Ke"
18-Ke"
20-Ke"
21-Ke*
3.48
3.78
3.91
23X23
24X24
25X25
26X26
5' 3
5' 6
5' 9
6'0*
Q3X
IOH
11
0.813
. 854
0.875
0.917
32- K e
35-Ke
39-Ke
42-Ke
5-Ke"
6-Ke"
5 Ke"
6 Ke"
18 Ke*
19-Ke*
21-Ke"
24-Ke"
24 -Ke"
26-Ke*
28-Ke"
31-Ke*
4.16
4.34
4.51
4.76
Superimposed load = 200 Ib. per sq. ft.
Panel size
(feet)
Capital
diameter
Depth
of slab
(inches)
Concrete
in cubic
feet per
sq. ft.
Round steel rods in each band
Steel in
Ib. per
sq. ft.
Direct
Direct over
column, add'l
each way
Across
direct
Diagonal
16X16
17X17
3' 6*
3' 9*
JM
0.625
0.667
22-%* 1 5-%*
25 %* 5-%*
12 %*
14-%*
19-%*
3.12
3.29
18X18
4' 0*
8^
0.708 29-%* 5-%*
16-%*
21-%*
3.49
19X19
4' 3*
9
0.750 23 Ke
5-Ke" 13-Kfi*
17-Ke"
3.66
20X20
21X21
4' 6*
4' 9*
10 2
0.791 26 Ke
0.833 29-Ke
4-Ke"
5-Ke*
14-Ke"
16-Ke"
19-Ke"
21-Ke"
3.88
4.04
22X22
5'0*
10^
0.875 ! 32-Ke
4-Ke"
17-Ke"
23-Ke*
4.20
23X23
5' 3*
\\y\
0.938 34-Ke
5-Ke*
19 Ke"
25-Ke"
4.37
24X24
5' 6*
12 1.000 j SS-Tie
4-Ke"
21-Ke"
28-7^6*
4.64
25X25
5' 9*
12% 1.063 41-Ke
4~Ke*
23-Ke*
4.78
26X26 6'0* 13J4 1.142 47~Ke i 5-Ke" 26 Ke" 34 -Ke" 5.23
35
FLAT
SLABS
TABLE 9
FLAT SLAB FLOORS
AMERICAN CONCRETE INSTITUTE RECOMMENDATIONS
INTERIOR SQUARE PANELS
CAP CONSTRUCTION
f c =650 for positive moment
f c =750 for negative moment
f s = 16,000
n = 15
Superimposed load = 250 Ib. per sq. ft.
Panel size
(feet)
Capital
diameter
Depth
of slab
(inches)
Concrete
in cubic
feet per
sq. ft.
Round steel rods in each band
Steel in
Ib. per
sq. ft.
Direct
Direct over
column, add'l
each way
Across
direct
Diagonal
16X16
3' 6"
8%
0.730
21-%
6-%"
n-%"
16-%"
3.00
17X17
3' 9"
0.771
26-%
4-%"
14 %"
19%"
3 30
18X18
4/0"
10
0.833
29-%
4-%"
16-%"
23-%"
3.61
19X19
20X20
4' 3"
4' 6"
}?|
0.896
0.959
23- H "
26 -H "
4-He"
4-He"
13-Ke"
15-He"
17- He"
19 He"
3.64
3.91
21X21
22X22
23X23
24X24
25X25
26X26
4 / 9 //
5' 0"
5' 3"
5' 6"
5' 9"
6' 0"
12
13
15 g 4
.000
.083
.146
.188
.250
.313
28-He"
31-He"
34-He"
38-He"
41 -He"
45-Ke*
2-Ke"
4-He"
5-He"
4-He^
4-He"
15- He"
17-He"
19-He"
21 He"
23-He"
25-He"
20-He"
23 He"
25-He"
28-He"
30-He"
33-He"
3.84
4.16
4.37
4.65
4.81
5.03
Superimposed load = 300 Ib. per sq. ft.
Panel size
(feet)
Capital
diameter
Depth
of slab
(inches)
Concrete
in cubic
feet per
sq. ft.
Round steel rods in each band
Steel in
Ib. per
sq. ft.
Direct over
Direct column, add'l
each way
Across
direct
Diagonal
!
16X16
3' 6"
10
0.833
23-%"
3-%" 13-%"
17-%"
3.17
17X17
3' 9"
10%
0.896
26-%"
2-%" 14-%"
19-%"
3.27
18X18
4' 0"
11 J^
0.958
29-%"
3-%"
16-%"
21 %"
3 45
19X19
4' 3"
12M
.042
32-%"
2-%"
23-%"
3.58
20X20
21X21
4 / 6 "
4' 9'^
13
14
.083
.174
27 He"
29 He"
3-He"
3 He"
15-He"
16-He"
19- He"
21-He"
3.88
4.02 .
22X22
23X23
5'0"
5' 3"
15
16
.250
.333
32- He"
34 He"
2-He"
4-He"
IB-He"
19 He"
23- He"
25-He"
4.20
4.33
24X24
25X25
26X26
5' 6"
5' 9"
6'Q"
17 2
18
.375
.417
.500
38-He"
42-He"
46-He"
3 He"
21-He"
24 -He"
25-He"
28-He"
31-He"
30-He"
4.64
4.76
4.84
Superimposed load = 350 Ib. per sq. ft.
Panel size
(feet)
Capital
diameter
Depth
of slab
(inches)
Concrete
in cubic
feet per
sq. ft.
Round steel rods in each band
Steel in
Ib. per
sq. ft.
Direct
Direct over
column, add'l
each way
Across
direct
Diagonal
16X16 3' 6"
HM
0.958
23-%"
2-%"
13-%"
17 %"
3.16
17X17 ! 3' 9"
12K
1.021
26-%"
2-%"
14-%"
19-%"
3.23
18X18 4' 0"
13
1.083
29 %"
3 %"
16-%"
21-%"
3.45
19X19 4' 3"
13%
1.146
33 %"
3-%"
18-%"
24-%"
3.74
20X20
21X21
22X22
23X23
24X24
4' 6"
4' 9"
5' 0"
5' 3"
5' 6" -
14%
15%
16%
17%
18%
1.230
1.313
1.396
1.480
1.563
27-He"
29-He"
32-He"
35-He"
37-He"
2-He"
3-He"
- 3-He
HK
3- He
14^He"
18~8 f6 "
20-He"
21-He"
19-He"
21- He"
23-He"
26-He"
27-He"
3.85
4.02
4.22
4.48
4.50
25X25
5' 9"
19%
1.646
41-He"
30-He"
4.79
26X26
6'0"
20%
1.730
45-He"
3-Ke"
25-He"
33-Ke"
5.00
36
FLAT SLAB FLOORS
NEW YORK CITY BUILDING CODE
INTERIOR SQUARE PANELS
f c =650 for positive moment
f c =750 for negative moment
f t = 16,000
FLAT
SLABS
Bending Moment Coefficients
Moment coefficients shown on diagram are to be multiplied by WL.
W = wL*
w = total dead and live load in pounds per square foot.
L = span center to center of columns for square panels, or average span for rectangular
panels where long dimension is not more than 1.1 times short dimension.
Values shown above coefficients are percentages of numerical sum of moments in one direction
across panel.
Numerical sum of moments in one direction across panel = 0.0587TFL.
Minimum size of drop = 0.33L.
Minimum diameter of capital = 0.225L.
'6
0.02L\/wJ_+ 1 with drop
0.024L\/w + IK without drop
L/32
t = total thickness of slab.
Minimum t =
(t in inches, L in feet)
37
FLAT
SLABS
TABLE 10
FLAT SLAB FLOORS
NEW YORK CITY BUILDING CODE
INTERIOR SQUARE PANELS
DROP CONSTRUCTION
f c = 650 for positive moment
f c =750 for negative moment
ft =16, 000
n=15
Superimposed load = 100 Ib. per sq. ft.
Panel
size
(feet)
Capital
diameter
Size of
drop
panel
Depth
of slab
(inches)
Depth
of drop
(inches)
Concrete
in cubic
feet per
sq. ft.
1
Round steel rods in each band
Steel in
Ib. per
sq. ft.
Direct
Across'
direct
Diagonal
i
16X16
3' 6"
5' 4"
6
3
0.528
13-%
9-%
9-%"
1.76
17X17
3' 9"
5' 8"
3
0.570
15-%
10-%"
1.89
18X18
4' 0"
6' 0"
6%
334
0.593
17-%
12-%
12-%"
2.04
19X19
4' 3'"
6' 4"
734
33^2
0.636
19-%
14-%
13-%"
2.14
20X20
4' 6"
6' 8"
7^|
3%
0.660
21-%
16-%
15-%"
2.30
21X21
4' 9"
7'0"
8
4
0.704
23 -%
17-%"
17-%"
2.40
22X22
5' 0''
7' 4"
4
0.725
26-%
19 %"
19-%"
2.57
23X23
24X24
5' 3"
5' 6"
7' 8"
8'0"
8%
*H
' 0.770
0.794
22-Ke"
24-Ke"
16-Ke"
16-Ke"
17-Ke"
2.85
2.95
25X25
5' 9"
8' 4"
9^<2
*H
0.835
26-Ke" 19-Ke*
3.10
26X26
6'0"
8' 8"
9%
5
. 858
29-Ke" 21-Ke"
21-Ke"
3.30
Superimposed load = 150 Ib. per sq. ft.
Panel
size
(feet)
Capital
diameter
Size of
drop
panel
Depth
of slab
(inches)
Depth
of drop
(inches)
Concrete
in cubic
feet per
sq. ft.
Round steel rods in each band
Steel in
Ib. per
sq. ft.
Direct
Across
direct
Diagonal
16X16
3' 6"
5' 4"
6
3
0.528
16-%
12-%
12-%"
2.24
17X17
3' 9"
5' 8"
63-4
334
0.571
18-%
13-%
13-%"
2.32
18X18
4' 0"
6' 0"
6%
. 595
20-%
15-%
15-%"
2.48
19X19
4' 3"
6' 4"
734
4
0.641
22-%
17-%
16-%"
2.54
20X20
4' 6"
6' 8"
7^|
4
0.662
25-%
19-%
19-%"
2.62
21X21
4' 9"
7' 0"
8
434
0.706
27-%
20 %
20 %"
2.82
22X22
5'0"
7' 4"
SM
0.727
23 Ke"
17-Ke"
3.15
23X23
5' 3"
7' 8"
4%
0.774
25 Ke"
19 Ke"
18-Ke"
3.24
24X24
5' 6"
8' 0"
934
5
0.817
27 Ke"
20-Ke"
20-Ke"
3.36
25 X 25
26X26
5' 9"
6' 0"
8' 4"
8' 8"
10
0.841
0.887
30-Ke''
32-Ke"
22-K 6 "
24-Ke"
22-Ke"
24-Ke"
3.58
3.72
Superimposed load = 200 Ib. per sq. ft.
j
~ Round steel rods in each band
Panel
size
(feet)
Capital
diameter
Size of
drop
panel
Depth
of slab
(inches)
Depth
of drop
(inches)
Concrete
in cubic
feet per
sq. ft.
Steel in
Ib. per
sq. ft.
Direct
Across
direct
Diagonal
16X16
3' 6"
5' 4"
6H
334
0.571
18-%"
13-%"
13-%"
2.46
17X17
3' 9"
5' 8"
7
0.618
20 %"
15 %"
14-%"
2.54
18X18
4' 0"
6' 0"
734
434
0.643
22-%"
17-%"
16-%"
2.67
19X19
4' 3"
6' 4"
434
0.685
24-%"
18-%"
18-%"
2.80
20X20
21X21
4' 6"
4' 9"
6' 8"
7' 0"
gg
JM
0.729
0.775
20-Ke"
15-Ke"
15 Ke"
16-Ke"
3.04
3.14
22X22
5' 0"
7' 4"
9
O '4.
0.799
25-Ke"
ig_7^ 6 "
18-Ke"
3.38
23X23
5' 3'
7' 8"
93^
5H
0.841
27-Ke"
21-Ke"
20-Ke"
3.54
24X24
25X25
5' 6"
5' 9"
8' 0"
8' 4"
10
$
0.887
0.954
31- Ke"
22-Ke"
24-Ke"
23-Ke"
3 . 66
3.77
26X26
6'0"
8' 8"
1 1 34
GH
1.002
34-Ke"
26-Ke"
25-Ke"
3 . 94
:
38
TABLE 10
FLAT SLAB FLOORS
NEW YORK CITY BUILDING CODE
INTERIOR SQUARE PANELS
DROP CONSTRUCTION
f e =650 for positive moment
f e =750 for negative moment
fs=16,000
FLAT
SLABS
Superimposed load = 250 Ib. per sq. ft.
Panel
size
(feet)
Capital
diameter
Size of
drop
panel
Depth
of slab
(inches)
Depth
of drop
(inches)
Concrete
in cubic
feet per
sq. ft.
Round steel rods in each band
Steel in
Ib. per
sq. ft.
Direct
Across
direct
Diagonal
16X16 3' 6
5' 4*
7M
4
0.662
17-%;
13-%*
13-%*
2.39
17X17 3' 9
5' 8*
8
4%
0.706
15-%*
15-%'
2.62
18X18 i 4'
19X19 4' 3
6' 0'
6' 4*
8*
4%
0.752
0.797
22-%*
25-%*
17-%*
19 %\
17%*
18-%*
2.76
2.87
20 X 20 4' 6
6' 8*
9%
5
0.859
21-^6"
15-Ke*.
3.11
21X21
4' 9
7' 0*
10%
0.906
23-He"
17 Ke".
3.29
22X22
5'0*
7' 4*
10%
6
0.953
25-Ke"
18 M
3.38
23X23
5' 3*
7' 8*
HM
6
1.014
27-He"
20-^g*
20-He
3.51
24X24
5' 6*
8' 0*
12
6H
1.060
30-He*
22 He".
22-^6
3.71
25X25
26X26
5' 9*
6'0*
8' 4*
8' 8*
12% 7%
13% m
1.129
1.215
32-^6*
27-M"
19-^*
3.80
3.98
Superimposed load = 300 Ib. per sq. ft.
Panel
size
(feet)
Capital
diameter
Size of
drop
panel
Depth
of slab
(inches)
Depth
of drop
(inches)
Concrete
in cubic
feet per
sq. ft.
Round steel rods in each band
Steel in
Ib. per
sq. ft.
Direct
Across
direct
Diagonal
16X16
17X17
3' 6*
3' 9*
5' 4*
5' 8*
8j*
J*
0.749
0.796
20-%*
i3-% :
13-%*
15-%*
2.46
2.62
18X18
4' 0*
6' 0*
9%
5
0.858
22-%*
17-%*
16-%*
2.67
19X19
4' 3"
6' 4*
5%
0.928
25-%*
19-%\
1 ?-^" / ,
2.87
20X20
4' 6*
6' 8*
lit!
6%
0.996
20-Ke"
3.04
21X21
4' 9*
7' 0*
n%
6%
1.043
22-Ke*
17-K6"
16 -He*
3.14
22X22
5' 0*
7' 4*
12 J^
6%
1.104
25-He"
18 T^R*
18-Ke"
3.36
23X23
24X24
5' 3*
5' 6*
7' 8*
8' 0*
13%
13%
7%
7 V*>
1.169
1.215
27-Ke*
30-He*
20-^6*
22-He*
20-K6*.
3.51
3.71
25X25
5' 9*
8' 4*
14^
8
1.283
32-Ke*
24-K6*
23 J^ *
3.80
26X26
6'0*
8' 8*
iS
9
1.375
19-8*
19-M*
3.90
Superimposed load = 350 Ib. per sq. ft.
Panel
size
(feet)
Capital
diameter
Size of
drop
panel
Depth
of slab
(inches)
Depth
of drop
(inches)
Concrete
in cubic'
feet per
sq.ft.
Round steel rods in each band
Steel in
Ib. per
sq. ft.
Direct
Across
direct
Diagonal
i
|
16X16
3' 6*
5' 4*
9^ 5
0.827
18-%*
13-%*
13-%* ! 2.46
17X17
3' 9*
5' 8*
10 5%
0.882
21-%*
15-%*
15-%* 2.68
18X18
4' 0* 6' 0*
10% 6
0.951
23-%'
17 %;
16-%* 2.74
19X19
4' 3* 6' 4*
11 4 6%
.017
26-%*
18-%*^ i 2.90
20X20
4' 6* 6' 8*
.101
21-He*.
1 5- K 6 *
21X21
4' 9* 7' 0* i 13% 7%
.169
17 "^i e*
16-Ke* 3^21
22X22
5' 0* 7' 4* 14 7%
.239
25-lil"
19-Ke*
IS-Mo" 3.38
23X23
5' 3* 7' 8* 15 8
.324
28-K 6 *
20 Ke*
24X24
5' 6* 8' 0* 15% 8%
.393
22- He*
21 7A*,"
3.64
25X25
5' 9* 8' 4*
16% 9% .483 32-T<"
24-Ke*
23 TY*
3.80
26X26
6' 0* 8' 8*
17% 9%
.569 27-H*
20-M*
19-M"
3.98
39
FLAT
SLABS
FLAT SLAB FLOORS
NEW YORK CITY BUILDING CODE
INTERIOR SQUARE PANELS
CAP CONSTRUCTION
f c =650 for positive moment
f c =750 for negative moment
f, =16,000
n = 15
Superimposed load = 100 Ib. per sq. ft.
Round steel rods in each band
Panel size
(feet)
Capital
diameter
Depth
of slab
(inches)
Concrete
in cubic
feet per
sq. ft.
Steel in
Ib. per
sq. ft.
Direct
Direct over
column, add'l
each way
Across
direct
Diagonal
16X16
3' 6"
W
0.562
14-%
8-%
8-%"
8-%"
1.91
17X17
18X18
4'0"
^
0.605
0.645
18-%
10-%
n-%
10-%"
9 %"
10-%"
2.04
2.14
19X19
4' 3"
8
0.667
21-%
n-%
12-%"
12-%"
2.34
20X20
4' 6"
8K
0.708
23-%
13-%
13-%"
13-%"
2.44
21X21
22X22
23X23
4' 9"
5' 0"
5' 3"
9
9K
10
0.750
0.791
0.833
19-K
21-K
24-K
IO-K
12-K
11-Ke"
12-K e "
13-Ke"
11-Ke"
12-Ke"
13-Ke"
2.66
2.78
2.95
24X24
5' 6"
IOK
0.875
26-K
15-Ke"
14-K e"
3.08
25X25
5' 9"
11
0.917
29-K
15-K
16-Ke"
15-K e"
3.22
26X26
0.937
32-K
16-K
18-Ke"
18-Ke"
3.56
Superimposed load =150 Ib. per sq. ft.
Panel size
(feet)
Capital
diameter
Depth
of slab,
(inches)
Concrete
in cubic
feet per
sq. ft.
Round steel rods in each band
Steel in
Ib. per
sq. ft.
Direct
Direct over
column, add'l
each way
Across
direct
Diagonal
16X16
3' 6*
7%
0.645
16-%"
8-%"
9-%
9-%"
2.12
17X17
3' 9"
S^A
0.687
18-%"
10 %"
10-%
10-%"
2.25
18X18
4'0"
O 1 *
0.708
21-%"
n-%"
12-%
12-%"
2.48
19X19
4' 3"
9
0.750
24-%"
13-%"
13 %
13-%"
2.62
20X20
4' 6"
9K
0.792
20-Ke"
10-Ke"
11-K "
11-Ke"
2.85
21X21
4' 9"
10
0.833
22-Ke"
12 K e"
12-K "
12-K e"
2.99
22X22
23X23
5' 0"
5' 3"
11
0.875
0.917
25-Ke"
27-Ke"
15-Ke"
14-K "
15-K "
13 K 6 "
14-K e "
3.20
3.30
24X24
5' 6"
UK
0.958
23-K"
13 K
3.60
25X25
5' 9"
12
1.000
26-K"
12-K"
14-K" 3.78
26X26
6'0"
12K
1.042
14-K"
15-K
15-K"
3.93
Superimposed load = 200 Ib. per sq. ft.
Panel size
(feet)
Capital
diameter
Depth
of slab
(inches)
Concrete
in cubic
feet per
sq. ft.
Round steel rods in each band
Steel in
Ib. per
sq. ft.
Direct
Direct over
column, add'l
Across
Diagonal
each way
16X16
3' 6"
8^
0.687
18-%"
10-%
10-%"
10-%"
2.39
17X17
3' 9"
8%
0.729
21-%"
11-%
12 %"
11-%"
2.55
18X18
19X19
4'0"
4' 3"
IH
0.771
0.812
18-Ke"
19-K e"
10-K "
ii-K "
IO-K e"
ll-K e"
9-Ke"
11-K e"
2.72
2.96
20X20
4' 6"
IOK
0.855
22-Ke"
12-K "
12-Ke"
12-K e "
3.27
21X21
22X22
4' 9"
5'0"
10
UK
0.896
0.958
25-Ke"
21-K"
13-K "
\&'
13-Ke"
11 K"
3.34
3.52
23X23
5' 3"
12
1.000
23-K"
12-K
13_^
12-K"
3.61
24X24
5' 6"
12K
1.042
25 K"
13-K
14-K"
3.90
25X25
26X26
5' 9"
6' 0"
13
1.083
1.145
QO I/ ' *
30-K"
16-K
15-K"
17-K"
15-K"
16-K"
4.09
4.25
40
TABLE 11
FLAT SLAB FLOORS
NEW YORK CITY BUILDING CODE
INTERIOR SQUARE PANELS
CAP CONSTRUCTION
f c =650 for positive moment
f e =750 for negative moment
f,=16,
n=15
FLAT
SLABS
Superimposed load = 250 Ib. per sq. ft.
Panel size
(feet)
Capital
diameter
Depth
of slab
(inches)
Concrete
in cubic
feet per
sq. ft.
Round steel rods in each band
Steel in
Ib. per
sq. ft.
Direct
Direct over
column, add'l
Across
direct
Diagonal
* 1
each way
16X16 i 3' 6"
9
0.750
19-%"
10-%"
11-H"
n-%"
2.53
17X17 i 3' 9*
9^
0.791
17^6*
9 ^" 9~J^e"
9 'T i R "
2.75
18X18 4' 0*
10
0.833
19 M 6*
10-Ke* 11-K"
10-J^e"
3.01
19X19 1 4' 3*
0.875
21-Jl 6*
12-Ke*
i2-Kfr
3.21
20X20
4' 6"
11%
0.937
23 Ms*
12 1A e"
13-K"
3.32
21X21
4' 9*
11%
0.979
20-}^"
11-^" 11-^|"
ii-%"
3.57
22X22
5'0"
12M
.042
oo \&
12 J^" 12^6"
12 J^"
3.74
23X23
5' 3*
13%
.104
24-y 2
13 V^" ! 13 J^"
13-^"
3.87
24X24
5' 6*
14
.167
13-^" I 15-J^"
1 5-J4 "
4.08
25X25
5' 9*
14%
.229
29-^
14 M" 16 J-*
16-H*
4.27
26X26
15%
.292
14-K"
17-K'
4.36
Superimposed load = 300 Ib. per sq. ft.
Panel size
(feet)
Capital
diameter
Depth
of slab
(inches)
Concrete
in cubic
feet per
sq. ft.
Round steel rods in each band
Steel in
Ib. per
sq. ft.
Direct
Direct over
column, add'l
each way
direct j
16X16
3' 6"
10%
0.854
19-%*
10-%"
11-%*
11-%*
2.53
17X17
3' 9*
11
0.917
17-He*
8 J^ "
9 J*f e*
9 M e*
2.81
18X18
4'0*
0.958
Q-T^g"
10-J^ 6 *
10-Ke*
2.95
19X19
4' 3*
12%
.021
21 J^ e*
H~J^6*
12-Ke*
3.12
20X20
4' 6*
13
.083
23 %K"
H-Ke*
13 J^e"
3.29
21X21
4' 9"
13% . 146
20-^
11 Jl
11-M"
3.55
22X22
5' 0*
14^ .208
22 %
11 "
12 J^
12 i^
3.69
23X23
5' 3*
15% .271
24 i^
12 W"
14 J^
13 J-^
3.87
24X24
5' 6*
16 .333
27~M
13-^"
15-M
14~M
4;07
25X25
5' 9*
17 .417
29-H
lg_i,^
Igi^,
4.22
26X26
6'0"
18 .500
its-
17-M"
17-H
4.36
Superimposed load = 350 Ib. per sq. ft.
Panel size
(feet)
Capital
diameter
Depth
of slab
(inches)
Concrete
in cubic
feet per
sq. ft.
Round steel rods in each band
Steel in
Ib. per
sq. ft.
Direct
Direct over
column, add'l
each way
Across
direct
Diagonal
16X16
17X17
3' 6*
3' 9"
12%
0.958
1.021
83f-
9~/8
n : ?|;.
11-%" 2.58
9-Jie* 2.81
18X18
4'0"
13
1.083
19- JH*
9-He"
10-Jie"
10-H" 2.95
19X19
4' 3*
13%
1.146
10 Ji e*
12 J^e*
12 Ke" 3.18
20X20
4' 6*
14%
1.229
23 IA R"
11 Me*
13 J^is"
13-Ke" 3.29
21X21
4' 9*
15^
1T292
20-M*
9 .H
n-H
11-M* 3.52
22X22
5' 0*
16^
1.375
22-K*
10 V
12 J^
12->i" 3.69
23X23
5' 3*
17%
1.437
11 i^
14_i^
13-M"
3.84
24X24
5' 6*
18%
1.521
27-M"
12-M
15 J-^
4.11
25 X 25
5' 9*
1.604
29-M"
16 H
16-1^"
4.22
26X26
6'0"
20
1.667 32-M*
14->r
17-K
17-M"
4.41
41
FLAT
SLABS
FLAT SLAB FLOORS
CHICAGO BUILDING CODE
INTERIOR SQUARE PANELS
f c = 700 for positive moment
f c =805 for negative moment
f s =18,000
.--4-
&m
l^p
-+
i
^dT\ i
#;vo
5 i ^
^4.
wj
Drop Conatuction
X
-J D!
<Q
a.
ft
^i l
q
;i N
^4-' x/
T Cap Construction
?r^ri/^ R
U>
Section on C-C
^-^
Bending Moment Coefficients
Moment coefficients shown on diagram are to be multiplied by WL.
W = wL*
w = total dead and live load in pounds per square foot.
L = span center to center of columns for square panels, or average span for rectangular
panels where long dimension is not more than 1.05 times short dimension.
Values shown above moment coefficients are percentages of numerical sum of moments in one
direction across panel.
Numerical sum of moments in one direction across panel:
for drop construction O.OS25TFL
for cap construction 0.0679 WL
Minimum size of drop = \%L
Minimum diameter of capital = 0.225L
(6
Minimum t = j VW/44
lL/32
t = total thickness of slab.
t is in inches, L is in feet.
42
TABLE 12
FLAT SLAB FLOORS
CHICAGO BUILDING CODE
INTERIOR SQUARE PANELS
DROP CONSTRUCTION
f e = 700 for positive moment
f e =805 for negative moment
f s =18,000
n = 15
FLAT
SLABS
Superimposed load = 100 Ib. per sq. ft.
Panel
size
(feet)
Capital
diam-
eter
Sise of
drop panel
Depth
of slab
(inches)
Depth
of drop
(inches)
Concrete
in cubic
feet per
sq. ft.
Round steel rods in each band
Steel in
Ib. per
sq.ft.
Direct
Across
direct
Diagonal
16X16
3' 6*
5' 4*X5'4*
6
3M
0.54
13-%*
Q a/
10-%
1.83
17X17
3' 9*
5'8*X5'8*
3$i
0.58
15 %*
10%
11 %
1.94
18X18
4'0*
6' 0* X 6' 0*
6?4 411
0.60
H-%
12 %
2.04
19X19
4' 3*
6' 4*X6' 4*
7J4 4 \s
0.65
19-%*
13-%
14%
2.19
20X20
21X21
4' 6*
4' 9*
6' 8* X 6' 8*
7'0*X7'0*
8 * 4X.
0.67
0.72
22-%*
24-%*
14-%
16-%
16-% ! 2.35
17 % ! 2.45
22X22
5' 0*
7' 4*X7' 4*
5
0.74
27-%*
18-%
19-%
2.63
23X23
5' 3*
7' 8*X7'8*
8^i
51-4
0.78
22-Ke*
14 Ke"
16-K *
2.81
24X24
5' 6*
8' 0*X8' 0*
9 / 5H
0.81
25- K 6*
16-K e*
17-K "
2.99
25X25
26X26
5' 9*
6'0*
8'4*X8'4*
8' 8*X8'8*
6
6
0.85
0.87
27-Ke*
30-Ke*
%-%l"'
18-K *
21-Ke"
3.04
3.33
Superimposed load 150 Ib. per sq. ft.
Panel
size
(feet)
Capital
diam-
eter
Size of
drop panel
Depth
of slab
(inches)
Depth
of drop
(inches)
Concrete
in cubic
feet per
sq. ft.
Round steel rods in each band
Steel in
Ib. per
sq. ft.
Direct
Across
direct
Diagonal
16X16
3' 6*
5'4*X5'4*
6
*y*
0.54
17-%
n-%
12-%
2.31
17X17
3' 9*
5'8*X5'8*
6K
3%
0.58
19-%
13 %
14-%
2.46
18X18
4'0*
6' 0* X 6' 0*
4
0.61
21-%
15-%
16-%
2.63
19X19
4' 3*
6' 4*X6' 4*
7j^
0.65
25-%
17-%
18 %
2.84
20X20
4' 6*
6' 8* X 6' 8*
71,4
4%
0.67
27-%
18-%
20-%
2.95
21X21
4' 9*
7'0*X7'0*
8
5
0.72
30-%
20-%
22-%
3.09
22X22
5' 0*
7'4*X7'4*
0.74
25-Ke*
16 y\
17-K 6
3.23
23X23
5' 3*
7' 8*X7'8*
8^| 5$i
0.79
17-K
18-Ke
3.33
24X24
5' 6*
8' 0*X8' 0*
9 5% 0.81
30-Ke*
20-K
21-Ke
3.56
25X25
5' 9*
8'4*X8'4*
9K 6 0.85
34-Ke*
22 -K
23-Ke
3.83
26X26
6'0*
8'8*X8'8*
10 6 0.89
36-Ke*
24-K
25-K.
3.94
Superimposed load = 200 Ib. per sq. ft.
Panel
size
(feet)
Capital
diam-
eter
Size of
drop panel
Depth
of slab
(inches)
Depth
of drop
(inches)
Concrete
in cubic
feet per
sq. ft.
Round steel rods in each band
Steel in
Ib. per
sq. ft.
1 direct
Diagonal
16X16
3' 6
5'4*X5' 4*
6J4
3H
0.56 j 21-%
13-%*
14-%*
2.74
17X17
3' 9
5' 8*X5'8*
6^
o *x
. 58 24-%
16-%*
17-%*
3.01
18X18
4'
6' 0* X 6' 0*
7
4^i
0.62 27-%
18-%*
20-%*
3.25
19X19
4' 3
6'4*X6'4*
7J4
4L
0.67
31-%
21-%*
22-%*
3.47
20X20
4' 6
6' 8* X 6' 8*
8
4i
0.72
24-K
17-Ke
18-Ke*
3.52
21X21
4' 9
7' 0* X 7' 0*
8J^
5J4
0.76
26-K
18-Ke"
3.54
22X22
5'0
7'4*X7'4*
9
5^|
0.80
28-K
18-Ke
20-K e"
3.66
23X23
5' 3
7' 8*X7'8*
9J^
6
0.85
30-K
20-K 6
21-Ke*
3.71
24X24
5' 6
8'0'XS'O*
10
0.89
34-K
22-Ke
24-K e*
4.03
25X25
26X26
5' 9*
6' 0*
8'4*X8'4*
8' 8*X8' 8*
11
i
0.94
0.98
37-K
39- K
24-K 6
28-K
25-Ke*
29-Ke*
4.13
4.39
43
FLAT
SLABS
TABLE 12
FLAT SLAB FLOORS
CHICAGO BUILDING CODE
INTERIOR SQUARE PANELS
DROP CONSTRUCTION
f e =700 for positive moment
f e =805 for negative moment
f s =18,000
n=15
Superimposed load = 250 Ib. per sq. ft.
Round steel rods in each band
Panel
size
(feet)
Capital
diam-
eter
Size of
drop panel
Depth
of slab
(inches)
Depth
of drop
(inches)
Concrete
in cubic
feet per
sq. ft.
Steel in
Ib. per
sq. ft.
Direct
Across
direct
Diagonal
16X16
3' 6"
5' 4"X5' 4"
6%
4K
0.60
23-%"
14-%"
16-%"
3.03
17X17
3' 9"
5' 8" X 5' 8"
7 1/:
4/4
0.65
24-%"
17-%"
18-%"
3.12-
18X 18
4' 0"
6' 0" X 6' 0"
7 3 i
4 3 1
0.69
27-%"
18-%"
19-%"
3.21
19X19
4' 3"
6' 4" X 6' 4"
8J4
5M
0.74
30-%"
20-%"
21-%"
3.33
20X20
21X21
22X22
23X23
24X24
4' 6"
4' 9"
5' 0"
5' 3"
5' 6"
6 8" X 6' 8"
7' 0" X 7' 0"
7' 4" X 7' 4"
7' 8" X 7' 8"
8' 0" X 8' 0"
8M
10>|
5/"4
5*
88'
0.78
0.82
0.87
0.92
0.96
Al
8$j
37-Ke*
18 -He"
20-Ke"
22-Ke"
24-Ke"
18-Ke*
20-Ke"
24l#
3.63
3.77
3.91
4.16
4.31
25X25
26X26
5' 9"
6'0"
8' 4"X8' 4"
8' 8"X8' 8"
12
7*4
7M
1.03
1.08
39-He"
42-Ke*
25-Ke"
28-Ke"
30-Ke"
4.41
4.63
Superimposed load = 300 Ib. per sq. ft.
Round steel rods in each band
Panel
size
(feet)
Capital
diam-
eter
Size of
drop panel
Depth
of slab
(inches)
Depth
of drop
(inches)
Concrete
in cubic
feet per
sq. ft.
Steel in
Ib. per
sq. ft.
Direct
Across
direct
Diagonal
16X16
3' 6"
5' 4"X5' 4"
7X
4M
0.65
24-%"
16-%"
17-%"
3.20
17X17
3' 9"
5' 8" X 5' 8"
8
4%
0.72
27-%"
17-%"
18-%"
3.28
18X18
4' 0"
6' 0" X 6' 0"
si*
0.77
21-Ke"
14-Ke"
3.49
19X19
4' 3"
6' 4"X6'4"
9
5/-^
0.81
24-Ke"
16-Ke"
17 H e"
3.66
20X20
4' 6"
6' 8" X 6' 8"
9M
6
0.85
27-He"
19_7^ 6 *
3.85
21X21
4' 9"
7' 0" X 7' 0"
10
6/4
0.89
20 -He"
21-Ke"
4.09
22X22
5' 0"
7' 4" X 7' 4"
6*4
0.94
33-Ke"
4.20
23X23
5' 3"
7' 8" X 7' 8"
1 1
7
0.99
35 He"
23-He"
25 He"
4.40
24X24
5' 6"
8' 0"X8' 0"
11%
7K
1.05
39-Ke"
25-Ke"
26-He"
4.55
25X25
5' 9"
8' 4"X8' 4"
I2H
7 3 '
1.10
33-M"
23-^"
4.78
26X26
6' 0"
8'8"X8' 8"
8
1.15
35-^"
25-K"
26-K"
5.15
Superimposed load = 350 Ib. per sq. ft.
Round steel rods in each band
Panel
size
(feet)
Capital
diam-
eter
Size of
drop panel
Depth
of slab
(inches)
Depth
of drop
(inches)
Concrete
in cubic
feet per
sq. ft.
Steel in
Ib. per
sq. ft.
Direct
Across
direct
Diagonal
16X16
3' 6"
5'4"X5' 4"
8
4H
0.71
24-%"
16-%"
17-%"
3.20
17X17
3' 9"
5' 8"X5' 8"
8/^
5%
0.76
27-%"
18-%"
19-%"
3.36
18X18
4' 0"
6' 0" X 6' 0"
9
5/-^
0.80
23-He"
16-Ke"
3.64
19X19
20X20
4' 3"
4' 6"
6' 4" X 6' 4"
6' 8" X 6' 8"
10 2
6
0.84
0.89
25 He"
27-H'e"
17-Ke"
19-Ke"
18-Ke"
20- 1{ 6 "
3.82
4.00
21X21
22X22
23 X 23
24X24
4' 9"
5' 0"
5' 3"
5' 6"
7'0"X7'0"
7' 4"X7' 4"
7' 8"X7'8"
8' 0"X8' 0"
12 *
p
0.95
.00
.07
.12
31-Ke"
Ijirk
20-Ke"
22-Ke"
25-Ke"
22-He"
24-He"
ttfy"
4.24
4.42
4.63
4.76
25X25
5' 9"
8' 4"X8' 4"
13
8
.16
34- \/ "
23i^"
5.00
26X26
6' 0*
8' 8"X8' 8"
13?i
.22
38-M"
25-H"
26-M"
5.29
44
TABLE 13
FLAT SLAB FLOORS
CHICAGO BUILDING CODE
INTERIOR SQUARE PANELS
FLAT
SLABS
CAP CONSTRUCTION
f c = 700 for positive moment
f c =805 for negative moment
f s =18,000
n=15
Superimposed load = 100 Ib. per sq. ft.
Panel size
(feet)
Capital
diameter
Depth
of slab
(inches)
Concrete
in cubic
feet per
sq. ft.
Round steel rods in each band
Steel in
Ib. per
sq. ft.
Direct
Add'l in each
band over
each column
Across
direct
Diagonal
16X16
3' 6*
6%
0.562
13-%
o S/
9-%
9-%
2.17
17X17
3' 9*
0.604
14%
10^
10-%
10-%
2.34
18X18
4'0*
7%
0.646
16-%
H-%
H-%
H-%
2.46
19X19
4' 3*
8
0.667
12-%
13-%
13-%
2.69
20X20
4' 6"
8K
0.708
21%
14-%
14-%
14-%
2.85
21X21
4' 9"
9
0.750
17-Ke*
12-K
3.04
22X22
5'0*
0.792
19-Ke"
13-K
13_j^ 6 *
3.23
23X23
5' 3* 9%
0.812
21-Ke"
15-K
14 K 6*
14-K
3.40
24X24
5' 6* 10%
0.854
24-K6*
16-K
16-K 6*
16-K
3.65
25X25
5' 9* 10%
0.896
26-K6"
17-K
18 ~K K"
18-K
3.85
26X26
6'0* UX
0.937
19-K
19-He'
19-K *
3.97
Superimposed load = 150 Ib. per sq. ft.
Panel size
(feet)
Capital
diameter
Depth
of slab
(inches)
Concrete
in cubic
feet per
sq. ft.
. Round steel rods in each band
Steel in
Ib. per
sq. ft.
Direct
Add'l in each
band over
Across Diagonal
each column
16X16
3' 6"
7K
0.625
15-%
10-%*
10-%
10-%
2.50
17X17
3' 9"
8
0.667
17-%
11-%*
H-%
11-%
2.65
18X18
4'0*
0.708
19-%
12-%*
13-%
13-%
2.83
19X19
4' 3*
9
0.750
21-%
14-%*
14-%
14-%
2.96
20X20
4' 6"
0.771
24-%
16-%*
17-%
17-%
3.32
21X21
4' 9"
10
0.833
20-K"
13-Ke"
13 K
13 K
3.46
22X22
0.875
22-Ke*
15 K
15 K
3.67
23X23
5' 3"
11
0.917
24-Ke"
lg_7^ K "
16-K
3.83
24X24
5' 6*
0.958
26-K*
17-K"
18-K
18-K
3.96
25X25
5' 9*
12
1.000
29-Ke"
19 KB*
20-K
20-K 6
4.26
26X26 i 6' 0*
1.042
16-H"
4.54
Superimposed load = 200 Ib. per sq. ft.
Panel size
(feet)
Capital
diameter
Depth
of slab
(inches)
Concrete
in cubic
feet per
sq. ft.
Round steel rods in each band
Steel in
Ib. per
sq. ft.
Direct
Add'l in each
band over
each column
Across
direct
Diagonal
16X16
3' 6*
8^
0.687
16-%*
n-%"
H-%
n-%
2.76
17X17
3' 9"
8%
0.729
18-%*
13-%
13-%
2.95
18X18
4'0*
0.771
15-K 6
10 Ks*
ll-K
3.21
19X19
4' 3*
o &/
0.813
17-K
12-K 6*
12 K
12-K
3.42
20X20
4' 6"
10^4
0.854
20-K 6
13-K
13-K
3.60
21X21
4' 9"
10%
0.896
22-Kc
14-K e"
15-K
15-K
3.82
22X22
5' 0"
11 \^L
0.937
24-Ke
16 K
16-K
4.00
23X23
5' 3*
12
1.000
13 1 ^"
14 14
4.21
24X24
5' 6"
12M
1.042
23->i*
14 *
15~M
15~M
4.46
25X25
5' 9*
13 1.083
25-M*
1 Q1,4 "
17 M
17_i^
4.76
26X26
6'0* 13H 1-125
27->i*
i8-y z "
i*4j
18-H
4.94
45
FLAT
SLABS
TABLE IS
FLAT SLAB FLOORS
CHICAGO BUILDING CODE
INTERIOR SQUARE PANELS
CAP CONSTRUCTION
/ c =700 for positive moment
f c =805 for negative moment
f s =18,000
n=15
Superimposed load = 250 Ib. per sq. ft.
Panel size
(feet)
Capital
diameter
1
Depth
of slab
(inches)
Concrete
in cubic
feet per
sq. ft.
Round steel rods in each band
Steel in
Ibs. per
sq. ft.
Direct
Add'l in each
band over
each column
Across
direct
Diagonal
16X16
3' 6"
9
0.750
17-%"
n-%"
12-%"
12-%"
2.92
17X17
3' 9"
0.792
13_s^/>
13-%"
13-%"
3.12
18X18
19X19
20X20
4' 0"
4' 3"
4' 6"
10
1 1 \A
0.833
0.896
0.937
19-Me"
21-He"
jjjjjj:
13-Ke"
13-Ke"
14-J-le"
3.42
3.67
3.86
21X21
4' 9"
11%
0.979
15 7.Y"
1 6- 7-<" c "
16-Ke"
4.05
22X22
5' 0"
1.042
20-3-i"
13-3-2"
13-3-2"
13->2
4.29
23X23
5' 3"
133-1
1.104
21 \4t"
14-jJ*
153-2"
15_L
4.51
24X24
5' 6"
14
1.167
24-3-2 "
Jg-l^l'
16-3-2
4.71
25X25
5' 9"
143-2
1.208
26-3-2"
16 !,"
173-2 "
173-2
4.91
26X26
6' 0"
15^
1.271
28-3-2"
18-X 2 "
19-H"
19->2
5.13
Superimposed load = 300 Ib. per sq. ft.
Panel size
(feet)
Capital
diameter
Depth
of slab
(inches)
Concrete
in cubic
feet per
sq. ft.
Round steel rods in each band
Steel in
Ib. per
sq. ft.
Direct
A4d'l in each
band over
each column
Across
direct
Diagonal
I
16X16
3' 6"
103-4
0.854
18-%"
H-%"
12-%"
12-^"
3.01
17X17
3' 9"
11
0.917
10-Kc
3.20
18X18
4' 0"
113-2
0.958
17-Me"
11 M
1 1-J.fg
ii-Ko
3.42
19X19
4' 3"
1224
1.021
19-Ke"
12-K
13 J-Y
3.67
20X20
4' 6"
13
1.083
13-H
14-Ke
14-Ke
3.80
21X21
4' 9"
133-2
1.125
23 J-f e"
15-H
4.05
22X22
5' 0"
1434
1.187
20^2"
13 3-2
13 3-2"
4.27
23X23
5' 3"
15
1.250
22-3V'
14-3*2
14-3-2
14-3-2"
4.47
24X24
5' 6"
16
1.333
24-3-2"
15 l-o'
Igi^
jgi,^"
4.71
25X25
5' 9"
17
1.417
16-3-2
17-3-2
17-3-2"
4.84
26X26
6'0"
17%
1.479
28-3-2"
18-J-2
19-H
19->2"
5.13
Superimposed load = 350 Ib. per sq. ft.
Panel size
(feet)
Capital
diameter
Depth
of slab
(inches)
Concrete
in cubic
feet per
sq. ft.
Round steel rods in each band
Steel in
Ib. per
sq. ft.
Direct
Add'l in each
band over
each column
Across
direct
Diagonal
16X16 3' 6"
17X17 3' 9"
18X18 4' 0"
19X19 4' 3"
!$
13
0.958
1.021
1.083
1.146
18-%"
15-Ke"
17-Ke"
19-Ke"
io-K*
12-He"
11 ~? i C
H-Ke"
13-He"
3.01
3.28
3.42
3.67
20X20 4' 6"
14> 2
1.208
14 J-f e"
14-Me"
3.86
21X21 4' 9"
15J4
1.271
23 J--f "
15 M e"
16 M e"
4.05
22X22
5' 0"
163^
1.354
20 V2 "
133^"
133-2"
133-2"
4.29
23X23
5' 3"
17K
1.437
22-^"
14-3-2"
14-3-2"
14-3-2"
4.47
24X24
5' 6"
1.521
23-3-2"
15-3-2"
lg_ i^"
jg_i^^
4.64
25X25
5' 9"
19
1.583
17-3-2"
17_i<"
173-2 "
4.91
26X26
6' 0*
20
1.667
28-M"
19-3-2"
19-M"
5.13
46
SECTION 3
RECTANGULAR BEAMS
Table 14 and Diagram 18 may be used in the design of rectangular beams. Dia-
gram 18 may also be employed to determine the safe resisting moment of a given beam
and the greatest unit stresses due to a given bending moment.
Example of Design of Rectangular Beam
Design a simply supported rectangular beam to carry a total load, of 3000 Ib. per ft. on
a span of 20ft.;f e = 650; /. = 16,000; n = 15.
Reading from the intersection of lines representing f c = 650 and /, = 16,000 in
Diagram 18, it is found that ^ = 107.5 and j = 0.875 (Table 14 gives values of
107.7 and 0.874 respectively).
a - f = (300 s )(20); (12) - 1,800,000 in.*.
o o
- 16 ' 75
Assuming b = 14 in. d = 34.5 in.
M ' _ 1,800,000 o 7
"A/a " (16,000) (0.875) (34.5) "
or A s = (0.0077) (14) (34.5) = 3.72 sq. in.
From Table 15 which gives areas and perimeters of combinations of four rods, we
find that the area of three 1^-in. and one 1-in. round rods is 3.77 sq. in.
To make a complete design, the bond stress and shearing stress should also be
investigated.
Reviewing Design of Rectangular Beam
Given a beam 12 in. wide, 30 in. deep to steel, reinforced with four l-in. round rods
and subjected to a bending moment of 1,500,000 in.-lb. Find the unit stresses in the
steel and concrete, n = 15.
M_ 1,500,000 _
bd* (12) (30) 2
'- KF - - - 87
From Diagram 18
f e = 805 and /. = 18,200
Using Diagrams for Rectangular Beams One Inch Wide
Design a rectangular beam to resist a moment of 1,000,000 in.-lb., assuming f c = 750
andf, = 18,000.
Taking b = 12 in., the bending moment per inch of width is
^00 = 83,333 in,lb.
Then from Diagram 24
d = 26 in. and A, = (12) (0.204) = 2.448 sq. UL,
47
RECTANGULAR BEAMS
Finding Points to Bend Horizontal Steel
Diagram 25 is for use in determining the points at which horizontal steel in beams
or slabs can be bent so that the steel remaining will not be less than that required to
take the bending moment. The curves in the lower left hand corner are maximum
bending moment curves for the center and supports of beams for different conditions of
loading and restraint. They give the proportion of the steel required at different
points along the beam from support to center.
How far from the support of a simple beam of 2Q-ft. span, uniformly loaded, can four
tenths (0.4) of the steel be bent up?
Using the scale which reads up from the bottom, enter at 0.4 and follow hori-
zontally to the curve marked "uniform load, simple span, bottom steel." The bend
point is shown to be 0.183 of the span length from the support. Following up to the
line for a 20-ft. span and then horizontally to the right hand scale, this distance is
found to be 44 in. from the support.
48
TABLE 14
RECTANGULAR
BEAMS
VALUES OF Ar, /, p AND K
nf c
K =
n = 12
/
fc
k
3
P
K
/.
fc
k
3
P
K
500
0.300
0.900
0.0054
67.5
.
500
0.261
0.913
0.0038
59.6
550
0.320
0.893
0.0063
78.7
550
0.280
0.907
0.0045
69.4
600 0.340
0.887
0.0073
90.5
600
0.298
0.901
0.0053
80.5
650 0.358
0.881
0.0083
102.5
650
0.315
0.895
0.0060
91.6
14,000
17,000
700 0.375
0.875
0.0094
114.8
700
0.331
0.890
0.0068
103.1
750 0.391
0.870
0.0105
127.6
750
0.346
0.885
0.0076
114.7
800
0.407
0.864
0.0116
140.6
800
0.361
0.880
0.0085
127.1
850
0.421
0.860
0.0128
154.0
850
0.375
0.875
0.0094
139.5
900
0.435
0.855
0.0140
167.4
900
0.389
0.870
0.0103
152.2
500
0.286
0.905
0.0048
64.7
500
0.250
0.917
0.0035
57.2
550
0.306
0.898
0.0056
75.5
550
0.268
0.911
0.0041
67.2
600
0.324
0.892
0.0065
86.7
600
0.286
0.905
0.0048
77.6
650
0.342
0.887
0.0074
98.6
650
' 0.302
0.899
0.0055
88.4
15,000
18,000
700
0.359
0.880
0.0084
110.4
700
0.318
0.894
0.0062
99.6
750
0.375
0.875
0.0094
123.4
750
0.333
0.889
0.0069
111.1
800
0.390
0.870
0.0104
135.7
800
0.348
0.884
0.0077
123.0
850 0.405
0.865
0.0115
149.2
850
0.362
0.879
0.0085
135.2
I 900 0.418
0.861
0.0125
162.0
900
0.375
0.875
0.0094
147.7
500
0.273
0.909
0.0043
62.0
500
0.231
0.923
0.0029
53.3
550
0.292
0.903
. 0050
72.5
550
0.248
0.917
0.0034
62.6
600
0.310
0.897
0.0058
83.5
600
0.265
0.912
0.0040
72.6
650
0.328
0.891
0.0067
94.9
650
0.281
0.906
0.0046
82.7
16,000
20,000
700
0.344
0.885
0.0075
106.7
700
0.296
0.901
0.0052
93.3
750
0.360
0.880
0.0084
118.8
750
0.310
0.897
0.0058
104.3
800
0.375
0.875.
0.0094
131.3
800
0.324
0.892
0.0065
115.6
850
0.389
0.870
0.0103
144.0
850
0.338
0.887
0.0072
127.4
900
0.403
0.866
0.0113
157.0
900
0.351
0.883
0.0079
139.4
n = 15
/. fc
k
i
P
K f.
fc
k
3
P
K
500
0.349
0.884
0.0062
77.1
500
0.306
0.898
0.0045
68.7
550
0.371
0.876
0.0073
89.4
550
0.327
0.891
0.0053
80.1
600
0.391
0.870
0.0084
102.1
600
0.346
0.885
0.0061
91.8
650
0.411
0.863
0.0095
115.2
650
0.365
0.878
0.0070
104.2
14,000
17,000
700
0.429
0.857
0.0107
128.6
700
0.382
0.873
0.0079
116.7
750
0.446
0.851
0.0120
142.2
750
0.398
0.866
0.0088
129.2
800
0.462
0.846
0.0132
156.3
800
0.414
0.862
0.0097
142.7
850
0.477
" 0.841
0.0145
170.4
850
0.429
0.857
0.0107
155.9
900
0.491
0.836
0.0158
184.8
900
0.443
0.853
0.0117
169.7
500
0.333
0.889
0.0056
74.1
500
0.294
0.902
0.0041
66.3
550
0.355
0.882
0.0065
86.4
550
0.314
0.895
0.0048
77.4
600
0.375-
0.875
0.0075
98.4
600
0.333
0.889
0.0056
88.9
650
0.394
0.869
0.0085
111.3
650
0.351
0.883
0.0063
100.8
15,000
18,000
700
0.412
0.863
0.0096
124.4
700
0.368
0.877
0.0072
113.1
750
0.428
0.857
0.0107
137.6
750
0.385
0.872
0.0080
125.7
800
0.444
0.852
- 0.0118
151.2
800
0.400
0.867
0.0089
138.7
850
0.460
0.847
0.0130
165.1
850
0.415
0.862
0.0098
151.9
900
0.474
0.842
0.0142
179.5
900
0.429
0.857
0.0107
165.3
500
0.319
0.894
0.0050
71.3
500
0.273
0.909
0.0034
62.0
550
0.339
0.887
0.0058
82.9
550
0.292
0.903
0.0040
72.5
600'
0.360
0.880
0.0068
95.0
600
0.310
. 897
0.0047
83.5
650
0.379
0.874
0.0077
107.7
650
0.328
0.891
0.0053
94.9
16,000
20,000
700
0.396
0.868
0.0087
120.4
700
0.344
0.885
0.0060
106.6
750
0.413
0.862
0.0097
133.5
750
0.360
0.880
0.0068
118.8
800
0.429
,0.857
0.0107
146.9
800
0.375
0.875
0.0075
131.2
850
0.443
0.852
0.0118
160.6 i'
850
0.389
0.870
0.0083
144.0
900
0.458
0.847
0.0129
174.5
900
0.403
0.866
0.0091
157.0
49
RECTANGULAR
BEAMS
DIAGRAM 18
VALUES OF k, j, p AND K
71=75
rercentaqe of steel
DIAGRAM 19
\
RECTANGULAR
BEAMS
MOMENT OF RESISTANCE AND AREA OF STEEL
FOR
BEAMS ONE INCH WIDE
f e =650
f s =16,0
= 15
Area or steel in so. in.
RECTANGULAR
BEAMS
DIAGRAM 20
f c =650
f s =18,0
n=15
MOMENT OF RESISTANCE AND AREA OF STEEL
FOR
BEAMS ONE INCH WIDE
DIAGRAM 21
RECTANGULAR
BEAMS
MOMENT OF RESISTANCE AND AREA OF STEEL
FOR
BEAMS ONE INCH WIDE
f e =700
f,=16,
Area of stee in sg. in.
RECTANGULAR
BEAMS
DIAGRAM 22
f c =700
f s =18,0
n=15
MOMENT OF RESISTANCE AND AREA OF STEEL
FOR
BEAMS ONE INCH WIDE
Area or steel m sa. in
RECTANGULAR
BEAMS
MOMENT OF RESISTANCE AND AREA OF STEEL
FOR
BEAMS ONE INCH WIDE
f e = 750
f, = 16,000
Area or steel in sq. in.
RECTANGULAR
BEAMS
DIAGRAM 24
/ =750 MOMENT OF RESISTANCE AND AREA OF STEEL
f t =18,000 FOR
n=15 BEAMS ONE INCH WIDE
Area of stee m sa. in.
DIAGRAM 25
RECTANGULAR
BEAMS
DIAGRAM FOR LOCATING POINTS
TO BEND HORIZONTAL STEEL
RECTANGULAR
BEAMS
AREAS AND PERIMETERS
OF
COMBINATIONS OF FOUR RODS
Square rods
Number and size Round rods
II
Area
(sq. in.)
Perimeter
(in.)
M
H
H
y*
1
1H IK
Area
(sq. in.)
Perimeter
(in.)
1 00
80 4
1
79
6 28
l!l4
8 . 5 3
l
0.89
6^68
1.28
9.0 2
2
1.01
7.07
1 31
90 i 3
1
1 03
7 07
l'42
9.5 1
3
1.12
7^46
1.52
9.5
3
i
1.19
7.46
1.56
10.0
4
1.23
7.85
1.63
10.0
2'
2
1.28
7 85
1.73
10.5
3
1
1.36
8.25
1.91
11.0
2
2
1.50
8.64
1.94
11.0
3
i
1.52
8.64
1.94
11.0
l"
3
1.52
8 64
2.03
11.0
2
2
;; \ '.'.
1.60
8.64
2.08
11.5
i
3
1.63
9.03
2.17
11.5
3
i
1.71
9.03
2.25
12.0
4
1.77
9.43
2.31
' 12.0
2
2
1.82
9.43
2.45
12.5
3
1
1.93
9.82
2.55
12.5
'l
3
2.00
9 82
2.66
13.0
2
2
2.09
10.21
2.69
13.0
1
3
2.11
10.21
2.69
13.0
3
i ....
2.11
10.21
2.78
13.0
2
2 ! .- ; -
2.18
10 21
2.86
13.5
1
3
2.24
10.60
2.95
13.5
3
" "
1
2.32
10 . 60
3.06
14.0
-
4
2.41
11.00
3.13
14.0
2
2 . .
2.45
11 .00
3.30
14.5
3 1 . .
2.59
11 39
3.39
14.5
"l
3
2.66
11.39
3.53
15.0
2 2
2.77
11.78
3.56
15.0
1
3
2.80
11.78
3.56
15.0
3 .. 1
2.80
11.78
3.66
15.0
2
. . i . . i 2
2.87
11.78
3.77
15.5
1 3 I ..
2.96
12. 17
3.86
15.5
. . . .
3 ....
'l
3.03
12.17
4.00
16.0
_
.. 1 ..
4
3.14
12.56
4.06
16.0
I
2 . ; 2
3.19
12,56
4.27
16.5
_
31
3.35
12.96
4.36
16.5
1
. . | . . 3
3.42
12.96
4.53
17.0
2 2
3.56
13.35
4.56
17.0
3 ;
1
3.58
13.35
4.56
17.0
i
3
3.58
13.35
4.66
17.0
2
2
3.66
13.35
4.80
17.5
V
3
3.77
13.74
5.06
18.0
4
3.98
14.14
5.13
18.0
2
2
4.02
14.14
5.36
18.5
3
1
4.21
14.53
5.45
18.5
1
3
4.28 14.53
5.66
19.0
2
2
4.44
14.92
5.69
19.0
1
3
4.47
14.92
5.95
19.5
1
3
4.67
15.32
6.25
20.0
4
4.91
15.71
58
TABLE 16
RECTANGULAR
BEAMS
AREAS AND PERIMETERS
OF
COMBINATIONS OF SIX RODS
1
|
Square rods
Number and size
Round rods
Square rods
Number and size
Round rods
Area
Perim-
Area
Perim-
Area
Perim-
Area
Perim-
(sq. 1 eter
N
^
%
1
IK
IK
(sq.
eter
(sq.
eter
N
;! i
H
1
IK
IK
(sq.
eter
in.)
(in.)
in.)
(in.)
in.)
(in.)
in.)
(in.)
2.34
15.0
ft
1.84
11.78
5.39
22.5
* "
5
1
4.23
17.67
2.52
15.5
5
I
\' m
\\
1.98
12.17
5.48
22.5
3
3
4.31
17.67
2.69
16.0
4
9
2.11
12.57
5.53
23.0
2
4
4.34
18.07
2.72
16.0
5..
1
2.14
12.57
5.56
23.0
1
5
4.37
18.07
2.86
16.5
3
3
2.25
12.96
5.59
23.0
4
2
4.39
18.07
2.95
16.5
5
1
2.32
12.96
5.77
23.5
1
5
4.53
18.46
3.03
17.0
2
4
2.38
13.35
6.00
24.0
6
4.71
18.85
3.09
17.0
4
. t
2
2.43
13.35
6.09
24.0
3
3
4.79
18.85
3.20
17.5
1
5
2.52
13.74
6.19
24.0
2
4
4.86
18.85
3.38
18.0
6
2.65
14.14
6.19
24.0
4
2
4.86
18.85
3.47
18.0
3
3
2.72
14.14
6.27
24.5
..
..
..
5
1
4.92
19.24
3.56
18.0
4
2
2.80
14.14
6.53
25.0
4
2
5.13
19.64
3.58
18.5
5
1
']
2.81
14.53
6.56
25.0
5
1
5.15
19.64
3.78
19.0
4
2
2.97
14.92
6.59
25.0
2
4
5.18
19 64
3.81
19.0
6
1
2.99
14.92
6.80
25.5
3
3
5.34
20.03
3.84
19.0
2
4
..
3.02
14.92
6.89
25.5
1
5
.
.5.41
20.03
3.98
19.5
.
3
3
.
3.13
15.32
6.98
25.5
3
.
3
5.48
20.03
4.08
19.5
5
1
. .
3.20
15.32
7.06
26.0
2
4
5.55
20.42
4.17
19.5
3
3
3.28
15.32
7.09
26.0
1
5
5.57
20.42
4.19
20.0
2
4
3.29
15.71
7.13
26.0
-
4
2
5.60
20.42
4.22
20.0
1
5
3.31
15.71
7.33
26.5
1
5
5.76
20.81
4.25
20.0
4
2
3.34
15.71
7.59
27.0
6
5.96
21.20
4.39
20.5
.
1
5
3.45
16.10
7.69
27.0
3
3
6.04
21.20
4.59
21.0
6
3.61
16.49
7.78
27.0
2
4
6.11
21.20
4.69
21.0
3
3
3.68
16.49
7.89
27.5
5
1
6.19
21.60
4.78
21.0
2
4
3.76
16.49
8.19
28.0
4
2
6.43
21.99
4.78
21.0
4
2
3.76
16.49
8.25
28.0
2
4
6.48
21.99
4.83
21.5
5
1
; .
3.79
16.89
8.48
28.5
3
3
6.66
22.38
5.06
22.0
. .
4
2
3.98
17.28
8.58
28.5
1
5
6.74
22.38
5.09
22.0
5
1
4.00
17.28
8.78
29.0
2
4
6.90
22.78
5.13
22.0
3
4
4.03
17.28
8.81
29.0
1
5
6.92
22.78
5.30
22.5
3
3
! 4.16
17.67
9.08
29.5
1
5
7.13
23.17
5.39
22.5
1
5
4.23
17.fi7
9.38
30.0
6
7.36
23.56
59
RECTANGULAR
BEAMS
TABLE 17
AREAS AND PERIMETERS
OF
COMBINATIONS OF EIGHT RODS
Square rods
Number and size
Round rods Square rods
Number and size
I
; Round rods
Area
Perim-
Area
Perim- Area
Perim-
Area
Perim-
(sq.
eter
H
7 A
1
IK
iH
(sq-
eter (sq.
eter
3 A
y*
1
1M
1J-4
(sq.
eter
in.)
(in.)
in.)
(in.) in.)
(in.)
in.)
(in.)
4.50
24.0
8
3.53
18.85 8.12
32.0
4
4
6.38
25.14
4.70
24.5
7
l
3.69
19.24 8.27
32.5
7
1
6.49
25.53
4.91
25.0
6
2
3.85
19.64 8.52
32.5
5
3
6.69
25.53
4.94
25.0
7
1
3.88
19.64 8.53
33.0
6
2
6.70
25.92
5.11
25.5
5
3
4.01
20.03 8.56
33.0
7
1
6.72
25.92
5.20
25.5
7
1
4.09
20.03 8.62
33.0
3
5
..
6.77
25.92
5.31
26.0
4
4
4.17
20.40 8.72
33.0
2
6
6.85
25.92
5.38
26.0
6
2
4.22
20.40 8.80
33.5
5
3
6.91
26.31
5.52
26.5
3
5
4.33
20.81 9.06
34.0
4
4
7.12
26.70
5.72
27.0
2
6
4.49
21.20 9-12
34.0
2
6
7.17
26.70
5.81
27.0
5
3
4.57
21.20 9.13
34.0
6
2
7.17
26.70
5.91
27.0
6
2
4.64
21.20 9.31
34.0
4
4
7.31
26.70
5.92
27.5
1
7
.
4.65
21.60 9.33
34.5
3
5
7.33
27.10
6. 12
28.0
8
.
4.81
21.99 9.42
34.5
1
7
7.40
27.10
6.25
28.0
4
4
4.91
21.99 9.59
35.0
2
6
7.53
27.49
6.36
28.5
7
1
4.99
22.38 9.62
35.0
1
7
7.56
27.49
6.59
29.0
6
2
5. 18
22.78 9.69
35.0
5
3
7.61
27.49
6.61
28.5
5
3
5. 19
22.38 9.86
35.5
1
7
7.74
27.88
6.62
29.0
7
1
5.20
22.78 10.11
35.5
3
5
7.94
27.88
6.69
29.0
3
5
5.25
22.78 10.12
36.0
8
7.95
28.28
6.83
29.5
5
3
5.36
23.17 10.25
36.0
4
4
8.05
28.28
6 92
29.5
7
1
5.44
23.17 10.42
36.5
7
1
8.19
28.67
7.06
30.0
4
4
5.55
23.56 10.72
37.0
, ,
6
2
8.42
29.06
7.12
30.0
6
2
5.60
23.56 10.81
37.0
3
5
8.49
29.06
7.13
30.0
2
6
5.60
23.56 10.91
37.0
2
6
8.56
29.06
7.30
30.5
3
5
..
5.73
23.96 11.02
37.5
..
5
3
8.65
29.45
7.31
30.0
4
4
5.74
23.56 11.31
38.0
. .
4
4
8.88
29.85
7.53
31.0
2
6
5.91
24.35 11.38
38.0
.
2
6
8.93
29.85
7.56
31.0
1
7
5.94
24.35 11.61
38.5
3
5
9.12
30.24
7.63
31.0
5
3
5.9
24.35 11.70
38.5
1
7
9.19
30.24
7.72
31.0
6
2
6.06
24.35 11.91
39.0
2
6
9.35
30.63
7.77
31.5
1
7
6.10
24. 74 111 1.94
39.0
1
7
9.37
30.63
8.00
32.0
8
6.28
25. 14 12.20
39.5
1
7 I
9.58
31.02
8.02
31.5
3
5
6.30
24.74 12.50
1
40.0
8 ' 9.82'
31.42
60
TABLE 18
RECTANGULAR
BEAMS
AREAS AND PERIMETERS
OF
GROUPS OF RODS OF UNIFORM SIZE
Number
Size of rods
H
H
M
M
H
H
1
1M
IK
1H
1H
1
1
1
1
1
. 0625
1.0
0.1406
0.2500
0.3906
0.5625
0.7656
3.5
1.000
4.0
1.266
1.563
1.891
2.250
2
. 1250
2.0
0.2812
3.0
0.5000
4.0
0.7812
5.0
1.125
6.0
1.531
7.0
2.000
8.0
2.531
9.0
3.125
10
3.781
11.0
4.500
12.0
3
0.1875
3.0
0.4218
4.5
0.7500
6.0
1.172
7.5
1.688
9.0
2.297
10.5
3.000
12.0
3.797
13.5
4.688
15.0
5.672
16.5
6.750
18
4
0.2500
4.0
. 5624
6.0
1.000
8.0
1.563
10.0
2.250
12.0
3.062
14.0
4.000
16.0
5.062
18.0
6.250
20.0
7.562
22.0
9.000
24.0
5
0.3125
5.0
0.7030
7.5
1.250
10.0
1.953
12.5
2.813
15.0
3.828
17.5
5.000
20.0
6.328
22.5
7.813
25.0
9.453
27.5
11.25
30
6
. 3750
60
0.8436
9.0
1.500
12.0
2.344
16.0
3.375
18.0
4.594
21.0
6.000
24.0
7.594
27.0
9.375
30.0
11.34
33.0
13.50
36.0
7
0.4375
7.0
0.9842
10.5
1.750
14.0
2.734
17.5
3.938
21.0
5.359
24.5
7.000
28
8.859
31.5
10.94
35.0
13.23
38.5
15.75
42.0
8
0.5000
80
1.125
12.0
2.000
16.0
3.125
20.0
4.500
24.0
6.125
28.0
8.000
32.0
10.12
36.0
12.50
40.0
15.12
44.0
18.00
48
9
. 5625
90
1.265
13 5
2.250
18.0
3.516
22.5
5.063
27.0
6.890
31.5
9.000
36.0
11.39
40.5
14.06
45.0
17.02
49.5
20.25
54.0
10
0.6250
10.0
1.406
15.0
2.500
20
3.906
25.0
5.625
30
7.656
35.0
10.00
40.0
12.66
45
15.63 118.91
50.0 55.0
22.50
60.0
1
0.0491
0.785
0.1105
1 18
0.1964
1.571
0.3068
1 96
0.4418
2 35
0.6013
2 75
0.7854
3.14
9940
3 53
1.227 1.485
3 93 4 32
1.767
4.71
2
0.0982
1.57
. 2209
2 36
0.392*7
3.14
0.6136
3 93
0.8836
4 71
1.203
5.50
1.571
6.28
1.988
7.07
2.454
7 85
2.970
8 64
3.534
9.42
3
0.1473
2.36
0.3313
3 53
0.5890
4.71
. 9204
5 89
1.325
7.07
1.804
8 25
2.356
9 43
2.982
10.6
3.681
11.8
4.455
13.0
5.301
14.1
4
1964
3.14
0.4418
4.71
. 7854
6.28
1.227
7.85
1.767
9 42
2.405
11.0
3.142
12.6
3.976
14.1
4.908
15.7
5.940
17.3
7.068
18.8
5
. 2455
3.93
. 5522
5.89
0.9817
7.85
1.534
9 82
2.209
11.8
3.006
13.7
3.927
15.7
4.970
17.7
6.135
19.6
7.425
21.6
8.835
23 6
6
0.2946
4.71
0.6627
7.07
1.178
9 43
1.841
11 8
2.651
14.1
3.608
16.5
4.712
18 9
5.964
21.2
7.362
23 6
8.910
25.9
10.60
28.3
7
0.3437
5.50
0.7731
8.25
1.374
11.0
2.148
13.7
3.093
16.5
4.209
19.2
5.498
22.0
6.958 8.589
24.7 27.5
10.39
30.2
12.37
33.0
8
0.3928
6.28
0.8836
9 42
1.571
12 6
2.454
15 7
3.534
18.8
4.810
22
6.283
25.1
7.952 | 9.816
28.3 ! 31.4
11.88
34 6
14.14
37.7
9
0.4419
7 07
0.9940
10.6
1.767
14 1
2.761
17.7
3.976
21.2
5.412
24.7
7.069
28 3
8.946
31.8
11.04
35 3
13.37
38 9
15.90
42 4
10
0.4910
7.85
1.105
11.8
1.964
15.7
3.068
19.6
4.418 ! 6.013
23 . 6 27 . 5
7.854 1 9.940
31.4 ! 35.3
I
12.27
39 3
14.85
43.2
17.67
47.1
61
RECTANGULAR
BEAMS
TABLE 19
AREAS, PERIMETERS AND WEIGHTS OF RODS
Round rods
Square rods
Size (inches)
Area
(square
inches)
Perimeter
(inches)
Weight
per foot
(pounds)
Area
(square
inches)
Perimeter
(inches)
Weight
per foot
(pounds)
H
0.0491
0.785
0.167
0.0625
1.00
0.212
KG
0.0767
0.982
0.261
0.0977
1.25
0.333
H
0.1104
1.178
0.375
0.1406
1.50
0.478
KG
0.1503
1.374
0.511
0.1914
1.75
0.651
y 2
0.1963
1.571
0.667
0.2500
2.00
0.850
MG
0.2485
1.767
0.845
0.3164
2.25
1.076
%
0.3068
1.964
1.043
0.3906
2.50
1.328
%
0.3712
2.160
1.262
0.4727
2.75
1 . 608
H
0.4418
2.356
1.502
0.5625
3.00
1.913
13 Ae
0.5185
2.553
1.763
0.6602
3.25
2.245
7 /8
0.6013
2.749
2.044
. 7656
3.50
2.603
^6
0.6903
2.945
2.347
. 8789
3.75
2 . 989
1
O.V854
3.142
2.670
1.0000
4.00
3.400
1M
0.9940
3.534
3.379
1 . 2656
4.50
4.303
\y
1.2272
3.927
4.173
1.5625
5.00
5.312
l 3 /8
1.4849
4.320
5.049
1 . 8906
5.50
6 . 428
IX
1.7671
4.712
6.008
2.2500
6.00
7.650
1%
2.0739
5.105
7.051
2.6406
6.50
8.978
1%
2.4053
5.498
8.178
3.0625
7.00
10.41
1%
2.7612
5.891
9.388
3.5156
7.50
11.95
2
3.1416
6.283
10.68
4.0000
8.00
13.60
2M
3.9761
7.069
13.52
5.0625
' 9.00
17.22
2H
4.9087
7.854
16.69
6.2500
10.00
21.25
2%
5 . 9396
8.639
20.20
7.5625
11.00
25.71
3
7.0686
9.425
24.03
9.0000
12. CO
30.60
62
SECTION 4
DOUBLY REINFORCED BEAMS
Diagrams 26 to 30 inclusive are particularly useful in checking the supports of con-
tinuous T-beams when the value of -j- is approximately 3^i o- The results are on the
safe side when -r is less than %Q. For different values of j-^ they give directly the
amounts of compressive and tensile steel required.
When the value of -j- does not approximate Ho? the formulas given below may
be used. These are based on the fundamental fact that for any given values of
f e and /,, k has exactly the same value regardless of the shape or type of beam. It
follows from this that if steel is added to the section without changing the extreme
fiber stresses, this added tensile and compressive steel must form a balanced couple
whose stresses conform to the stresses already in the section.
Let pi = steel ratio for the beam, without compressive steel.
p-2 = steel ratio for the added tensile steel.
Pf = Pi + P*
p' = steel ratio for compressive steel.
Mi = moment of the beam without compressive steel.
M z = moment of the added steel couple.
M = Mi + M 2
Then
I J-
Pl ^ 2f*
^=/*i(i-gw
3/o = M - Mi
P2 =
1 - A
P
Diagram 31 is of general use. By means of this diagram and Table 20 it is possible
to readily determine the stresses in the concrete and steel of a doubly reinforced
rectangular beam for a given bending moment.
Diagram 32 is used to determine the length of embedment necessary to develop the
actual compressive stress in the rods in the bottom of a continuous T-beam at the
63
DOUBLY REINFORCED BEAMS
supports. The upper part of the diagram is general, and may be used to find length
of embedment to provide for bond when the stress is the steel is either tension or
compression.
Finding Percentages of Tensile and Compressive Steel
M
~_ What percentages of tensile and compressive steel will be required when f ,., = 200,
t oa~
d'
iff c is not to exceed 750 and / is not to exceed 18,000? j- = 0.10. n = 15.
From Diagram 28 we find that for f c = 750, / = 18,000, and ^ = 200
p = 0.0127 and p' - 0.010
If p should be increased to 0.0143, /, will be lowered to 16,000 and p' to 0.0086.
Given: b = 12 in., d = 18 in., j = 0.15, M = 750,000 in.-lb., f c = 750 and / =
16,000, n = 15. Determine the required percentages of tensile aud compressive steel.
From Table 14,
k = 0.413 pi = 0.0097, and K = 133.5
M[ = (133.5) (12) (18) 2 = 519,000 in.-lb.
M 2 = 750,000 - 519,000 = 231,000 in.-lb.
231,000
* (16,000) (0.85) (12) (18) 2
P = Pi + p 2 = 0.0141
' = (0.0044) _ = 0.0097
Finding Length of Embedment of Compressive Steel
Given a continuous beam reinforced with 1-in. rods (either square or round) in com-
pression so that f c = 750; / = 16,000; -7- = 0.10; n = 15; u = 80. Find required
length of embedment of compressive steel.
From the lower part of Diagram 32, the compressive stress// is found to be 8540 Ib.
per sq. in. The upper diagram shows the length of embedment for 1-in. plain rods,
with u = 80, to be 26>2 in.
Finding Stresses in Concrete and Steel
A continuous T-beam, uniformly loaded, has a bending moment at the center of each
span of 356,300 in.-lb. Negative bending moment at the supports and the positive bending
wl 2
moment at the center of span are figured by the formula, M = ^r. The tensile steel at the
center of span consists of four %-in. round bars, b' = 10 in. d 15 in. Design
the supports.
At the supports the flange of the T-beam, being in tension, is negligible and the
T-beam changes into a rectangular beam with steel in top and bottom. Two of the
tension bars on each side of the supports will be bent up and made to lap over the top
of the supports, while the other two bars on each side will be continued straight and
lapped over supports at the bottom of beam.
64
DOUBLY REINFORCED BEAMS
The ratios of steel in tension and compression are the same, and are respectively :
a 118
(1.77 in above equation taken from Table 18.)
d ' - 2 - o m
T U
From Diagram 31, knowing p' = p, we obtain
d' k = 0.361
For - 0.10....
d' k = 0.377
For = 0.15...
Thus,
k =0 ' 372
= 0.873
(It is usually well within the precision of the actual work, and on the safe side, to use the
curves for the value of -r next larger than the actual value. Thus in this problem the
values of k and j for -j =0.15 could be used with sufficient accuracy.)
Then
M 356,300
(1.77X0.873X15)
and, using Table 20,
f c = n(l k _ fc) /, = (0.0394) (15,400) = 607 Ib. per sq. in.
The stresses in the concrete and steel are within the allowable and no haunch or
additional steel is necessary.
The moment of resistance at the supports may be found as follows:
f e n(l - k} 650
fc- = 0^394 = 16,500 Ib. per sq.m.
Thus the moment of resistance depends on the steel and
Ms = bd%pj = (10) (15) 2 (16,000) (0.0118) (0.873) = 371,000 in.-lb.
65
DIAGRAM 26
DOUBLY
REINFORCED
BEAMS
DOUBLY REINFORCED RECTANGULAR BEAMS
VALUES OF ^p, p, ANDp'
*' JL
d, 10
f c =650
f ,=16,000
f s = 18,000
n=15
Percentage of -tensile steel, p
DOUBLY
REINFORCED
BEAMS
DIAGRAM 27
f t =7 00
f,=16,
f.= 18,000
n=15
DOUBLY REINFORCED RECTANGULAR BEAMS
VALUES OF ~t, p, ANDp'
Percentage of tensile steel, p
DIAGRAM 28
DOUBLY
REINFORCED
BEAMS
DOUBLY REINFORCED RECTANGULAR BEAMS
VALUES OF ~, p, AN Dp'
f e =750
f s =16,000
f s =18,000
= 15
Percentage of tensile steel , p
DOUBLY
REINFORCED
BEAMS
DIAGRAM 29
f c =800
f s =16,000
f s = 18,000
15
DOUBLY REINFORCED RECTANGULAR BEAMS
VALUES OF , p, ANDp'
Percentage of tensi le steel , p
DIAGRAM 30
DOUBLY
REINFORCED
BEAMS
DOUBLY REINFORCED RECTANGULAR BEAMS
VALUES OF ^ p, ANDp'
<*L=L
d~ 10
, f e =850
f,=16,000
f, = 18,000
71 = 15
DOUBLY
REINFORCED
BEAMS
DIAGRAM 31
DOUBLY REINFORCED RECTANGULAR BEAMS
VALUES OF k AND j
DIAGRAM 31
DOUBLY
REINFORCED
BEAMS
DOUBLY REINFORCED RECTANGULAR BEAMS
VALUES OF k AND j
DOUBLY
REINFORCED
BEAMS
VALUES OF
IN FORMULA f c
TABLE 20
J*
48
<c
1
-
rig
5'
1
rH
-
2T
1
lH
"s
^
-
3e
1
si
-4J
iJS
5?
1
^
r4J
48
5
1
rH
"c
-ie
*
-^
1
V
ri
-Si
ST
1
^
|
I
0.200
0.0
106
0.2500.0
222
0.300
0.0
286
0.350
0.0
35!)
0.400
0.0
444
0.450
0.0
545
0.500
0.0
6660.550
().(
815
0.202
0.0169
0.2520.0224
0.302
. 0288
0.352
0.0362
0.402
0.0447
0.452
0.0549
0.502
0.0671
0.5520.0821
0.204
0.0171
0.2540.0226
0.304
0.0291
0.354
0.0365
0.404
0.0451
0.454
0.0554
0.5040.0677
. 554
0.0827
0.206
0.0173
0.256
. 0229
0.306
0.0293
0.356
. 0368
0.406
0.0455
0.456
0.0558
0.506
. 0682
. 556
0.0834
0.208
0.0175
0.258
0.0231
0.308
. 0296
0.358
0.0371
0.408
. 0459
0.458
0.0562
0.508
. 0688
0.558
0.0841
0.210
0.0177
0.260
0.0234
0.310
0.0299
0.360
0.0375
0.410
0.0463
0.460
0.0567
0.510
. 0694
0.560
. 0848
0.212
0.0179
0.262
0.0236
0.312
0.0301 0.362
. 0378
0.412
. 0466
0.462
0.0571
0.512
0.0699
0.562
0.0855
0.214
0.0181
0.264
0.0238
0.314
0.0305
0.364
0.0381
0.414
. 0470
0.464
0.0576
0.514
0.0705
0.564
. 0862
0.216
0.0183
0.266
0.0241
0.316
. 0308
0.366
. 0384
0.416
0.0474
0.466
0.0581
0.516
0.0711
. 566
0.0869
0.218
0.0186
0.268
0.0243
0.318
0.0311
0.368
. 0387
0.418
0.0478
0.468
. 0586
0.518
0.0717
0.568
0.0876
0.220
0.0188
0.270
0.0246
0.320
0.0314
0.370
0.0391
0.420
. 0482
0.470
0.0591
0.5200.07230.570
. 0884
0.222
0.0190
0.272
0.0248
0.322
0.0317
0.372
0.0394
0.422
0.0486
0.472
0.0595
0.5220.07280.572
0.0891
0.224
0.0192
0.274
0.0251
0.324
0.0319
0.374
0.0398
0.424
. 0490
0.474
0.0600
0.5240.0733ji0.574
. 0898
0.226
0.0194
0.276
0.0254
. 326
. 0322
0.376
0.0401
0.426
. 0494
0.476
0.0605
. 526
0.0739 0.576
. 0905
0.228
0.0196
0.278
. 0257
0.328
0.0325
0.378
0.0404
0.428
. 0498
0.478
0.0610
0.5280.07450.578
0.0912
0.230
0.0199
0.280
0.0259
0.330
0.03280.380
. 0408
0.430
. 0502
0.480
0.0615
0.5300.0751j|0.580
0.0920
0.232
0.0201
0.282
0.0261
0.332
0.0331 0.3820.0411
. 432 . 0506
0.482
0.0620
0.532 j 0.0757 0.582
. 0927
0.234
. 0203
0.284
. 0264
0.334
0.0334 0. 384^0.0415
0.4340.0511
0.484
. 0625
. 534
0.0763 0.584
0.0935
0.236
. 0205
0.286
0.0267
0.336
0.03370.3860.0419
. 436
0.0515
0.486
. 0630
0.536
0.07700.586
. 0943
0.238
. 0207
0.288
0.0269
0.338
0.0340
0.388
. 0422
0.438
. 0520
0.488
. 0635
0.538
0.07760.588
0.0951
0.240
0.0210
0.290
0.0272
0.340
0.03440.390
0.0426
0.440
0.0524
0.490
. 0640
0.540
0.0783 0.590
0.0959
0.242
0.0212
0.292
. 0275
0.342
0.03470.392
0.0429
0.442
. 0528
0.4920.0645
0.542(0.07890.592
0.0967
0.244
0.0214
0.294
0.0278
0. 344 0.0350J 0.394
0.0433
0.444
. 0532
0.4940.0650
0.544
0.0795 0.594
. 0975
0.246
0.0217
0.296
1.0280
0.346
0.0353||0.396
0.0437
0.446
0.0536
0.4960.0656
0.546
. 0802 . 596 . 0984
0.248
0.0219
. 298
. 0283
0.348
0.03560.398
0.0440
0.488
0.0540
0.4980.0660
0.548
0.0808JO. 5980. 0993
74
DIAGRAM 32
DOUBLY
REINFORCED
BEAMS
LENGTH OF EMBEDMENT OF RODS IN COMPRESSION
UNIT STRESS IN COMPRESSIVE STEEL
10
D
<5.?o n ""s" s s~" "*s"
, = \Q 000
V X, "IX. >s > o
" ^S. ^"^X. ^ * -1 X- ^ S ^x_*
n * 5
o.is .35! >JjIS ZS ' nS^
"X. X^ ^ . 1 y X^?/")
"* s "^x ^ix^i- ^h*?
1 Xv
xj X ^'Tp^p ^t
s. VN
x /e~ n^O ^X
B^^ s k
0.10 ^?P N > "
v v
x ^^xT
^ s^ ^xl <s s
s s X.
I^V ' "* v ^ ^v
X ^
X^ x. Xs^ ^^
s v
S X_ ^^X "N. ^^^
o.o5 ::::::;::
S^ ^S X^ "* s " *^
020 V ^ V X \
S "XL ^V ^\ ^^
f s = 16,000
>^ ^ T* ^ x "*< &
_ _ . . f~
Lii"" s" '^~ "^ ; r"&:
n = ID
o.is ISIIIS !.!uj ^ ; ^
X, ' v ^ rTrPf
** I ' ^v S X^
S ** V
^ > ' S "^l ' TrS
s. X.
^^S^^ l^i ^
^X_ ^s
9.10 sPM x
X s^ ^ i
^s ""^ ^
^^V 'V^ V
V ^^
s X X. s v^
s s^
**,. *S S <i > >
^v s ^ X, ^s s
005 I
s ** i J__L ^. s > s i ik
O O O S?
\T) *O r ~ <O
i I II
Values of i' S) Unit compress
ve stress in steel, Ib.persq.tn.
75
SECTION 5
T-BEAMS
Diagrams 33 and 34 should be used for designing T-beams when the neutral axis is
in the stem and when the compression in the stem is to be neglected. The left hand
side of the diagram gives the values of r^, / c , and ^- The right hand side gives values
of j and p, to be used in finding the area of steel required.
Diagram 35* is for general use and may be employed either for design or for
determining stresses in existing designs.
Design of T-B earns
Assuming f a = 16,000, f c = 650, n = 15, t = 5% in., and M = 3,000,000 in.-U>.,
find the section of stem required.
Consider the stem width to be 12 in., and the width of flange as found from the
Joint Committee recommendations to be 56 in.
M t
To obtain the value of r^> it is necessary to know the value of -v Since this is
unknown it must be assumed. For -, = 0.2, Diagram 33 shows rnr; = 87.6. and
d oa 2
3^000,000 , t 5.5
= 24 - 8 m - and = = -
Taking = 0.23, = 94, and
d = J'M^OW 23.9 or 24 in. and'.
- 222
0.229
a
The required depth therefore is 24 in.
Entering the right hand side of Diagram 33 with -i = 0.229 and K = 93, it is found
that j = 0.902, and
M - 3,000,000
" JITd ~ (16,000) (0.902) (24) ~
Diagram 35 may also be used in making this design. The value of -5 is assumed as
before. Entering at the lower right hand scale with / = 16,000, follow vertically to
f e = 650 and then to the left to ^ = 0.23. The percentage of steel is 0.0065. Now
follow vertically along -\ = 0.23 to p = 0.0065 in the upper left hand part of the dia-
gram. From there follow to the right to/ = 16,000 and then vertically to obtain the
value of f-T^ = 94.
oa 2
A.
* From Vol. I of "Bridge Engineering," by Waddell.
77
T-BEAMS
Usually the section of the stem of a T-beam is controlled by the shearing stresses.
The procedure in ordinary building design is to design the stem to take the shear at the
support and then determine the concrete stress in the flange at the center of span,
using the value of -j already determined.
Reviewing T-Beams
M t
In reviewing a beam already designed, the values of r-> 3> and p are known. From
these the value of f s is found from the upper half of Diagram 35. Then using the
values of -v p and/ s , the value of f c is found from the lower half of this diagram.
78
DIAGRAM 33
T-BEAMS
DESIGN OF T-BEAMS
VALUES OF L, f c , p, ANDj
f a =16,000
71=15
79
T-BEAMS
DIAGRAM 34
f s =18,000
n=15
DESIGN OF T-BEAMS
VALUES OF **, , f c , p, ANDj
80
DIAGRAM 35
T-BEAMS
DESIGN OR REVIEW OF T-BEAMS*
15
* From Vol. 1 of "Bridge Engineering,'
by Waddell.
81
SECTION 6
SHEAR REINFORCEMENT
Diagram 36 may be used to find unit shear or bond stress for any beam.
Uniformly Loaded Beams
Diagram 37 gives the total number of stirrups in each end of a uniformly loaded
beam, assuming the concrete to take one-third of the total shear, as recommended by
the Joint Committee. The total number -of stirrups at each end of beam is found by
entering the diagram with the unit shear at the support and the clear span in feet,
and following the directions of the arrows to the upper left hand part of the diagram.
Note that Diagram 37 is made for U-stirrups only with the exception of the K-in.
W-stirrup which has a total cross-sectional area equal to the %6-in. square U-stirrup.
The number of W-stirrups required in any given case will be one-half the number of
U-stirrups of the same size.
Diagram 38 gives the distance (I') from the face of support to the point where v =
40 Ib. per sq. in., beyond which no stirrups are required.
Diagram 39 is used for locating the stirrups in the beam. It is so constructed that
if any one of the horizontal light lines is assumed to pass through the face of the sup-
port and the top line marked "center of span" is assumed to pass through the center
of span, the intermediate light lines will divide the triangular shear diagram into equal
areas and the heavy lines will pass through the centers of gravity of these areas. The
heavy lines therefore represent the location of the stirrups.
A convenient scale is placed with the zero on the fine line marked with a number
corresponding to N s . The scale is then rotated until it reads (in inches) at the top
z
line (center of span line). The distances from the face of support to the heavy lines
are then read directly from the scale, stopping when I' is reached. One side of a
triangular engineers' scale may be used for all ordinary cases.
Required to space %-4n. round U-stirrups in a beam 10 in. wide and of IS-ft. clear
span, having a shear at the support of 118 Ib. per sq. in.
From Diagram 37
Ns = 12
From Diagram 38
I' = 71 in.
Placing scale on Diagram 39 to read zero at N g = 12 and 108 on line marked
"center of span," the distances in inches from the face of support to the points where
stirrups should be placed are: 2^, 7, 12, 17, 2% 28^, 35, 42, 50, 59, and 70. This
theoretical spacing will usually be modified by practical considerations, such as the
maximum spacing allowable for the depth of beam. The spacing of stirrups should
not be greater than about one-half the beam depth.
Beams with Concentrated Loads
Diagrams 40 and 41 may be used to find the theoretical spacing of stirrups for
beams with concentrated loads, the concrete assumed to take one-third of the total
shear. Diagram 40 is based on unit shear and Diagram 41 on total shear. The
spacing of stirrups will ordinarily be made uniform between load concentrations.
83
SHEAR
REINFORCEMENT
DIAGRAM 36
UNIT SHEAR AND BOND STRESS
j = 0.875
-. \L n, V
bid u ZQJZ
?&
^?
#^^
DIAGRAM 37
SHEAR
REINFORCEMENT
STIRRUPS FOR UNIFORMLY LOADED BEAM
f a =16,000
Unit shear at support
AT, = Total Number of
Stirrups in Each End
of Uniformly Loaded
Beam From Support
to Center Concrete
Taking One-third of
Total Shear.
vbl
6AJ,
f a = 16,000 Ih. per sq. in.
85
SHEAR
REINFORCEMENT
DIAGRAM 38
UNIFORMLY LOADED BEAMS
LENGTH OF BEAM REQUIRING SHEAR REINFORCEMENT
Clear span in feet. .
86
DIAGRAM 39
SHEAR
REINFORCEMENT
DIAGRAM FOR LOCATING STIRRUPS
IN
UNIFORMLY LOADED BEAMS
^-Center of span
^
I
<5
I
v v
2
3
4-
T
5
^
r
6
1
7
T
Q
1
9
i
10
II
1
j
f \
\z
\
I
/
13
N
= 1
14
87
SHEAR
REINFORCEMENT
DIAGRAM 40
SPACING OF U-STIRRUPS
CONCRETE TAKING ONE-THIRD OF TOTAL SHEAR
f s = 16,000
DIAGRAM 41
SHEAR
REINFORCEMENT
SPACING OF STIRRUPS
CONCRETE TAKING ONE-THIRD OF TOTAL SHEAR
f s = 16,000
89
SECTION 7
COLUMNS
The following tables of safe loads on columns are based on the requirements of the
respective codes in regard to maximum and minimum percentages of vertical steel and
spiral, and also on such practical considerations as the minimum spacing of vertical
steel. The number of rods in the square cored columns is limited to eight because
every rod should be tied back into the column by the binders and it is ordinarily better
practice to iise a spiraled column if more than eight rods are found necessary.
The tables for round cored hooped columns are so complete that it should be
possible to select a satisfactory design for any condition of concentric loading without
additional computation. The values of safe loads given in Tables 35 to 42 inclusive
are based on the percentages of spiral listed and, if desired, another spiral of equal
volume may be substituted from Table 46.
Diagrams 42 and 43 will be found valuable for determining building column loads
for preliminary work.
For the design of columns which are eccentrically loaded, see Section 8. Diagrams
for the design of round columns subjected to bending and direct stress have been
constructed and are published here for the first time.
What size of square cored column and what amount of longitudinal steel will be re-
quired to support a centratty applied load of 200,000 lb., assuming the recommendations of
the Joint Committee to govern? Ratio of unsupported length of .column to column side is
less than 15.
Tables 21, 22 and 23 show the following possible designs:
2000-to. concrete.
( 6-134 in- square
22-m. column So,,/.
I 8-1 Y% in. square
( 6-1 in. square
23-in. column \ - . ,
I 8-1 in. round
2500-&. concrete.
- n. square
20-in. column < ,* .
181>B in. square
f 6-1 in. square
21-m. columns _ ., .
I 8-1 in. round
3000-&. concrete.
19-in. column { 8-1 ^ in. round
- n. square
20-m. column < ' .
( 6-1 in. round
Lateral ties must be used of not less than 34 in. in diameter and spaced not over
12 in. apart. For %-in. rods the spacing should never be more than 10 in.
What size of round column and what amount of longitudinal steel will be required by
the Joint Committee Recommendations to support a load of 1,100,000 lb.? A 3000-lb.
concrete is to be used with 1 % of spiral reinforcement. Unsupported length of column is
less ttian 10 diameters.
91
COLUMNS
From Table 34, page 114, it is found that a 37-in. round column with 33-in.
core, and with fourteen l^-in. square longitudinal rods will safely support a load of
1,105,000 Ib.
Table 47 shows that a spiral of 7/0 gage and 2%-m. pitch will give 1 % of reinforce-
ment; or that a %-in. spiral may be used with 2%-in. pitch. Table 46, page 188, gives
other satisfactory sizes and pitch of spirals to obtain the required 1% of spiral re-
inforcement. This table also gives the weight in pounds per foot of column for each
spiral. Table 45 gives the volume and weight of columns per foot and Table 44 gives
the weights of column rods per foot.
What would be the design of the column of the preceding problem assuming the American
Concrete Institute recommendations to govern?
A number of satisfactory designs may be taken from Table 37. One possible
design is to- use a 37-in. column with 33-in. core and a spiral of 7/0 gage, 2^-in. pitch,
sixteen IJ^-in. round longitudinal rods.
Reduction Formula for Long Columns. Where long columns must be used, the
reduction which follows, taken from the Los Angeles Building Code, may be employed
in the design of columns whose unsupported length (1} is between 15 and 30 times the
least dimension of effective section (d). Let r represent the quantity by which the
working stress for columns with -i less than 15 should be multiplied to give a working
stress which may be used for long columns. Then
r-l.6-H.fi
92
TABLE 21
COLUMNS
^ .Gi'umn size J
SQUARE CORED COLUMNS
SAFE LOAD IN THOUSANDS OF POUNDS
JOINT COMMITTEE RECOMMENDATIONS
Max.
/unsupported length\
side
15
2000- Ib. concrete
1:6 mixture
n = 15
f t =450
"of*
column
(.inches)
Size
of
core
(inches)
Number
of
rods
Square rods Round rods
X
H H
1
1H IK K H
H i
IK
IK
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
8
9
10 .
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
4
4
4
6
8
8
4
6
8
4
6
8
4
6
8
4
6
8
4
6
8
4
6
8
4
6
8
4
6
8
4
6
8
4
6
8
4
6
8
4
6
8
6
8
4
6
8
6
8
38.6
46.3
i 54.8
i 59.7
; 64.7
64.3
69.2
1 74.1
74.6
79.5
84.5
'90^8
i 95.7
102.9
107.9
iie.6
120.9
134.9
i49.7
43.0
50.6
59.2
66.3
36.5
44^2
52.7
56.6
60.4
62.2
66.0
69.9
"76 A
80.2
87.6
91.5
103.6
40.0
47.6
56.2
61.7
67.2
65.6
71.1
76.7
76.0
81.5
87.0
87.2
92.7
98.3
i04.9
110.4
44.0
51.6
60.2
67.7
69.6
77.2
84.8
80.0
87.5
95.1
91.2
98.8
106.4
103.4
110.9
118.5
116.4
124.0
131.6
56.2
64.8
74.2
84.1
84.6
94.5
95.8
105.7
115.6
108.0
117.9
127.8
121.0
130.9
140.8
135.0
144.9
154.8
149.8
159.7
169.6
70.1
79.5
89.9
101.1
113.6
113.3
125.7
126.3
138.8
151.3
140.3
152.8
165.3
155.1
167.6
180.1
170.9
183.3
195.9
187.5
200.0
212.5
205.1
217.5
230.1
95.7
107.0
119.1
134.6
132.2
147.6
146.1
161.6
177.1
161.0
176.4
191.9
176.7
192.2
207.7
193.4
208.8
224.3
210.9
226.4
241.9
229.4
244.8
260.3
248.7
264.2
279.7
284.4
299,9
305.6
321.1
327.6
343.1
350.6
366.0
55.7
64.3
70.2
68.6
75.7
82.8
79.0
86.1
93.2
90.2
97.3
104.4
102.4
109.5
116.6
115.4
122.5
129.6
i36.5
143.6
ioi.3
158.4
73.7
83.4
79.7
84.1
93.7
95.3
105.0
114.6
107.5
117.1
126.8
120.5
130.2
139.8
134.5
144.1
153.8
149.3
159.0
168.6
90.0
96.1
101.3
113.9
113.4
126.0
107.9
115.4
i
120.1 127.6
136.0
126.5
139.1
151.7
140.4
153.0
165.6
155.3
167.9
180.5
171.0
183.6
196.2
187.7
200.3
212.9
205.2
217.8
230.4
133.1
149.1
147.1
163.0
179.0
161.9
177.9
193.8
177.7
193.6
209.6
194.3
210.3
226.2
211.9
227.8
243.8
230 3
140.6
117.9
123.5
154.6
174.3
116.7
131.9
137.4
137.9
145.5
i52'.8
160.4
169.4
189.1
185.2
204.9
224.6
201.8
221.5
241.2
219.4
239.1
258.8
237 8
i52.3
:::::
167.1
174.2
174.7
184.4
168.5175.5
176.1 185.4
168.0
191.4
201.0
185.2 192.1
192.8202.0
190.8
. . 208.9
208.4218.6
209.7
219.6
210.3
227.4
237.0
236.3
248.9
246.3
262.2
249.7
265.6
281.6
285 '.9
301.8
257.5
277.2
257.2
276.9
296.6
277.4
297.1
316.8
298.6
318.3
338.0
320.6
340.6
360.0
363.3
383.0
228.1
238.0
236.0
248.5
226.8
228.8
255.6
268.2
275 '.9
288.5
255.3
267.9
275.6
288.1
296.7
309.3
33i'.3
354.3
256.4
257.4
277 ".6
i"
276 '.6
i . . . .
297.0
309.6
307.0
323.0
297.8
::;
;;;;;
298.8
320 '.8
33i'.7
329.1
345.0
352.0
368.0
354.6
93
COLUMNS
TABLE 22
SQUARE CORED COLUMNS
SAFE LOAD IN THOUSANDS OF POUNDS
JOINT COMMITTEE RECOMMENDATIONS
2500-lb. concrete
1:4% mixture
n = 12
f c =565
Max.
/unsupported length^
side
15
Size
of
column
(inches)
Size
of
core
(inches)
Number
of
rods
Square rods
Round rods
H
H
y*
1
IK
IK
H
H
V*
1
IK
IK
12
13
14
15
16
17
18
19
20
21
22
23
24
25
20
27
28
29
30
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
4
4
4
6
8
4
6
8
4
6
8
4
6
8
4
6
8
4
6
8
4
6
8
4
6
8
4
6
8
4
6
:
i
4
6
8
4
6
8
4
6
8
4
6
8
4
6
8
6
8
45.9
55.5
! 66.2
71.1
75.9
1 78.1
! 82.9
87.8
91.1
95.9
;100.8
50.1
59.8
70.5
77.5
82.4
89.3
96.3
95.3
102.3
129.3
109.5
116.5
123.5
124.7
131.7
138.7
141.1
148.1
155.1
ies'.e
172.6
184 3
64.8
75.5
!
43.8
53.4
64.1
67.9
71.8
76.0
79.8
83.6
'92 '.8
96.6
ioe>'.9
110.7
47.1
56.8
67.5
73.0
78.5
79.4
84.8
90.3
92.3
97.8
103.3
106.5
112.0
117.5
i27! 2
132.7
51.1
60.7
71.5
78.9
83.3
90.8
98.3
96.3
103.8
111.3
110.4
117.9
125.4
125.7
133.2
140.6
142.1
149.6
157.0
i<37\i
174.5
185' 7
65.3
76.0
87.9
97.7
100.9
110.7
115.0
124.8
134.5
130.3
140.0
149.8
146.7
156.4
166.2
164.2
173.9
183.7
182.8
192 6
81.2
93.1
106.1
120.2
132.6
135.5
147.8
151.8
164.2
176.6
169.4
181.7
194.1
188.0
200 4
111.9
126.0
141.3
156.5
157.6
172.9
175.2
190.4
205 . 7
193.8
209 1
81.4
87.4
96.9
93.2
100.4
109.9
106.2
112.8
114.5
124.0
133.6
129.8
139.3
148.8
146.2
155.7
165.2
163 . 7
173.2
182.7
182.3
191 8
120.4
132.8
135.6
148.0
127.0
142.2
157 9
134.3
149.6
J110.1
1114.9
i25.3
130.2
i4i'.7
146.6
iei'.i
126.0
152.0
164.4
176.9
169.5
181.9
194.4
188.2
200 6
158.6
174.3
176.1
191.8
207.6
194.8
210.5
166.0
183.5
202.9
202.1
221 6
l42'.4
143.6
149.1
iei '. i
166.6
182.7
191.3
204 '.6
211.0
201.4
2ii'.6
22}. 1
213.0
207.9
220.4
232.8
228.8
241.3
253.7
250 9
226.2
214.5
230.3
246.0
235.4
251.2
266.9
257 5
185.3
193.2
202.3
212.7
207.8
220.1
232.5
228.7
241.0
253.4
250.7
263.1
275.4
224.3
213.6
228.8
244.1
234.5
249.7
265.0
256.5
271.8
287.0
279.7
294.9
310.2
304.0
319.2
334.5
344.7
359.9
371.2
386.5
398.9
414.1
427.7
443.0
221.9
241.3
260.8
242.8
262.2
281.7
264 8
'.'.'.'.'.
205 '.6
205.5
213.0
226 '.4
233.9
212.4
222.1
233.3
243.0
1
231 '.9
232.5
242.0
254.6
264.1
277 '.7
287.2
263.3
275.7
286 '.5
298.9
273.2
288.9
280.6
296.4
312.1
304.9
320.7
336.4
284.3
303.7
288.0
307.4
326.9
312.3
331.7
351.2
337.7
357.2
376.6
364.3
383.7
403.1
392.0
411.4
430.8
440.2
459.6
255.9
255.3
265.1
1
254.0
277'.!
\
279 . i
278.5
288.2
286.2
298.6
310.5
322.9
336.0
348.3
362.5
374.9
402 '.6
43i.4
3ii.5
310.8
323.2
312.5
336.2
348.6
362 '.7
375.2
346.1
361.8
372 '.6
388.4
400 '.3
416.1
429 .1
444.9
337.6
363 . 5
337.9
364 '.5
392 '.2
1
402 '.9
43i'.7
94
TABLE 23
COLUMNS
, Cotumnsizf
SQUARE CORED COLUMNS
SAFE LOAD IN THOUSANDS OF POUNDS
JOINT COMMITTEE RECOMMENDATIONS
/unsupported length\
Max. [ - T3 I = 15
V side /
3000- Ib. concrete
1:3 mixture
n = 10
f c =675
Size
of
column
(inches)
Size
of
core
(inches)
Number
of
rods
Square rods
Round rods
K
H
H
1
IX
IK
%
y*
H
1
IK
IK
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
4
4
4
6
8
4
6
8
4
6
8
4
6
8
4
6
8
4
6
8
4
6
8
4
6
8
4
6
8
4
6
8
4
6
8
4
6
8
4
6
8
4
6
8
4
6
8
4
6
8
6
8
52.7
64.2
78.0
81.7
86.5
91.2
95.9
100.7
'106.7
111.4
116.2
'i28'.3
133.1
i46.5
1151.3
iee'.i
170.9
igi'.s
2i4'.i
56.9
68.3
81.2
86.0
50.7
62.1
75.0
78.7
82.4
89.1
92.9
96.6
i08.4
112.1
i25'. 3
129.0
53.9
65.4
78.2
83.6
89.0
92.4
97.8
103.2
107.9
113.3
118.7
124.8
130.2
135.6
57.8
69.3
82.1
89.4
96.3
103.6
110.9
111.8
119.1
126.4
128.7
136.0
143.3
146.9
154.2
161.5
166.5
173.8
181.1
73.8
86.6
100.8
110.3
116.3
125.8
133.2
142.7
152.3
151.4
160.9
170.5
171.0
180.5
190.1
191.9
201.4
211.0
214.6
223.7
233.3
91.7
105.7
121.4
138.2
150.3
156.5
168.5
180.6
176.0
188.1
200.2
197.0
209.0
221.1
219.2
231.3
243.4
242.9
254.9
267.0
267.8
279.9
292.0
294.2
306.2
318.3
127.0
143.9
162.1
177.0
181.7
196.6
202.6
217.5
232.4
224.9
239.8
254.7
248.5
263.4
278.3
273.5
288.4
303.3
299.8
314.7
329.6
327.5
73.3
86.1
91.8
95.3
102.2
109.0
110.9
117.7
124.5
127.7
134.6
141.4
146.0
152.8
159.6
165.5
172.4
179.2
i93.3
200.1
2is'.6
222.4
100.3
109.6
106.0
115.8
125.1
121.5
128.0
132.7
142.0
151.3
150.9
160.2
169.5
170.5
179.8
189.1
191.4
200.7
210.0
213.7
223.0
232.3
138.4
150.5
144.8
152.0
156.6
168.8
163.1
178.4
170.3
148.4
153.8
ies'.o
173.4
147.2
iee'.s
176.2
188.3
200.5
197.1
209.3
221.4
219.4
231.5
243.7
243.0
255.2
267.3
268.0
280 1
182.6
198.0
203.6
218.9
234 3
189.8
210.8
229.8
188.9
194.3
194.7
202.0
225.8
241.2
256.6
249.5
264.8
280.2
274.4
289 8
233.0
252.0
256.7
275.7
294.6
281.6
300 6
217.0
224.3
216.6
:::::
239.2
246.0
246.6
255.9
27i 6
240.2
240.6
247.9
247.3
256.9
i
265.6
272.9
299 '.2
272.3
281.9
298 '.6
308.2
:;!"!!
271.0
297 '.3
280.9
297.9
307.2
325 '.6
334.9
363 '.9
292.3
294,3
306.5
318.6
334. i
346.3
363 '.2
375.3
305.2
300.8
316.1
331.5
328.4
343.8
359.2
357.5
372.8
388.2
319.6
308.0
327.0
345.9
335.5
354.6
373.6
364.7
383.7
402.6
395.0
414.0
433.0
426.8
445.8
464.7
459.8
478.8
497.8
513.3
532.2
326.3
335.9
364 '.9
395.3
333.9
346.0
362 '.9
375.0
393.3
405.4
425.0
437.1
470 '.2
504 '.6
342.3
357.3
356.5
371.4
386.3
401.8
416.7
433.5
448.4
466.3
481.5
501.0
515.9
325.0
326.9
:::::
|
394 '.3
393.5
405.7
403.2
418.6
434 '.9
450.3
::::.:
426.6
425.3
437.4
i
427.0
460. i
'.'.'.'.'.
470 '.5
504.9
468.0
483.4
502.4
517.8
95
COLUMNS
TABLE 24
SQUARE CORED COLUMNS
SAFE LOAD IN THOUSANDS OF POUNDS
AMERICAN CONCRETE INSTITUTE RECOMMENDATIONS
AND
NEW YORK CITY BUILDING CODE REQUIRE-
MENTS
2000 -Ib. concrete P =Af c [l + (n-l)p]
1:6 mixture ,_ (unsupported length\
n = 15 Max.(- -J =15
f c =500
( Column cize
j?
sksSs^
ip.^
iCV.-.-.--o-.-.-:i J
^liftl
x ConrSize >
Size
of
column
(inches)
Size
of
core
(inches)
Number
of
rods
Square rods
Round rods
H
'H
y*
1
1H
IK
%
H
14
i
1H
iy*
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
4
4
4
e
8
4
6
8
4
6
8
4
6
.8
4
6
8
4
6
8
4
6
8
4
6
8
4
6
8
4
6
8
4
6
8
4
6
8
4
6
8
4
6
8
4
6
8
4
6
8
4
6
8
42.9
51.4
60.9
66.4
71.9
71.4
76.9
82.4
82.9
88.4
93.9
95.4
'100.9
106.4
108 9
1 14 . 4
119.9
123.4
128.9
134.4
138.9
144.4
149.9
155.4
160.9
166.4
178.4
183.9
igeig
202.4
2ie'.4
221.9
236 '.9
242.4
47.8
56.3
65.8
73.6
40.6
49.1
58.6
62.9
67.2
69.1
73.4
77.7
80.6
84.9
89.2
93.1
97.4
101.7
106.6
110.9
115.2
121.1
125.4
129.7
146 '.9
145.2
i57.4
161.7
174 '.9
179.2
i93.'4
197.7
44.4
52.9
62.4
68.6
74.7
72.9
79.1
85.2
84.4
90.6
96.7
96.9
103.1
109.2
110.4
116.6
122.7
124.9
131.1
137.2
140.4
146.6
154.7
156.9
163.1
169.2
174.4
180.6
186.7
199. 'i
205.2
48.8
57.3
66.8
75.3
77.3
85.8
94.2
88.8
97.3
105.7
101.3
109.8
118.2
114.8
123.3
131 . 7
129.3
137.8
146.2
144.8
153.3
161.7
161.3
169.8
178.2
178.8
187.3
195.7
197.3
205.8
214.2
216.8
225.3
233.7
237.3
245.8!
254.2
267.3
275.7
289 '.8
298.2
sis. 3
321.7
62.5
72.0
82.5
93.5
94.0
105.0
106.5
117.5
128.5
120.0
131.0
142.0
134.5
145.5
156.5
150.0
161.0
172.0
166.5
177.5
188.5
184.0
195.0
206.0
202.5
213.5
224.5
222.0
233.0
244.0
242.5
253 . 5
264.5
264.0
275.0
286. ;
286.5*
297.5
308.5
310.0
321.0
332.0
334.5
345.5
356.5
77.8
88.3
99.8
112.3
126.3
125.8
139.8
140.3
154.3
168.2
155.8
169.8
183.7
172.3
186.3
200.2
189.8
203.8
217.7
208.3
222.3
236.2
227.8
241.8
255.7
248.3
262.3
276.2
269.8
283.8
297.7
292. 3 1
306.3
320.2
315.8
329.8;
343.7
340.3
354.3
368.2
365.8
379.8
393.7'
106.4
118 .9
132.4
149.5
146.9
164.0
162.4
179.5
196.7
178.9
196.0
213.2
196.4
213.5
230.7
214.9
232.0
249.2
234.4
251.5
268.7
254.9
272.0
289.2
276.4
293.5
310.7
298.9
316.0
333.2
322.4
339.5
356.7
346.9
364.0
381.2
372.4
3S9.5
106.7
61.9
71.4
78.0
! 76.3
84.1
92.0
87.8
95.6
103.5
100.3
108.1
116.0
113.8
121.6
129.5
128.3
136.1
144.0
143.8
151.6
159.5
160.3
168.1
176.0
177.8
185.6
193.5
196.3
204.1
212.0
215.8
223.6
231.5
236.3
244.1
252.0
81.9
92.7
88.5
93.4
104.2
100.0
105.4
105.9
116.7
127.4
119.4
130.2
140.9
133.9
144.7
155.4
149.4
160.2
170.9
165.9
176.7
187.4
183.4
194.2
204.9
201.9
212.7
223.4
221.4
232.2
242.9
241.9
252.7
263.4
263.4
274.2
284.9
285.9
296.7
307.4
309.4
320.2
330.9
344 . 7
355.4
112.5
126.5
126.0
ITO.O
119.9
128.3
133.4
151.2
141.8
140.5
154.5
168.5
156.0
170.0
184.0
172.5
186.5
200.5
190.0
204.0
218.0
208.5
222.5
236.5
228.0
242.0
256.0
248.5
262.5
276.5
270.0
284.0
298.0
292.5
306.5
320.5
316.0
330.0
344.0
340.5
354.5
368.5
366
147.9
165.7
156.3
163.4
181.2
198.9
179.9
197.7
215.4
197.4
215.2
232.9
215.9
233.7
251.4
235.4
253.2
270.9
255.9
273.7
291.4
277.4
295.2
312.9
299.9
317.7
335.4
323.4
341.2
358.9
347.9
365.7
383.4
373 4
171.8
193.6
188.3
210.1
205.8
227.6
249.5
224.3
246.1
268.0
243.8
265.6
287.5
264.3
286.1
308.0
285.8
307.6
329.5
308.3
330.1
352.0
331.8
353.6
375.5
356.3
378.1
400.0
381 8
2i7'.2
237 '.7
259.2
28i .-7
218.6
224.7
239. i
245.2
260 . 6
266.7
283 '.i
289.2
263 '.9
286 '.4
309.9
334 '.4
265.6
273.5
288 '.1
296.0
3ii.6
319.5
336! 1
344.0
::::
3i2'.7
....
337 '.2
337.8
346.2
36i.6
369.5
376.2386.6|391.2403.6
380.9394.0,408.9 425.5
363.3
371.7
371.0
382.0
362.7
96
TABLE 25
L Colur^n sira J
COLUMNS
SQUARE CORED COLUMNS
SAFE LOAD IN THOUSANDS OF POUNDS
AMERICAN CONCRETE INSTITUTE
RECOMMENDATIONS
Max.
/unsupported length^
side
15
2500 -Ib. concrete
1:4% mixture
n=12
f c = 625
Size
of
column
(inches)
Size
of
core
(inches)
Number
of
rods
Square rods
1 I IK I IK
Round rods
K
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
50. 7j
61.4
73.2
78.6
84.0:
86. 4J 91.1
91.7 98.8
55.5
66.1
78.0
85.7
71.7
83.6
107.2
97.5
103.1
97.1 loee ....
100.7105.51111.1
106.1 113.2121.6
111.5 120 9
117.5124.8 .
116
121
127
| 133
; 138
I 144
151
156
162
170,
176,
181.
191.
196.
202.
218
224
241
247
4 121
7 128
1 136
2!l38
6; 145
0153
4' 156
7 163
1171
7|175.
11183.
5190.
4J196.
7203.
211.
218.
6225.
0233.
241.
.7248.
256.
48.4
59.1
70.9
75.2
79.4
84.1
88.3
92.5,
52.2
62. 8 !
74.7J
56.5
67.2
79.0
80.71 87.3
86.8J
87. 8i 92.2
93.9 100.4
99.9 108.7
1 IK IK
72.2
84. l'
89.8
97.2103.0
108.0
98.4 102.2 106.5 111.6117.3
102.7108.2 114.8122.4
106.9 114.3 123.1
.l'l26.7 132
.8137.2146
.6J147.7 . ..
.0!l43.6il50.o'l57.3 i 165.5 130.9
.7154.1163.8174.7 135.2
41164.6 | 139.4
1 161.7
8172.2
6182.7
181.1
2 191
202
201
8:212
6 J 222
1 140.4 148.6 114.1 117
9 i 118.3 123
.| i ! 122.5129
134
140
146
8 122.2J127.2
9 130.4 138.0
9 ! 138.7148.8
123.8
133.0 139.4
146.6
168.
181.
195.
187.
l'l75.4183
9 192.8 ...
6'..
. 6
5 194.8203
6201.3212.2224
0^29.6,
266.1
271.5
291.7
297.1
352.1
38i'
7234
4244
l!246,
8257.
6267
215.
7
2|221
7J235.6250.2
61230
1 243
6257
1215. 4^223.
9232.8J245.
265.5271
273.2281
280.9:292
291.1296
298.8307
306.6317
.J323
325.7,334
324.0333.4344
7,243
2 ! 266
.71280,
.1277,
.6291,
. 1 305 ,
.7303.
.2316.
.7,330.
.6330.
.1 343.
.6357.
0237.3245.5
8:254.7267.0
5272.1 288.4
l'260.4268.6
9277.8290.1
6295.2311.6
.351.7358
353.8362.2371
361.6372.7385
.'381
383 2391.6401
5390.9402
.1
413.8422
421.6432
445 7 454
453.4464
415
418
2431
.7445
450
463
6|477
5284
3302
OJ319
11310
9327.
6345.
0337.
8354.
5372.
1365.
9382.
6,400.
5! 394 .
3*412.
OJ429.
T425.
9442.
6460.
0457.
8474.
5:492.
.8293.0
.2314.5
.6335.9
.4318.6
.8340.1
.2.361.6
s'345.5
7'367.0
1 388.4
4373.6
8 395 . 1
2j 416.6
8403.0
21424 5
6J445.9!
4433.6'
8455.1
2476.6
3465.5
7487.0
1 508.4
7 139
7147
8155
149.1 152.8157
9 165
9 173
.
153.3 158
157.5164
172
172.7 178
176.9 184
192
193.3 198
197.5204
2 176.
2184.
3193.
8197.
9 205.
9213.
0144
3 ! 154
6 165
2162
4 173
7 183
5181
8192
1 203
2202
4J213
7223
1149
9 163
7 |
2 168
0181
8 195
6187
4 201
2.214
2' 208
0221
8235
.8156.3
.5173.1
.0 174.4
.6191.3
.31193.8
.OJ210.6
.7227.5
,0!214.4
.6231.3
.3 248.1
214.7219.0224.1 229.8 ! 236.3
215.2220.7|227.3234.9:243.5253.1
219. 41226.8235.6245.71257.2 270.0
242. 2247. 2^53. 0*259. 4
238.3243.9250.4258.0266.6276 3
242.5249.9 258. 7 268. 8280. 3J293.1
266.5271.6277.3283.8
268.2,274.8282.4 291.0300.6
266.9 274 .3|283 . l!293 .2 304 .7*317 .5
!292.2297.2 ! 303.0309.4
293.9300.4308.0316.6:326.3
292 .5 299 .9j308 .7 318 .8|330 .3 343 . 1
324.r329.s'336.3
334.91343.5353.1
319.4326.8335.6345.71357.2370.0
320.7327.3
347
. 348
5354
3S4
414
446
9355
I) 303
. 384
.3393
. 415
.9423
. 447
8455
. 352 .
.4 363.
.7J373.
.381.
.8392.
.1408.
. ! 412.
4423.
7433.
3454.
6 465 .
2358
0371
8J385
6387.
4401.
2414.
2,418.
0|431.
8445.
. 449'.
9463.
7477.
.0364.4
.6381.3
.3398.1
.3(393.8
.0410.6
.7427.5
.0424.4
.6441.3
.3458.1
8456.3
5473.1
2490.0
97
COLUMNS
TABLE 26
SQUARE CORED COLUMNS
SAFE LOAD IN THOUSANDS OF POUNDS
AMJttKK
I
3000-lb. concrete
1:3 mixture -
7i 12 Max.
f 750
JAJN UUJNUK..&J..& 1HS11J
RECOMMENDATIONS
P = Af c [l + (n l)p]
/unsupported length\
U1H,
15
Cofumn size
&*$$]*
siny
! j
N,
\ side )
Size
of
column
(inches)
Size
of
core
(inches)
Number
of
rods
Square rods
Round rods
H
K
%
1
IK
IK
H
K
Vs
i
IK
IK
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
8
9
10
11
12
13
14
15
10
17
18
19
20
21
22
23
24
25
26
4
4
4
6
8
4
6
8
4
6
8
4
6
8
4
6
8
4
6
8
4
6
8
4
6
8
4
6
8
4
6
8
4
6
8.
4
6
8
4
6
8
4
6
8
4
6
8
4
6
8
4
6
8
60.9
73.6
87.9
94.3
100.8
103.6
110.1
116.5
120.9
127.3
133.8
139.6
146.1
152.5
159.9
166.3
172.8
181.6
188.1
194.5
204.9
211.3
217.8
229.6
236.1
242.5
262.3
268.8
290.1
296.5
3i9'.3
325.8
350 '.i
356.5
66.6
79.3
93.6
102.8
86.0
100.3
58.1
70.9
85.1
90.2
95.3
100.9
105.9
111.0
118.1
123.2
128.3
136.9
141.9
147.0
157.1
162.2
167.3
178.9
183.9
189.0
207.2
212.3
23i'.9
237.0
258 '.2
263.3
285.9
291.0
320.3
62.6
75.3
89.6
96.9
104.2
105.3
112.6
119.9
122.6
129.9
137.2
141.3
148.6
155.9
161.6
168.9
176.2
183.3
190.6
197.9
206.6
213.9
221.2
231.3
238.6
245.9
257.6
264.9
272.2
292 '.6
299.9
32i'.9
329.2
67.8
80.6
94.8
104.8
110.6
120.4
130.4
127.8
137.8
147.7
146.6
156.5
166.4
166.8
176.8
186.7
188.6
198.4
208.4
211.8
221.8
231.7
236.6
246.5
256.4
262.8
272.8
282.7
290.6
300.5
310.4
319.8
329.8
339.7
350.6
360.5
370.4
392 '.8
402.7
86.7
100.9
116.7
129.6
133.9
146.9
152.7
165.6
177.6
172.9
185.9
198.8
194.7
207.6
220.6
217.9
230.9
243.8
242.7
255.6
268.6
268.9
281.9
294.8
296.7
309.6
322.6
325.9
338.9
351.8
356.7
369.6
382.6
388.9
401.9
414.8
422.7
435.6
448.6
457.9
470.9
483.8
494.7
507.6
520.6
107.8
123.6
140.8
159.6
176.0
179.8
196.1
201.6
218.0
234.4
224.8
241.2
257.7
249.6
266.0
282.4
275.8
292.2
308.7
303.6
320.0
336.4
332.8
349.2
365.7
363.6
380.0
396.4
395.8
412.2
428.7
429.6
446.0
462.4
464.8
481.2
497.7
501.6
518.0
534.4
539.8
556.2
572.7,
148.5
167.3
187.5
207.7
209.3
129.5
232.5
252 . 8
273.0
257.3
277.5
297.8
283.5
303.8
324.0
311.3
331.5
351.8
340.5
360.8
381.0
371.3
391.5
411.8
403 . 5
423.8
444.0
437.3
457.5
477.8
472.5
492.8
513.0
509.3
529.5
549.8
547.5
567.8
588.0
108.0
109.3
118.6
127.9
126.6
135.8
145.1
145.3
154.6
163.9
165.6
174.8
184.1
187.3
196.6
205.9
210.6
219.8
229.1
235.3
244.6
253.9
261.6
270.8
280.1
289.3
298.6
307.9
318.6
327.8
337.1
349.3
358.6
367.9
116.0
128.7
123.8
133.3
145.9
141.0
149.8
152.0
164.7
177.3
172.3
184.9
197.5
194.0
206.7
219.3
217.3
229.9
242.5
242.0
254.7
267.3
268.3
280.9
293.5
296.0
308.7
321.3
325.3
337.9
350.5
356.0
368.7
381 -.3
388.3
400.9
413.5
422.0
434.7
447.3
457.3
469.9
482.5
506 '.7
518.3
544.9
557.5
159.8
176.3
168.5
178.3
180.0
196.5
188.8
209.7
198.6
201.8
218.3
234.8
225.0
241.5
258.0
249.8
266.3
282.8
276.0
292.5
309.0
303.8
320.3
336.8
333.0
349.5
366.0
363.8
380.3
396.8
396.0
412.5
429.0
429.8
446.3
462.8
465.0
481.5
498.0
501.8
518.3
534.8
540.0
556.5
573.0
210.5
231.4
220.3
233.8
244.7
275.5
258.5
279.4
300.3
284.8
305.7
326.5
312.5
333.4
354.3
341.8
362.7
383.5
372.5
393.4
414.3
404.8
425.7
446.5
438.5
459.4
480.3
473.8
494.7
515.5
510.5
531.4
552.3
548.8
569.7
590.5
243.6
269.3
268.3
294.1
294.6
320.3
346.1
322.3
348.1
373.9
351.6
377.3
403.1
382.3
408.1
433.9
414.6
440.3
466.1
448.3
474.1
499.9
483.6
509.3
535.1
520.3
546.1
571.9
558.6
584.3
610.1
351.0
383 '.3
4i7.6
352.6
359.9
384 '.9
392.2
388 '.8
422.5
390.8
400.1
424 '.6
433.9
418.6
425.9
426.5
436.4
457 '.8
494 . 5
459.8
469.1
496 '.6
505.9
534.8
544.1
: : ; ; ;
46i.2
46i.8
471.7
497.9
498.5
508.4
536 '.2
536.8545.9
546.7^58.8
98
TABLE 27
COLUMNS
Column size
SQUARE CORED COLUMNS
SAFE LOAD IN THOUSANDS OF POUNDS
NEW YORK CITY BUILDING CODE
REQUIREMENTS
mixture
= 12
Size
of
column
(inches)
Size
of
core
(inches)
Number
of
rods
Square rods
Round rods
H
H \ X \ H
1H
12
13
14
15
16
17
18
19
20
21
22
23
24
25
20
27
28
29
30
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25.
20
I 48. 7| 53.3
j! 58.91 63.5 68.8
i 70. 3 ! 54. 9 ! 80.2
! 75.5! 82.3 ..
82.9
87.5! 92.8
94.9 102 9
93.2 102. 3|
96.7 101.3106.6
'101.9 108.7,116.7
|107. 0116.1
111. 7 116.3121.6
86.4
99
112.8
127
116.9 123.7|131.7 141
122.0 131.1141.8 .. -
8134
0. ..
127.9
133.1
138.2
142.7
132.5 137. 8' 144
139.9'l47.9 157
147.3,158.0 ....
! 151
2 167
145.3149.9 155.2161
150.5 157.3 165.3 174
155.6164.71175.4^87
163. 9! 168.5; 173. 8 180
169.1 175.9 183.9 193
,184.21183. 3 194. 0206
.0158.
.7 ....
183.7 188
188.91195
194. 0| 203
'209
209.9'216
215.0J224
.....231
232.1 238
237.2246
3193
7203
1,213
3214
7224
1 234
5*236
9246
3257
.6199
.7213
.8226
.6 ! 220
.7234
.8,247
. 8*243
.9 256
.0269
254.9260.21266
255.5262.3270.3:279
260.6269.7280.41292
279.5284
!280.1J286.9294
285.2294.3305
. . . 310
312.7320
311.0320.1
330
,337
339.71347
338.0347.1357
365
367.9375
366.2375.3386
.8291
.930-4
.0317
.6316
.7330
.8343
.6343
.7357
.8370
.8372
. . 401
168
6 185
o'l87
2203
4220
8 ( 206
0223
2240
8227
0244
2261
01250
2266
4J283
4273
6290
8306
0298
2314
4 331
s'323
0340
8350
0367
2384
0379
2395
4412
4408
.4176.
.1 ____
.o'l94.
.7215.
.8214.
.5235.
.2255.
.8235
.5256
.2276
.o'257
.7278
.4299
.4381
.1 301
.8322
o'sos
.7326
,4|347
.s'331
5352
.2372
.8358
.4379
.2399
.0386
.7407
.4428
46.5
56.7
68.1
72.2
76.2
80.7
84.7
88.8
94.5
98.6
102.6
109.5
113.6
117.6
50.1
60.3
71.7
77.5
83.3
84.3
90.1
95.9 104
98.1
103.9
109.
125.7129
129.8 135
133.8,140
143.1 146
147.2152
151.2 158
54.3
64.5
75.9
83.8
69.3
80.7
.5 93.3
.4 103.7
. 4|
102.3 107.1
110.2 117.5
7118.2
117.3 122.1
113
118.9 125.2 132.5140.8!
124.7133.2,142.9
86.2
98.8
112.6 118.8
127.6133.8
..,,133. 5 138. 3 143. 8 150.0
.1 141.4 148. 7J157.0 166.2
.9 149.4 159.1
.7
!3|166.8 176.5ll87.5i
150.9,155.7161.2167.4
158.8 I 166.1!174.4 183.6
.3
185
189
206
210
!165.3'l69.5 174.3 179.8 186.0
.8 171. l|l77. 4 184.7 193.0202.2
.8 176.9 185.4,195.1:206.1 218.4
6190
6196
.206
6212
6227
189.
197.
1 210.
0|218.
7226.
3193
2204
7205.2214
3215
2225
2235
228
232
8234.
8239.
256
2SO
232 .
240.
248.
5 237
4247
4258
1 199
5212
9 225
l' 220
5233
9,246
3 '242
7256
i;269
.6205.8
.81222.0
.9238.2
.6226.8
.8243.0
.9,259.2
.9^249.0
.0265.2
.1281.4
? :::
397.3405.3414
395.6404.7415.4
427
432
427.9435.9J445
435.3446.0458
6425
,8 ( 441
0439
,2455
4472
1436
,8457,
01447
7J467,
4488.
.. 255.9260.7266.2272.4
. . 257.5 263 .8 271 . 1 279 .4 288.6
.2263.3271.8^81.5292.5304.8
..':.... 280. 5285. 3i290. 8297.0
. . 282. H288. 4 295. 7^304.0313. 2
.8 287. 9 296. 4 306.1 347. 1 ( 329. 4
. .'311.l'316.6322.8
. . 307.9314.2321.5329.8339.0
.6 313.7 322.2 331 .9 342.9 355.2
333
. 334
6340
361
9341
7349
.9,377
I
8368
'. 398.3406
! 428
. 429
,9437
. 338
.2348
.2358
.1366
,4376
.4387.
.395
8406
8416.
4436
4447
1343
5356.
9369.
3371.
7385.
1 ( 398.
7401.
1414.
5427.
.6349.8
.8366.0
.5372.2
.8378.0
.0394.2
.1410.4
2407.4
4 423 . 6
5439.8
. 431.8438.0
7445.0454.2
1 458.1 470.4
99
COLUMNS
TABLE 28
SQUARE CORED COLUMNS
SAFE LOAD IN THOUSANDS OF POUNDS
CHICAGO BUILDING CODE REQUIREMENTS
2000-lb. concrete
1: 6 mixture
71=15
f c =400
Ma X .( lenff * h }=12
\ side I
Size
of
column
(inches)
Size
of
core
(inches)
Number
of
rods
Square rods Round rods
M
H
14
1 IK
IK
H
H
K
1
IK
IK
12
g
4
41 .2
45
39.3 42 3
45.9
13
10
4
48.8
52.6
46.9
49.9
53.5
14
4
57.2
61
65.6
55 3
57.3
61.9
66.0
6
6l'5
67^3
58^7
63.2
68.6
g
65.9
62.2
68.2
15
12
4
66.4
70.2
74.8
80.0
64.5
67.5
71.1
75.2
79.9
70 7
76.5
67 9
72 4
77.8
8
75 .'l
71 !4
77 'A
16
13
4
76.4
80.2
84.8
90.0
96.0
74.5
77.5
81.1
85.2
89.9
95.1
6 80 7
86.5
93.3
77.9
82.4
87.8
94.0
8 1 HS ' 1
92^8
81 .4
87.4
94 .5
17
14
4
87.2
91.0
95.6
100.8106.8
85.3
88.3
91.9
96.0
100.7
105.9
6 ! 91.5
97.3
104.1
88.7
93.2
98.6
104.8
8 ! 95.9
103.6
92.2
98.2
105.3
18
15 4 99.8
102.6
107.2
112.4118.4 125.0
96.9
99.9
103.5
107.6
112.3
117.5
6 103.1'108.9
115.7
123.6| 100.3104.8110.2116.4
123.4
8
107.5 115.2
124.3
i
103.8109.8116.9 125.2
19
16
4
111.2 115.0
119.6
124.8 130.8 137.4
.. 112.3 115.9 120.0
124.7 129.9
6 115^5 121.3 128.1
136.0 144.9 112.7117.2 122. 6! 128. 8
135.8 143.6
8 1119.9127.6
136.7
116.2 122.2 329.3 137.6
20
17
4 124.4128.2
132.8
138.0144.0150.6
. . 125.5 129.1 133.2
137. 9 : 143.1
6 , 128.7 134.5
141.3
149.2158.1
; 125. 9130. 4135. 8142.0
149.0156.8
i
8 133.1
140.8
149.9
160.4
129.4135.4
142.5 150.8
160.1
1
21
18
4 '
142.2
146.8
152.0 158.0
164,61 139.5
143.1 149.2
151.9 157.1
6 142.7148.5
8 147. 1 154.8
155.3 163.2
163 9 174 4
172.1
182.1 1139. 9|144. 4
J143 4 14Q 4.
149.8
156.5
156.0163.0170.8
1fU S 174 1
22 19
4 157.0
161.6
166.8172.8
. . J.40.4
179. 4 1 .
157.9 162.0
166.7
171.9
6 157.5163.3
8 161.9169.6
170.1
178.7
178.0 186.9 196.9 154.7 159.2 164.6:170.8 177.8 185.6
189.2201.1 (158.2164.2171.3179.6188.9199.4
23 20
4 172.6177.2182.4188.4 195.0
173.5 177.6
182.3
187.5
6 173.1178.9185.7193.6202.5212.5
..174.8180.2186.4
193.4201.2
8 177 5 185 2 194 3 9n4 s 21 fi 7 17 ^ fi 17Q 8 1Rfi Q 10.1 9
9fU A 91.1 H
24 21
4 |l 189.0 193.6
198.8204.8
211.4' .
. . 189.9 194.0198.7203.9
6
189.5 195.3 202.1 210.0218.9 228.9 191 .2196 .6 202 .8
209.8217.6
1
8
193.9 201.6210.7
221.2233.1246.4
190.2196.2203.3211.6
220.9 231.4
25 22
4
210.8
216.0222.0228.6
. . 211.2215.91221.1
6-
'. '. 212.5 219.3 I 227.2 236.1 246.1
208.4,213.8220.0
227.0234.8
1
8
211.1218.8227.9238.4
250.3263.6
207.4 213.4,220.5228.8238.1 248.6
26 23
4
. . 228 . 8
234.0
240.0246.6
229.2
233.9
239.1
6
'.'.'.'.'. 230.5237.3245.2
254.1
264.1
226.4231.8238.0
245.0i 252. 8
8
229.1 236.8245.9 256.4
268.3
281.6
231.4238.5246.8
256.1
266.6
27 24
4 1 247.6
252.8
258. 8 265. 4 !
l248.0 ! 252.7
257.9
6 !| 249.3 256.1 264.0
272.9282.9
250.6256.8263.8
271.6
8 247.9255.6,264.7
275.2
287.1 300.4
'.'. '.'. '. 250.2257.3265.6274.9
285.4
28 25
4
272.4
278.4
285.0
267.6272.3
277.5
6
268 '.9 275. 7
283.6
292.5302.5
. . 270.2276.4
283.4
291.2
8 267.5
275.2284.3
294.8
306.7320.0
269.8276.9285.2,294.5
305.0
29
26
4
292.8
298.8305.4
292.7
297.9
6
8
289.3296.1 304.0
295.6304.7315.2
312.9
327.1
322.9
340.4
'.'. '.'. ^290.2
290^6296.8303.8
297.3305.6,314.9
311.6
325.4
30
27
4
292.8
298.8
305.4
292.7
297.9
6
296 '.i
304.0
312.9
322.9
296.8
303.8'311.6
! 8
'..... 295.6304.7
315.2
327.1 340.4
'.'.'.'.'. 297.3 305.6 | 314.9|325.4
100
TABLE 29
K
J COLUMNS
SQUARE
SAFE LOAD IN
CHICAGO BUILD
Ma.
V
"*
CORED COLUMNS
THOUSANDS OF POUNDS
ING CODE REQUIREMENTS
Af[l + (n l)p] 2400-lb. concrete
/length\ 19 1:4 % mixture
ic; ' * *> J ? *
-lilt
*'\ side )
/* JL6
f c =480
Size Size
of of
column core
(inches) (inches)
Number
of
rods
Square rods Round rods
H
%
K
1 i 1,4
IK i! *A
1
1
IK
IK
12 9
13 10
14 11
15 12
16 13
17 14
18 15
19 16
20 17
21 18
22 19
23 20
24 21
25 22
26 23
27 24
28 25
29 26
30 27
4
4
4
6
8
4
6
8
4
6
8
4
6
8
4
6
8
I
I
8
4
6
8
4
6
8
4
6
8
4
6
8
4
6
8
4
6
8
4
6
8
A
6
8
4
6
8
4
6
8
47.1
56.3
66.3
70.5
74.6
77.4
81.5
85.6
89.4
93.5
97.6
102.3
108.5
110.6
116.3
120.4
124.5
131.1
135.3
139.4
147.0
151.1
155.2
50.8
59.9
69.0
75.9
74.3
45.4
54.5
64.6
67.8
71.0
75.6
78.8
82.1
87.6
90.8
94.1
100.6
103.8
107.0
114.5
117.7
121.0
132.6
135.8
l48'.4
151.7
48.2
57.3
67.4
72.1
76.7
78.5
83.1
87.8
90.5
95.1
99.8
103.4
108.1
112.7
117.3
122.0
126.7
132.2
136.9
141.5
148.1
152.7
157.4
164.9
51.1
60.7
70.8
77.1
81.8
88.2
93.8
100.2
106 5
106.8
113.-1
119.5
120.7
127.1
133.4
135.6
141.9
148.3
151.4
157.8
164.1
168.2
74.7
85.7
97.7
106.0
110.7
119.0
124.6
132.9
141.2
139.5
147.8
156.1
155.3
163.6
171.9
172.1
90.1
102.1
115.1
129.0
139.5
143.9
154.4
159.7
170.2
180.7
176.5
107.0
120.0
133.9
148.8
161.8
164.6
177.6
181.4
81.0
86.9
85.3
90.2
93.0
98.9
104.9
106.0
111.9
117.8
119.9
125.8
131.8
134.8
140.7
146.6
150.6
156.5
162.5
167.4
97.3
105.4
102.2
107.9
110.3
118.3
115.2
120.8
124.2 129.1
132.3139.7
140.3!
139.1 144.0
147.1 154.6
155.2
154.9159.8
163.0170.4
171.1 181.0
171.7176.6
134.7 141.0
149.6
163.0
165.5
178.8
182.3
155.9
171.7
188.5
167.9
172.0
173.3 179.8 187.2
179.3 187.9197.8
185 2 189 5 194 4
195.6
200.0
205.0
206.3
165.2
168.5
169.5
174.2
174.6
180.9
186.0
192.3
198.7
204.7
211.1
217.4
224.4
180.4
188.7
189.9
198.2
206.5
208.6
216.9
225.2
228.3
236.6
244.9
248.9
257.2
265.5
270.5
278.8
287.1
283.1
301.4
309.7
316.6
324.9
333.2
349.4
357.7
187.0|194.4
197.5
194.3 199.2
204.8212.2
215.3225.1
213.0217.9
223.5230.9
234.0243.8
232.7237.6
243.21250.6
253.7263.5
253.3258.2
263.81271.2
274.3284.2
274.9278.8
285.4292.8
295.9305.8
297.5302.4
308.0315.4
318.5328.3
321.0325.9
331.5338.9
342.0351.8
345.5350.4
356.0363.4
366.5^76.3
370.9375.8
381.4388.8
391.9401.8
185.7
189.8
204 '.4
208.5
191.1 197.5205.0
197.0205.6215.5
203.9208.2'213.1
209.8:216.3223.7
215.8224.3234.2
223.6227.9'232.8
213.4
226.7
218.7
232.1
245.5
238.4
222.8
225.0
241.5
244.7
183.0
186.2
205 '.6
187.3
191.9
206 '.6
210.7
224.1
228.2
248 '.8
229.5
235.4
250 '.i
256.1
235.9
244.0
248.5
256.6
264.7
270.1
278.2
286.3
292.7
300.7
308.8
324 '.3
332.3
348 '.7
356.8
243.4
253.9
253.4
264.0
274.6
275.0
285.6
296.2
297.6
308.2
318.7
321.1
331.7
342.2
345.6
356.2
366.7
371.0
381.6
392.2
251.8
265.1
259.1
272.4
285.8
280.7
294.0
307.4
303.2
316.6
329.9
326.7
340.1
353.5
351.2
364.6
377.9
376.7
390.0
403.4
261.2
277.7
265.3
281.8
298.3
286.9
303.4
319.9
309.5
326.0
342.5
333.0
349.5
366.0
357.5
374.0
390.5
382.9
399.4
415.9
224 . 6
245 '.3
225.7
230.3
246 '.3
251.0
230.7
237.1
25i'.4
257.7
271.7
277.7
267.9
272.6
273.0
279.3
270.4
293.6
3ie>'.5
294.3
300.2
3i7'.8
323.8
342 '.3
348.2
295.5
301.9
sig'.i
325.4
343.5
349.9
295.1
sis '.7
.....
343.1
374.2
'373.7382.3
374.8
375.3 ( 383.1
101
COLUMNS
TABLE 30
U V H
1 J
SQUARE
LOAD IN
JO BUILD
Ma
CORED COL1
THOUSANDS
ING CODE RI
Af c [l + (n-l)p
/length}
JMNS
OF POUNDS
SQUIREMENTS
]
2
- Column $fr e >
SAFE
CHICAC
2900- Ib. concrete
1:3 mixture
n 1 ft
1
1
71 J.U
f c = 580
*' V side ) ~
JJ3SSS
Size
of
column
(inches)
Size
of
core
(inches)
Number
of
rods
Square rods
Round rods
X|
%
1
m
IK
H
X
H
i
. | .
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
4
4
4
6
8
4
6
8
4
6
8
4
6
8
4
6
8
4
6
8
4
6
8
4
6
8
4
6
8
4
6
8
4
6
8
4
6
8
4
6
8
4
6
8
4
6
8
4
6
8
4
6
8
55.1
66.2
78.3
82.4
86.5
91.7
95.7
99.8
106.2
110.2
114.3
121.8
125.9
130.0
138.7
142.7
146.8
156.6
!l60.7
164.8
175.8
179.8
183.9
266 '.i
204.2
22i.6
225 7
58.7
69.8
81.9
87.8
53.4
64.4
76.6
79.8
83.0
89.9
93.1
96.3
104.4
107.6
110.8
120.1
123.3
126.5
136.9
140.1
143.3
iss'.i
161.3
177 '.2
180.4
i97.5
200.7
219 .0
222 2
56.2
67.2
79.4
84.0
88.6
92.8
97.4
102.0
107.3
111.9
116.5
122.9
127.5
132.1
139.7
144.3
149.0
157.7
162.3
166.9
176.9
181.5
186.1
197.2
201.8
206.4
223 '.2
227 8
59.5
70.6
82.7
89.0
96.1
102.4
110.6
116.9
123.1
126.2
132.5
138.8
143.1
149.3
155.6
161.0
167.3
173.6
180.2
186.5
192.7
200.5
206.8
213.0
221.9
228.2
234 5
86.6
99.9
114.4
122.6
130.1
138.3
146.9
155.1
163.3
164.9
173.1
181.3
184.0
192.2
200.4
204.3
212.5
220.7
225.8
234.0
242.2
104.3
118.8
134.4
151.3
161.6
169.2
179.6
188.4
198.8
209.2
208.7
219.1
229.5
230.1
240.5
251.0
123.6
139.3
156 . 1
174.1
186.9
193.2
206.1
213.5
226.4
235.0
247.8
260 . fi
86.2
95.3
101.1
109.8
115.6
121.5
125.4
131.3
137 2
99.5
104.4
114.0
122.0
118.9
124.5
129.7
137.7
134.6
140.1
142.3
148.1
154.0
160.2
166.1
172.0
179.4
185.2
191.1
199.7
205.5
211.4
221.1
227.0
232.9
146'5
154.5
162 5
151.4
161.8
156.9
163.1
164.5
172.5
180.5
183.6
191.6
199.6
203.9
211.9
219.9
225.4
233.4
241.4
169.4
179.8
188.5
198.9
209.4
208.8
219.2
229.7
230.3
240.7
251.1
174.9
188.1
181.1
194.1
207.3
214.4
227.6
235.8
249.0
262.2
200.3
220.6
236.9
242.0
258.3
243.8
249.6
255.5
267.5
273.4
279.3
248.0
256.0
264.0
271.8
279.8
287.8
296.7
304.7
312.7
322.8
330.8
337.9
350.1
358.1
366.1
252.9
263.3
273.8
276.7
287.1
297.5
301.6
312.0
322.5
327.7
338.1
348.6
355.0
365.4
375.8
383.4
393.8
404.3
413.0
423.4
433.8
443.7
454.1
464.6
258.4
271.6
284.9
282.2
295.4
308.6
307.2
320.4
333.6
333.3
346.5
359.7
360.5
373.7
386.9
388.9
402.1
415.4
418.5
431.7
444.9
449.3
462.5
475.7
264.6
280.9
288.4
304.7;
321.0|
313.4
329.7
346.0!
339.5
355.9
372.1
366.7
383.0!
399.3
395.1
411.4
427.8,
424.71
441.0
457.3;
455.5
471.8
488.1
245 '.8
250.5
244.6
250.8
257.1
268.3
274.6
280.9
248.4
256.6
264.8
272.2
280.4
288.6
297.1
305 . 3
313.5
323.2
331.4
339.6
350.5
358.7
366.9
378.9
387.1
395.3
4i6'.7
424.9
252.8 ! 257.6
263.1 270.4
273.6,283.3
276.5281.4
286.9294.2
297.4307.0
301.5 306.3
311.9319.2
322.3 332.0
327.6332.4
338.0345.3
348.4358.1
354.8359.7
365.2372.5
375.7385.3
383.3388.1
393.6400.9
404.1 413.8
412.8417.7
423 . 2 430 . 5
433.7|443.3
443.8448.4
454.0461.3
464.4474.1
244.2
248.3
268 ! 6
272.1
244.8
268 '.6
293 . 5
269.6
274.2
298.3
304.2
294.6
299.2
299.6
305.8
325 '.7
831.9
352 '.9
359.2
38i'.3
387.6
4i6.9
417.2
297.0
323 '.i
324.4
330.3
320.7
325.3
351.7
357.6
350.4
352.5
378 '.8
380.1
386.0
409 '.7
415.6
386.5
393.5
iie'.i
424.1
38i.6
iiois
446 '.3
446.8
454.8
447.4
455.6
447.9
102
TABLE 31
( Column sire J
SQUARE CORED COLUMNS
COLUMNS
SAFE LOAD IN THOUSANDS OF POUNDS
.OS ANGELES BUILDING CODE REQUIREMENTS
1:6 mixture
P = Af c (l + (n-l)p} n =15
f c =550
j: e' '.'. -a- "
BVJ
<:$*
mm
- i^-SliXs.
3M
Jj'l
l J
Size
of
column
(inches)
Size
of
core
(inches)
Number
of
rods
Square rods
Round rods
H
X
H
1
1H
IK
H
H
K
1
1M
IK
12
13
14
15
16 *
17
18
19
20
21
22
23
24
25
26
27
28
29
30
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
4
4
6
8
4
6
8
4
6
8
4
6
8
4
6
8
4
6
8
6
8
4
6
8
4
6
8
4
6
8
4
6
8
4
6
8
4
6
8
4
6
8
4
6
8
4
6
8
6
8
6
8
56.6
67.0
73.0
79.0
78.6
84.5
90.6
91.2
97.2
103.2
111.0
117.0
125.8
131.8
141.8
147.8
61.9
72.3
81.0
89.7
83.9
92.6
101.2
96.5
105.2
113.9
110.3
119.0
127.6
125.1
133.8
142.5
141.1
149.8
158.4
iee'.s
175.5
iss'.o
193.6
204 '.2
212.9
233.2
254 '.7
68.1
78.6
75.4
85.8
54.0
64'. 5
69.2
73.9
76.0
80.7
85.4
93.4
98.1
107.1
111.8
58.2
68.6
75.4
82.2
80.2
87.0
93.7
92.8
99.6
106.4
106.6
113.4
120.1
63.1
73.5
82.8
I 92.0
85.1
94.3
103.6
97.8
107.0
116.2
111.5
120.7
130.0
126.4
135.6
144.8
142.3
151.5
160.8
68.7
79.2
| 75.2
85.6
92.8
J 90.3
J 91.3
90.7
102.8
103.4
116.5
97.2
104.4
90.1
101.9
97.4
105.5
112.8
112.4
109.8
117.0
102.8
114.5
Il26.3
116.5
128.3
140.1
131.4
143.1
154.9
147.3
159.1
170.9
164.4
176.1
187.9
182.5
194.3
206.1
2i3'.5
225.3
233.9
245.7
255.3
267.1
110.0
118.2
127.3
J125.4
125.1
130.8
J149.6
145.6
164.5
1127.6
117.1
129.2
141.3
132.0
144.1
156.2
147.9
160.0
172.1
165.0
177.1
189.2
183.1
195.2
207.3
2i4'.5
226.6
234 '.8
246.9
256 '.3
268.4
123.6
138.8
J154.2
138.4
153.7
123.8
139.2
|154.6
138.6
154.0
131.9
141.1
151.4
146.8
166.2
155.9
180.0
126.7
128.2
135.0
169.4
154.6
170.0
185.4
171.6
187.0
202.4
189.8
205.2
220.6
209.0
224.4
239.8
229.4
244.8
260.2
250.8
266.2
281.6
|169.0 183.4
154.4161.6
169.6180.4
185.0|199.4
171.4 178.6
186.7197.5
202.0216.4
189.6196.8
204.8215.6
220.2234.6
208.8 ! 216.0
224.1 234.8
239.4253.8
229.2'236.4
244.4255.2
259.8274.2
250.6257.8
265.9276.7
281.2295.6
. .280.4
162.7
182.2
201.7
179.8
199.2
218.7
197.9
217.4
236.9
217.2
236.6
256.1
237.5
257.0
276.5
259.0
278.5
297.9
281.5
301.0
320.5
305 2
171.9
196.0
142.6
144.2
150.9
188.9
213.0
237.1
207.1
231.2
255.2
226.3
250.4
274.5
246.7
270.8
294.8
268.1
292.2
316.3
290.7
314.8
338.8
314 3
161.2
168.0
168.6
177.8
i86'.7
196.0
206.6
215.2
226 '.3
235.6
257 '.6
164.8
iss'.o
186.1
205 '.4
:::::
'
277 '.2
277.9
289.7
288.8
304.2
279 '.6
278.8
290.9
288.4
303.8
299.2
318.2
304.0
322.9
341.8
347.6
366.5
373.4
392.4
400.4
419.4
428.5
447.4
457.6
476.6
312.4
327.8
324 . 6
344.1
338.4
362.5
339.1
363.2
387.2
364.9
389.0
413.1
391.9
416.0
440.0
444.0
4fi8 1
312.1
327.4
336.8
352.2
362.7
378.0
405.0
313.3
3i4.6
337.2
352.6
349.4
368.9
338.1
:....
339.3
365 '.2
392.1
.'.'.'.'.
363 '.9
363.0
378.4
375.2
394.7
402.2
421.7
430.2
449 7
.....
.....
405.4
433 4
433.0
459.4473.2
478.9,497.2
462.6
462. 2j
Below and to right of zig-zag lines, reinforcement is more than 4 per cent.
103
COLUMNS
TABLE 32
ROUND CORED HOOPED COLUMNS
Column size
2000 -Ib.
1:6 mixti
nje
JOINT C01V
concrete Volume of
Max.
1MITTEE RECOMMENI
P = Af c (l + (n-l}p]
Hooping = 1% of Volume
/unsupported length\
)ATIONS
of Core
10
1
f 7nn
\ core diameter /
t^&r
Size
of
column
(inches)
Diameter
of
core
(inches)
Number
of
rods
Square rods
Round rods
H
H
14
1
1H 1>4
H
H
7 A
l
1H
1M
12
13
14
15
16
17
18
19
20
21 .
22
23
24
25
8
9
10
11
12
13
14
15
16
17
18
19
20
21
6
6
8
6
8
6
8
10
6
8
10
6
8
10
6
8
10
12
' 6
8
10
12
8
10
12
14
8
10
12
14
8
10
12
14
8
10
12
14
16
8
10
12
14
16
10
12
14
16
53.2
62.5
68.6
73.0
79.1
84.5
90.6
96.6
97.2
103.3
109.3
110.9
116.9
123.0
125.7
131.8
137.8
143.8
141.7
147.8
153.8
159 .8
164.9
170.9
176.9
182.9
183.0
189.0
195.0
201.0
208 '.3
214.3
220.3
81.0
92.5
101.1
105.2
113.8
122.5
118.9
127.5
136.2
133.7
142.3
151.0
159.7
149.7
158.3
167.0
175.7
175.4
184.1
192.8
201.4
193.5
202.2
210.9
219.5
212.8
221.5
230.2
238.8
233.1
241.8
250.5
259 . 1
267.8
254.5
263.2
271.9
280.5
289.2
285.8
294.5
303.1
311.8
101.9
114.6
128.3
140.0
143.1
154.8
166.6
159.1
170.8
182.6
187.9
199.7
211.5
206.0
217.8
229.6
241.4
225.3
237.1
248.9
260:7
245.6
257.4
269.2
281.0
292.8
267.0
278.8
290.6
302.4
314.2
301.4
313.2
325.0
336.8
139.1
153.9
169.9
185.3
202.4
217.8
220.5
235.9
239.8
255.2
270.6
260.1
275.5
290.9
306.3
281.5
296.9
312.3
327.7
343.1
319.5
334.9
350 . 3
365.7
166.1
182.1
218.7
236.8
256.1
275.6
276.4
295.9
297.8
317.3
336.8
339.9
359.4
.
274.4
294.7
316.1
340 . 1
362.7
67.5
78.0
85.6
89.5
97.1
102.2
109.8
117.5
115.9
123.5
131.2
130,7
138.3
146.0
153.6
146.7
154.3
162.0
169.6
171.4
179.1
186.7
19r?4
189.5
197.2
204.8
212.5
208.8
216.5
224.1
231.8
229.1
236.8
244.4
252 . 1
259.8
250.5
258.2
265.8
273.5
281.2
280.8
288.4
296.1
303.8
99.6
112.3
123.3
126.0
137.0
137.9
140.8
151.8
162.8
156.8
167,8
178.8
189.9
184.9
195.9
206.9
2ig":o
203.0
214.0
225.0
236 1
152.7
167.7
166.5
168.7
183.7
182.5
. . f>
:
200.8
215.8
219.2
218.9
2 3L- 9
237.3
222.3
233.3
244.4
255.4
-
242.6
253.6
264.7
275.7
286.7
264.0
275.0
286.1
297.1
308.1
297.6
308.7
319.7
330.7
238.2
253.2
268.2
256.6
276.2
277.4
258.5
273.5
288.5
303.5
m
309.9
32T.9
339.9
317.5
332.5
347.5
362.5
276.9
296.5
298.3
317.9
337.5
340.5
360 . 1
297 7
319.1 342.4
343.9 ...
366 . 5
j
228.6
234.6
240.6
246.6
256 '.6
262.0
268.0
278 '.6
284.6
290.6
104
TA^LE 32
Column Size ^
ROUND CORED HOOPED COLUMNS
SAFE LOAD IN THOUSANDS OF POUNDS
JOINT COMMITTEE RECOMMENDATIONS
Volume of Hooping = 1% of Volume of Core
,_ /unsupported length\
Max. I j-. I = 10
\ core diameter /
COLUMNS
2000- Ib. concrete
1:6 mixture
71=15
f c =700
Size I Diameter
of of
column i core
(inches) I (inches)
Number
of
rods
Square rods
Round rods
?s
L>7
28
29
SO
lio
27
20
10
12
14
16
18
10
12
14
16
18
10
12
14
16
18
10
12
14
16
18
20
12
14
16
18
20
12
14
16
18
20
22
12
14
16
18
20
22
12
14
16
18
20
22
12
14
16
18
20
22
24
304.4 .321.21341.1 364.1 390.1
312.0332 3!356 1 383.7414.9
319.7 343. 31 371.1 403?
327.4354.3
335.0365.3
346.0
357.1
368.1
379.1
390.1
365.9388.9414
380.91408.5439
395.9J428.1
410.9447.7
425.9
1309.4325.0343
J318.1 336.8
308.2 326.7 348.6
314.2335.4360.4
320.2 344.0 372.2
444.0
469.8
371.8391.7414.7440.7
382. 9 406. 7 434. 31465. 5
393.9 421.7 453.9:490.3
404. 91436.71473. 5;
315. 9!451. 7J493.1 ..
398.7:418.6441.6476.6496.7!
409.8 433.6 461 .2 ! 492.4 ! 527. 4
420.8 1 448.6480.8517.2
431.8463.6500.4
442.8478.6520.0
453.9493.7
437.8461.6489.2520.4
448.8 476.6508.81545.2
459.8491.6528.4 570.0
470.8 506.6548.0
481.9521.7:567.6
467.0490
478.01505.
489.0520
500.0 535
511.1 550
522 . 1 565
.6
615.2
8518.4549.6584
8538.0574.4
8557.6599.2
8]577.2 624.1
9596.8
9616.4
|
. 497.3521
. 508.3536
, 519.3551
. 530.3566
. 541.4581
. 552.4596.2646.7 ..
555.4
1548.7579.9614.9
1 568.3 604.7645.5
1 587.9:629.5 ......
1 607.5654.4
2627.1
, 528.6552.4580.0611.2646.2
.539.6567.4599.6636.0676.8
. 550.6582.4619.2660.8707.4
. 561 .6 597.4 638.8 685. 7J |,
572. 7 612.5|658. 4'710. 5i j,
583.7627.5678.0'..
... 584.8:612.4:643.6678.6
572.0 599.81632.0 668.4 709.2
583.0614.8651.6|693.2 739.8
594. 0629. 8^671. 2718.1 770 .4
605.1 644.9690.8742.9
616.1 659.9710.4 767.7
627.1 674.9730.0,...
349.8367.9388.3411.1
8435.2
334.2
342.9 361
351.5373.
360.2 385.2 414
368.8397.0429.4
375.6
.7387.4
393.7414
409.1
3399.2424.5
0439.9
.2
368
377.
386.0411
394.6422
402.5420.6
6414.3436.0
.11363.5386.3
358.5 383.01410.4
373.9402.5
389.3
404.6
383.3
398.7
407.
427.3
446.8
8455.
395.
404.2426.1
412.9 437.9466
421.5449
430.2461.5497
423.6442.3464
432.2454
440.9465.9494
449.5477
458.2489.5525
.0
479.4
.8
510.1
.5
471.5493.2517.754
483.3
495.1
461.4
470.1
478.7506.9539
487.4518
496.1
.7
530.4
508.6
524.0 556
.3
554.7595
570.1
501
491.7513
500.4 525
509.0537
517.7549
526.4560
544
531.7556
540.3568
549.0580
557.7592
'564.1
.8523,
.6538,
.4'554
.2569
.0585
.7600
.1;554,
.9570.
.7585.
.5J600,
.3'616.
.0631.
433.
453.1
472.6
492.0
436.9
6461.0
485.0
441.0463
460 . 5 487
451.4 480.0
499.5 536
518.9
488.
508.0539
527.5
546.9
566.4
537.2
.7
576.1
.6
615.1
5548.
9|567.
3587.
6606.
0625.
4645.
8579.
2,598.
61618.
9,637.
3 657.
7676.
.s
.9
511.9
.0
5 51;
.9
564.0
5.1
569.1
593.2
617.2
0575.4
5599.4
623 . 5
4647.5
9671.6
4 1
3 606.7
8 630'. 7
3 654.8
7678.8
2 702.9
7
565.51587.2 611.7 639.1
577.3602.6631.2663.1
589.1 618.0650.7687.2
1572.7600.9633.3670.1 711.2
581 .4 612.7 648.7 689.6 735.3
590.1 624.4 664.1 709.1 759.3
598.7636.2 ! 679.5;728.6
105
COLUMNS
TABLE 32
ROUND CORED HOOPED COLUMNS
SAFE LOAD IN THOUSANDS OF POUNDS
JOINT COMMITTEE RECOMMENDATIONS
Column size ._.>
2000 -lb. concrete
1:6 mixture
n = 15
f c =700
l}p]
Volume of Hooping =1% of Volume of Core
Max
unsu PP rted
core diameter /
Size
of
column
(inches)
3f>
36
37
38
Diameter
of
core
(inches)
10
31
32
33
34
35
3(1
37
38
Number
of
rods
Hi
18
20
22
24
26
28
Hi
18
20
22
21
26
28
Hi
18
20
22
21
26
28
30
Square rods
1605.6 633. 4,665. 6i702.0 742.8
616.6 648.4)685.2 726.8 773.4
.627.6663.4
704. 8 751. 71804.0
638 7678.5 724.4 776.5
.649.7693.5744.0801.3
.660.7708.5763.6'
667.9700,
682.9719,
697.9 739,
713.0758
728.01778,
743.01798,
703.7i735.
718.7755.
733.7 775.
748.8794.
763.8 ! 814.
778.8 : 833.
>793.8'853.
740.5772.
i 755.5| 792.
770.5811.
1785.61831.
'800.6:851.
815.6870.
830.6890.
778.5810.
793.5J830.
808.5849.
823.6 ; 869.
. '838.6'889.
853.6908.
. I868.6J928.
,832.5869,
'847. 5(888,
862.6;908
i877.6i928
I892.6J947
;907. 61967
922.61986
1 736
7 761
3786
9811
5835
1 860
9772
5,797
11822
7!846
3 871
9 896
5 921
5777.3
3807.9
2838.5
0869.2
3813.1
1 843 . 7
0874.3
8905.0
7 809.11849.9
3833.9880.5
9i858. 8)911.1
51883.6)941.8
1:908.4)972.4
71933.2 .....
3 958.0).
7847.1887.9
3 871.9918.5
9 896.8,949.1
5 921.6979.8
1 946.4
7971.2
3 996.0
3 910.91957.5
,9 935.8)988.1
1010
1041
5 960.6
1 985.4
71 1010
3) 1035
9 1060
872.6909.4 951.0997.6
887.6929.0975.9
902.7 948.6
'917.7'968.2
^932.7987.8
1947.7 1007
! 962.7 1027
1001
1025
1050
1075
1100
1019
1049
1080
1111
913.9950.7992.3
928. 9970. 3' 10171
1944.0 989.9) 1042)
959.0) 1009 1067
974.0 1029 1092
989.0
1004
1019
1049 1116
1068
1088
1141
1166
1028
1059
1089
1120
1151
1039
1069
1100
1131
1161
1192
1223
Round rods
606.
615.
623.
632.
610.9636.2 664.8696.7
622.7651.6684.3 720.8
3 634.5 666.9 703.7|744.8
0646.3682.3723.21768.9
7658.0697.7742.7792.9
3669.8713.1 762.2 817.0
645.
657.2 686
680.8
692.
704
4670.7699.3 731.2
718.8755.3
0701.4 738.2 779.3
716.8757.7J803.4
5732.2 777.2827.4
.3747.6796.7851.5
753.4
765.1
693.0
704.8737.2
716.6752
728.3
740.1
751.9
706.5735.1 767.0
721.9 754.6791.1
774.0815.1
.6 793.5)839.2
768.0:813.0863.2
783.4 832.5:887.3
798.8,852.0911.3
743.3j771.9803.8
729.8758.7 791. 4 ; 827. 9
741.6774.0)810.8:851.9
789.4l830.3 1 876.0
804.81849.8)900.0
776. 9 820. 2'869. 31924.1
788.7835.6 ! 888.8948.1
781.3 809.9 841.8
767.8)796.7i829.4865.9
779.6812.0848.8i889.9
791.4)827.4,868.3 914.0
803.1 842.8:887.8938.0
814.9)858.2 907.3 962.1
826.7873.6926.8,986.1
835.7868.4 ; 904.9
818.6851.0.887.8928.9
830.4866.4 907.3953.0
842.1(881.8926.8977.0
853.9 897.2 946.3
865.7912.6965.8
877.51928.0985.3
1001
1025
1049
875.8908.5945.0
858.71891.1 927.9969.0
870.5906.5947.4993.1
882.2921.9966.9 "
894.0937.3986.4
905.8952.2
917.6968.1
1006
1025
1017
1041
1065
1089
...1917.1949.8986.3
...1932.4969.2 1010
911.8 I 947.8988.7
923.5963.2
935.3978.6
947.11994.0
958.9 1009
970.7 1025
1008
1028
1047
1067
1086
1034
1058
1083
1107
1131
1155
100
TABLE 32
COLUMNS
ROUND CORED HOOPED COLUMNS
SAFE LOAD IN THOUSANDS OF POUNDS
JOINT COMMITTEE RECOMMENDATIONS
Volume of Hooping
Max.
1% of Volume of Core
**ngth\ ==w
\ core diameter I
2000 -Ib. concrete
1:6 mixture
n=15
f c =700
Size
of
column
(inches)
Diameter
of
core
(inches)
Number
of
rods
Square rods
Round rods
H
H
T4 : l
i
IX
U4
X
H
H
1
IX
IK
43
44
45
46
47
48
49
50
39
40
41
42
43
44
45
46
16
18
20
22
24
26
28
30
16
18
20
22
24
26
28
30
18
20
22
24
26
28
30
18
20
22
24
26
28
30
18
20
22
24
26
28
30
18
20
22
24
26
28
30
18
20
22
24
26
28
30
20
22
24
26
28
30
956.2
971.2
986.3
1001
1016
1031
1046
1061
993.0
1012
1032
1052
1071
1091
1111
1130
1036
1056
1076
1095
1115
1134
1154
1174
1101
1120
1140
1159
1179
1199
1218
1146
1166
1186
1205
1225
1244
1264
1193
1213
1232
1252
1271
1291
1311
1241
1260
1280
1300
1319
1339
1358
1290
1309
1329
1349
1368
1388
1407
1359
1379
1399
1418
1438
1457
1035
, 1060
1084
1109
1134
1159
1184
1208
1078
1103
1128
1153
1178
1202
1227
1252
1148
1172
1197
1222
1247
1272
1296
1193
1218
1243
1268
1292
1317
1342
1240
1265
1289
1314
1339
1364
1389
1288
1313
1337
1362
1387
1412
1437
1337
1361
1386
1411
1436
1461
1485
1411
1436
1461
1486
1511
1535
1081
1112
1143
1173
1204
1234
1265
1296
1125
1155
1186
1217
1247
1278
1308
1339
1200
1231
1261
1292
1322
1353
1384
1245
1276
1307
1337
1368
1399
1429
1292
1323
1353
1384
1415
ii
1340
1371
1401
1432
1463
1493
1524
1389
1420
1450
1481
1511
1542
1573
1470
1500
1531
1561
1592
1623
959.4
974.7
990.1
1005
1021
1036
1052
1067
1003
1018
1034
1049
1064
1080
1095
1110
1063
1078
1094
1109
1124
1140
1155
1108
1124
1139
1155
1170
1185
1200
992.1
1012
1031
1051
i 1070
1090
1109
; 1128
1036
1055
1074
1094
1 1113
1133
1152
1172
1100
1119
1139
1158
1178
1197
1216
1145
1165
1184
1204
1223
1243
1262
1192
1211
1231
1250
1270
1289
1309
1240
1259
1279
1298
1318
1337
1357
1289
1308
1328
1347
1367
1386
1406
1358
1378
1397
1417
1436
1456
1029
1053
1077
1101
i 1125
1149
1173
1197
1072
1096
1120
1144
1168
1192
1216
1240
1141
1165
1189
1213
1237
1261
1285
1186
1210
1234
1258
1282
1307
1331
1233
1257
1281
1305
1329
1353
1377
1281
1305
1329
1353
1377
1401
1425
1330
1354
1378
1402
1426
1450
1474
1404
1428
1452
1476
1500
1524
i
954.1
965.8
977.6
989.4
1001
1013
ioog
1021
1033
1045
1056
1654
1066
1077
1089
1101
iiii
1123
1135
1147
1
P
1015
1030
1045
1060
1075
1090
1105
1059
1074
1089
1104
1119
1134
1149
1
1
: : : : .
- -
1120
1135
1150
1165
1180
1195
iiee
1181
1196
1211
1226
1441
i2i4
1229
1244
1259
1274
1289
i
1170
1186
1201
1217
1232
1247
1170
1182
1193
:::::
'1218
1229
1241
1218
1234
1249
1265
1280
1295
1278
1293
1308
1323
1338
i328
1343
1358
1373
1388
1283
1298
1313
1329
1344
'1278
1290
1333
1348
1363
1379
1394
1328
1340
107
COLUMNS
TABLE 33
2500 -Ib. concrete
1:4% mixture
n=12
f c =870
ROUND CORED HOOPED COLUMNS
SAFE LOAD IN THOUSANDS OF POUNDS
JOINT COMMITTEE RECOMMENDATIONS
P=Af e [l+(n-l)p]
Volume of Hooping 1% of Volume of Core
Max ( unsu PP rted length\ = w
' \ core diameter I
fc Column size >i
Size
of
column
(inches)
Diameter
of
core
(inches)
Number
of
rods
Square rods
Round rods
H
K
1
1H
IK
1
%
K
K
1
IK
l l A
12
13
14
15
16
17
18
19
20
21
22
23
24
^
25
8
9
10
11
12
13
14
15
16
17
18
19
20
21
6
6
8
6
8
6
8
10
6
8
10
6
8
10
6
8
10
12
6
8
10
12
8
10
12
14
iS
12
14
X 8
10
12
14
ii
12
14
16
8
10
12
14
16
10
12
14
16
1
61
73
79
86
92
100
106
112
116
122
128
133
139
145
152
157
163
169
171
177
183
189
198
204
210
216
221
227
233
239
; - 2&i
257
263
"276
282
288
294
"309
314
320
337
342
348
94
108
116
124
132
141
141
149
158
159
168
176
185
179
188
196
204
209
217
226
234
231
240
248
257
255
264
272
281
280
289
297
306
314
307
316
324
333
341
344
352
361
369
117
133
150
161
168
180
191
188
200
211
221
233
244
244
255
267
278
267
279
290
302
293
304
316
327
339
319
331
342
354
365
359
370
382
393
161
179
199
214
235
250
258
273
282
297
312
307
322
337
352
333
349
364
379
394
377
392
407
422
191
211
251
274
298
317
323
342
349
368
388
396
416
3ir,
341
367
391
419
78
91
98
105
113
115
121
128
136
138
145
153
156
164
171
179
176
184
191
199
205
212
220
227
! 227
1 235
1 242
i 250
251
259
266
274
; 277
i 284
292
299
306
303
311
318
326
333
339
346
354
361
131
141
148
158
166
177
189
186
197
208
218
218
229
240
250
241
251
262
273
264
275
286
297
290
300
311
322
333
316
327
238
349
359
355
366
377
388
:::: ....
159
178
193
198
212
234
248
191
211
252
256
271
280
295
309
305
320
335
349
332
347
361
376
391
375
389
404
419
274
298
317
323
342
350
369
388
;:::
397
416
318
344
....
370
394
422
108
TABLE 33
^ Columr> sift? tt
ROUND
SAFE LOAI
JOINT CO1V
Volume of
Max.
CORED HOOPED COLl
) IN THOUSANDS OF ]
IMITTEE RECOMMENI
P=Af e (l + (n-l)p]
Hooping =1% of Volume
/unsupported length\
IMNS
>OUN
)ATIC
of a
10
COLUMNS
DS
)NS
9re
2500 -lb. concrete
1:4]^ mixture
n = 12
f c =870
H
\ core diameter /
Tt*J&r
Size
of
column
(inches)
Diameter
of
core
(inches)
Number
of
rods
Square rods
Round rods
H
%
H
1
IK \Vi
H
H
7 A
1
IH
IH
26
27
28
29
30
31
32
33
34
22
23^
24
25
26
27
28
29
30
10
12
14
16
18
10
12
14
16
18
10
12
14
16
18
10
12
14
16
18
20
12
14
16
18
20
12
14
16
18
20
22
12
14
16
18
20
22
12
14
16
18
20
22
12
14
16
18
20
22
24
368
376
383
391
398
385
395
406
417
428
415
426
437
448
458
447
458
469
480
490
481
492
502
513
524
535
526
537
548
559
570
563
574
584
595
606
617
600
611
622
633
643
654
639
650
661
672
682
693
404
419
433
448
463
435
449
464
479
493
467
482
496
511
525
500
515
530
544
559
574
550
564
579
594
608
586
601
615
630
645
659
624
638
653
668
682
697
663
677
692
707
721
736
703
718
732
747
762
776
791
426
452
373
381
390
398
407
404
412
421
429
438
'444
453
461
470
'478
486
495
503
512
513
521
530
538
546
'557
566
574
583
594
'595
603
612
620
629
'e>4i
651
659
668
683
691
700
708
716
388
400
411
423
434
419
431
442
454
465
451
463
474
486
497
485
496
508
519
531
542
531
542
554
565
577
567
579
590
602
613
625
605
616
628
639
651
662
644
655
667
678
690
701
684
696
707
719
730
743
753
406
421
436
451
466
437
452
467
482
497
469
484
499
514
529
502
517
532
547
562
577
552
567
582
597
612
588
603
618
633
648
664
626
641
656
671
686
701
665
680
695
710
725
740
705
720
735
750
765
780
795
426
445
464
457
476
495
514
489
508
527
546
565
522
541
560
579
598
517
576
595
614
633
650
612
631
650
669
688
707
650
669
688
707
726
745
689
708
727
746
765
784
729
748
767
786
805
824
843
448
472
479
502
511
535
558
545
568
592
615
603
626
647
639
663
686
710
677
700
724
747
771
716
739
763
786
810
756
779
803
826
850
873
446
476
372
378
384
457
476
495
515
483
507
511
489
508
528
547
566
523
542
561
580
599
515
539
563
543
....
548
572
597
577
607
577
596
615
634
653
613
632
651
670
689
709
651
670
689
708
727
746
689
709
728
748
766
785
730
749
768
787
806
826
845
607
631
656
641
644
668
692
716
678
708
681
705
730
754
715
745
....
720
744
768
793
817
760
785
809
833
857
881
754
784
814
794
824
854
884
.''
690
701
712
723
733
744
109
COLUMNS
TABLE 33
2500- Ib. concrete
I'AV^ mixture
n = 12
f c =870
ROUND CORED HOOPED COLUMNS
SAFE LOAD IN THOUSANDS OF POUNDS
JOINT COMMITTEE RECOMMENDATIONS
P=Af e [l+(n-iyp]
Volume of Hooping =1% of Volume of Core
(unsupported length\ _
Max. [ j-. ] =10
\ core diameter I
Column sire ,
Size
of
column
(inches)
Diameter
of
core
(inches)
Number
of
rods
Square rods
Round rods
H
H
H
1
IX
1H
H
H
H
1
IH
IK
" 35
36
37
38
39
40
41
42
31
32
33
34
35
36
37
38
14
16
18
20
22
24
14
16
18
20
22
24
14
16
18
20
22
24
26
14
16
18
20
22
24
26
14
16
18
20
22
24
26
16
18
20
22
24
26
28
16
18
20
22
24
26
28
16
18
20
22
24
26
28
30
732
743
754
765
775
786
760
774
789
804
819
833
802
817
832
846
861
876
847
861
876
891
905
920
935
892
907
922
936
951
966
980
940
954
969
984
998
1013
1028
1003
1017
1032
1047
1061
1076
1091
1053
1067
1082
1097
1111
1126
1141
1104
1119
1133
1148
1163
1177
1192
1206
791
810
829
848
868
887
834
853
872
891
910
929
878
897
916
936
955
974
993
924
943
962
981
1000
1020
1039
971
990
1009
1028
1048
1067
1086
1039
1058
1077
1096
1115
1134
1154
1089
1108
1127
1146
1165
1184
1203
1140
1159
1178
1197
1216
1235
1255
1274
827
851
875
899
924
866
896
926
'733
742
750
759
738
749
761
772
784
795
780
792
803
815
826
838
'836
848
860
871
882
894
'881
893
905
916
928
939
'929
941
952
964
975
987
'989
1001
1012
1024
1035
1047
i039
1051
1062
1074
1085
1097
iio2
1113
1125
1136
1148
1159
762
777
792*
807
822
837
805
820
835
850
865
880
849
864
879
894
909
925
940
895
910
925
940
955
970
985
942
957
972
987
1002
1017
1032
1006
1021
1036
1051
1066
1081
1096
1056
1071
1086
1101
1116
1131
1146
1107
1122
1137
1152
1167
1182
1197
1212
790
809
828
847
866
885
833
852
871
890
909
928
877
896
915
934
953
972
991
923
942
961
980
999
1018
1037
970
989
1008
1027
1046
1065
1084
1038
1057
1076
1095
1114
1133
1152
1088
1107
1126
1145
1164
1183
1202
1139
1158
1177
1196
1215
1234
1253
1272
821
845
868
892
915
939
864
888
911
935
958
982
909
932
956
979
1002
1026
1049
954
978
1001
1025
1048
1072
1095
1001
1025
1048
1072
1095
1119
1142
1073
1097
1120
1144
1167
1191
1214
1123
1147
1170
1194
1217
1241
1264
1175
1198
1222
1245
1269
1292
1316
1339
869
893
918
942
966
990
914
938
962
986
1011
1035
1060
959
984
1008
1032
1056
1081
1105
1007
1031
1055
1079
1103
1128
1152
1079
1104
1128
1152
1176
1200
1225
1129
1154
1178
1202
1226
1250
1275
1180
1205
1229
1253
1277
1302
1326
1350
909
939
969
999
953
983
1013
1043
999
1029
1059
1089
1119
1046
1076
1106
1136
1166
1196
1125
1155
1185
1215
1244
1274
'
....
1175
1205
1234
1264
1294
1324
1226
1256
1286
1316
1346
1375
1405
110
TABLE 33
Column size
COLUMNS
ROUND CORED HOOPED COLUMNS
SAFE LOAD IN THOUSANDS OF POUNDS
JOINT COMMITTEE RECOMMENDATIONS
Volume of Hooping
/unsupported length\
Max. [
\
1% of Volume of Core
10
j-.
core diameter I
2500 -Ib. concrete
1:4% mixture
n=12
f c =870
Size
of
column
(inches)
Diameter
of
core
(inches)
Number
of
rods
Square rods
Round rods
H
H
y*
1
1H
IK
H
H
y*
1
1H
IK
43
44
45
46
47
48
49
50
39
40
41
42
43
44
45
46
16
18
20
22
24
26
28
30
16
18
20
22
24
26
28
30
18
20
22
24
26
28
30
18
20
22
24
26
28
30
18
20
22
24
26
28
30
18
20
22
24
26
28
30
18
20
22
24
26
28
30
20
22
24
26
28
30
1157
1171
1186
1200
1215
1230
1244
1259
1192
1212
1231
1250
1269
1288
1307
1326
1246
1266
1285
1304
1323
1342
1361
1380
1321
1340
1359
1378
1397
1417
1436
1378
1397
1416
1435
1454
1473
1492
1436
1455
1474
1493
1512
1531
1551
1495
1514
1533
1553
1572
1591
1610
1556
1575
1594
1613
1632
1652
1671
1637
1656
1676
1695
1714
1733
1233
1257
1282
1306
1330
1354
1378
1403
1287
1311
1335
1360
1384
1408
1432
1457
1367
1391
1415
1439
1464
1488
1512
1423
1448
1472
1496
1520
1544
1569
1481
1506
1530
1554
1578
1603
1627
1541
1565
1589
1614
1638
1662
1686
1602
1626
1650
1674
1699
1723
1747
1688
1712
1736
1761
1785
1809
1279
1308
1338
1368
1398
1428
1458
1488
1332
1362
1392
1422
1452
1482
1512
1542
1418
1448
1478
1508
1537
1567
1597
1474
1504
1534
1564
1594
1624
1654
1533
1562
1592
1622
1652
1682
1712
1592
1622
1652
1682
1712
1742
1771
1653
1683
1713
1743
1772
1802
1832
1745
1775
1805
1835
1865
1894
1160
1175
1190
1205
1220
1235
1250
1265
1214
1229
1244
1259
1274
1289
1304
1319
1284
1299
1314
1329
1344
1359
1374
1341
1356
1371
1386
1401
1416
1431
1192
1211
1230
1249
1268
1287
1306
1325
1245
1264
1283
1303
1322
1341
1360
1379
1320
1339
1358
1377
1396
1415
1434
1377
1396
1415
1434
1453
1472
1491
1435
1454
1473
1492
1511
1530
1549
1494
1513
1532
1551
1570
1589
1608
1555
1574
1593
1612
1631
1650
1669
1636
1655
1674
1693
1712
1731
1227
1251
1274
1298
1321
1345
1368
1392
1281
1305
1328
1352
1375
1399
1422
1446
1360
1384
1407
1431
1454
1478
1501
1417
1440
1464
1487
1511
1534
1558
1475
1498
1522
1545
1569
1592
1616
1534
1558
1581
1605
1628
1652
1675
1595
1619
1642
1666
1689
1712
1736
1681
1704
1728
1751
1775
1798
1154
1166
1177
1189
1200
1212
::::
1225
1240
1254
1269
1284
1298
1313
1281
1295
1310
1325
1339
1354
1368
i352
1366
1381
1396
1410
1425
iiio
1425
1438
1454
1469
1483
1469
1484
1499
1513
1528
1543
i220
1231
1243
1254
1266
1275
1287
1298
1310
1321
....
'.'.::
1343
1355
1366
1378
....
1413
1425
1436
1414
1429
1444
1459
1474
1489
'.'.'.'.
i472
1484
1495
1473
1488
1503
1518
1533
1548
1545
1560
1574
1589
1603
1549
1564
1579
1594
1609
1545
1556
....
1607
1622
1636
1651
1666
....
1611
1626
1641
1656
1671
ieo7
1618
111
COLUMNS
TABLE 34
ROUND CORED HOOPED COLUMNS
SAFE LOAD IN THOUSANDS OF POUNDS
JOINT COMMITTEE RECOMMENDATIONS
3000- Ib. concrete
1:3 mixture
n = 10
-p
Volume of Hooping =1% of Volume of Core
Max /unsupported length\
\ core diameter )
Size
of
column
(inches)
Diameter
of
core
(inches)
Number
of
rods
Square rods
Round rods
H
H
%
1
IK
U4
H
H
H
1
1H 1>4
12
13
14
15
16
17
18
19
20
21
22
23
24
25
8
9
10
11
12
13
14
15
16
17
18
19
20
21
6
6
8
6
8
6
8
10
6
8
10
6
8
10
6
8
10
12
6
8
10
12
8
10
12
14
8
10
12 -
14
8
10
12
14
8
10
12
14
16
8
10
12
14
16
10
12
14
16
70
84
90
100
105
117
123
129
136
142
148
157
163
168
179
185
191
196
203
209
215
220
234
240
246
252
262
267
273
279
107
125
133
144
152
161
164
173
181
187
195
203
212
211
219
227
236
245
253
. 261
271
272
280
289
298
301
309
317
327
331
339
348
357
364
363
372
380
389
397
405
414
423
431
134
153
173
185
196
207
218
219
231
242
257
268
279
284
295
307
318
313
324
335
347
343
355
366
377
389
375
387
398
409
421
421
432
443
455
184
206
230
245
271
285
298
313
327
341
356
357
372
387
402
389
404
419
434
449
438
453'
468
482
218
242
286
314
342
361
373
392
405
424
443
458
476
360
390
423
446
480
89
105
112
122
129
132
141
148
156
161
169
176
184
191
199
206
208
215
222
230
241
248
255
263
268
275
283
290
297
304
312
319
327
335
342
349
357
359
367
374
382
389
401
408
415
423
151
161
171
182
193
204
215
217
228
239
249
243
254
264
275
281
292
302
313
310
320
331
342
340
351
361
372
383
372
383
394
404
415
417
428
438
449
183
205
219
218
229
243
242
269
284
287
296
311
314
....
325
340
354
356
370
384
399
343
362
373
392
363
393
296
302
308
'327
332
338
344
'365
371
376
'399
404
410
388
402
417
431
446
436
451
465
479
406
424
443
426
450
448
458
477
483
112
TABLE 34
COLUMNS
ROUND CORED HOOPED COLUMNS
SAFE LOAD IN THOUSANDS OF POUNDS
JOINT COMMITTEE RECOMMENDATIONS
Volume of Hooping =1% of Volume of Core
)p]
Vol
Max.
/unsupported length\
\ core diameter )
10
3000 -Ib. concrete
1:3 mixture
n = 10
f c =1050
Size
of
column
(inches)
Diameter
of
core
(inches)
Number
of
rods
Square rods
Round rods
K
H
1
IK
IK
H
H
H
1
1H
IK
2(3
27
28
29
30
31
32
3.3
34
22
23
24
25
26
27
28
29
30
10
12
14
16
18
10
12
14
16
18
10
12
14
16
18
10
12
14
16
18
20
12
14
16
18
20
12
14
16
18
20
22
12
14
16
18
20
22
12
14
16
18
20
22
12
14
16
18
20
22
24
436
443
451
458
466
452
463
474
484
495
489
500
511
521
532
528
539
549
560
571
569
579
590
601
611
622
621
632
643
653
664
665
676
686
697
708
718
710
721
732
742
753
764
757
768
779
789
800
810
'817
827
838
849
859
870
471
486
500
515
529
509
523
538
552
567
547
562
576
591
605
588
602
617
631
646
660
644
659
673
688
702
688
703
717
731
746
760
733
748
762
777
791
806
780
795
809
824
838
853
829
844
858
872
887
901
916
494
513
531
519
543
441
449
458
466
474
478
487
496
503
511
"525
534
542
550
456
467
479
490
501
493
504
516
527
539
532
543
555
566
577
572
584
595
606
618
629
626
637
648
660
671
669
681
692
704
715
726
715
726
738
749
760
772
762
773
784
796
807
819
810
822
833
845
856
867
879
473
488
503
518
533
511
525
540
555
570
549
564
579
594
609
590
605
619
634
649
664
647
661
67Q
691
706
690
705
720
735
750
765
736
751
765
780
795
810
783
797
812
827
842
857
831
846
861
876
891
906
920
493
512
531
530
549
568
587
569
588
607
625
644
609
628
647
666
685
670
689
708
727
745
714
733
752
770
789
808
759
778
797
816
834
853
806
825
844
863
881
900
855
874
893
911
930
949
968
515
538
552
575
591
614
637
631
655
678
701
697
720
743
740
764
787
810
786
809
832
855
879
833
856
879
902
925
881
905
928
951
974
997
440
445
451
531
550
569
587
556
580
584
570
588
607
626
645
610
629
648
667
686
595
619
642
635
659
683
623
663
693
!
566
575
582
591
599
608
617
624
633
641
671
690
709
728
746
715
734
752
771
790
809
760
779
798
817
836
854
807
826
845
864
883
901
856
875
893
912
931
950
969
701
725
749
745
769
793
817
790
814
838
862
837
861
885
909
933
886
910
934
958
981
1005
735
....
778
808
....
661
668
676
685
693
'706
713
722
730
738
760
769
777
785
824
853
871
900
930
919
949
979
1008
'.'.'.'.
809
817
826
834
842
....
113
COLUMNS
TABLE 34
ROUND CORED HOOPED COLUMNS
SAFE LOAD IN THOUSANDS OF POUNDS
JOINT COMMITTEE RECOMMENDATIONS
.^Column sire ^
3000 -lb. concrete
1:3 mixture
n = 10
f c =1050
Volume of Hooping =1% of Volume of Core
M I unsupported length\ =lg
\ core diameter I
Size
of
Diameter
of
Number
Squar
e rods
Roun<
irods
column
(.inches)
core
(inches)
of
rods
H
H
K
1
IK
IK
^
H
K
1
1H
IK
35
31
14
867
894
925
960
999
872
896
924
955
16
878
908
944
984
1029
883
911
943
978
18
888
923
963
1008
1058
'868
895
926
962
1001
20
899
937
982
1032
877
906
941
980
1024
22
909
952
1000
1056
884
918
956
999
1048
24
920
966
1019
893
929
971
1018
1071
36
32
14
946
977
1012
1051
924
948
976
1007
16
960
996
1036
1081
935
963
995
1030
18
975
1015
1060
1110
947
978
1014
1053
20
989
1033
1084
1140
958
993
1032
1076
22
1004
1052
1108
969
1008
1051
1100
24
1018
1071
1131
981
1023
1070
1123
37
33
14
999
1030
1066
1105
1002
1030
1060
16
1014
1049
1089
1135
'989
1017
1048
1084
18
1028
1068
1113
1164
1000
1032
1067
1107
20
1043
1087
1137
1193
1012
1047
1086
1130
22
1057
1106
1161
1023
1061
1105
1153
24
1072
1125
1185
1034
1076
1124
1176
26
1086
1144
1209
1046
1091
1142
1200
38
34
14
1055
1086
1121
1160
1057
1085
1116
16
1069
1105
1145
1190
1044
1072
1104
1139
18
1084
1123
1169
1219
1056
1087
1122
1162
20
1098
1142
1192
1249
1067
1102
1141
1185
22
1112
1161
1216
1278
1078
1117
1160
1208
24
1127
1180
1240
1090
1131
1179
1232
26
1141
1199
1264
1101
1146
1198
1255
39
35
14
1111
1143
1178
1217
1114
1142
1173
16
1126
1161
1202
1246
iioi
1129
1161
1196
18
1140
1180
1225
1276
1112
1144
1179
1219
20
1155
1199
1249
1306
1124
1159
1198
1242
22
1169
1218
1273
1335
1135
1173
1217
1265
24
1184
1237
1297
1365
1147
1188
1236
1289
26
1198
1256
1321
1158
1203
1254
1312
40
36
16
1185
1220
1260
1305
1188
1219
1254
18
1199
1239
1284
1335
ii7i
1202
1238
1278
20
1213
1258
1308
1364
1182
1217
1257
1301
22
1228
1277
1332
1394
1194
1232
1275
1324
24
1242
1296
1356
1423
1205
1247
1294
1347
26
1257
1315
1380
1453
1217
1262
1313
1370
28
1271
1333
1404
1228
1277
1332
1394
41
37
16
1245
1280
1320
1365
1248
1279
1315
18
1259
1299
1344
1395
i23i
1263
1298
1338
20
1274
1318
1368
1424
1243
1277
1317
1361
22
1288
1337
1392
1454
1254
1292
1336
1384
24
1303
1356
1416
1483
1265
1307
1354
1407
26
1317
1375
1464
1513
1277
1322
1373
1430
28
1332
1394
1488
1288
1337
1392
1454
42
38
16
1307
1342
1382
1427
1310
1341
1376
18
1321
1361
1406
1457
1324
1360
1400
20
1336
1380
1430
1486
1304
1339
1379
1423
22
1350
1399
1454
1516
1316
1354
1397
1446
24
1364
1418
1478
1545
1327
1369
1416
1469
26
1379
1437
1502
1575
1339
1 384
1435
1492
28
1393
1455
1526
1605
1350
1398
1454
1516
30
1408
1474
1550
1361
1413
1473
1539
114
TABLE 34
^Column si
COLUMNS
ROUND CORED HOOPED COLUMNS
SAFE LOAD IN THOUSANDS OF POUNDS
JOINT COMMITTEE RECOMMENDATIONS
p
Volume of Hooping =1% of Volume of Core
._ /
' \
unsupported length\ _
core diameter )
3000-lb. concrete
1:3 mixture
/i = 10
f c =1050
Size
of
column
(inches)
Diameter
of
core
(inches)
Number
of
rods
Square rods-
Round rods
*A
H
H
1 i 1W
IK
M
H
H
1
IK i IK
43
44
45
46
47
48
49
50
39
40
41
42
43
44
45
46
16
18
20
22
24
26
28
30
16
18
20
22
24
26
28
30
18
20
22
24
26
28
30
18
20
22
24
26
28
30
18
20
22
24
26
28
30
18
20
22
24
26
28
30
18
20
22
24
26
28
30
20
22
24
26
28
30
1370
1385
1399
1414
1428
1442
1457
1471
1450
1464
1479
1493
1508
1522
1536
1517
1531
1545
1560
1574
1589
1603
1599
1614
1628
1643
1657
1672
ie7o
1684
1698
1713
1727
1742
l74i
1756
1770
1785
1799
1814
i829
1844
1858
1873
1887
1904
1919
1933
1948
1962
1406
1424
1443
1462
1481
1500
1519
1538
1471
1490
1508
1527
1546
1565
1584
1603
1556
1575
1594
1613
1632
1651
1670
1625
1644
1663
1681
1700
1719
1738
1695
1714
1733
1752
1771
1789
1808
1767
1786
1804
1823
1842
1861
1880
1840
1859
1878
1897
1916
1935
1953
1934
1953
1972
1991
2010
2029
1446
1470
1494
1517
1541
1565
1589
1613
1511
1535
1559
1583
1606
1630
16.54
1678
1602
1626
1649
1673
1697
1721
1745
1670
1694
1718
1742
1766
1790
1813
1740
1764
1788
1812
1836
1860
1884
1812
1836
1860
1884
1907
1931
1955
1885
1909
1933
1957
1981
2005
2029
1984
2008
2032
2056
2080
2104
1491
1520i
1550
1579
1609
1638
1668
1697
1556
1585
1615
1644
1674
1703
1733
1762
1652
1682
1711
1741
1770
1800
1829
1720
1750
1780
1809
1839
1868
1898
1791
1820
1850
1879
1909
1938
1968
1862
1892
1921
1951
1980
2010
2039
1936
1965
1995
2024
2054
2083
2113
2040
2070
2099
2129
2159
2188
i368
1379
1391
1402
1413
1425
1373
1388
1403
1418
1432
1447
1462
1477
1438
1453
1468
1483
1498
1512
1527
1542
1520
1535
1550
1564
1579
1594
1609
1588
1603
1618
1633
1648
1662
1677
1(373
1688
1703
1718
1733
1747
i745
1760
1775
1790
1804
1819
1405
1423
1442
1461
1480
1499
1517
1536
1470
1489
1507
1526
1545
1564
1582
1601
1555
1574
1593
1612
1631
1649
1668
1624
1643
1661
1680
1699
1718
1736
1694
1713
1731
1750
1769
1788
1807
1766
1784
1803
1822
1841
1860
1879
1839
1858
1877
1895
1914
1933
1952
1933
1952
1970
1989
2008
2027
1440
1463
1486
1509
1533
1556
1579
1602
1505
1528
1551
1575
1598
1621
1644
1667
1595
1618
1641
1665
1688
1711
1734
1663
1687
1710
1733
1756
1779
1803
1734
1757
1780
1803
1826
1850
1873
1805
1828
1852
1875
1898
1921
1944
1879
1902
1925
1948
1971
1995
2118
1977
2000
2023
2047
2070
2093
'.'.'.'.
-
i444
1456
1467
1479
1490
. .*. .
isii
1523
1534
1545
1557
:::
is9i
1602
1614
1625
....
1673
1684
1695
i744
1756
1767
'.'.'.'.
::::
1833
1848
1863
1878
1893
i908
1923
1938
1953
1968
1829
1840
|
::::
i904
1915
115
COLUMNS
TABLE 35
2000- Ib. concrete
1:6 mixture
n = 15
f c =500
ROUND CORED HOOPED COLUMNS
SAFE LOAD IN THOUSANDS OF POUNDS
AMERICAN CONCRETE INSTITUTE
RECOMMENDATIONS
= Af c [(l+4np'}+(n-l}p]
/unsupported length\
\ diameter /
. Column Size
Size
of
column
inches)
Diam-
eter
of core
(inches)
Spirals
Number
of
rods
Size of vertical round rods
Size No.
(A. S. &
W. Co.)
Pitch
(inches)
Per cent
of core
H
K
M
1
1H
IK
12
8
6
1M
1
6
53
13
9
5
1M
1
6
8
64
68
14
10
4
IH
1
6 76
8 80
81
15
11
3
1*8
1
6
8 -
10
89
93
97
95
101
101
16
12
2
3/0
^K
l$i
1
2
6
8
10
6
8
10
103
108
112
'i42
146
109
115
121
143
149
155
116
150
17
13
1
4/0
IK
1%
1
2
6
8
10
6
8
10
119
123
128
'l67
125
131
137
165
171
177
131
140
171
180
139
179
18
14
1
4/0
IK
IK
1
2
6
8
10
12
6
8 '
10
12
136
140
145
149
142
148
154
160
148
157
165
195
203
211
156
202
'i6i
195
194
200
206
19
15
5/0
1%
1%
1
2
6
8
10
12
6
8
10
12
154
159
163
167
'220
160
166
172
178
'2ig
225
231
166
175
183
220
228
236
174
185
227
238
183
236
20
16
2/0
6/0
2H
2
1
2
Q
10
12
14
8
10
12
14
178
182
187
191
'251
186
192
198
204
'252
258
265
195
203
211
255
263
272
205
216
265
276
217
277
116
TABLE 35
COLUMNS
Column size >
ROUND CORED HOOPED COLUMNS
SAFE LOAD IN THOUSANDS OF POUNDS
AMERICAN CONCRETE INSTITUTE
RECOMMENDATIONS
P = Af e [(l+4np') + (n-
._ /unsupported length\ ,_
Max. [ -- I =15
\ diameter /
2000 -Ib. concrete
1:6 mixture
n = 15
f c =500
Size
of
column
(inches)
Diam-
eter
of core
(inches)
Spirals
Number
of
rods
Size of vertical round rods
Size No.
(A. S. &
W. Co.)
Pitch
(inches)
Per cent
of core
H
H
H
1
1H
1H
2 1
17
2/0
6/0
2
I
1
2
8
10
12
14
8
10
12
14
199
203
207
212
206
213
219
225
215
224
232
241
283
292
300
309
226
237
294
305
237
305
....
'287
293
22
18
3/0
7/0
2H
2
1
2
8
10
12
14
8
10
12
14
8
10
12
14
16
8
10
12
14
16
'225
229
234
228
235
241
247
'317
323
237
246
254
263
'322
330
339
248
259
270
324
335
346
259
273
336
350
272
349
23
19
3/0
7/0
2K
1
1
2
'248
253
257
261
252
258
264
270
276
'355
361
260
269
277
286
294
'354
362
370
379
271
282
293
304
356
367
378
389
282
296
368
381
296
381
24
20
3/0
7/0
2
m
1
2
8
10
12
14
16
8
10
12
14
16
277
281
286
276
282
288
295
301
'395
285
293
302
310
319
396
405
413
295
306
317
328
339
390
401
412
423
434
307
321
335
401
415
429
320
337
414
432
25
21
4/0
7/0
2X
IH
1
2
10
12
14
16
10
12
14
16
'303
307
311
308
314
320
327
319
328
336
344
'432
440
448
332
343
354
365
436
447
458
469
347
361
451
465
363
467
430
117
COLUMNS
ROUND CORED HOOPED COLUMNS
SAFE LOAD IN THOUSANDS OF POUNDS
AMERICAN CONCRETE INSTITUTE
RECOMMENDATIONS
L. Column size >
2000 -Ib. concrete
1:6 mixture
n=15
f c =500
/unsupported length\
v I - ^ ~ - ~ I
V diameter /
Spirals Size of vertical round rods
Size
of
Diam-
eter
Number
~r
column
(inches)
of core
(inches)
Size No.
(A. S. &
W. Co.)
Pitch
(inches)
UI
Per cent rods
of core
[I
H
H
H
1
1H
IK
26
22
4/0
2H
1
10
335
346
359
374
390
12
....
341
355
370
387
407
14
334
347
363
381
401
16
338
354
371
392
18
343
360
380
403
7/0 \Y %
2
10
473
488
504
12
484
502
521
14
'477
495
516
16
485
506
18 i
474
494
517
27
23
4/0
2K
1 10
363
374
387
402
418
12 ....
370
383
398
416
435
14
362
376
391
409
430
16
367
382
400
420
444
18 371 388
408
431
7/0
1H
2 10
i 527
543
*
12
523
540
560
14
'516
534
554
16
524
545
568
18
....
533
556
28
24 4/0
2 1 10 404
417
431
448
12
j : 399 412
428
445
465
14
405
421
439
459
482
16
'396
411
429
450
473
18
401
418
438
461
487
7/0
\y, 2 10
567
584
12
....
'564
581
601
14
575
595
618
16
565 586
609
18
573
597
623 j
29
25 5/0
2M
1 10
435
448
462
479
12 I
'436
443
459
476
496
14
436
452
470
490
513
16
427
442
460
481
504
530
18
431
448
468
492
20
436
455
477
504
7/0
1H
2
10
609
626
12
623
643
14
'eii?
637
660
16
....
628
651
677
18
616
639
665
20
624
650
30
26
5/0
2H
1 12
462
475
491
508
528
14
468
484
502
522
545
16
474
492
513
536
562
18
'463
480
500
524
550
20
468
487
509
535
564
7/0
1H
1.93 12
656
676
14
'650
670
693
16
661
684
710
18
'649
672
698
20
657
683
712
118
TABLE 35
COLUMNS
ROUND CORED HOOPED COLUMNS
SAFE LOAD IN THOUSANDS OF POUNDS
AMERICAN CONCRETE INSTITUTE
RECOMMENDATIONS
P=Af c ((l+4np'
(unsupported length\
MaX '( -- diameter - ) =15
2000-lb. concrete
1:6 mixture
n = 15
f c =500
Size
of
column
(inches)
Diam-
eter
of core
(inches)
Spirals
Number
of
rods
Size of vertical round rods
Size No.
(A. S. &
W. Co.)
Pitch
(.inches)
Per cent
of core
y*
H
1
IK | IK
31
27
5/0
7/0
2H
IK
1
1.86
12
14
16
18
20
22
12
14
16
18
20
22
12
14
16
18
20
22
12
14
16
18
20
22
501
505
5oi
508
514
520
526
509
517
525
534
542
550
524
535
546
557
568
579
"683
694
705
716
727
542
555
569
583
597
611
689
703
717
731
745
759
561
578
595
613
709
726
743
760
"682
690
698
32
28
5/0
7/0
2
IX
1
1.80
543
552
560
568
577
585
559
570
581
592
603
614
576
590
604
618
632
646
723
737
751
765
779
793
596
613
630
647
664
743
760
777
795
812
829
. . . .
'MO
536
542
548
554
561
....
717
728
739
750
761
724
733
33
29
6/0
7/0
2K
1H
1
1.73
12
14
16
18
20
22
12
14
16
18
20
22
'576
'578
584
590
596
579
587
596
604
613
621
594
605
616
627
638
649
612
626
640
654
668
681
756
770
784
798
812
826
631
649
666
683
700
776
793
810
828
845
....
....
'757
765
761
772
783
794
34
30
6/0
7/0
9X
iy*
1
1.67
12
14
16
18
20
22
24
12
14
16
18
20
22
24
'ei7
'615
621
627
634
640
616
624
633
641
650
658
667
631
642
653
664
675
686
697
649
663
677
691
705
719
733
791
805
819
833
847
861
875
669
686
703
720
737
755
811
828
845
862
879
897
792
800
809
796
807
818
829
840
119
COLUMNS
TABLE 35
2000 -lb. concrete
1:6 mixture
n = 15
f c =500
ROUND CORED HOOPED COLUMNS
SAFE LOAD IN THOUSANDS OF POUNDS
AMERICAN CONCRETE INSTITUTE
RECOMMENDATIONS
P=Af c ((l+4np')+(n-l)p]
__ /unsupported lengtn\ ,_
Max. I -=-. 1 =.Zo
\ diameter /
Spirals
Size of vertical round rods
Size
of
Diam-
eter
Number
_r
1
column
(inches)
of core
(inches)
Size No.
(A. S. &
W. Co.)
Pitch
(inches)
Per cent
of core
or
rods
H
H
H
1
1H
1H
35
31
6/0
2M
1
14
662
680
701
724
16
671
691
715
741
18
'659
679
702
729
758
20
665
687
713
742
774
22
671
696
724
756
792
24
678
704
735
770
710
7/0
IK
1.62
14
842
864
16
'832
856
882
18
843
869
899
20
854
883
916
22
'837
865
897
933
24
845
876
971
950
36
32
6/0
'2
1
14
702
720
741
764
16
711
731
755
781
18
719
742
769
798
20
'705
728
753
783
815
22
711
736
764
796
832
24
718
744
775
810
850
7/0
IK
1.57
14
878
901
16
'869
892
918
18
880
906
935
20
891
920
953
22
'873
902
934
970
24
881
913
948
987
37
33
7/0
2H
1
14
761
782
805
16
'752
772
796
822
18
760
783
809
839
20
'746
768
794
823
856
22
752
777
805
837
873
24
758
785
816
851
890
26
765
794
827
865
908
7/0
IK
1.52
14
915
938
16
929
955
18
'9i7
943
972
20
928
957
989
22
'gib
939
971
1007
24
919
950
985
1024
26
927
961
999
1041
38
34
7/0
2H
1
14
803
824
847
16
'794
814
838
864
18
802
825
852
881
20
810
836
865
898
22
'794
819
847
879
915
24
801
827
858
893
932
26
807
836
869
907
950
7/0
IK
1.48
14
954
977
16
968
994
18
'956
982
1012
20
967
996
1029
22
978
1010
1046
24
'958
989
1024
1063
26
966
1000
1038
1080
120
TABLE 35
COLUMNS
ROUND CORED HOOPED COLUMNS
SAFE LOAD IN THOUSANDS OF POUNDS
AMERICAN CONCRETE INSTITUTE
RECOMMENDATIONS
= Af c [(l+4np'
(unsupported length\
( diarnettr )
2000-lb. concrete
1:6 mixture
n = 15
f c =500
Size
of
column
(inches)
Diam-
eter
of core
(inches)
Spirals
Number
of
rods
Size of vertical round rods
Size No.
(A. S. &
W. Co.)
Pitch
(inches)
Per cent
of core
^
K
%
1
IX
IK
39
35
7/0
7/0
IK
i
1
1.43
14
16
18
20
26
14
16
18
20
22
24
26
....
'.'.'.'.
'845
854
862
871
879
847
858
869
880
891
902
913
867
881.
895
909
923
937
951
991
1005
1019
1033
1047
1061
1075
890
907
924
941
959
976
993
1014
1031
1048
1066
1083
1100
1117
844
850
::::
995
1003
993
1004
1015
1026
1037
40
36
7/0
7/0
2
ftM
1
1.40
:
16
18
20
22
24
26
28
16
18
20
22
24
26
28
....
'895
901
'899
907
915
924
932
902
913
924
935
946
957
968
926
940
953
967
981
995
1009
1048
1062
1076
1089.
1103
1117
1131
952
969
986
1003
1020
1038
1055
1074
1091
1108
1125
1143
1160
1177
1637
1046
1054
i646
1057
1068
1079
1090
11
37
7/0
7/0
2
IK
1.36
16
18
20
22
24
26
28
16
18
20
22
24
26
28
936
944
953
961
970
978
948
959
970
981
992
1003
1014
i086
1097
1108
1119
1130
971
985
999
1013
1027
1041
1055
1088
1101
1115
1129
1143
1157
1171
998
1015
1032
1049
1066
1083
1101
1114
1131
1148
1165
1182
1200
1217
*934
941
947
1086
1094
121
COLUMNS
TABLE 35
ROUND CORED HOOPED COLUMNS
SAFE LOAD IN THOUSANDS OF POUNDS
AMERICAN CONCRETE INSTITUTE
RECOMMENDATIONS
Column size
2000-lb. concrete
1:6 mixture
n = 15
f c =500
,_ /unsupported length\
Max.\ - jr; - - - I =15
\ diameter /
Spirals
Size of vertical round rods
Size
of
Diam-
eter
Number
-r
|
column
(inches)
of core
(inches)
Size No.
i (A. S. &
W. Co.)
Pitch
(inches)
Per cent
of core
OI
rods K
H
K 1
1H
1>4
42
38
7/0
2
1
16
995
1019
1045
18
1006
1032
1062
20
99i
1017
1046
1079
22
1000
1028
1060
1096
24
1008
1039
1074
1113
26
988
1017
1050
1088
1131
28
'.'.'.'. 994
1025
1061
1102
1148
30
1000
1033
1072
1116
1165
7/0
IK
1.32
16
1127
1154
18
I
1141
1170
20
ii26
1155
1188
22
.... ! . . . .
1137
1169
1205
24
....
1148
1183
1222 ,
26
ii26
1159
1197
1239
28
1134
1170
1211
1257
30
i - -
1142
1181
1225
1274
43
39
7/0
l%
1
16
1044
1067
1093
18
1055
1081
1110
20
1640
1066
1095
1127
22
1048
1077
1109
1145
24
1057
1088
1123
1162
26
1065
1099
1137
1179
28
1042
1073
1110
1151
1196
30
'.'.'.'. 1048
1082
1121
1164
1213
7/0
IK
1.29
16
1171
1197
I
18
1185
1214
j
20
ii7o
1199
1231
22
1181
1213
1249
24
1192
1227
1266
26
ii69
1203
1241
1283
28
1177
1214
1254
1300
30
1186
1225
1268
1317
44
40
7/0
IH
1
16
1093
1117
1143
18
1104
1130
1160
20
1115
1144
1177
22
io98
1126
1158
1194
24
1106
1137
1172
1211
26
1115
1148
1186
1229
28
i692
1123
1159
1200
1246
30
1098
1132
1170
1214
1263
7/0
IX
1.25
16
1211
1237
18
1225
1254
20
1209
1239
1271
22
1220
1253
1288
24
1231
1266
1306
26
1242
1280
1323
28
i217
1253
1294
1340
30
1226
1264
1308
1357
122
TABLE 36
COLUMNS
Ca/umn size
ROUND CORED HOOPED COLUMNS
SAFE LOAD IN THOUSANDS OF POUNDS
AMERICAN CONCRETE INSTITUTE
RECOMMENDATIONS
P=Af c ((l+4np')+(n-l)p]
.. (unsupported length\
Max. I -=-: 1 =15
\ diameter J
2500 -Ib. concrete
1:4% mixture
n = 12
f c =625
Size
of
column
(inches)
Diam-
eter
of core
(inches)
Spirals
Number
of
rods
Size of vertical round rods
Size No.
(A. S. &
W. Co.)
Pitch
(inches)
Per cent
of core
M
H
K
1
IH
IH
12
8
6
1M 1
6
59
13 9
g
1^
1
6
8
71
76
14 10
4
1M
1
6
8
85
89
91
15 11
3
IH
1
6
8
10
100
105
109
106
112
113
16
12
2
3/0
IH
IH
1
2
6
8
10
6
8
10
117
121
126
'i55
160
123
129
135
157
163
169
129
163
17
13
1
4/0
IX
IK
1
2
6
8
10
6
8
10
135
140
144
'i84
141
147
153
181
187
193
148
156
187
196
195
18
14
4/0
l
IH
2
6
8
10
12
6
8
10
12
155
159
163
168
'210
214
161
167
173
179
'2i3
219
225
167
175
184
213
222
230
175
221
19
15
5/0
IK
1J4
1
2
6
8
10
12
6
8
10
12
176
180
184
189
"242
182
188
194
200
'24i
247
253
188
196
205
241
250
258
196
207
249
260
204
258
20
16
2/0
6/0
2H
2
2
8
10
12
14
8
10
12
14
203
207
211
216
'276
210
216
222
229
'277
283
289
219
227
236
279
288
296
229
240
289
300
241
301
123
COLUMNS
TABLE 36
ROUND CORED HOOPED COLUMNS
SAFE LOAD IN THOUSANDS OF POUNDS
AMERICAN CONCRETE INSTITUTE
RECOMMENDATIONS
^Column size
2500-lb. concrete
1:4% mixture
n = 12
f c =625
,_ (unsupported length\ _
IrlttX* I -j7 7 ~- I 15
\ diameter /
Spirals
Size of vertical round rods
Size
of
Diam-
eter
Number
. column
(inches)
of core
(inches)
Size No.
(A. S. &
W. Co.)
Pitch
(inches)
Per cent
of core
of
rods
H
H
H
1
IK
IK
21
17
2/0
2
1
8
227
234
243
253
265
10
231
240
251
264
12
235
246
260
14
240
253
268
6/0
1%
2
8
311
321
333
10
....
319
332
12
314
328
14
321
336
22
18
3/0
2^
1
8
260
268
279
290
303
10
'257
266
277
289
304
12
261
272
285
300
14
265
278
293
7/0
2
2
8
355
366
379
10
'353
366
380
12
'348
361
377
14
354
370
23
19
3/0
2K
1
8
286
295
305
317
330
10
'283
293
304
316
331
12
288
299
312
327
14
292
305
320
338
16
296
311
328
7/0
IK
2
8
391
402
415
10
'389
401
416
12
397
412
14
'390
405
423
16
396
414
24
20
3/0
2
1
8
315
324
334
345
358
10
321
332
345
359
375
12
'316
327
340
355
373
14
320
333
348
366
16
324
339
357
377
7/0
IK
2
8
428
440
452
10
439
453
469
12
'435
450
467
j
14
443
461
16
434
451
471
25
21
4/0
ty*
1
10
350
361
374
388
404
12
'345
356
369
385
402
14
349
362
378
395
16
354
368
386
406
7/0
ix
2
10
478
492
508
12
'474
489
506
14
482
500
16
473
490
510
124
TABLE 36
COLUMNS
ROUND CORED HOOPED COLUMNS
SAFE LOAD IN THOUSANDS OF POUNDS
AMERICAN CONCRETE INSTITUTE
RECOMMENDATIONS
P=Af c [(l+4np')+(n-l)p]
Max.
'unsupported length\
diameter
= 15
2500 -Ib. concrete
1:4% mixture
n = 12
f c =625
Size
of
column
(inches)
Diam-
eter
of core
(inches)
Spirals
Number
of
rods
Size of vertical round rods
Size No.
(A. S. &
W. Co.)
Pitch
(inches)
Per cent
of core
%
H
H
1
IH
IX
26
22
4/0
7/0
zy*
i%
1
2
10
12
14
16
18
10
12
14
16
18
'38i
385
389
382
388
394
400
406
393
401
409
418
426
405
416
427
438
449
520
531
542
552
563
420
433
447
534
548
562
435
453
550
567
524
532
540
*52i
27
23
4/0
7/0
2H
1%
2
10
12
14
16
18
10
12
14
16
18
'4i4
418
422
414
420
427
433
439
425
434
442
450
458
438
449
460
470
481
452
466
480
493
576
590
604
617
468
485
592
609
I
.'.' :
'566
574
582
573
584
594
605
28
24
4/0
7/0
2
IX
1
2
10
12
14
16
18
10
12
14
16
18
460
468
476
484
493
472
483
494
505
515
487
500
514
527
541
623
637
650
664
678-
503
519
536
639
656
673
"452
456
455
461
467
473
....
619
630
641
652
....
621
629
29
25
5/0
7/0
Wt
iy*
1
2
10
12
14
16
18
20
10
12
14
16
18
20
'487
492
496
'490
496
502
508
514
495
503
512
520
528
537
508
519
529
540
551
562
522
536
549
563
577
670
683
697
711
724
686
703
719
736
.. ;
::::
'676
684
677
688
699
709
30
26
5/0
7/0
w
IX
1
1.93
12
14
16
18
20
12
14
16
18
20
'529
533
528
534
540
546
552
541
549
557
566
574
556
567
578
589
599
'715
725
736
747
573
587
601
614
628
721
735
748
762
776
593
609
626
740
757
774
....
....
'7i3
722
125
COLUMNS
TABLE 36
ROUND CORED HOOPED COLUMNS
SAFE LOAD IN THOUSANDS OF POUNDS
AMERICAN CONCRETE INSTITUTE
RECOMMENDATIONS
Column Size
2500 -lb. concrete
1:4% mixture
n = 12
f c =625
/unsupported length\
Max. I - -j-; - - - } = 15
\ diameter /
Spirals
Size of vertical round rods
Size
of
Diam-
eter
Number
_ e
column
(inches)
of core
(inches)
Size No.
(A. S. &
W. Co.)
Pitch
(inches)
Per cent
of core
OI
rods
H
H
Ys
1
1H
IK
31
27
5/0
2^
1
12
579
594
612
631
14
'572
587
605
625
648
16
578
596
616
639
664
18
584
604
627
653
681
20
'572
590
612
638
666
22
576
596
621
648
680
7/0
1H
1.86
12
759
778
14
....
'753
773
795
16
764
787
812
18
'752
774
800
829
20
760
785
814
22
768
796
828
32
28
5/0
2
1
12
619
634
651
670
14
ei2
627
645
665
687
16
618
635
656
679
704
18
....
624
644
666
692
721
20
630
652
677
706
738
22
616
636
660
688
720
7/0
IK
1.80
12
799
819
14
793
813
835
16
804
827
852
18
815
840
869
20
800
825
854
886
22
808
836
868
33
29
6/0
2>i
1
12
660
675
693
712
14
669
686
706
729
16
659
677
697
720
746
18
665
685
708
734
763
20
671
693
719
747
779
22
'667
677
702
729
761
7/0
IK
1.73
12
837
856
14
851
873
16
'84i
864
890
18
852
878
907
20
'838
863
892
924
22
846
874
905
34
30
6/0
2>i
1
12
704
719
736
755
14
712
730
750
772
16
703
720
740
763
789
18
709
728
751
777
806
20
715
737
762
791
823
22
721
745
773
804
840
24
'705
727
753
784
718
7/0
IK
1.67
12
878
897
14
891
914
16
'882
905
931
18
893
919
948
20
'878
904
932
964
22
887
914
946
981
!
24
895
925
960
126
TABLE 36
COLUMNS
ROUND CORED HOOPED COLUMNS
SAFE LOAD IN THOUSANDS OF POUNDS
AMERICAN CONCRETE INSTITUTE
RECOMMENDATIONS
,_ /unsupported length\ 1C
Max. \ 7^ I = lo
\ diameter
2500-lb. concrete
1:4% mixture
n = 12
Spirals
Size of vertical round rods
Size
of
Diam- j
eter
Number
f.
column
(inches)
of core
(inches)
Size No.
(A. S. & W.
Co.)
Pitch
(inches)
Per cent
of core
OI
rods
H
K
ft
1
IH
1H
35
31
6/0
2M
1
14
756
774
794
816
16
764
784
807
833
18
753
772
795
821
850
20
759
781
806
835
867
22
765
789
817
848
884
24
771
797
828
862
901
7/0
1H
1.62
14
933
956
16
'. '. '. '.
924
947
972
,
18
935
961
989
20
946
974
1006
22
'929
956
988
1023
24
937
967
1002
1040
36
32
6/0 2
1
14
802
820
840
862
16
810
830
853
879
18
818
841
867
896
20
'805
827
852
881
913
22
811
835
863
894
930
24
817
843
874
908
947
7/0
IH
1.57
14
977
999
16
'968
991
1016
18
979
1004
1033
20
989
1018
1050
22
"972
1000
1032
1067
24
981
1011
1045
1084
37
33
7
2>
1
14
867
887
909
16
857
878
901
926
18
866
888
914
943
20
'852
874
899
928
960
22
858
882
910
942
977
24
864
890
921
955
994
26
870
899
932
969
1011
f/0
1M
1.52
14
1020
1042
16
1033
1059
18
io2i
1047
1076
20
1032
1061
1093
22
iois
1043
1074
1110
24
1023
1054
1088
1127
26
1031
1064
1102
1144
38
34
7/0
2H
1
14
.... I ....
916
936
958
16
'906
926
949
975
18
914
937
963
992
20
923
948
977
1009
22
'967
931
959
990
1026
24
913
939
970
1004
1043
26
919
947
980
1018
1059
7/0
iy z
1.48
14
1065
1088
16
1079
1104
18
i067
1093
1121
20
1078
1106
1138
22
1088
1120
1155
24
1669
1099
1134
1172
26
1077
1110
1147
1189
127
^>
,
!
COLUMNS
]
& SAI
<-/
',500 -Ib. concrete \J
':4% mixture V
TABLE 36
ROUND CORED HOOPED COLUMNS
SAFE LOAD IN THOUSANDS OF POUNDS
AMERICAN CONCRETE INSTITUTE
RECOMMENDATIONS
Column size ^
P=Af c [(l+4np') + (n-
.,
max,
(unsupported length\
f c =625
diameter
/
**
m *
V
}
:>
^-
Size
of
column
(inches)
Diam-
Spirals
Number
of
rods
Size of vertical round rods
eter
of core
(inches)
Size No.
(A. S. &
W. Co.)
Pitch
(inches)
Per cent
of core
H
H
H
1
IH
U4
39
35
7/0
7/0
2H
IH
1
1.43
14
16 '
18
20
22
24
26
14
16
18
20
22
24
26
'963
969
'956
964
973
981
989
997
966
976
987
998
1009
1020
1030
986
999
1013
1026
1040
1054
1068
1109
1122
1136
1150
1163
1177
1191
1008
1025
1042
1059
1076
1093
1109
1131
1148
1165
1182
1199
1216
1233
iii2
1120
iiio
1121
1132
1143
1153
40
,
36
7/0
7/0
2
IH
1
1.40
16
18
20
22
24
26
28
16
18
20
22
24
26
28
i020
1027
i024
1033
1041
1049
1057
1028
1039
1050
1060
1071
1082
1093
1051
1065
1078
1092
1106
1119
1133
1173
1187
1200
1214
1228
1241
1255
1076
1093
1110
1127
1144
1161
1178
1198
1215
1232
1249
1266
1283
1300
'.'.:
lies
1171
1179
ii72
1182
1193
1204
1215
V 41
H>
^
V
*
37
7/0
7/0
' !
2
\H
j
1
1.36
16
18
20
22
24
26
28
16
18
20
22
24
26
28
1067
1073
1080
1669
1077
1086
1094
1102
1110
1081
1092
1103
1113
1124
1135
1146
1104
1118
1131
1145
1159
1172
1186
1219
1233
1246
1260
1274
1287
1301
1129
1146
1163
1180
1197
1214
1231
1244
1261
1278
1295
1312
1329
1346
1217
1225
1218
1228
1239
1250
1261
TABLE 36
COLUMNS
ROUND CORED HOOPED COLUMNS
SAFE LOAD IN THOUSANDS OF POUNDS
AMERICAN CONCRETE INSTITUTE
RECOMMENDATIONS
P=Af e ((l+4np'
,_ /unsupported length\
Max '( diameter )
15
2500 -Ib. concrete
1:4% mixture
n = 12
f e =625
Size
of
column
(inches)
Diam-
eter
of core
(inches)
Spirals
Number
of
rods
Size of vertical round rods
Size No.
(A. S. & W.
Co.)
Pitch
(inches)
Per cent
of core
M
H
M
1
IK
IK
42
38
7/0
7/0
2
1^
1
1.32
16
18
20
22
24
26
28
30
16
18
20
22
24
26
28
30
1136
1147
1158
1168
1179
1190
1201
1212
1159
1173
1186
1200
1214
1227
1241
1255
1268
1282
1296
1309
1323
1337
1350
1364
1184
1201
1218
1235
1252
1269
1286
1303
1294
1311
1328"
1345
1362
1378
1395
1412
....
ii28
1135
1141
1132
1141
1149
1157
1165
1174
....
1267
1278
1289
1299
1310
1321
i266
1274
1283
43
39
7/0
7/0
IK
IX
1.29
16
18
20
22
24
26
28
30
16
18
20
22
24
26
28
30
'. '.'.
iiss
1196
1204
1212
1220
1229
1191
1202
1213
1224
1235
1245
1256
1267
1214
1228
1242
1255
1269
1283
1296
1310
1318
1332
1345
1359
1373
1386
1400
1414
1240
1257
1274
1291
1308
1324
1341
1358
1344
1361
1377
1394
1411
1428
1445
1461
'.'.'.'.
iioo
1196
1317
1327
1338
1349
1360
1371
1316
1324
1333
44
40
7/0
7/0
1H
IX
1
1.25
16
18
20
22
24
26
28
30
16
18
20
22
24
26
28
30
!!!?
....
i253
1261
1269
1277
1286
1248
1259
1270
1280
1291
1302
1313
1324
1271
1285
1298
1312
1326
1339
1353
1367
1366
1380
1393
1407
1421
1434
1448
1462
1296
1313
1330
1347
1364
1381
1398
1415
1392
1409
1425
1442
1459
1476
1493
1510
....
1247
1253
1365
1375
1386
1397
1408
1419
1372
1381
129
COLUMNS
TABLE 37
3000-lb. concrete
1:3 mixture
n=12
f c =750
ROUND CORED HOOPED COLUMNS
SAFE LOAD IN THOUSANDS OF POUNDS
AMERICAN CONCRETE INSTITUTE
RECOMMENDATIONS
P=Af c [(l+4np')+(n-l)p]
,_ /unsupported length\
Max. I ^-. I =25
\ diameter I
Column size *
Size
of
column
(inches)
Diam-
eter
of core
(inches)
Spirals
Number
of
rods
Size of vertical round rods
Size No.
(A.S.&W.
Co.)
Pitch
(inches)
Per cent
of core
H
H
K
1
.IM
1H
12
8
6
IK
1
6 71
13
9
5
IH
1
6
8
86
91
14
10
4
iH
1
6 102
8 107
109
15
11
3
IH
1
6 121
8 126
10 131
127
135
135
16
12
2
3/0
1%
IH
1
2
6
8
10
6
8
10
141
146
151
'ise
191
147
155
162
188
195
203
155
196
17
13
1
4/0
1%
m
1
2
6
8
10
6
8
10
162
167
172
'226
169
176
184
217
224
231
177
187
225
235
186
234
18
14
1
4/0
1%
iH
1
2
6
8
10
12
6
8
10
12
186
191
196
201
'251
257
193
200
207
215
255
263
270
201
210
220
256
266
276
210
265
19
15
5/0
1%
i%
1
2
6
8
10
12
6
8
10
12
211
216
221
226
'290
218
225
233
240
'289
296
303
226
236
246
289
299
309
235
248
299
312
245
309
20
16
2/0
6/0
2y*
2
1
2
8
10
12
14
8
10
12
14
243
248
254
259
'331
252
260
267
274
332
339
347
263
273
283
335
345
355
275
288
347
360
289
361
130
TABLE 37
COLUMNS
Column
ROUND CORED HOOPED COLUMNS
SAFE LOAD IN THOUSANDS OF POUNDS
AMERICAN CONCRETE INSTITUTE
RECOMMENDATIONS
P=Af e ((l+4np'
/unsupported length\
* \ diameter /
3000-lb. concrete
1:3 mixture
n = 12
f e =750
Spirals
Size of vertical round rods
Size
of
Diam-
eter
Number
nf
column
(inches)
of core
(inches)
Size No.
(A. S. & W.
Co.)
Pitch
(inches)
Per cent
of core
OI
rods
M
K
K
1
IK
1H
I !
21
17
2/0
2
1
8
272 281
292
304
318
10
277
288
302
317
12
282
296
312
14
287
303
321
6/0
IK
2
8
373
385
399
10
383
398
12
'377
393
14
385
403
22
18
3/0
2K
1
8
312
322
334
348
363
10
308
319
332
347
364
12
313
326
342
360
14
318
333
352
7/0
2
2
g
426
440
455
10
424
439
456
12
iis
434
452
14
425
444
23
19
3/0
2K
1
8
344
354
366
380
396
10
340
351
364
379
397
12
345
358
374
392
14
350
366
384
405
16
355
373
394
7/0
IK
2
8
469
482
498
10
....
'466
481
499
12
476
494
14
"468
486
507
16
475
496
24
20
3/0
2
1
8
378
388
401
414
430
10
385
398
413
431
450
12
379
392
408
426
447
14
384
400
418
439
16
389
407
428
452
7/0
IK
2
8
514
528
543
10
527
544
563
12
'522
540
560
14
531
553
16
520
541
566
25
21
4/0
2K
1
10
421
434
449
467
486
12
415
428
444
462
483
14
420
436
454
475
16
425
443
464
488
7/0
1%
2
10
574
591
610
12
"570
587
60S
14
579
600
16
'568
589
613
131
COLUMNS
TABLE 37
ROUND CORED HOOPED COLUMNS
SAFE LOAD IN THOUSANDS OF POUNDS
AMERICAN CONCRETE INSTITUTE
RECOMMENDATIONS
^Column
)-lb. concrete
1:3 mixture
n = 12
f c = 750
P=Af c [(l+4np') + (n-
,_ /unsupported length\ ,_
Max. I - ^ - I =J.o
\ diameter /
Spirals
Size of vertical round rods
Size
of
Diam-
eter
Number
_r
column
(inches)
of core
(inches)
Size No.
(A. S. &
W. Co.)
Pitch
(inches)
Per cent
of core
of
rods
H
H
H
1
iy*
1M
26
!
22
4/0
2H
1
10
458
472
487
504
523
12
466
481
500
520
543
14
'457
473
491
513
537
16
462
480
501
526
18
467
488
511
539
7/0
\*A
2
10
623
641
660
A /8
12
636
657
680
14
'628
649
674
16
....
638
662
18
624
648
675
27
23
4/0
2H
1
10
498
511
526
543
562
12
505
521
539
560
583
14
'497
512
531
552
576
16
502
520
541
565
592
18
507
527
551
578
7/0
1%
2
10
693
712
12
688
709
732
14
680
701
726
16
690
714
742
18
700
727
28
24
4/0
2
1
10
552
567
584
603
12
546
562
580
601
623
14
553
572
593
617
644
16
543
560
581
606
633
18
548
568
591
619
650
7/0
IK
2
10
747
766
A /2
12
743
763
786
14
756
780
806
16
'744
769
796
18
754
782
813
29
25
5/0
2M
1
10
594
610
627
646
12
'589
604
623
643
f>60
14
596
614
636
660
687
16
'585
603
624
648
676
707
18
590
610
634
661
692
20
595
618
644
674
7/0
114
2
10
804
823
* /2
12
820
843
14
'812
836
863
16
825
853
884
18
'sii
838
869
20
821
851
30
26
5/0
2?<t
1
12
633
649
667
688
711
14
640
659
680
704
731
16
648
669
693
720
751
18
'635
655
678
706
737
20
640
662
688
719
753
7/0
IK
1.93
12
867
890
14
'859
883
910
16
872
900
930
18
'858
885
916
1
20
....
868
898
932
132
TABLE 37
COLUMNS
Column 3L2S.
ROUND CORED HOOPED COLUMNS
SAFE LOAD IN THOUSANDS OF POUNDS
AMERICAN CONCRETE INSTITUTE
RECOMMENDATIONS
Max.
/unsupported length\
diameter
15
3000-lb. concrete
1:3 mixture
n = 12
Size
of
column
(inches)
Diam-
eter
of core
(inches)
Spirals
Number
of
rods
Size of vertical round rods
Size No.
(A. S. &
W. Co.)
Pitch
(inches)
Per cent
of core
H
H
M
1
IK
IK
31
27
5/0
7/0
2K
IK
1
1.86
12
14
16
18
20
22
12
14
16
18
20
22
686
691
'687
694
701
708
716
695
705
715
725
735
745
713
726
739
752
765
778
'962
915
928
941
954
734
750
767
783
800
816
910
926
943
959
976
992
757
777
797
818
933
953
974
994
901
911
921
32
28
5/0
7/0
2
IK
1
1.80
12
14
16
18
20
22
12
14
16
18
20
22
'739
'735
742
749
756
764
743
753
763
773
783
793
761
774
787
800
813
826
'956
963
976
989
1002
782
798
815
831
848
864
957
974
990
1007
1023
1039
805
825
845
866
886
981
1001
1021
1041
1061
'958
968
33
29
6/0
7/0
2K
l
1.73
12
14
16
18
20
22
12
14
16
18
20
22
'789
'791
799
806
813
793
803
812
822
832
842
811
824
837
850
863
876
832
848
864
881
897
913
1004
1020
1037
1053
1070
1086
855'
875
895
915
936
1027
1047
1067
1088
1108
1009
1022
1035
1048
ioos
1015
....
....
34
30
6/0
7/0
2K
IK
1
1.67
12
14
16
18
20
22
24
12
14
16
18
20
22
24
844
854
864
874
884
894
904
862
875
888
901
914
927
940
883
899
916
932
949
965
981
1053
1069
1086
1101
1118
1135
1151
906
926
946
967
987
1007
1076
1096
1116
1137
1157
1177
! ....
'845
843
850
857
865
872
1058
1071
1084
1097
1110
::::
::::
i654
1063
1073
133
COLUMNS
TABLE 37
3000- Ib. concrete
1:3 mixture
n=12
f c=7 50
ROUND CORED HOOPED COLUMNS
SAFE LOAD IN THOUSANDS OF POUNDS
AMERICAN CONCRETE INSTITUTE
RECOMMENDATIONS
P=Af c [(l+4np'}+(n-l}p\
Max /unsupported length\
\ diameter /
Column Size ^
Spirals
Size of vertical round rods
Size
of
Diam-
eter
Number
column
(inches)
of core
(inches)
Size No.
(A. S. &
I W. Co.)
Pitch
(inches)
Per cent
of core
of
rods
$i
H
H
1
1H
IK
35
31
6/0
2>6
i
14
907
929
953
980
16 ....
917
941
969
1000
18
'963
927
954
985
1020
20
911
937
967
1002
1040
22
918
947
980
1018
1061
24
925
957
993
1035
1081
7/0
1H
].62
14
1123
1150
16
iiii
1139
1170
18
....
1124
1155
1190
20
1137
1172
1210
22
iii7
1150
1188
1231
24
1127
1163
1205
1251
36
32
6/0
2
1
14
962
983
1007
1034
16
972
996
1024
1055
18
982
1009
1040
1075
20
'965
992
1022
1056
1095
22
973
1002
1035
1073
1115
24
980
1012
1048
10.89
1136
7/0
IK
1.57
14
1173
1200
16
ii<52
1189
1220
18
1175
1206
1240
20
1187
1222
1260
22
ii67
1200
1239
1280
\
24 I ....
1177
1213
1256
1301
37
33 7/0
2M
1 14
1040
1064
1091
16 ,
i028
1053
1080
1111
18 ....
1038
1066
1097
1131
20 ....
1022
1048
1079
1113
1151
22
1029
1058
1092
1130
1172
24
1037
1068
1105
1146
1192
26
1044
1078
1118
1164
1212
7/0
U2
1.52
14
1225
1251
16
1241
1272
18
i226
1257
1292
20
....
1239
1274
1312
22
i2ij>
1252
1290
1332
24
1229
1265
1307
1353
26
1239
1278
1323
1373
38
34
7/0
2Y&
1 14
1098
1123
1149
16
io87
1111
1139
1170
18 : ....
1097
1124
1155
1190
20 ....
1107
1137
1172
1210
22 ....
1088
1117
1150
1188
1230
24
1095
1127
1163
1205
1251
26
1102
1137
1176
1221
1271
7/0
1>2
1.48
14
1279
1306
16
1296
1326
18
. . . .
i2si
1312
1347
20
1294
1328
1367
22
1307
1345
1387
24
1283
1320
1361
1407
26
1293
1333
1378
1428
134
TABLE S7
COLUMNS
ROUND .CORED HOOPED COLUMNS
SAFE LOAD IN THOUSANDS OF POUNDS
AMERICAN CONCRETE INSTITUTE
RECOMMENDATIONS
-- /unsupported length\ ,_
Max. [ - j-. - - - J = 15
\ diameter /
3000-lb. concrete
1:3 mixture
n = 12
f f =750
Size
of
column
(inches)
Diam-
eter
of core
(inches)
Spirals
Number
of
rods
Size of vertical round rods
i
Size No.
(A. S. &
W. Co.)
Pitch
(inches)
Per cent
of core
K
H
%
1
IX
1M
39
35
7/0
7/0
2K
l)i
1
1.43
14
16
18
20
22
24
26
14
16
18
20
22
24
26
il47
1157
1167
1177
1187
1197
1158
1172
1185
1197
1210
1223
123G
1183
1199
1216
1232
1248
1265
1281
1334
1351
1367
1383
1400
1416
1433
1210
1230
1250
1270
1291
1311
1331
1361
1381
1402
1422
1442
1462
1483
1148
1155
1163
1336
1349
1362
1375
1388
1339
1348
40
36
7/0
7/0
cy
1H
1.40
16
18
20
22
24
26
28
16
18
20
22
24
26
28
1233
1246
1259
1272
1285
1298
1311
1261
1277
1294
1310
1327
1313
1359
1406
1423
1439
1455
1472
1488
1505
1292
1312
1332
1353
1373
1393
1413
1437
1457
1477
1498
1518
1538
1558
i225
1231
1229
1239
1249
1259
1269
1404
1417
1430
1443
1456
1394
1404.
1414
41
37
7/0
7/0
2
1H
1.36
16
18
20
22
24
26
28
16
18
20
22
24
26
28
i2si
1288
1295
....
i283
1293
1303
1312
1322
1332
i4o9
1469
1297
1310
1323
1336
1349
1361
1375
i-iso
1473
I486
1499
1512
1325
1341
1357
1374
1390
1407
1423
1462
1478
1495
1511
1527
1544
1560
1355
1376
1396
1416
1436
1457
1477
1492
1513
1533
1553
1573
1594
1614
135
COLUMNS
TABLE 37
3000 -lb. concrete
1:3 mixture
ROUND CORED HOOPED COLUMNS
SAFE LOAD IN THOUSANDS OF POUNDS
AMERICAN CONCRETE INSTITUTE
RECOMMENDATIONS
= Af c [(l+4np')+(n-l}p]
(unsupported length\ _
' \ diameter /
Column Size ^
Spirals
Size of vertical round rods
Size
of
Diam-
eter
Number
column
(inches)
of core
(inches)
Size No.
(A. S. &
W. Co.)
Pitch
(inches)
Per cent
of core
of
rods
H
H
%
1
IH
IK
42
38
7/0
2
1 16 ! ...
1362
1390
1421
18
1375
1406
1441
20
i358
1388
1423
1461
22
1368
1401
1439
1482
24
1378
1414
1456
1502
26
1354
1388
1427
14*72
1522
28
1360
1398
1440
1488
1542
30
1368
1408
1453
1504
1563
7/0
IK
1.32
16
1520
1551
18
1537
1571
20
1519
1553
1591
22
1532
1570
1612
24
1545
1586
1632
26
isis
1558
1603
'1652
28
1528
1571
1619
1673
30
1538
1583
1635
1693
43
39
7/0
iy*
1
16
1430
1457
1488
18
1443
1474
1508
20
1425
1456
1490
1528
22
1435
1469
1506
1549
24
1445
1482
1523
1569
26
1455
1494
1539
1589
28
i428
1465
1507
1556
1609
30
1435
1475
1520
1572
1630
7/0
IK
1.29
16
1583
1613
18
1599
1634
20
1581
1615
1654
22
1594
1632
1674
24
1607
1648
1694
26
isso
1620
1665
1715
28
1590
1633
1681
1735
30
1600
1645
1697
1755
44
40
7/0
1%
1
16
1498
1526
1557
18
1511
1542
1577
20
1524
1559
1597
22
is b-4
1537
1575
1618
24
1514
1550
1592
] 638
26
1524
1563
1608
1658
28
1496
1534
1576
1624
1678
30
1504
1544
1589
1641
1699
7/0
IK
1.25
16
1639
1670
18
1656
1690
20
1(337
1672
1710
22
1650
1688
1731
24
1663
1705
1751
26
1670
1721
1771
28
1647
1689
1738
1791
30
1657
1702
1754
1812
130
TABLE 38
COLUMNS
Column size
ROUND CORED HOOPED COLUMNS
SAFE LOAD IN THOUSANDS OF POUNDS
NEW YORK CITY BUILDING CODE
REQUIREMENTS
P =Af c (l + (n -l)p] +2f s p'A
f t =20,000
1:6 mixture
n = 15
f e =500
Size
of
column
(inches)
Diam-
Spirals
Number
of
rods
Size of vertical round rods
eter
of core
(inches)
Size No.
(A. S. &
W. Co.)
Pitch
(inches)
Per cent
of core
X
K
H
1
1H
IK
12
8
6
IK
1
6
58
13 9 5
1M
1
6
8
70
74
14 10
4
IK
1
6
8
83
88
89
15 11
3
IH
1
6
8
10
98
103
107
104
110
ill
16
12
2
3/0
IK
1H
1
2
6
8
10
6
8
10
115
119
123
'iei
168
120
126
133
166
172
178
127
172
17
13
1
4/0
IK
IVs
1
2
6
8
10
6
8
10
132
137
141
'i94
138
144
150
191
197
203
145
153
198
206
152
205
18
14
1
4/0
IK
IK
1
2
6
8
10
12
6
8
10
12
151
156
160
164
"222
226
157
163
169
176
'225
231
237
164
172
181
225
234
242
171
233
19
15
5/0
Ul
1%
1
2
6
8
10
12
6
8
10
12
172
176
180
185
'255
178
184
190
196
'254
261
267
184
193
201
255
263
272
192
203
263
274
201
271
20
16
2/0
6/0
2H
2
1
2
8
10
12
14
8
10
12
14
198
202
207
211
'29i
206
212
218
224
'292
299
305
215
223
231
295
303
312
225
236
305
316
237
317
137
COLUMNS
TABLE 38
1:6 mixture
n = 15
f c =500
ROUND CORED HOOPED COLUMNS
SAFE LOAD IN THOUSANDS OF POUNDS
NEW YORK CITY BUILDING CODE
REQUIREMENTS
-l)p]+2f,p'A
f s = 20,000
Spirals
Size of vertical round rods
Size
of
Diam-
eter
Number
column
(inches)
of core
(inches)
Size No.
(A. S. &
W. Co.)
Pitch
(inches)
Per cent
of core
rods
M
M
14
1
IK
IX
21
17
2/0
1
8
221
229
238
248
260
10
226
235
246
259
12
230
241
255
14
234
248
263
6/0
114
2
8
329
339
351
10
337
350
12
'332
346
14
338
354
22
18
3/0
2>4
1
8
254
263
273
285
298
10
'256
260
271
284
299
12
255
266
280
295
14
259
272
288
7/0
2
2
8
375
386
400
10
'373
386
400
12
'368
381
397
14
374
390
23
19
3/0
2V &
1
8
280
289
299
311
324
10
'277
286
297
310
325
12
281
292
306
321
14
285
298
314
332
16
289
305
322
7/0
114
2
8
412
424
437
10
411
423
438
12
419
434
14
'412
427
445
16
418
436
24
20
3/0
2
1
8
307
316
327
338
351
10
314
325
338
352
369
12
'308
320
333
349
366
14
313
326
342
360
i !
16 317
332
350
371
7/0
114
2 8
452
464
477
10
. 463
478
494
12
'459
474
492
14
467
485
16
'458
476
496
25
21
4/0 2K
1 10
343
354
367
381
398
12
'337
349
362
378
395
1
14 342
355
371
389
16 346
361
379
400
7/0 1?4
l' 10
505
520
536
12
'soi
516
534
14
509
527
16
500
518
538
138
TABLE 88
COLUMNS
ROUND CORED HOOPED COLUMNS
SAFE LOAD IN THOUSANDS OF POUNDS
NEW YORK CITY BUILDING CODE
REQUIREMENTS
f ,
1:6 mixture
71=15
f e =500
Size
of
column
(inches)
Diam-
eter
of core
(inches)
Spirals
Number
of
rods
Size of vertical round rods
Size No.
(A. S. &
W. Co.)
Pitch
(inches)
Percent
of core
K
H
H
1
I.H
1>4
26
22
4/0
7/0
2 ?-8
1
1
2
10
12
14
16
18
10
12
14
16
18
'372
376
381
373
379
385
391
398
384
393
401
409
418
397
408
419
430
441
549
560
571
582
593
412
425
439
564
578
592
428
445
580
597
550
'553
561
570
27
23
1
4/0
7/0
2H
1^
2
10
12
14
16
18
10
12
14
16
18
"404
408
413
405
411
417
423
430
416
424
433
441
450
429
440
451
462
473
443
457
171
485
610
624
638
651
460
477
626
643
'599
607
616
606
617
628
639
28
24
4/0
7/0
2
IH
1
2
10
12
14
16
18
10
12
14
16
18
10
12
14
16
18
20
10
12
14
16
18
20
441
446
444
450
457
463
449
458
466
474
483
'655
664
462
473
484
495
506
'654
665
676
687
477
491
505
518
532
658
672
686
699
713
493
510
527
674
691
708
29
25
5/0
7/0
2X
iy z
1
2
'476
480
485
479
485
491
497
504
484
492
501
509
518
526
497
508
519
530
541
551
511
525
539
553
567
708
722
736
749
763
528
545
562
579
724
741
758
776
'714
722
715
726
737
748
30
26
5/0
7/0
2
1H
1
1.93
12
14
16
18
20
12
14
16
18
20
'sie
521
515
521
527
533
540
528
537
545
554
562
544
555
566
577
588
'752
763
774
785
501
575
589
603
759
773
787
801
815
581
598
615
778
796
813
'75i
760
139
COLUMNS
TABLE 38
1:6 mixture
n=15
f c =500
ROUND CORED HOOPED COLUMNS
SAFE LOAD IN THOUSANDS OF POUNDS
NEW YORK CITY BUILDING CODE
REQUIREMENTS
-l)p]+2f s p'A
f s =20,000
length \
* \diameterl
= 15
!
Spirals
Size of vertical round rods
Size
of
Diam-
eter
Number
column
(inches)
of core
(inches)
Size No.
(A. S. &
W. Co.)
Pitch
(inches)
Per cent
of core
of
rods
H
%
%
1
Ui
1M
31
27
5/0
2V
1
12
566
581
599
618
^7a
14
559
574
592
613
636
16
565
583
603
627
653
18
571
591
614
641
670
20
'558
577
599
625
654
22
563
583
608
636
668
7/0
1M
1.86
12
796
816
14
'796
810
833
16
801
824
850
18
'789
812
838
868
20
797
823
852
22
806
834
866
32
28
5/0
2
1
12
605
620
638
657
14
'597
613
631
652
674
16
604
622
642
666
692
18
610
630
653
679
709
20
616
638
664
693
726
22
'eoi
622
647
675
707
7/0
1H
1.80
12
834
854
14
'827
' 848
871
16
838
862
888
18
849
876
905
20
'835
860
890
922
22
843
871
904
33
29
6/0
2H
1
12
645
660
678
697
14
653
671
692
715
16
'644
662
682
706
732
18
! ! . .
650
670
693
720
749
20
656
679
704
734
766
22
*642
662
687
715
747
7/0
1H
1.73
12
869
889
14
883
906
16
'874
897
923
18
885
911
940
20
'870
896
925
958
22
878
907
939
34
30
6/0
2X
1
12
687
702
720
739
14
695
713
734
756
16
'686
704
724
748
774
18
692
712
735
761
791
20
698
720
746
775
808
22
704
729
757
789
825
24
'688
710
737
768
803
7/0
\H
1.67
12
908
928
14
922
945
16
'913
936
962
18
924
950
980
20
909
935
964
997
22
917
946
978
1014
24
926
957
992
140
TABLE 38
COLUMNS
Column size
ROUND CORED HOOPED COLUMNS
SAFE LOAD IN THOUSANDS OF POUNDS
NEW YORK CITY BUILDING CODE
REQUIREMENTS
P = Af e [l + (w -l)p] +2f s p'A
f,=20,000
I length \
Max.
\diameteri
= 15
1:6 mixture
n = 15
f e =500
Size
of
column
(inches)
Diam-
eter
of core
(inches)
Spirals
Number
of
rods
Size of vertical round rods
Size No.
(A. S. &
W. Co.)
Pitch
(inches)
Per cent
of core
*A
H
H
1
1H
t#
35
31
6/0
7/0
2^
1H
1
1.62
14
16
18
20
22
24
14
16
18
20
22
24
'735
741
747
754
738
747
755
763
772
780
756
767
778
789
800
811
777
791
805
818
832
846
964
978
992
1006
1020
1033
800
817
834
851
868
885
987
1004
1021
1038
1055
1073
954
965
976
987
998
959
967
36
32
6/0
7/0
2
IK.
1
1.57
14
16
18
20
22
24
14
16
18
20
22
24
'786
792
798
783
791
799
808
816
825
801
812
823
834
845
856
'994
1005
1016
1026
1038
821
835
849
863
877
891
1003
1017
1031
1045
1059
1073
844
861
878
896
913
930
1026
1043
1060
1078
1095
1112
'999
1007
37
33
7/0
7/0
2tf
1H
1
1.52
14
16
18
20
22
24
26
14
16
18
20
22
24
26
847
858
869
880
891
902
913
867
881
895
909
923
937
951
1043
1057
1071
1085
1099
1113
1127
890
907
924
942
959
976
993
1066
1083
1101
1118
1135
1152
1169
....
'832
838
844
850
837
845
854
862
871
879
1045
1056
1067
1078
1089
1039
1047
1055
68
34
7/0
7/0
2H
1>2
1
1.4S
14
16
18
20
22
24
26
14
16
18
20
22
24
26
'885
891
898
....
'884
893
901
909
918
927
1692
1100
894
905
916
927
938
949
960
1690
1101
1112
1123
1134
915
928
942
956
970
984
998
1088
1102
1116
1130
1144
1158
1171
937
955
972
989
1006
1023
1-040
1111
1128
1146
1163
1180
1197
1214
141
COLUMNS
TABLE 38
ROUND CORED HOOPED COLUMNS
SAFE LOAD IN THOUSANDS OF POUNDS
NEW YORK CITY BUILDING CODE
REQUIREMENTS
Cofumn size ^
1:6 mixture
n = 15
f c =500
-l)p]+2f s p'A
f s =20,000
/ length \
\diameter
Spirals
Size of vertical round rods
Size
of
Diam-
eter
kT 1 '
Number ~
nf
column
(inches)
of core
(inches)
Size No.
(A. S. &
W. Co.)
Pitch
(inches)
Per cent
of core
rods ^ ^
7 A
1
1H
1>4
39
35 7/0 2>
1 14 1
943
963
986
16
933
954
977
1003
j |
18
942
964
991
1020
20
950
975
1005
1038
22 934
958
986
1019
1055
24 940
967
997
1033
1071
26 ' i 946
975
1008
1047
1089
7/0
\Y 2 1.43 14
1129
1152
16
1143
1169
18
iisb
1157
1187
20
1141
1171
1204
22
1152
1185
1221
24
iis3
1164
1199
1238
26
1141
1175
1213
1255
40 36 7/0 2 1
16
1005
1028
1055
18
'992
1016
1042
1072
20
1001
1027
1056
1089
22
1010
1038
1070
1106
24 990
1018
1049
1084
1123
26 997
1027
1060
1098
1140
28 1004
1035
1071
1112
1158
7/0
IH
1.40
16
1190
1216
18
....
1204
1234
20
iis9
1218
1251
22
1200
1232
1268
24
iisb
1211
1246
1285
26
1188
1222
1260
1302
28 '
1197
1233
1274
1320
41 37
7/0
2 1
16
1056
1079
1105
18
1643
1067
1093
1122
20
1052
1078
1107
1139
22
1060
1089
1121
1157
24 1042
1069
1100
1135
1174
26 1048
1077
1111
1149
1191
28 1054
1085
1122
1162
1208
! ,
7/0 \K
1.36
16
1233
1259
!
18
1247
1277
20
1232
1261
1294
22 1 1
1243
1275
1311
24
1254
1289
1328
26
i23i
1265
1303
1345
28
1240
1276
1317
1362
142
TABLE 38
COLUMNS
Column Size
ROUND CORED HOOPED COLUMNS
SAFE LOAD IN THOUSANDS OF POUNDS
NEW YORK CITY BUILDING CODE
REQUIREMENTS
f,=20,
1:6 mixture
n=15
f c =500
Size
of
column
(inches)
Diam-
eter
of core
(inches)
Spirals
Number
of
rods
Size of vertical round rods
Size No.
(A. S. &
W. Co.)
Pitch
{.inches)
Per cent
of core
H
y*
1
IX
M
42
38
7/0
7/0
2
1
1
1.32
16
18
20
22
24
26
28
30
16
18
20
22
24
26
28
30
hoi
1107
1113
iios
1113
1122
1130
1138
1147
1109
1120
1131
1142
1153
1164
1175
1186
1132
1146
1160
1174
1188
12D2
1215
1229
1277
1291
1305
1319
1333
1347
1361
1375
1158
1175
1192
1210
1227
1244
1261
1278
1303
1321
1338
1355
1372
1389
1407
1424
1276
1287
1298
1309
1320
1331
1275
1284
1292
43
39
7/0
7/0
IH
IX
1
1.29
11
20
22
24
26
28
30
16
18
20
22
24
26
28
30
iie2
1168
il59
1168
1176
1185
1193
1201
1163
1174
1185
1196
1207
1218
1229
1240
1186
1200
1214
1228
1242
1256
1270
1284
1323
1337
1351
1365
1379
1392
1407
1421
1212
1230
1247
1264
1282
1298
1316
1333
1349
1367
1384
1401
1418
1435
1453
1470
i32i
1330
1338
1322
1333
1344
1355
1366
1377
44
40
7/0
7/0
IK
1H
1
1.25
16
18
20
22
24
26
28
30
16
18
20
22
24
26
28
30
1219
1230
1241
1252
1263
1274
1285
1296
1242
1256
1270
1284
1298
1312
1326
1340
1367
1381
1395
1409
1423
1437
1451
1465
1268
1286
1303
1320
1337
1354
1371
1389
1393
1411
1428
1445
1462
1479
1497
1514
1224
1232
1240
1249
1257
1217
1224
i,374
1382
1366
1377
1388
1399
1410
1421
143
COLUMNS
TABLE 39
1:4Y 2 mixture
n=12
f c =600
ROUND CORED HOOPED COLUMNS
SAFE LOAD IN THOUSANDS OF POUNDS
NEW YORK CITY BUILDING CODE
REQUIREMENTS
n-l)p]+2f s p'A
f s =20,000
}=15
,^ Column size o
Size
of
column
(inches)
Diam-
eter
of core
(inches)
Spirals
Number
of
rods
Size of vertical round rods
Size No.
(A. S. &
W. Co.)
Pitch
(inches)
Per cent
of core
*A
H
14,
1
1M
Ui
12 8
6
IK
1
6
62
13
9
5
lYz
1
6
8
76
80
14 10
4
iy*
1
6
8
91
95
96
15
11
3
IK
1
6
8
10
107
111
115
112
118
119
16
12
2
3/0
IK
IH
1
2
6
8
10
6
8
10
125
129
133
'i75
179
131
136
142
176
182
187
J37
182
17
13
1
4/0
1H
IK
1
2
6
8
10
6
8
10
145
149
153
'206
150
156
162
203
209
215
157
164
210
217
164
217
18
14
1
4/0
1H
1%
1
2
6
8
10
12
6
8
10
12
166
170
174
178
'236
240
171
177
183
189
'239
245
250
178
186
194
239
247
255
185
247
19
15
5/0
IK
IK
1
2
6
8
10
12
6
8
10
12
189
193
197
201
'272
194
200
206
212
'27i
276
282
201
208
216
271
279
287
208
218
278
289
216
237
20
16
2/0
6/0
2^
2
1
2
8
10
12
14
8
10
12
14
217
221
225
229
'SIO
224
230
236
242
'sii
316
322
233
241
249
313
321
329
243
253
323
333
254
334
144
TABLE 39
COLUMNS
Column size >
ROUND CORED HOOPED COLUMNS
SAFE LOAD IN THOUSANDS OF POUNDS
NEW YORK CITY BUILDING CODE
REQUIREMENTS
-l)p]+2f,p'A
f,=
1:4]4 mixture
n = 12
f c =600
Size
of
column
(inches)
Diam-
eter
of core
(inches)
Spirals
Number
of
rods
Size of vertical round rods
Size No.
(A. S. &
W. Co.)
Pitch
(inches)
Per cent
of core
*8
H
H
1
IK
iy*
21
17
2/0
6/0
2
IK
2
8
10
12
14
8
10
12
14
243
247
251
255
250
256
262
268
353
359
259
267
275
283
350
357
365
373
268
289
359
370
279
370
22
18
3/0
7/0
2H
2
1
2
8
10
12
14
8
10
12
14
'275
279
283
278
284
289
295
286
294
302
310
296
306
317
398
408
419
307
320
409
422
319
421
396
404
412
391
397
23
19
3/0
7/0
2H
IK
1
2
8
10
12
14
16
8
10
12
14
16
*304
308
312
316
307
313
318
324
330
315
323
331
339
347
'437
445
452
460
325
335
346
366
438
449
459
469
336
349
449
463
348
462
'
'438
444
24
20
3/0
7/0
2
IK
1
2
8
10
12
14
16
8
10
12
14
16
'338
343
347
337
343
349
355
361
346
354
362
370
378
356
366
376
387
397
481
492
502
512
523
367
380
393
492
505
519
379
395
505
521
487
495
503
::::
'486
25
21
4/0
7/0
2x
'*.
1
2
10
12
14
16
10
12
14
16
37i
375
379
376
381
387
393
386
394
402
410
'533
540
548
398
409
419
429
537
547
557
568
412
425
551
564
427
566
532
145
COLUMNS
ROUND CORED HOOPED COLUMNS
SAFE LOAD IN THOUSANDS OF POUNDS
NEW YORK CITY BUILDING CODE
REQUIREMENTS
1:4}^ mixture
n = 12
f c =600
f g =20,000
I length \
Max. ( -T-. ) = 15
\diameterj
Spirals
Size of vertical round rods
Size
of
Diam-
eter
Number
r
I
^
column
(inches;
of core
(inches)
Size No.
(A. S. &
W. Co.)
Pitch
(inches^
Per cent
of core
OI
rods
y*
H
1H
26
22 4/0 2Ys,
1
10
409 420 432
446
461
12
415
428 442
459
477
14
'408
421
436
453
472
16
412
427
444
463
18
417
433
452
473
7/0
IH
2
10
584
598
613
12
594
611
629
14
'588
605
624
16
596
615
18
585 ! 604
625
27
23
4/0
2K
1 10
445 455
467
481
496
12
450
463
478
494
513
14
444
456
471
488
507
16
448
462
479
498
520
18
452
468 487 509
7/0
1%
2 10
647
663
12
'644
660
679
14
037 654
673
16
*
645 ! 665
686
18
653 ! 675
28 24
4/0
2
1 10
492 504
518
533
12
487 500 515
531
550
14
493 508 525
544
566
16
'485
499 516 535
557
18
489
505 | 524 546
570
7/0
IK
2
10
699
714
12
i 696
712
14
706
725 1 747
16
697 716
738 1
18
705 727
751 !
29 25 5/0
2>
1 10
531 543
557 572
1 1
12
526
539 553
570 588
14
532
546 ! 563
583
604
16
523
538
554
574
596
620
18
527
543
562
584
609
20
531
549
570 595
7/0
IK
2
10
753
768
12
766
784
14
'760
779
801
16
770
792
817
18
759 781
805
20
767 791
30 26
5/0
2% 1
12
.... I 566
579 593
010
628
14
572
586
603
023
644
16
578
594
614
636
660
18
'567
583
602
624
649
20
571
589 610
635
662
7/0
IK
1.93
12
807
825
14
1 ....
'800
820
841
16
! ....
811
833
857
18
799
821
846
20
807
832
859
146
TABLE 39
COLUMNS
ROUND CORED HOOPED COLUMNS
SAFE LOAD IN THOUSANDS OF POUNDS
NEW YORK CITY BUILDING CODE
REQUIREMENTS
(n-l)p]+2f s p'A
f g =20,000
,_ / length \
Max - (diameter) =K
mixture
n = 12
f c =60
Size
of
column
(inches)
Diam-
eter
of core
(inches)
Spirals
Number
of
rods
Size of vertical round rods
Size No.
(A. S. &
W. Co.)
Pitch
(inches)
Per cent
of core
i
H
H 1
IK
Ifc
31
27
5/0
7/0
2M
1M
1
1.86
12
14
16
18
20
22
12
14
16
18
20
22
eis
617
6i3
619
625
631
637
620
628
636
644
652
660
635
645
656
666
676
687
651
664
678
691
704
717
848
861
875
888
901
914
670
686
702
718
867
883
899
915
842
853
863
873
884
'841
849
857
32
28
5/0
7/0
2
IX
1
1.80
12
14
16
18
20
22
12
' 14
16
18
20
22
660
657
662
668
674
680
663
671
679
687
695
703
678
688
699
709
719
730
'885
896
906
916
927
695
708
721
734
747
760
892
905
918
931
944
957
713
729
745
762
778
910
926
942
959
975
:::
"892
900
33
29
.
6/0
7/0
2M
IX
1.73
12
14
16
18
20
22
12
14
16
18
20
22
12
14
16
18
20
22
24
12
14
16
18
20
22
24
705
"707
713
719
725
708
716
724
732
740
748
723
733
743
754
764
775
739
752
765
778
792
805
932
945
958
971
985
998
758
774
790
806
822
951
967
983
999
1015
1 .
936
947
957
967
i ;;;; ;;;;
'934
941
34
30
6/0
7/0
*K
IX
1
1.67
....
755
754
759
765
771
777
755
762
770
778
786
794
802
769
779
790
800
811
821
831
786
799
812
825
838
851
864
975
988
1001
1014
1028
1041
1054
804
820
836
853
869
885
994
1010
1026
1042
1058
1075
'.'.'.'.
'976
984
992
979
990
1000
1010
1021
147
COLUMNS
ROUND CORED HOOPED COLUMNS
SAFE LOAD IN THOUSANDS OF POUNDS
NEW YORK CITY BUILDING CODE
REQUIREMENTS
.^ Column size ^
% mixture
12
600
Max.
-l)p]+2f t p'A
f ,=20, 000
I length \
\diameter
15
Spirals
Size of vertical round rods
Size
of
Diam-
eter
Number
~f
column
(inches)
of core
(inches)
Size No.
(A. S. &
\\ . Co.)
Pitch
(inches)
Per cent
of core
OI
.rods
H
X
V*
1
1H
IK
35
31 6/0
2H
1
14
1
810
827
847
868
16
818
838
860
884
18
'807
826
848
873
901
20
813
834
858
886
917
22
819
842
869
899
933
24
825
850
879
912
949
7/0
1H
1.62 14
1034
1055
16
1625
1047
1072
18
1035
1060
1088
20
1046
1073
1104
22
i029
1056
1086
1120
24
1037
1066
1099
1136
36
32
6/0
2
1
1 :
14
860 877
896
918
16
868 887
909
934
18
876 898
922
950
20
'863
884 908
935
966
22
868
892 j 918
949
982
24
874
899 i 929
962
999
7/0
1H
1.57.
14
1079
1101
16
io7o
1092
1117
18
i . . . .
1081
1106
1133
20
1091
1119
1149
22
i675
1102
1132
1166
24 i
1083 : 1112
1145
1182
37
33
7/0
2H 1
14
: 928
947
969
16 !
919 938
960
985
18
927 949
973
1001
20
914
935 959
987
1017
22
919
943 969
1000
1033
24
925
951 980
1013
1050
26
931
958 | 990
1026
1066
7/0
1H
1.52 14
1125
1146
16
1138
1163
18
1126
1151
1179
20
1137
1164
1195
22
ii20
1147
1177
1211
24 ...
1128
1157
1190
1227
1
26 1 ....
1136
1168
1204
1243
38
34 7/0
2H
1
14
980
1000
1021
16
971 991
1013
1037
18
'
979 1001
1026
1054
20
987 j 1012
1039
1070
22 ...
972
995
1022
1052
1086
24
978
1003
1032
1065
1102
26
984
1011
1013
1078
1118
7/0
IH
1.48
14
1174
1196
16
1187
1212
18
ii"6
1200
1228
20
1186
1214
1244
22
1196
1227
12G1
24
ii78
1207
1240
1277
26
1186
1217
1253
1293
148
TABLE 39
COLUMNS
ROUND CORED HOOPED COLUMNS
SAFE LOAD IN THOUSANDS OF POUNDS
NEW YORK CITY BUILDING CODE
REQUIREMENTS
n-l)p]+2f e p'A
f s =20,000
length \ ,_
-
mixture
f c =600
Size
of
column
(inches)
Diam-
eter
of core
(inches)
Spirals
Number
of
rods
Size of vertical round rods
Size No.
(A. S. &
W. Co.)
Pitch
(inches)
Per cent
of core
H
X
%
1
IH
IK
39
35
7/0
7/0
2H
1>*
1
1.43
14
16
18
20
22
24
26
14
16
18
20
22
24
26
i026
1034
1041
1049
1057
1065
1035
1045
1055
1066
1076
1087
1097
1054
1067
1080
1093
1106
1120
1133
1219
1232
1245
1258
1271
1284
1298
1075
1092
1108
1124
1140
1156
1173
1240
1257
1273
1289
1305
1321
1338
1626
1032
1038
. . . .*
1220
1231
1241
1251
1262
i222
1230
40
36
7/0
7/0
2
IH
1
1.40
16
18
20
22
24
26
28
16
18
20
22
24
26
28
....
1101
1111
1122
1132
1142
1153
1163
1123
1136
1149
1162
1175
1188
1202
1286
1299
1312
1325
1338
1352
1365
1147
1164
1180
1196
1212
1228
1245
1311
1327
1343
1359
1375
1392
1408
i094
1100
1097
1105
1113
1121
1129
i284
1295
1305
1316
1326
1276
1284
1292
41
37
7/0
7/0
2
m
1
1.36
16
18
20
22
24
26
28
16
18
II
11
28
ii47
1155
1163
1170
1178
1186
1158
1169
1179
1189
1200
1210
1220
1180
1193
1206
1220
1233
1246
1259
1334
1347
1360
1373
1386
1399
1413
1205
1221
1237
1253
1270
1286
1302
1359
1375
1391
1407
1423
1440
1456
....
ii4o
1151
1157
1333
1343
1353
1364
1374
i.332
1340
149
COLUMNS
ROUND CORED HOOPED COLUMNS
SAFE LOAD IN THOUSANDS OF POUNDS
NEW YORK CITY BUILDING CODE
REQUIREMENTS
Column size
1:4% mixture
n = 12
f c =600
f, = 20,000
Max (tewth\ 15
\diameter)
Spirals
Size of vertical round rods
Size
of
Diam-
eter
Number
f\f
column
(inches)
of core
(inches)
Size No.
(A. S. &
W. Co-.)
Pitch
(inches)
Per cent
of core
OI
rods
: %
K
H
1
1H
IK
42 38 7/0
2
1
16
1217
1239
1264
18
1227
1252
1280
20
1213
1238
1265
1296
22
1221
1248
1278
1312
24
1229
1259
1292
1328
26
i2ib
1237
1269
1305
1345
28
1216
1245
1279
1318
1361
30
1222
1253
1290
1331
1377
' 7/0
IK
1.32 16
1362
1384
1409
18
1372
1397
1425
20
1358
1383
1410
1441
1
22
1366
1393
1423
1457
i
24
1374
1403
1436
1473
26
1382
1414
1450
1490
28
isei
1390
1424
1463
1506
30
1366
1398
1435
1476
1522
43 39 7/0 l 7 ^
1 16
1278
1300
1324
18
1288
1313
1340
20
.
1274
1298
1326
1357
22
1282
1309
1339
1373
24
1290
1319
1352
1389
26
1298
1329
1365
1405
28
1276
1306
1340
1378
1421
30
1282
1314
1350
1391
1438
7/0 V/4 1.29 1T>
1438
1463
18
1451
1479
20
1437
1464
1495
22
1447
1477
1511
24
1457
1490
1527
26
i436
1468
1504
1543
28
1444
1478
1517
1560
30
1452
1489
1530
1576
44 40 7/0 1J 8 ' 1 16
1340
1362
1386
18
1350
1375
1402
1
20
1360
1388
1419
22
1344
1371
1401
1435
24
1352
1381
1414
1451
26
1360
1391
1427
1467
28
1338
1368
1402
1440
1483
30
1344
1376
1412
1453
1499
7/0 1> 1-25 16
1487
1511
1
18
1500
1528
20
i ....
'. '. '.
i486
1513
1544
22
1496
1526
1560
24
1506
1539
1576
26
1517
1553
1593
28
1493
1527
1566
1609
30
1501 1538 1579 1625
150
TABLE 40
COLUMNS
Column size
ROUND CORED HOOPED COLUMNS
SAFE LOAD IN THOUSANDS OF POUNDS
CHICAGO BUILDING CODE REQUIREMENTS
/ length \
MaxA-T^ I =12
\diameter
1:2:4 mixture
n = 15
f c =500
Size
of
column
(inches)
Spirals
Size of vertical round rods
eter
of core Size No.
(inches) (A. S. &
W. Co.)
!
Pitch
(inches
of
Per cent rods
of core
H
%
K
1
ix iy*
15 12 9 IK
0.5 8
10
88
93
97
104
16 13 8 Hi 0.5 8
10
99
104
108
115
119
17
14 7
\X
IX
0.5 8
10
12
1.5 8
10
I 12
112
117
122
147
154
161
121
128
135
159
168
178
131
141
173
186
1
-
18
15 6
2/0
IX
IX
0.5 8
10
12
1.5 8
10
12
125
130
136
'i72
178
134
142
149
177
186
196
145
155
191
204
157
207
19
16 G
3/0
\H
ix
0.5 8
10
12
14
1.5 8
10
12
14
140
145
150
155
igi
197
204
149
156
164
171
196
205
215
225
159
169
179
210
223
236
172
185
226
243
185
244
'
20
17 5
3/0
IX
IX
0.5 8
10
If
1.5 8
10
12
14
155
160
165
170
"2is
224
164
171
179
186
216
226
235
245
175
185
195
205
230
243
256
269
187
200
246
263
201
264
21
18 4
3/0
i?i
' ' '.
IX
0.5 8
10
12
14
1.5 8
10
12
14
172
177
182
187
180
188
195
203
191
201
211
221
251
265
278
291
203
216
230
268
285
302
217 233
234
286 306
307
246
"247
257
266
151
COLUMNS
ROUND CORED HOOPED COLUMNS
SAFE LOAD IN THOUSANDS OF POUNDS
CHICAGO BUILDING CODE REQUIREMENTS
TABLE 40
. Column size yi
1:2:4 mixture
n = 15
f c =500
= Af c (l+2.5np'
12
Spirals
Size of vertical round rods
Size
of
Diam-
eter
Number
f
column
(inches)
of core
(inches)
Size No.
(A. S. &
W. Co.)
Pitch
(inches)
Per cent
of core
ot
rods
y&
H
+
H
1
IK
IK
22
19
4
IH
0.5
8
189
198
208
221
234
250
10
194
205
218
234
251
12
199
213
228
247
14
204
220
238
260
16
! 209
227
248
4/0
IH
1.5
8
i 274
290
308
329
10
270 287
307
330
12
280
301 325
14
268
289
314 342
16
275
299
327 i
2.3 20
3
1M 0.5
8
207
216
226
239
253
268
j , :
10
212
223
236
252
269
289
12
217
231
246
265
277
14
222
238
257
278
16
227
245
267
291
5/0
1%
1.5
8
298
314
332
353
10
311
331
354
379
12
'SOS
324
349
376
14
313
337
366
i
16
'299
323
351
383
24
21
3
iH
0.5
10
231
242
256
271
288
308
12
236
250
266
284
305
14
241
257
276
297
16
I 246
264
286 310
5/0
IH
1.5
10
336
357
379
405
1
12
'329
350
374
401
14
338
363
391
I 16
348
376
408
25 22
2
IK
0.5 10
251
262
276
291
308
328
12
256
270
286
304
325
348
II 14
261
277
296
317
341
16
267
284
306
330
18
272
292
316
343
0/0
2
1.5 10
363
383
406
431
12
376
400
427
458
14
'365
369
417
449
16
374
402
435
! || 18
384
416
452
26
23
2
Ui
0.5 10
272
283
297
312
329
349
12
277
291
307
325
346
369
14
283
298
317
338
362
16
288
305
327
351
379
18
293
313
337
364
6/0
1%
1.5
10
411
433
459
12
'464
428
455
486
14
417
445
477
16
'462
430
462
499
!
18
411
443
479
152
TABLE 40
COLUMNS
Column Size <.
ROUND CORED HOOPED COLUMNS
SAFE LOAD IN THOUSANDS OF POUNDS
CHICAGO BUILDING CODE REQUIREMENTS
I length \
A-r. ) =12
\diameterj
1:2:4 mixture
n = 15
f e =500
Size
of
column
(inches)
Diam-
eter
of core
(inches)
Spirals
Number
of
rods
Size of vertical round rods
Size No.
(A. S. &
W. Co.)
Pitch
(inches)
Per cent
of core
H
H
H
1
IX
IH
27
24
7/0
2
2
0.5
1.5
10
12
14
16
18
10
12
14
16
18
294
299
304
310
315
305
313
320
327
335
318
329
339
349
359
'432
446
459
472
334
347
360
373
386
439
457
474
491
508
351
368
384
401
417
462
484
506
527
549
370
391
411
487
514
541
431
440
28
25
1
7/0
2
2
0.5
1.5
10
12
14
16
18
20
10
12
14
16
18
20
317
322
327
332
337
343
328
335
343
350
358
365
341
351
361
371
381
391
'476
489
502
515
357
370
383
396
409
422
469
487
504
521
538
555
374
391
407
424
440
492
514
536
558
579
393
414
434
455
518
545
571
598
470
480
29
26
7/0
2K
m
0.5
1.5
12
14
16
18
20
12
14
16
18
20
346
351
356
361
366
359
366
374
381
389
502
512
375
385
395
405
415
'507
520
533
546
393
407
420
433
446
518
536
552
570
588
414
431
447
464
481
545
567
589
610
632
438
458
478
576
602
630
30
27
7/0
2X
IH
0.5
1.5
12
14
16
18
20
22
12
14
16
18
20
22
371
376
381
386
391
396
384
391
399
406
413
421
400
410
420
430
440
450
418
431
445
457
471
484
550
568
585
602
620
636
439
456
472
489
505
522
578
600
622
643
664
686
462
483
503
524
608
635
662
689
'552
566
579
592
544
554
153
COLUMNS
TABLE 40
ROUND CORED HOOPED COLUMNS
SAFE LOAD IN THOUSANDS OF POUNDS
CHICAGO BUILDING CODE REQUIREMENTS
Column siz
1:2:4 mixture
n=15
f c =500
,_ / length \
Max. T - ) =12
\diameter
Spirals Size of vertical round rods
Size
of
Diam- ' -vr
eter 1 Number
column
of core Size No. p- h P t H
(inches)
(inches) $-S.& (inches) oTcor" H % ^ l
1M
1>4
I
i
31
28 2/0 2?^ 0.5 12 '396
410
425
444
465 488
14
401
417
435
457 481 i 508
16
407
424
445
470 498 529
18
312
432
455
483 514
549
20
417
439
466
496 531
569
22 422
447
476
509
548
7/0 ] 1.5 12
584
612
642
14
602
633
669
i 16
'586
619
655
696
18
600
646
677
722
20
613
653
698
749
22 .... | 588
626
670
720
32 29 2/0 2*4 0.5 12 423
436
452
471
491
514
14 428
444
462
484
508
535
16 433
451
472
497
524
556
18 438
458
482
509 541
576
20 443
466
492
523
557
596
22 448 473 502
536
574
7/0 \% 1.5 12
646
677
|| 14
637
668
704
16 !
654
690
731
18
'635
670
712
758
20
648
688
734
784
22 ....
661
705
755
33 30 2/0 2^ 0.5 12 450
464
479
498
519
542
14
456
471
490
511
537
563
16
461
479
500
524
552
583
18
466
486
510
537
568
603
20
471
493
520
550
585
624
22
476
500
530
563
602
644
24
481
508
540
576
618
7/0 16 1-5 12
672
713
14
'672
704
740
16
690
726
767
18
670
707
748
794
20
684
724
770
821
22 ....
697
741
791
847
24 i
'668
710
758
813
34 31 3/0 2^ 0.5 14 || 484
500
518
540
564
591
16 ! 489
507
528
552
581
611
18 494
514
538
566
597
632
20
499
522
548
579
613
652
; 22
504
529
558
592
630
672
24
510 536
568
605
(346
693
: 7/0 l$i 1.5 14
710
742
778
| 16
727
764
805
18
'708
744
785
832
20
722
762
807
858
22
734
779
829
885
24
748
796
851
912
154
TABLE 40
COLUMNS
Column size ^
ROUND CORED HOOPED COLUMNS
SAFE LOAD IN THOUSANDS OF POUNDS
CHICAGO BUILDING CODE REQUIREMENTS
Af e (l+2.5np')(l + (n-
/ length \ =
Max.
\diameter
12
1:2:4 mixture
n = 15
f c = 500
Spirals Size of vertical round rods
Size
Diam- : I %__i
of
eter
rxumuer
^r
column
(inches)
of core
(inches)
Size No.
(A. S. &
W. Co.)
Pitch
(inches)
Per cent
of core
OI
rods
X
H
X
1
IK
IK
35
32 3/0 2K 0.5 14
513
529
547
569
593
620
16
518
536
557
582
610
641
18
524
544
567
595
626
661
20
529
551
577
608
642
681
22
534
558
587
621
659
702
24
539
566
597
634
676
722
7/0
iX
1.5
14
780
816
16
'766
802
843
18
782
824
870
20
800
846
896
22
'773
818
867
924
24
786
834
889
950
36 33 3/0 2^ 0.5 14 544
559
578
599
623
650
16 549
566
588
612
640
671
18 , 554
574
598
625
656
691
20
559
581
608 | 638
673
712
22
564
589
618 ! 651
690
732
24
569
596
628 1 664
706
752
26
574
603
638 677
723
772
7/0
IK
1.5
14
820
856
16
842
883
18
823
864
910
20
840
886
936
22 . .
sis
857
907
963
,
24
826 874
929
990
:
26
839 892
951
1017
37 34 3/0 2H
0.5
14
591
609 630
655
682
16
580
598
619 644
671
702
18
585
605
629
657
688
723
20
590
613 ! 639
669
704
743
22
595
620 649 683
721
763
24 600
627 659 696
737
784
26
606
635 669 709
754
804
7/0
IX
1.48
14
857
893
16
879
920
18
860
901
946
20
876
922
973
22
894
944
1000
24
863 911 | 966
1027
26 ....
876 928 I 988
1053
38 35 3/0 2H 0.5
14
623
641 663
687
714
16 1 612
630
651 676
703
734
18 617
638
661 689
720
755
20 622
645
671 702
737
775
22 628
652
681 1 715
753
795
24 633
660
691 728
769
816
26
638
667
701 ! 741
786
836
7/0
IK
1.43
14
1
890
925
16
911
951
18
892
932
977
20
909
954
1003
22
926
975
1031
24
895 943
996
1057
26 , ....
908 959
1018
1082
155
COLUMNS
TABLE 40
ROUND CORED HOOPED COLUMNS
SAFE LOAD IN THOUSANDS OF POUNDS
CHICAGO BUILDING CODE REQUIREMENTS
Column Size
1:2:4 mixture
n=75
f c =500
/ length \
\diameterj
Spirals
Size of vertical round rods
Size
of
Diam-
eter
Number
column
(inches)
of core
(inches)
Size No.
(A. S. &
W. Co.)
Pitch
(inches)
Per cent
of core
of
rods
*A
H
14
1
IK
iy*
39
36
4/0 2%
0.5
16
663
684
709
735 768
18
'65i
671
694
722
753
788
20
656
678
704
735
769 808
22
661
685
714
748
786
829
24
666
693
724
761
803
849
26
! 671
700
734
774
819
870
28 676
707
744
787
836
890
7/0
m
1.40
16
943
985
18 ' . .. .
966
1012
20
943
987
1037
22
959
1008
1063
24 || .
930
976
1030
1089
26
....
942
993
1051
1116
28
955
1010
1072
1142
40
37
4/0
2*A
0.5
16
697
718
743
771
802
18
'685
705
728
756
787
822
20 690
712
738
769
803
842
22 695
719
748
782
820
863
24 700
727
758
795
837 884
26 . 705
734
768
808
854 905
28 710
741
778
821
869 925
7/0
1M
1.36 ! 16
980 1019
18
1001
1045
j 20
'978
1022
1071
22
994
1043
1097
24
1011
1064
1123
26
'976
1027
1085
1148
I
28
989
1044
1105
1174
41
38 4/0 2H 0.5 16
732 753
778
806
836
18
740 763
791
822
857
20 725
747
773
804
839
877
22 730
754
783
817
856
898
24 735
762
793
830
873
919
26 740
769
803
843
889
939
28 745
776
813
856
906
960
30 750
784
823
870
922
980
7/0
iy 2 1.32
16
1015
1054
18
1035
1079
20 ....
i6l2
1057
1105
22
1029
1077
1131
24
1045
1098
1157
26
ioi2
1062
1118
1183
28
1024
1078
1140
1209
30
1037 1095
1101
1234
156
TABLE 40
COLUMNS
ROUND CORED HOOPED COLUMNS
SAFE LOAD IN THOUSANDS OF POUNDS
CHICAGO BUILDING CODE REQUIREMENTS
,_ / length \
Max. [-T-. -) =12
\dianieteri
1:2:4 mixture
n=15
f c = 500
Size
of
column
(inches)
Diam-
eter
of core
(inches)
Spirals
Number
of
rods
Size of vertical round rods
Size No.
(A. S. &
W. Co.)
Pitc-h
(inches)
Per cent
of core
K
H
H
1
1^
IH
42
39
4/0
7/0
2H
1H
0.5
1.29
|
i
16
18
20
22
24
26
28
30
16
18
20
22
24
26
28
30
'76i
766
771
776
781
786
768
776
783
790
798
805
812
820
789
799
809
819
829
839
849
859
813
827
840
853
866
879
892
905
841
858
875
892
908
924
941
957
1052
1073
1093
1114
1134
1155
1175
1196
873
894
914
934
954
975
996
1016
1091
1117
1142
1167
1193
1218
1244
1269
1649
1065
1082
1098
1115
1131
::::
1648
1061
1074
43
40
4/0
7/0
2H
IK
0.5
1.25
16
18
20
22
24
26
28
30
16
18
20
22
24
26
28
30
803
808
813
818
823
805
813
820
827
835
842
849
857
826
836
846
856
866
876
886
896
851
864
877
890
903
916
929
942
879
895
911
928
944
961
978
995
1087
1107
1127
1147
1168
1188
1208
1228
909
930
950
970
991
1011
1032
1052
1124
1150
1175
1200
1225
1250
1275
1300
i096
1108
i085
1100
1116
1133
1148
1164
157
COLUMNS
TABLE 41
mixture
ROUND CORED HOOPED COLUMNS
SAFE LOAD IN THOUSANDS OF POUNDS
CHICAGO BUILDING CODE REQUIREMENTS
P = Af c (l+2.5np'}[l + (n-
Column Size *
12
600
\diameterl
Spirals
Size of vertical round rods
Size
of
Diam-
eter
Number
_r
column
(inches)
of core
(inches)
Size No.
(A. S. &
W. Co.)
Pitch
(inches)
Per cent
of core
OI
rods
H
H
H
1
1H
1M
15 12 9 Us' 0.5
8 97
105
10 101
112
10 13 8 IM 0.5 8 110
118
10 115
125
17
14 7
IH 0.5
8 125
133
143
10 130
140
152
.
12 134
146
\H
1.5 8 157
168
180
10 163
176
191
12
169
185
IS 15 6
1> 0-5 8
141
149
158
170
!
10
145
155
168
!
12
150
162
2/0
Ik' 1.5 8
188
200
214
10
'l83
196
211
12
189
204
19 16 6 ]? j 0.5 8 157
166
175
186
199
10
162
172
184
198
1 1
12
167
179
194
14
; 171
186
3/0
1%
l!5
8
209
221
235
251
10
'264
217
233
250
12 210
226
244
|
14 1 216
234
20
17 5
1>2
0.5 8 175
183
193
204
217
10
ISO
190
202
216
12
185
197
211
14
189
204
221
1 3/0
IH
1.5 8
231
244
258
274
10
240
255
273
12
233
248
267
|
14
239
257
278
21
18 4
iH
0.5
8
194
202
212
224
236
250
10
199
209
221
235
251
12
204
216
230
247
14
208
223
239
3/0
1>2
1.5
8
267
282
298
315
10
'264
279
297
317
12
272
290
312
14
'263
281 302
158
TABLE 41
COLUMNS
Column size
ROUND CORED HOOPED COLUMNS
SAFE LOAD IN THOUSANDS OF POUNDS
CHICAGO BUILDING CODE REQUIREMENTS
12
._
A/ax.
/ length \
(-^ )
\diameterl
1:1%:3 mixture
n = 12
f c =600
Size
of
column
(inches)
Diam-
eter
of core
(inches)
Spirals
Number
of
rods
Size of vertical round rods
Size No.
(A. S. &
W. Co.)
Pitch
(inches)
Per cent
of core
K
K
1
IH
IK
22
19
4
4/0
1^
I*
0.5
1.5
10
12
14
16
8
10
12
14
16
214
219
224
228
233
'288
294
222
229
236
243
249
'289
297
306
314
232
241
250
259
269
293
304
316
327
339
243
255
267
279
307
322
337
352
256
271
323
342
270
341
23
20
3
5/0
IK
IK
0.5
1.5
8
10
12
14
16
8
10
12
14
16
227
231
' 245
249
254
244
250
257
264
270
253
263
271
281
290
319
331
342
354
365
265
276
288
300
312
333
349
364
379
394
277
292
307
349
368
388
291
310
367
391
"326
324
333
341
24
21 3
5/0
1
1
0.5
1.5
10
12
14
16
10
12
14
16
262
267
272
276
272
279
286
293
'352
361
369
285
294
303
313
359
370
382
393
299
311
322
334
377
392
407
422
314
330
396
416
332
419
25
22
2
6/0
IK
2
0.5
1.5
10
12
14
16
18
10
12
14
16
18
286
290
295
299
304
296
302
309
316
322
308
317
326
335
344
388
400
411
423
434
322
334
346
358
370
406
421
436
451
466
338
353
368
426
445
464
356
374
-448
472
1
390
398
407
26
23
2
6/0
IK
IK
0.5
1.5
10
12
14
16
18
10
12
14
16
18
310
315
319
324
329
320
327
334
340
347
332
342
350
360
369
346
358
370
382
394
437
452
467
482
497
362
377
392
408
457
476
495
514
380
398
479
502
.' : : :
'429
438
431
442
454
465
159
TABLE 41
COLUMNS
ROUND CORED HOOPED COLUMNS
SAFE LOAD IN THOUSANDS OF POUNDS
CHICAGO BUILDING CODE REQUIREMENTS
Column size
mixture
= 600
Spirals
Size of vertical round rods
Size
of
Diam-
eter
Number
column
(inches)
of core
(inches)
Size No.
(A. S. &
W. Co.)
Pitch
(inches)
Per cent
of core
of
rods
H
H
H
1
1H
IK
27
24
1
2
0.5 10
335
346
358
372
388
405
12
340
352
367
384
403
424
14
345
359
376
396
418
443
16
849
366
385
408
433
18
354
372
394
420
448
7/0
2
1.5
10
469
489
511
12
463
484
508
535
14
474
499
527
558
16
461
486
514
546
; 18
470
497
529
565
28
25 1
1
2
0.5
10 362
372
384
399
414
432
12 367
379
394
410
429
451
14
371
386
403
423
444
469
16
376
392
412
434
459
488
18
380
399
421
446
474
20
i 385
406
430
458
7/0
2
1.5 10
502
522
545
12
517
541
568
14
j
'508
532
560
592
16 ....
519
547
579
615
18
'503
531
562
598
20 |
512
542
577
29 26
2M
0.5
12 394
407
421
438
457
478
14 399
413
430
450
472
497
16 404
420
439
462
487
516
i 1 1
18 408
427
448
473
502
20 413
433
458
485
516
7/0
1H
1.5
12 j . ..
552
576
603
14
'542
567
595
626
I j
16 li . ..
554
582
614
650
! 1
is :j . ..
'538
565
597
633
i
20 ! . ..
546
577
612
652
30
27
2H
0.5
12 423
435
450
467
486
507
14 ! 428
442
459
479
501
525
16
432
449
468
491
516
544
i
18
437
455
477
502
. 531
563
1
20
442
462
486
514
546
22
446
469
495
526
561
7/0
IK
1.5
12
588
612
639
14 |i
603
631
663
16
'596
618
650
686
18 ....
602
633
669 710
20
'583
613
648
688
22
591
624
664
707
160
TABLE 41
Column size ^
COLUMNS
ROUND CORED HOOPED COLUMNS
SAFE LOAD IN THOUSANDS OF POUNDS
CHICAGO BUILDING CODE REQUIREMENTS
P = Af c (l +2.5np')U + (n -
I length \
Max.
-;-.
\diameterj
12
1:1)4:3 mixture
n = 12
f c =600
Size
'of
column
(inches)
Diam-
eter
of core
(inches)
Spirals
Number
of
rods
Size of vertical round rods
I Size No.
(A. S. &
W. Co.)
Pitch
(inches)
Per cent
of core
%
\
K
H
1
IX
IK
31
1
28
2/0
7/0
2H
IK
0.5
1.5
12
14
16
18
20
22
12
14
16
18
20
22
453
458
462
467
471
476
465
472
479
485
492
499
480
489
498
507
516
525
497
508
520
532
544
556
626
641
656
671
686
701
515
530
546
561
576
591
650
669
688
707
726
745
545
555
574
593
611
687
700
724
747
771
628
639
651
662
'629
32
29
2/0
7/0
2H
IM
0.5
1.5
12
14
16
18
20
22
12
14
16
18
20
22
484
488
493
498
502
507
496
503
509
516
523
530
510
520
529
538
546
556
527
539
551
563
575
587
547
562
577
592
606
622
689
708
727
746
765
784
568
586
605
624
642
716
739
763
786
810
680
695
710
725
740
678
690
701
33
30
2/0
7/0
2K
i*
0.5
1.5
12
14
16
18
20
22
24
12
14
16
18
20
22
24
516
520
525
530
534
539
544
528
535
541
548
555
562
568
542
552
561
570
579
588
597
559
571
583
595
607
619
631
578
593
608
624
639
654
669
729
748
767
786
805
824
843
599
618
637
656
674
693
756
779
803
826
850
873
720
735
750
765
780
795
....
....
719
730
742
753
716
34
31
3/0
7/0
2H
l)i
0.5
1.5
14
16
18
20
22
24
.14
16
18
20
22
24
553
558
563
567
572
577
568
574
581
588
595
602
585
594
603
612
622
631
605
617
629
641
653
665
762
777
792
807
822
837
627
642
657
672
687
702
790
809
828
847
866
885
651
670
688
707
726
745
821
845
868
892
915
939
'7ei
772
784
795
( '
11
161
COLUMNS
TABLE 41
1:1^4:3 mixture
n = 12
f c = 600
ROUND CORED HOOPED COLUMNS
SAFE LOAD IN THOUSANDS OF POUNDS
CHICAGO BUILDING CODE REQUIREMENTS
P=Af c (l+2.5np'
Max.
, Column si.
Size
of
column
(inches)
Diam-
eter
of core
(inches)
Spirals
Number
of
rods
Size of vertical round rods
Size No.
(A. S. &
W. Co.)
Pitch
(inches)
Per cent
of core
%
H
%
1
IH
IK
35
32
3/0
7/0
2H
IK
0.5
1.5
14
16
18
20
22
24
14
16
18
20
22
24
587
592
597
601
606
611
602
608
615
622
629
635
619
628
637
646
655
664
638
650
662
674
686
698
661
676
691
706
721
736
833
852
871
890
909
928
685
704
722
741
760
779
864
888
911
935
958
982
'826
838
820
835
850
865
880
36
33
3/0
7/0
2M
IX
0.5
1.5
14
16
18
20
22
24
26
14
16
18
20
22
24
26
623
627
632
637
641
646
652
637
644
650
657
664
670
677
654
663
673
682
691
700
709
674
685
697
709
721
733
745
696
711
726
741
756
771
786
877
896
915
934
953
972
991
721
739
758
777
795
813
832
909
932
956
979
1002
1026
1049
....
'87i
882
894
'879
894
909
925
940
37
34
3/0
7/0
2H
1H
0.5
1.48
14
16
18
20
22
24
26
14
16
18
20
22
24
26
' '664
; 668
673
678
682
687
673
680
687
693
700
707
714
690
699
708
717
727
736
745
710
722
734
746
758
770
782
732
747
76?
777
792
807
822
919
937
956
975
994
1013
1031
757
775
794
813
831
850
868
949
973
996
1019
1042
1065
1089
'923
935
921
936
950
965
980
38
35
3/0
7/0
2H
IH
0.5
1.43
14
16
18
20
22
24
26
14
16
18
20
22
24
26
'761
706
710
715
720
725
711
717
724
731
738
744
751
727
737
746
755
764
773
782
747
759
771
783
794
806
819
769
784
800
815
830
845
860
956
975
994
1013
1031
1050
1069
794
813
832
851
869
887
906
987
1010
1033
1056
1080
1103
1126
'96i
973
958
973
988
1003
1018
162
TABLE 41
COLUMNS
Column Size
ROUND CORED HOOPED COLUMNS
SAFE LOAD IN THOUSANDS OF POUNDS
CHICAGO BUILDING CODE REQUIREMENTS
P=Af c (l+2.5np')[l + (n-
Max.
I length \
{diameter/
12
%: 3 mixture
12
600
Size
of
column
(inches)
Diam-
eter
of core
(inches)
Spirals
Number
of
rods
Size of vertical raund rods
Size No.
(A. S. &
W. Co.)
Pitch
(inches)
Per cent
of core
H
H H 1 iM 1M
39
36
4/0
7/0
*M
iK
0.5
1.40
16
18-
20
22
24
26
28
16
18
20
22
24
26
28
16
18
20
22
24
26
28
16
18
20
22
24
26
28
'744
749
754
758
763
768
756
763
769
776
783
789
796
775
784
794
803
812
821
830
798
810
821
833
845
857
869
823
838
853
869
884
899
914
1016
1035
1054
1073
1092
1110
1129
851
870
889
908
926
945
964
1052
1075
1098
1121
1145
1168
1191
-
iois
1030
1044
1059
1074
; ;;;
ioos
1014
1025
40
37
4/0
7/0
2%
IH
0.5
1.36
"784
788
793
798
803
807
795
802
809
816
822
829
836
815
824
833
842
851
860
869
837
850
861
873
885
897
909
863
878
893
909
924
939
954
1056
1074
1093
1111
1130
1148
1167
891
909
928
947
965
984
1003
1091
1113
1136
1159
1182
1205
1228
;; :
1054
1065
1055
1070
1084
1098
1113
41
38
1
4/0
7/0
*H
IK
0.5
1.32
16
18
20
22
24
26
28
30
16
18
20
22
24
26
28
30
'829
834
839
844
, 848
852
836
843
850
856
863
870
876
883
856
865
874
883
892
901
910
919
879
890
902
914
926
938
950
962
903
918
934
949
964
979
994
1009
1096
1115
1133
1152
1170
1188
1207
1225
932
951
970
988
1007
1025
1044
1063
1131
1154
1176
1199
1221
1244
1267
1289
'
i094
1105
1116
16&5
1109
1124
1138
1153
1167
163
COLUMNS
TABLE 41
1:1%:3 mixture
n = 12
ROUND CORED HOOPED COLUMNS
SAFE LOAD IN THOUSANDS OF POUNDS
CHICAGO BUILDING CODE REQUIREMENTS
12
fnlnmrt size %.
Max.
Size
of.
column
(inches)
Diam-
eter
of core
(inches)
Spirals
Number
of
rods
Size of vertical round rods
Size No.
(A. S. &
W. Co.)
Pitch
(.inches)
Per cent
of core
ys
H
7 A
1
IH
IK
42
39
4/0
7/0
2M
1}'2
0.5
1.29
16
18
20
22
24
26
28
30
16
18
20
22
24
26
28
30
'S71
876
880
885
889
894
878
885
891
898
905
911
918
924
897
906
916
925
934
943
953
962
920
932
944
956-
967
979
991
1003
945
960
975
990
1004
1019
1034
1050
1140
1158
1176
1194
1212
1230
1249
1267
973
992
1010
1029
1048
1066
1084
1103
1172
1196
1219
1241
1264
1286
1309
1331
ii37
1148
1159
li38
1152
1167
1181
1195
1210
43
40
4/0
7/0
2H
IH
0.5
1.25
16
18
20
22
24
26
28
30
16
18
20
22
24
26
28
30
"gis
923
928
932
1 937
921
927
934
941
947
954
961
968
940
949
958
968
977
986
995
1004
962
974
986
998
1010
1022
1034
1046
988
1003
1018
1033
1048
1062
1077
1092
1181
1199
1217
1235
1253
1271
1289
1307
1016
1035
1053
1072
1090
1109
1128
1146
1215
1237
1259
1282
1304
1326
1348
1371
1179
1193
1207
1222
1236
1250
....
ii90
1200
164
TABLE 42
Column size
COLUMNS
ROUND CORED HOOPED COLUMNS
SAFE LOAD IN THOUSANDS OF POUNDS
CHICAGO BUILDING CODE REQUIREMENTS
1:1:2 mixture
n=10
f c =725
Spirals
Size of vertical round rods
Size
of
Diam-
eter
Number
column
(inches)
of core
(inches)
Size No.
(A. S. &
W. Co.)
Pitch
(inches)
Per cent
of core
of
rods
H
H
H
1
IX
IH
15
12
9
1H
0.5
8
110
118
1
10
115
125
16
13
8
IH
0.5
8
126
134
!
10
; 131.
141
17
14
7
IK
0.5
8
144
151-
161
10
148
158
170
12
153
164
IH
1.5
8
175
185
197
10
181
193
207
12
186
201
18 15 .6
1H
0.5
8 162
170
179
190
10 167
177
188
12
171
183
2/0
1H
1.5
8
208
219
233
10
'264
216
230
12
209 224
19
16
6
IH
0.5
8
182
190
199
210
223
10
186
196
208
222
12
191
203
217
14
195
211
3/0
i^
1.5
8
232
244
257
272
10
'228
240
254
271
12
233
248
265
14
239
257
20
17
5
1H 0.5
8
203
211
220
231
243
10
208
217
229
243
12
212
224
238
14
217
231
247
3/0
m
1.5
8
258
269
283
298
10
266
280
296
12
'259
274
291
14
265
282
302
21
18
4
IK
0.5
8 225
234
243
254
266
280
10 230
240
252
265
280
12
235
247
260
277
14
239
254
269
3/0
IK
1.5
8
297
310
325
342
10
'293
308
324
343
12
301
318
338
1
14
'292
310
329
165
COLUMNS
TABLE 42
ROUND CORED HOOPED COLUMNS
SAFE LOAD IN THOUSANDS OF POUNDS
CHICAGO BUILDING CODE REQUIREMENTS
Column size
1:1:2 mixture
'ri = 10
f c = 725
Max l lw"L\ =12
\diameter /
Spirals
Size of vertical round rods
Size
of
Diam-
eter
Number
_r
column
(inches)
of core
(inches)
Size No.
(A. S. &
W. Co.)
Pitch
(inches)
Per cent
of core
OI
rods
*A
H
V*
1
IH
IH
22
19
4
IH
0.5
8
249
257
266
277
290
303
10
254
264
275
289
304
12
258
270
284
300
14
263
277
293
312
16
267
283
302
4/0 1%
1.5 8
326
339
354
370
10
'322
336
353
372
12
330
347
367
14
'321
338
358
381
16 327
346
369
23
20 3 IH 0.5 8 i 274
282
291
302
315
328
10 i 279
289
300
314
329
346
12 ; 283
295
309
326
344
14
i 288
302
318
337
16
292
808
327
349
5/0 1%
1.5 8
356
369
384
401
10
367
384
402
423
12
'sei
378
398
420
14
369
389
412
1
i 16 357
377
399
426
24
21 3
1%
0.5 10
305
315
326
340
356
372
12
309
321
335
352
370
14 ' 314
328
344
363
16
319
334
353
375
5/0 IM
1.5 10
399
416
435
455
12
393
410
430
452
14
401
421
444
16
409
432
458
25
22 2 1% 0.5 10 333
342
354 1 368
383
400
12 337
349
363 379
398
418
: j
14 341
356
372
391
412
16 346
362
381
402
18
350
368
389
414
6/0
2
1.5 10
433
449
468
490
12
444
463
486
511
14
'434
454
478
504
16
442
465
492
18
450
476
506
1
26
23
2
IH 0.5 10 i 361
372
383
396
412
429
12 366
378
392
408
427
447
14 370
385
401
420
442
16 375
391
410
431
456
18 1 379
397
418
443
6/0 1% ' 1.5
10
485
503
525
12
'479
499
521
546
14
490
513
539
16
'478
501
527
557
18 |; ....
485
512
541
.
lf>6
TABLE 42
COLUMNS
Column size
ROUND CORED HOOPED COLUMNS
SAFE LOAD IN THOUSANDS OF POUNDS
CHICAGO BUILDING CODE REQUIREMENTS
Max. -- =12
n=10
f c = 725
Size
of
column
(inches)
Diam-
eter
of core
(inches)
Spirals
Number
of
rods
Size of vertical round rods
Size No.
(A. S. &
W. Co.)
Pitch
(inches)
Per cent 1
of core
*A
H
H
1
IK
in
27
24
7/0
Q
2
0.5
1.5
10
12
1 4 6
18
10
12
14
16
18
392
396
401
305
410
401
408
415
421
428
413
422
431
440
449
'515
526
537
548
427
438
450
461
473
522
536
550
564
578
442
457
471
486
500
540
558
576
594
612
459
477
495
561
583
605
:::.'
'si 5
522
28
25
1
7/0
2
0.5
1.5
10
12
14
16
18
20
10
12
14
16
18
20
423
428
432
437
441
446
433
440
447
453
459
465
445
453
462
471
480
489
458
470
481
493
504
516
560
574
588
602
616
630
473
488
503
517
532
578
596
614
632
650
490
508
527
545
599
621
644
666
'56i
569"
'565
576
587
597
29
26
7/0
2M
m
0.5
1.5
12
14
16
18
20
12
14
16
18
20
460
464
469
473
478
472
479
485
491
498
'eoi
608
486
495
504
512
521
'605
616
626
637
502
513
525
537
548
613
628
642
656
670
521
535
550
564
579
636
654
672
690
707
541
559
577
662
683
705
30
27
7/0
2H
IH
0.5
1.5
12
14
16
18
20
22
12
14
16
18
20
22
494
499
503
508
512
517
506
513
519
525
531
538
520
529
537
546
555
564
536
548
559
570
582
593
655
670
684
698
712
726
554
569
583
598
613
628
678
696
714
731
749
767
575
593
611
629
703
725
747
769
"650
658
'657
668
679
689
167
COLUMNS
1:1:2 mixture
n=10
f c=7 25
ROUND CORED HOOPED COLUMNS
SAFE LOAD IN THOUSANDS OF POUNDS
CHICAGO BUILDING CODE REQUIREMENTS
P=Af c (l+2.5np'j[l+(n-l)p]
Max. t-- =12
TABLE 42
i^ Co/if 777/7 size y.
Spirals
Size of vertical round rods
Size
of
Diam-
eter
Number
_*
column
(inches)
of core
(inches)
Size No.
(A. S. &.
W. Co.)
Pitch
(inches)
Per cent
of core
OI
rods
H
H
%
1
IK
IX
31
28
2/0
2%
0.5
12
530
541
555
571
590
610
14
534
548
564
583
605
628
16
539
554
573
595
619
647
18
543
560
582
606
633
665
20
548
567
590
618
648
682
22
552
573
599
629
663
7/0
IK
1.5
12
698
721
746
14
713
739
768
16
'766
727
757
790
18
711
741
775
812
20
722
755
792
834
22
'76!
733
769
810
32
29
2/0
2H
0.5
12
565
577
592
608
626
647
14
570
584
600
620
641
665
16
' 574
590
609
631
655
683
18
579
597
618
642
670
701
20
583
603
627
654
685
718
22
588
610
636
666
699
7/0 .
IK
1.5
12
765
792
14
'757
783
813
16
771
801
835
18
'756
785
819
857
20
767
800
837
879
22
777
814
855
33
30
2/0
2H
0.5
12
604
616
629
646
664
685
14
608
622
638
657
678
702
16
613
628
647
669
693
720
18
617
635
656
680
708
738
20
622
641
665
691
723
757
22
526
648
674
703
737
775
24
631
654
683
715
752
7/0 IK
1.5
12
812
836
14
'803
830
858
16
817
848
880
18
'802
832
866
902
' 20
813
846
883
925
22
824
860
901
947
24
'800
834
873
919
34
31
3/0
2%
0.5
14
647
661
677
696
718
742
16
652
668.
686
708
733
760
18
656
674
695
720
747
778
20
661
680
704
731
762
796
22
665
687
713
743
777
813
24
670
693
722
754
791
831
7/0
IK
1.5
14
851
878
907
1 16 !
865
895
929
18
'850
880
913
951
20
861
894
931
973
22
872
908
949
995
24
882
922
966
1017
168
TABLE 42
Column size <.
COLUMNS
ROUND CORED HOOPED COLUMNS
SAFE LOAD IN THOUSANDS OF POUNDS
CHICAGO BUILDING CODE REQUIREMENTS
P=Af c (l+2.5np')(l + (n-
I length \
) = 12
Max '
diameter
1:1:2 mixture
n=10
f c = 725
Size
of
column
(inches)
Diam-
eter
of core
(inches)
j
Spirals
Number
of
rods
Size of vertical round rods
Size No.
(A. S. &
W. Co.) !
Pitch
(inches)
Per cent
of core
K
%
H
1
IX
IH
35
32
3/0
7/0
2K
IK
0.5
1.5
14
16
18
20
22
24
14
16
18
20
22
24
688
692
697
701
706
710
702
708
715
721
728
734
717
727
736
745
753
762
737
748
760
771
782
795
758
773
787
802
817
831
927
945
963
981
998
1016
782
800
818
836
854
872
956
978
1000
1022
1045
1067
915
929
943
957
972
....
'921
931
36
33
3/0
7/0
2K
IK
0.5
1.5
14
16
18
20
22
24
26
14
16
18
20
22
24
26
729
734
738
743
747
752
756
743
749
756
762
769
775
782
759
768
777
786
795
804
812
778
790
801
813
825
836
848
800
814
829
843
858
873
887
978
996
1013
1031
1049
1067
1086
824
842
860
878
896
914
932
1007
1029
1051
1073
1095
1117
1140
'972
983
993
980
994
1008
1022
1036
37
38
34
3/0
7/0
99i
IK
0.5
1.48
14
16
18
20
22
24
26
14
16
18
20
22
24
26
'778
782
787
791
796
800
787
793
800
806
813
819
826
803
812
820
829
838
846
855
821
833
844
856
867
879
890
843
858
872
886
900
915
930
1027
1044
1061
1079
1097
1114
1132
867
885
903
920
938
956
975
1054
1077
1099
1121
1143
1165
1187
1628
1042
1056
1070
1084
ioso
1041
35
3/0
7/0
2H
IK
0.5
1.43
14
16
18
20
22
24
26
14
16
18
20
22
24
26
"82i
826
830
835
839
844
830
837
843
850
856
863
869
846
854
863
872
881
890
899
866
877
888
900
912
923
935
887
901
916
930
945
960
975
1072
1089
1107
1125
1142
1160
1178
911
929
947
965
983
1000
1018
1100
1122
1144
1166
1188
1209
1231
1673
1087,
1101
1115
1129
::::
|
i075
1086
169
COLUMNS
TABLE 42
ROUND CORED HOOPED COLUMNS
SAFE LOAD IN THOUSANDS OF POUNDS
CHICAGO BUILDING CODE REQUIREMENTS
Column size .^i
P
1:1:2 mixture
n = 10
Af e (l+2.5np')[l+(n-l)p]
Spirals
Size of vertical round rods
Size
Diam-
t
of
eter
JN umber
of
column
(inches)
of core
(inches)
Size No.
(A. S. &
W. Co.)
Pitch
(inches)
Per cent
of core
j
OI
rods
H
!
2i
H
1
IH
IX
39
36
4/0
2H
0.5
16
866
882
901
922
947
974
I 18
871
888
910
934
961
992
20
875
895
919
945
976
1010
22
880
901
928
957
991
1028
24
884
908
936
969
1005
1046
26
889
914
945
980
1020
1064
28
893
920
954
992
1034
1082
7/0 iy 2
1.40
16
1133
1167
18
1151
1188
20
ii32
1168
1210
22
1146
1186
1232
24
ii2i
1159
1204
1254
26
1131
1173
1221
1275
28
1141
1187
1239
1297
40
37
4/0
2H
0.5 16
929
948
968
993
1021
18
'6i8
935
956
980
1008
1039
20
922
942
965
991
1023
1057
22
927
948
974
1003
1037
1075
24
931
955
983
1015
1052
1093
26
936
961
991
1026
1066
1111
28
940
967
1000
1038
1081
1129
7/0
1>2
1.36 16
1183
1216
18
1201
1237
20
1181
1219
1259
22
1195
1236
1280
24
1209
1253
1302
26
iisi
1223
1271
1323
28 |
1191
1237
1289
1345
41
38
4/0
2^ 0.5 16
978
996
1017
1041
1069
18
984
1005
1029
1056
1087
20
97i
991
1013
1040
1071
1105
22
976
997
1022
1052
1086
1123
24
980
1004
1031
1063
1100
1141
26
985
1010
1040
1075
1115
1159
1
28
989
1016
1049
1086
1130
1177
30
994
1022
1058
1098
1144
1196
7/0
ll
1.32
16
1232
1264
* 7z
18
1249
1285
20
1230
1266
1306
22
1244
1284
1328
24
1257
1301
1350
26
1230
1271
1318
1371
28
.
1240
1285
1336
1393
30
1251
1298
1353
1415
170
TABLE 42
Column size
COLUMNS
ROUND CORED HOOPED COLUMNS
SAFE LOAD IN THOUSANDS OF POUNDS
CHICAGO BUILDING CODE REQUIREMENTS
19
12
.f-.
\diameter
1:1:2 mixture
n = 10
f e =725
Size
of
column
(inches)
Diam- i
eter
of core
(inches)
Spirals
Number
of
rods
Size of vertical round rods
Size No.
(A. S. &
W. Co.)
Pitch
(inches)
Per cent j
of core !
X
H
H
1
IH
I
42
39
4/0
7/0
2H
1H
0.5
1.29
16
18
20
22
24
26
28
30
16
18
20
22
24
26
28
30
1620
1025
1029
1034
1038
1042
1027
1033
1040
1046
1053
1059
1065
1072
1045
1054
1063
1071
1080
1089
1098
1107
1067
1078
1090
1101
1112
1124
1136
1147
1091
1106
1120
1135
1149
1163
1178
1193
1283
1300
1317
1334
1351
1368
1386
1403
1118
1136
1154
1172
1190
1208
1226
1244
1315
1336
1357
1378
1399
1420
1441
1463
1281
1294
1308
1321
1335
1349
'.'.'.'.
i
1280
1290
1300
43
40
4/0
7/0
2H
1H
0.5
,.
16
18
^0
22
24
26
28
30
16
18
20
22
24
26
28
30
i073
1078
1083
1088
1092
1
1077
1083
1090
1096
1103
1109
1116
1122
1096
1104
1113
1122
1131
1140
1149
1158
1117
1129
1140
1152
1163
1175
1186
1198
1142
1156
1171
1186
1200
1215
1229
1244
1333
1350
1367
1385
1402
1419
1436
1453
1169
1187
1205
1223
1241
1259
1277
1295
1366
1387
1408
1429
1450
1471
1492
1513
1332
1345
1359
1372
1386
1400
i
1340
1350
171
COLUMNS
TABLE 43
71=15
f c =800
ROUND CORED HOOPED COLUMNS
SAFE LOAD IN THOUSANDS OF POUNDS
LOS ANGELES AND MILWAUKEE BUILDING
CODE REQUIREMENTS
P=Af c [l+(n-l)p]
Cotumn size
Size
of
column
(inches)
Diameter
of
core
(inches)
Number
of
rods
Square rods
Round rods
IK
1M
H
H
|
H 1
IK
134
H
H
H
1
10
7
6
*57.0
*51.4
*60.5
11
8
6
*66.4
*78 . . .
60.8
*69.9
c
*7* 2;
*67.7
*79.8
12
9
6 77.1
71.5
8
'
78.4
13 10
6 j 89
83 4
92.5
8 j 97.8
90.3
14
11
6 102 2
1138
96.6
105.7
116.4
8 1111.
103.5
115.6
10
110.4
15
12 6
116.7
128.3
111.1
120.2
130.9
8
125.5
140.9
118.0
130.1
10
134 3
124.9
140.0
10
13 6
132.4
144.0
157.6
126.8
135.9
146.6
159.0
8
141.2
156.6
133.7
145.8
160.1
10
150.0
140.6
155.7
17
14 6
8
149.3
158.1
160.9 174.5
173.5 191.7
190.3
143.7
150.6
152.8
162.7
163.5
177.0
175.9
189.9
10
166.9
186.1 i ,
157.5 172.6
190.4
12
175.6
164.3
182.5
18
15 6
167.6
179.2
192.8
208. G !
162.0171.0
181.8
194.2
. 8
176.4
191.8
210.0
168.9 181.0
195.3
211.8
10
185.2
204.4
175.8
190.9
208.7
12
193.9
217.0
182.6
200.8
19 10 8
195.9
211.3
229.5
250.5
188.4
200.5
214.8
231.3'250.0
10
204.7
223.9
246.6
195.3
210.4
228.2
248.9
12
213.4
236.5
202.1
220.3
241.7
14
222.2
249.1
209.0
230.2
20 17
8
216.6
232.0
250.2
271.2 ..
209.1
221.2235.5
252.0270.7
10
225.4
244.6
267.3)
216.0
231.1 248.9
269.6,
12
234.1
257.2
...... 1
222.8
241.0 262.4
14
242.9
269.8
229.7
250.9
275.9
I
21 18
8
238.6
254.0
272.2
293.2'317.0
243.2
257.5
274.0292.7
313.5
10
247.4
266.6
289.3
315. 6j
238 '. 6
253.1
270.9
291.6314.9
12
256.1
279.2
306.5
244.8
263.0 984 4
309.2
14
264.9
291.8
251.7
272.9
297.9
22 19
8
261.8
277.2
295.4
316.4340.2
266.4
280.7
297.2315.9
336.7
10
270.6
289.8
312.5
338.8 ..-.[.I
26i!2
276.3
294.1
314.8338.1
12
279.3
302.4
329.7
1
268.0
286.2
307.6
332.4
14
16
288.1
296.8
315.0
327.6
346 8
274.9
281.8
296.1
306.0
321.1
334.6
350.0
23
20
8
10
286.4
295.2
301.8320.0341.0364.8
314.41337.1 363.4393.1
391.4
291.0
300.9
305.3
318.7
321.8340.5361.3
339.4362.7388.8
12 303.9
327. 0354.31 385. 8
262! 6
310.8
332.2
357.0 385. Oj
14 312.7
16 321.4
339.6
352.2
371.4
388.6
299.5
306.4
320.7(345.7
330.6359.2
374.6
392.1
These columns contain more than 4 % of steel.
172
TABLE 43
COLUMNS
i^ Column size ^
ROUND CORED HOOPED COLUMNS
SAFE LOAD IN THOUSANDS OF POUNDS
LOS ANGELES AND MILWAUKEE BUILDING
CODE REQUIREMENTS
= 15
\ \
1/4^^-?^ i k
**&&
oUU
Size
of
column
(inches)
Diameter
of
core
(inches)
Number
of
rods
Square rods
Round rods
H
H
M
1
IK
IK
.*
H
M
1
IK
IX
24
25
26
27
28
29
30
31
32
33
21
22
23
24
25
26
27
28
29
30
10
12
14
16
10
12
14
16
18
10
12
14
16
18
10
If
16
18
10
12
14
16
18
20
12
14
16
18
20
12
14
16
18
20
22
12
14
16
18
20
22
12
14
16
18
20
22
12
14
16
18
20
22
24
320.9
329.6
338.4
347.1
347.9
356.6
365.4
374.1
382.9
340.1
352.7
365.3
377.9
367.1
379.7
392.3
404.9
417.5
395.4
408.0
420.6
433.2
445.8
424.9
437.5
450.1
462.7
475.3
455.7
468.3
480.9
493 . 5
506.1
518.7
500.3
512.9
525.5
538.1
550.7
533.7
362.8
380.0
397.1
414.3
389.8
407.0
424.1
441.3
458.4
418.1
435.3
452.4
469.6
486.7
447.6
464.8
481.9
499.1
516.2
478.4
495.6
512.7
529.9
547.0
564.2
527.6
544.7
561.9
579.0
596.2
561 .
389.1
411.5
418.8
318.3
325.2
332.1
326.6
336.5
346.4
356.3
353.6
363.5
373.4
383.3
393.2
381.9
391.8
401.7
411.6
421.5
42i!3
431.2
441.1
451.0
344.4
357.9
371.4
384.9
371.4
384.9
398.4
411.9
425.3
399.7
413.2
426.7
440.2
453.6
429.2
442.7
456.2
469.7
483.1
460.0
473.5
487.0
500.5
513.9
527.4
505.5
519.0
532.5
545.9
559.4
538.9
552.4
565.9
579.3
592.8
606.3
573.4
586.9
600.4
613.8
627.3
640.8
609.2
622.7
636.2
649.6
663.1
676.6
646.3
659.8
673.3
686.7
700.2
713.7
727.1
265.1
382.7
400.3
417.8
392.1
409.7
427.3
444.8
462.4
420.4
438.0
455.6
473.1
490.7
449.9
467.5
485.1
502.6
520.2
480.7
498.3
515.9
533 . 4
551.0
568.6
530.3
547.9
565.4
583.0
600.6
563.7
581.3
598.8
616.4
634.0
651.6
598.2
615.8
633.3
650.9
668.5
686.1
634.0
651.6
669.1
686.7
704.3
721.9
671.1
688.7
706.2
723.8
741.4
759.0
776.6
388.4
410.7
415.4
437.7
460.0
443.7
466.0
488.3
510.5
473 . 2
495.5
517.8
540.0
562.3
504.0
526.3
548.6
570.8
593.1
558.3
580.6
602.8
625.1
647.4
591.7
614.0
636.2
658.5
680.8
703.0
626.2
648.5
670.7
693.0
715.3
737.5
662.0
684.3
706.5
728.8
751.1
773.3
699.1
721.4
743.6
765.9
788.2
810.4
832.7
414.5
441.5
469.0
469.8
497.3
499.3
526.8
554.3
530.1
557.6
585.1
612.6
589.6
617.1
644.6
623.0
650.5
678.0
705.5
657.5
685.0
712.5
740.0
767.4
693.3
720.8
748.3
775.8
803.2
730.4
757.9
785.4
812.9
840.3
867.8
416.1
438.5
460.9
445.8
474.2
507.4
352.2
359.1
366.0
444.4
466.8
489.2
511.6
473.9
496.3
518.7
541.1
563.5
504.7
527.1
549.5
571.9
594.3
559.1
581.5
603.9
626.3
648.7
592.5
474.1
502.5
503.6
532.0
560.3
536.9
534.4
562.8
591.1
567.7
602.7
452.1
462.0
471.9
481.8
491.7
484.1
494.0
503.9
513.8
523.7
594.8
623.1
651.5
628.2
634.7
668. 1
:::::
546.3578.1
558.9595.3
571.5612.4
584.1J629.6
596.7i646.7
568.2595.5
580.8612.6
593.4629.8
606.0;646.9
618.6664.1
631.2 681.2
604.0631.3
616.6 648.4
614.9
637.3
659.7
682.1
704.5
627.0
649.4
671.8
694.2
716.6
739.0
662.8
685.2
656.5
684.9
713.2
703.1
527.4
537.3
547.2
557.1
567.0
561 .9
571.8
581.7
591.6
601.5
:::::
662.7
691.0
719.4
747.7
698.5
726.8
702.6
737.6
738.4
773.4
! '.'.'.
: : : : :
629.2
641.8
654.4
667.0
665.6
682.7
699.9
717.0
66S 4
707.6
730.0
752.4
774.8
699.9
755.2
783.5
811.9
735.6
808.4
607.6
617.5
627.4
637.3
775.5
g
653.7685.5
666.3702.7
678.91719.8
691.51 737.0
704.1 754.1
716.7771.3
722.3
744.7
767.1
789.5
811.9
834.3
763.9
792.3
820.6
849.0
877.3
810.5
845.5
880.5
644.7
654.6
664.5
674.4
684.3
173
COLUMNS
TABLE 43
SAFE LOAD IN THOUSANDS OF POUNDS
LOS ANGELES AND MILWAUKEE BUILDING
CODE REQUIREMENTS
f c =800
jgaa*
IP I
Size
of
column
(inches)
Diameter Number
of of
(inches) rod8
!
Square rods
Round rods
M
H
K
1
IK
I*
M
K
H
1
1M
1M
34
35
36
37
38
3!)
40
41
31 14
16
18
20
22
24
32 14
16
18
20
22
24
33 14
16
18
20
22
24
26
34 14
16
18
20
22
24
26
35 14
16
18
i 20
22
24
26
36 16
18
20
; 22
24
26
28
37 16
18
20
22
24
26
28
38 16
18
! 20
22
24
26
28
30
:::::
692.0
704.6
717.2
729.8
742.4
755.0
723.8
741.0
758.1
775.3
792.4
809.6
763.4
780.6
797.7
814.9
832.0
849.2
804.2
760.6
783.0
805.4
827.8
850.2
872.6
800.2
822.6
845.0
867.4
889.8
912.2
841.0
802.2
830.6
858.9
887.3
915.6
848.8
883.8
918.8
692! 9
702.8
712.7
722.6
698.1
711.6
725.0
738.5
752.0
765.4
737.7
751.2
764.6
778.1
791.6
805.0
727.0
744.5
762.1
779.7
797.3
814.9
766.6
784.1
801.7
819.3
836.9
854.5
807.4
824.9
842.5
860.1
877.7
895.3
912.9
849.5
867.0
884.6
902.2
919.8
937.4
955.0
892.9
910.4
928.0
945.6
963.2
980.8
998.4
955.0
972.6
990.2
1008
1025
1043
1061
1001
1019
1036
1054
1071
1089
1107
1048
1066
1083
1101
1118
1136
1154
1171
759.7
781.9
804.2
826.5
848.7
871.0
799.3
821.5
843.8
866.1
888.3
920.6
840.1
862.3
884.6
906.9
929.1
951.4
973.7
882.2
904.4
926.7
949.0
971.2
993.5
1016
925.6
947.8
970.1
992.4
1015
1037
1059
992.4
1015
1037
1059
1082
1104
1126
1038
1061
1083
1105
1127
1150
1172
1085
1108
1130
1152
1175
1197
1219
1241
796.2
823.7
851.2
878.6
906.1
933.6
835.8
863.3
890.8
918.2
945.7
973.2
876.6
904.1
931.6
959.0
986.5
1014
1041
918.7
946.2
973.7
1001
1029
1056
1084
962.1
989.6
1017
1045
1072
1100
1127
1034
1062
1089
1117
1144
1172
1199
1080
1108
1135
1163
1190
1218
1245
1127
1155
1182
1210
1237
1265
1292
1320
841.8
870.2
898.5
926.9
955.2
983.6
882.6
888.4
923.4
958 4
993.4
929.2
821.4
838.5
855.7
872.8
890.0
907.1
846.3
863.5
880.6
897.8
914.9
932.1
949.2
889.7
906.9
924.0
941.2
958.3
975.5
992.6
951.5
968.6
985.8
1003
1020
1037
1054
997.4
1015
1032
1049
1066
1083
1100
1045
1062
1079
1096
1113
1130
1147
1165
863.4
885.8
908.2
930.6
953.0
975.4
883.1
905.5
927.9
950.3
972.7
995.1
1018
926.5
948.9
971.3
993.7
1016
1039
1061
993.5
1016
1038
1061
1083
1106
1128
1039
1062
1084
1107
1129
1151
1174
1087
1109
1131
1154
1176
1199
1221
1243
911.0
939.3
967.7
996.0
1024
1053
924.7
953.1
981.4
1010
1038
1067
1095
968.1
996.5
1025
1053
1082
1110
1138
1041
1069
1098
1126
1155
1183
1211
1087
1115
1144
1172
1200
1229
1257
1134
1162
1191
1219
1248
1276
1304
1333
964.2
999.2
1034
971.3
1006
1041
1076
1111
792.0
805.4
818.9
832.4
845.8
859.3
834 !i
847.5
861.0
874.5
887.9
901.4
877 '.5
890.9
904.4
917.9
931.3
944.8
1015
1050
1085
1120
1155
1190
1094
1129
1164
1199
1234
1269
1140
1175
1210
1245
1280
1315
935.5
949.0
962.5
975.9
989.4
1003
981.4
994.9
1008
1022
1035
1049
1187
1222
1257
1292
1327
1362
1397
1042
1056
1069
1082
1096
1109
174
TABLE 43
COLUMNS
ROUND CORED HOOPED COLUMNS
-srr^
SAFE LOAD IN THOUSANDS OF POUNDS
LOS ANGELES AND MILWAUKEE BUILDING
CODE REQUIREMENTS
P = Af e [l + (n-l)p] ?
fc
= 15
snn
IP
^^j&r
ouv
Size
of
column
(inches)
Diameter
of
core
(inches)
Number
of
rods
Square rods
Round rods
H
H
H
1
IK
IK
H
H
H ' i
m
lA
42
43
44
45
46
47
48
49
39
40
41
42
43
44
45
46
16
18
20
22
24
26
28
30
16
18
20
22
24
26
1093
1110
1127
1144
1162
1179
1196
1213
1135
1157
1180
1202
1225
1247
1269
1292
1185
1207
1229
1252
1274
1297
1319
1341
1258
1280
1303
1325
1347
1370
1392
1310
1332
1355
1377
1400
1422
1444
1363
1386
1408
1431
1453
1475
1498
1418
1440
1463
1485
1508
1530
1552
1474
1496
1519
1541
1563
1586
1608
1554
1576
1598
1621
1643
1666
1183
1211
1239
1268
1296
1324
1353
1381
1232
1260
1289
1317
1346
1374
1402
1431
1311
1340
1368
1396
1425
1453
1481
1363
1392
1420
1449
1477
1505
1534
1417
1445
1474
1502
1530
1559
1587
1472
1500
1528
1557
1585
1613
1642
1527
1556
1584
1613
1641
1669
1698
1613
1641
1670
1698
1726
1755
1236
1271
1306
1341
1376
1411
1446
1481
1285
1320
1355
1390
1425
1460
1495
1530
1371
1406
1441
1476
1511
1546
1581
1423
1458
1493
1528
1563
1598
1633
1477
1512
1547
1582
1617
1652
1687
1531
1566
1601
1636
1671
1706
1741
1587
1622
1657
1692
1727
1762
1797
1680
1715
1750
1785
1820
1855
I
1096
1114
1132
1149
1167
1184
1202
1220
1146
1164
1181
1199
1216
1234
1252
1269
1215
1232
1250
1267
1285
1303
1320
1267
1284
1302
1319
1337
1355
1372
1134
1156
1178
1201
1223
1245
1267
1290
1183
1206
1228
1250
1273
1295
1317
1339
1257
1279
1301
1323
1346
1368
1390
1309
1331
1353
1376
1398
1420
1442
1362
1385
1407
1429
1451
1474
1496
1417
1439
1461
1484
1506
1528
1550
1473
1495
1517
1540
1562
1584
1606
1552
1574
1597
1619
1641
1664
1176
1203
1231
1258
1286
1313
1341
1368
1225
1253
1280
1308
1335
1363
1390
1418
1304
1331
1359
1386
1414
1441
1469
1356
1383
1411
1438
1466
1493
1521
1409
1437
1464
1492
1519
1547
1574
1464
1491
1519
1546
1574
1601
1629
1520
1547
1575
1602
1630
1657
1685
1604
1632
1659
1687
1714
1742
'
1104
1117
1131
1144
1158
1160
1177
1194
1211
1228
1245
1262
1211
1228
1245
1262
1279
1296
1313
1154
1167
1180
1194
1207
28
30
18
20
22
24
26
28
30
18
20
22
24
26
28
30
18
20
22
24
26
28
30
18
20
22
24
26
28
30
18
20
22
24
26
28
30
20
22
24
26
28
30
.....
1204
1218
1231
1245
1258
-
1280
1297
1314
1331
1348
1366
'i270
1283
1297
1310
|
:::!
:::.
1333
1350
1368
1385
1402
1419
:::::;::::
'i337
1351
1364
1338
1355
1373
1391
1408
1426
1388
1405
1422
1439
1457
1474
1392
1410
1428
1445
1463
1480
1392
1405
1418
1461
1478
1495
1512
1530
1466
1483
1501
1519
1536
::::: :::::
1461
1474
i
1518
1535
1552
1570
1587
1523
1541
1558
1576
1593
1518
1532
175
COLUMNS
TABLE
AREAS AND WEIGHTS OF COLUMN RODS
Number of rods
Area of column rods
Number of rods
Weight of column rods per linear foot
Size of rods
Size of rods
H
H
M
1
IK
IH
H
K
H
1
IH
i*
4
1.56
2.25
3.06
4.00
5.06
6.25
4
5.313
7.650
10.41
13.60
17.21
21.25
6
2.34
3.38
4.59
6.00
7.59
9.38
6
7.969
11.48
15.62
20.40
25.82
31.88
8
3.13
4.50
6.12
8.00
10.1
12.5
8
10.63
15.30
20.82
27.20
34.42
42.50
10
3.91
5.63
7.66
10.0
12.7
15.6
10
13.28
19.13
26.03
34.00
43.03
53.13
1
12
14
4.69
5.47
6.75
7.88
9.19
10.7
12.0
14.0
15.2
17.7
18.8
21.9
12
14
15.94
18.59
22.95
26.78
31.24
36.44
40.80
47.60
51.64
60.24
63.75
74.28
16
6.25
9.00
12.2
16.0
20.2
25.0
16
21.25
30.60
41.65
54 . 40
68.85
85.00
1
18
20
7.03
7.81
10.1
11.3
13.8
15.3
18.0
20.0
22.8
25.3
28.1
31.3
18
20
23.91
26.56
34.43
38.25
46.85
52.06
61.20
68.00
77.45
86.06
95.63
106.3
22
8.59
12.4
16.8
22.0
27.8
34.4
22
29.22
42.08
57.27
74.80
94.67
116.9
24
9.38
13.5
18.4
24.0
30.4
37.5
24
31.88
45.90
62 47
81.60
103.3
127.5
26
10.2
14.6
19.9
26.0
32.9
40.6
26
34.53
49.73
67.68
88.40
111.9
138.1
28
10.9
15.8
21 .4
28.0
35.4
43.8
28
37.19
53 . 55
72.89
95.20
120.5
148.8
30
11.7
16.9
23.0
30.0
38.0
46.9
30
39.84
57.38
78.09
102.0
129.1
159.4
4
1.23
1.77
2.41
3.14
3.98
4.91
4
4.172
6.008
8.178
10.68
13.52
16.09
6
1.84
2.65
3.61
4.71
5.96
7.36
6
6.259
9.013
12.27
16.02
20.28
25.03
8
2.45
3.53
4.81
6.28
7.95
9.82
8
8.345
12.02
16.36
21.36
27.04
33.37
10
3.07
4.42
6.01
7.85
9.94
12.3
10
10.43
15.02
20.44
26.70
33.80
41.72
12
3.68
5.30
7.22
9.42
11.9
14.7
12
12.52
18.03
24.53
32.04
40.56
50.06
14
4.30
6.19
8.42
11.0
13.9
17.2
14
14.60
21.03
28.62
37.39
47.31
58.41
16
4.91
7.07
9.62
12.6
15.9
19.6
16
16.69
24.03
32.71
42.73
54.07
66 . 75
c
18
5.52
7.95
10.8
14.1
17.9
22.1
18
18.78
27.04
36.80
48.07
60.83
75 09
o
tf
20
6.14
8.84
12.0
15.7
19.9
24.5
20
20.86
30.04
40.89
53.41
67.59
83.44
22
6.75
9.72
13.2
17.3
21.9
27.0
22
22.95
33.05
44.98
58.75
74.35
91.78
24
7.36
10.6
14.4
18.8
23.9
29.4
24
25.03
36.05
49 07
64.09
81.11
100.1
26
7.98
11.5
15.6
20.4
25.8
31.9
26
27.12
39.06
53.15
69.43
87.87
108.5
28
8.59
12.4
16.8
22.0
27.8
34.4
28
29.21
42.06
57.24
74.77
94.63
116.8
30
9.20
13.3
18.0
23.6
29.8
36.8
30
31.29
45.06
61.33
80.11
110.4
125.2
176
TABLE 45
COLUMNS
AREA, VOLUME, WEIGHT AND PERIMETER
OF
SQUARE, ROUND AND OCTAGONAL COLUMNS
Square columns
Round columns
Octagonal columns
Diam-
eter of
Area
Volume
Weight
Perim-
Area
Volume
Weight
Perim-
Volume
Weight
Perim-
(sq.
(c. f.
(Ib.
eter
(sq.
(c.f.
(Ib.
eter
(c.f.
(Ib.
eter
in.)
per ft.)
per ft.)
(ft.)
in.)
per ft.)
per ft.)
(ft.)
per ft.)
per ft.)
(ft.)
10
100
0.69
104
3.3
78.54
0.55
82
2.62
0.58
86
2.76
11
121
0.84
126
3.7
95.03
0.66
99
2.88
0.70
104
3.14
12
144
1.00
150
4.0
113.1
0.79
118
3.14
0.83
124
3.31
13
169
1.17
175
4.3
132.7
0.92
138
3.40
0.97
146
3.57
14
196
1.36
204
4.7
153.9
1.07
160
3.66
1.13
169
3.87
15
225
1.56
234
5.0
176.7
1.23
184
3.93
1.29
194
4.14
16
256
1.78
267
5.3
201.1
1.40
209
4.18
1.47
221
4.42
17
289
2.01
302
5.7
227.0
1.58
236
4.45
1.66
249
4.70
18 324
2.25
338
6.0
254.5
1.77
265
4.71
1.86
280
4.97
19 361
2.51
377
6.3
283.5
1.97
295
4.97
2.08
312
5.25
20
400
2.78
417
6.7
314.2
2.18
327
5.23
2.30
345
5.52
21
441
3.06
459
7.0
346.4
2.41
361
5.50
2.54
381
5.80
22
484
3.36
504
7.3
380.1
2.64
396
5.76
2.78
418
6.08
2.3 529
3.68
552
7.7
415.5
2.89
433
6.02
3.04
457
6.35
24 ! 576
4.00
600
8.0
452.4
3.14
471
6.28
3.31
497
6.63
2.~> 025
4.34
651.
8.3
490.9
3.41
511
6.55
3.60
539
6.90
2(i 676
4.69
704_
8.7
530.9
3.69
553
6.81
3.89
583
7.18
27
729
5.06
758
9.0
572.6
3.98
596
7.07
4.19
629
7.45
28
784
5.44
816
9.3
615.8
4.28
641
7.33
4.51
677
7.73
29
841
5.84
877
9.7
660.5
4.59
688
7.58
4.84
726
8.01
30
900
6.25
938
10.0
706.9
4.91
736
7.86
5.18
777
8.29
31
961
6.67
1000
10.3 ! 754.8
5.24
786
8.12
5.53
829
6.56
32
1024
7.12
1067
10.7 804.2
5.58
838
.8.38
5.89
884
8.84
33
1089
7.56
1134
11.0 855.3
5.94
891
8.64
6.27
940
9.11
34
1156
8.02
1203
11.3 1 907.9
6.30
946
8.89
6.55
983
9.39
35
1225
8.50
1275
11.7 I 962.1
6.68
1002
9.16
7.05
1057
9.67
36
1296
9.00
1350
12.0
1018
7.07
1060
9.42
7.46
1118
9.94
37
1369
9.50
1425
12.3
1075
7.47
1120
9.68
7.88
1181
10.22
38
1444
10.03
1505
12.7
1134
7.88
1181
9.95
8.31
1246
10.50
39 1521
10.57
1586
13.0
1195
8.30
1244
10.21
8.75
1313
10.78
40 1600
11*11
1666
13.3
1257
8.73
1309
10.47
9.21
1381
11.05
41 1681
11.68
1753
13.7
1320
9.17
1375
10.72
9.67
1451
11.33
42 1764
12.25
1839
14.0
1385
9.62
1443
10.99
10.15
1522
11.60
43 1849
12.84
1926
14.3
1452
10.08
1513
11.26
10.64
1596
11 88
44 1936
13.45
2020
14.7
1520
10.56
1584
11.52
11.14
1671 j 12.17
45 2025
14.06
2110
15.0
1590
11.04
1657
11.79 11.65
1748 12.43
46 2116
14.69
2202
15.3
1662
11.54
1731
12.04 ! 12.17 : 1826
12.70
47 ; 2209
15.34
2300
15.7
1735
12.05
1807
12.31 I 12.71
1906
12.98
48
2304
16.01
2400
16.0
1810
12.57
1885
12.57 j 13.26
1988
13.26
49
2401
16.68
2502
16.3
1886
13.10
1964
12.83 j 13.81
2072
13.53
50
2500
17.36
2604
16.7
1964
13.64
2045
13.10 1 14.38
2158
13.81
j
177
COLUMNS
TABLE 46
COLUMN SPIRALS
PERCENTAGE OF VOLUME OF CORE
AND
WEIGHT IN POUNDS PER FOOT OF COLUMN
HEAVY TYPE GIVES PERCENTAGES WEIGHTS DO NOT INCLUDE SPACERS
LIGHT TYPE GIVES WEIGHTS WIRE SIZES ARE A. S. & W. CO. GAGE
o
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CD
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o
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re
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en oo
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d
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g
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178
TABLE 46
COLUMNS
COLUMN SPIRALS
PERCENTAGE OF VOLUME OF CORE
AND
WEIGHT IN POUNDS PER FOOT OF COLUMN
HEAVY TYPE GIVES PERCENTAGES
LIGHT TYPE GIVES WEIGHTS
WEIGHTS DO NOT INCLUDE SPACERS
WIRE SIZES ARE A. S. & W. CO. GAGE
179
COLUMNS
TABLE 46
COLUMN SPIRALS
PERCENTAGE OF VOLUME OF CORE
AND
WEIGHT IN POUNDS PER FOOT OF COLUMN
HEAVY
LIGHT
TYPE
TYPE
GIVES PERCENTAGES
GIVES WEIGHTS
WEIGHTS DO NOT INCLUDE SPACERS
WIRE SIZES ARE A. S. & W. CO. GAGE
i
1C
d
I
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CO
rH
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TH
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d
00
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d
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c
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X -v t v^v, S5 * ^-v.
P^\ COS. r-\
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84 04 e
h 15
Q <"=
CN
co
S
180
TABLE 46
COLUMNS
COLUMN SPIRALS
PERCENTAGE OF VOLUME OF CORE
AND
WEIGHT IN POUNDS PER FOOT OF COLUMN
HEAVY TYPE GIVES PERCENTAGES
LIGHT TYPE GIVES WEIGHTS
WEIGHTS DO NOT INCLUDE SPACERS
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TABLE 46
COLUMN SPIRALS
PERCENTAGE OF VOLUME OF CORE
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TABLE 46
COLUMNS
COLUMN SPIRALS
PERCENTAGE OF VOLUME OF CORE
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TABLE 46
COLUMN SPIRALS
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TABLE 46
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PERCENTAGE OF VOLUME OF CORE
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TABLE 46
COLUMNS
COLUMN SPIRALS
PERCENTAGE OF VOLUME OF CORE
AND
WEIGHT IN POUNDS PER FOOT OF COLUMN
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COLUMNS
TABLE 46
COLUMN SPIRALS
PERCENTAGE OF VOLUME OF CORE
AND
WEIGHT IN POUNDS PER FOOT OF COLUMN
HEAVY TYPE
LIGHT TYPE
GIVES PERCENTAGES
GIVES WEIGHTS
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TABLE 46
COLUMNS
COLUMN SPIRALS
PERCENTAGE OF VOLUME OF CORE
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COLUMNS
TABLE 46
COLUMN SPIRALS
PERCENTAGE OF VOLUME OF CORE
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CO CM CM CM
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: : : : eL^ : : : :
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1
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iO <M
CM IM
d d
i : : : : is : : : : ':
S5
o d
t^
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CO
d
d
::::::
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d :
: : : : : g ::::::
o
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00
co
i
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1
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d
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d
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s
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d
d
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=#=
d
d
(inches).
.9
Mi
NN V* V* \M N^l
rH rH CM IM IN (N CO
\N V*
TH TH
MCq N eO rHrHCMlMlMCMCO
TH TH
i-K iH\
<N M
N CO
I
Diameter
d*
a"o SB
b
"
^
5
192
TABLE 46
COLUMNS
COLUMN SPIRALS
PERCENTAGE OF VOLUME OF CORE
AND
WEIGHT IN POUNDS PER FOOT OF COLUMN
HEAVY TYPE GIVES PERCENTAGES
LIGHT TYPE GIVES WEIGHTS
WEIGHTS DO NOT INCLUDE SPACERS
WIRE SIZES ARE A. S. & W. CO. GAGE
-1< **" CO O OS CM CM
CO 00 IN I-H OS O 00
DenPl>ScOOO -4<Tt<OOCOCOOSCM
H 00 t- fl 10 OOlNOOOCOlO
oo t- 10 o eo IH o
co>u3M3ooeq<o * * eo o i> o d
TH <J> 00 t- 10 t(NCOCSCOrHCM
w (O <o n a> oo t-
sssssss
T-H CM CO I-H O CO O
co o * * co eo co
rHOOOOOO CO^t-CMb.^.-;
O "O "^ "^ CO CO CO
^OOOOOO SS^^c^c^S
^OOOOOO
O rft O O CM O O
CM > rjt T}< 10 CM CO
S2S3SSS ^os^cocsc^
^HOOOt-0eiO iCOO^COCOOCM
OD O CD <O (O fc
SSSSSS S^S2SS
isisiill
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lO O ^ CO CO CO CM
iHOOOOOO O^-iiOOCOCOO
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10 o eo o o co <N
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g^sssste
0) 00 f O 10 M9 M
CM 10 OS >O ^H 00 CO
1C ^ CO CO CM CM
o o o d o o p co co cs 10 CM cs =0
I 10 ^ ^ co co c^ Ic^i
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d d d d d d d
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Sto to e> n to vr r: t^- i" ri
t>oioie^i cMcoi-i^iosco
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t- vo 10 10 TH . eocMCsooioos
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cSScSSS : :
o o ojd o . o eo c^ o co . .
O oo_oo - : j*_g : ;
0000
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SS3 : : : : ^5 : : : :
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SS3 : : : : S2 : : : :
t- 00 O - . .
SS5 : : : :
Tf OS CO
CO <N (N kM
000 : : : : SSS : : : :
000 : : : : S : : : :
000
- 1 ....
10 on ....
5 5 : : : : : : : :
s s s
ro t5 K
523:-::2co::::
10 ^i - 00 T}( -
10 W
IN 1-- I^Jt
CO W Iri
: : : : co .CM : : : :
O O O CO OS iO
000
b rrn
16 : : : i : Si : : : : ':
Is ; ; : ; ; sss ; i \]
00 00
O KO ....
"ip : : : : : .8 : : : : :
00- 00 * .
S ::::::
3 :::::: S ::::::
a ::::::
- ' N '
* ^^^
XX* S 3JS
s xx ssr xsx
^ y v* >i \*
3
s
'
193
COLUMNS
TABLE 46
COLUMN SPIRALS
PERCENTAGE OF VOLUME OF CORE
AND
WEIGHT IN POUNDS PER FOOT OF COLUMN
HEAVY TYPE GIVES PERCENTAGES
LIGHT TYPE GIVES WEIGHTS
WEIGHTS DO NOT INCLUDE SPACERS
WIRE SIZES ARE A. S. & W. CO. GAGE
X
o
o
d
o
iO * O5 O ^H (N CN
00 * CO O5 IO O5 O5
10 d 05 CO 05 10 <N
TH (0 00 00 10 (0 <0
OCOTHMieO)"* O^-^CO1OOO<N
00 t- 10 10 (NCOr^OOCOcOCO
TH d d d d d d i> t>.' o * d co co
g
o
d
d
CO O <N CO ** O5 1-1
<N CN ** rH O5 -sJH CO
CO Tt< b- IN l> * i-H
t> 00 to 00 O> TH TK 1 1
WO>COO>t-NOO>OCOiOrt<INO5
OOOt-tOOlOIOiOCO^O!>(N(N
TH O O O O O O \ ^ iO CO Co' 00 10 (N
1 co 10 ^ * co co ro 1
\
10
CO
CO
00 1> O5 CO O Tf<
O O CO CO CO O
O t- b* O CO t> JIO
eoo>0>o4iooto 00 o o OJ rH K*
O>t(O(OIOIOMI (Ni-iO5T-ICO(NCO
o
d
10 rt< Tt< CO CO CO IN
, 1 iO Tt* TJH CO CO CO I<N
<D
IO
CO
o
10
O5 O O5 O5 Tf O5
CO <N t- iO (N ^
eOTHMIOOlO 5D iH O r-l 00 >
00 t- 1C US ^1 ^ TH ^ CO 00 JO
f\
d
d
O CO t>- CO O f
10 Tt< co co co N
OOOOOO i-H^OOTtHOOO
iO Tt< CO CO CO '(N
10
o
co
TH
d
I
d
00 00 CO 10 <N
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o
00
co
d
00
<N
d
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00 O CO (N
O IO O t-
rJH CO CO C^t
to o t- ITH ...
t- 00 O 10 TH 10 00 O
to IO IO Ml b- t^ IN IOO
6;
o
10
CO
8
d
SCO O5 ' ' ' '
t> h. . . . .
CO CO <N
41 to lo ....
THNO-.-.TtlCOoO....
toiok<-...oo^co-...
O O O t-(NOO
1 COCOtN-...
CO
CO
d
co
o
d
CO 05 ' ' '
TjJ 05 10
CO IN <N ....
eo TH
t-O> Tf<O5
^< COIN
O O iO d '. '. '. '. '.
co co
o
co
CO
d
d
CO IN
OO' Tji '. ' ' ' '
(N <N
:;;;;; ^
O 05
%0
CO
d
CO
O
d
p
o
co
00
co
&
o
o
51
o
CO
00
IN
d
O5
1
d
IN
(N
CO
<N
d
IO
o
d
^
o
iC
(N
d
05
o
CO
CO
IN
O
o
=*=
IN
(N
d
d
8
G
d
S ^^
i-H I-H CN (N IN <N CO
THTHC^CflC^NW i 1 tlNCNC^IC^CO
*0
Diameter
1
1
Q O ~
5
00
194
TABLE 47
COLUMNS
COLUMN SPIRALS
JOINT COMMITTEE RECOMMENDATIONS
Volume of spiral equal to 1% of volume of core
Maximum pitch = - or
6
m,
Diam. of core
(inches)
Am. S. & W. Co.'s gage Rod sizes
Size (No.)
Pitch (inches) Size (inches)
Pitch (inches)
8
6
IK
9
5
IK
10
4
IK
11
3
IN
X
m
12
2
i
H
IH
13
1
i
y*
IX
14
1
m
xt
2K
15
IK
Xs
2
16
2/0
2K
x*
IK
17
2/0
2
H
2K
18
3/0
2X
H
2H
19
3/0
2X
H
2K
20
3/0
2
H
2K
21
4/0
2X
H
2
22
4/0
2K
7 A*
2H
23
4/0
2H
K*
2%
24
4/0
2
7 A6
2H
25
5/0
2K
14s
2K
26
5/0
2K
^6
2y*
27
5/0
2K
H6
2K
28
5/0
2
He
2K
29
6/0
2K
Ke
2
30
6/0
2M
K 6
2
31
6/0
2^
H
2M
32
6/0
2
X
2H
33
7/0
2Yt
H
2H
34
7/0
2K
H
2K
35
7/0
2K
y*
2M
36 .
7/0
2
M
2H
37
7/0
2
x
2K
38
7/0
2
H
2
39
7/0
IK
y*
2
40
7/0
IK
y*
IK
41
7/0
IK
y*
IK
42
7/0
i
y*
IK
43
7/0
IX
H
iH
44
7/0
i%
H
m
45
7/0
1%
H
IK
46
7/0
i%
H
i
47
7/0
IK
H
i^
48
7/0
IK
H
i^
49
7/0
IK
H
IK
50
7/0
IH
X
IK
195
COLUMNS
TABLE 48
AMERICAN STEEL & WIRE CO.'S STEEL WIRE GAGE
Diameter
(inches)
Steel wire
gage
Diameter
(inches)
Area, square
inches
Pounds per
foot
Pounds per
mile
Feet per
pound
y>
. 5000
!
0.19635 0.6668
3,521.0
1.500
7/0
0.4900
0.18857 0.6404
3,381.0
1.562
%
0.46875
0.17257 0.5861
3,094.0
1.706
6/0
0.4615
0.16728 0.5681
2,999.0
1.760
He
0.4375
0.15033 0.5105
2,696.0
1.959
5/0
0.4305
0.14556
0.4943
2,610.0
2.023
13| 2
0.40625
0.12962
0.4402
2,324.0
2.272
4/0
0.3938
0.12180
0.4136
2,184.0
2.418
H
. 3750
0.11045
0.3751
1,980.0
2.666
3/0
0.3625
0.10321
0.3505
1,851.0
2.853
11,^2
0.34375
0.092806
0.3152
1,664.0
3.173
2/0
0.3310
0.086049 0.2922
1,543.0
3.422
Me
0.3125
0.076699
0.2605
1,375.0
3.839
. 3065
0.073782
0.2506
1,323.0
3.991
1
0.2830
0.062902
0.2136
1,128.0
4.681
%a
0.28125
0.062126
0.2110
1,114.0
4.74
2
0.2625
0.054119
0.1838
970.4
5.441
^
. 2500
0.049087
0.1667
880.2
5.999
3
0.2437
0.046645
. 1584
836.4
6.313
4
0.2253
0.039867
0.1354
714.8
7.386
3-32
0.21875
0.037583
0.1276
673.9
7.835
]
5
0.2070 0.033654
0.1143
603.4
8.750
6
0.1920 0.028953
0.09832
519.2'
10.17
He
0.1875 0.027612
0.09377
495.1
10.66
7
0.177( 0.024606
0.08356
441.2
11.97
8
0.162C
0.020612
0.07000
369.6
14.29
%2
0.15625
0.019175
0.06512
343.8
15.36
9
G.1483
0.017273
0.05866
309.7
17.05
10
0.1350
0.014314
0.04861
356.7
20.57
0.125
0.012272
0.04168
220.0
24.00
If
0.1205
0.011404
0.03873
204.5
25.82
12
0.1055
0.0087417
0.02969
156.7
33.69
Ma
0.09375
. 0069029
0.02344
123.8
42.66
13
0.0915
0.0065755
0.02233
117.9
44.78
14
0.0800
. 0050266
0.01707
90.13
58.58
15
0.0720
0.0040715
0.01383
73.01
72.32
16
0.0625
0.0030680
0.01042
55.01
95.98
17
0.0540
. 0022902
0.007778
41.07
128.60
196
JJ1AUKAM 42
WEIGHT OF TYPICAL SQUARE PANEL OF THREE-BE
FLOOR SYSTEM DESIGNED IN ACCORDANCE WITH J
RECOMMENDATIONS
(FOR ESTIMATING COLUMN LOADS
COLUMNS
AM-AND-GIRDER
OINT COMMITTEE
)
(0
10
/
/
/
t
/
f
/
/
j
/
j
f
j
J
j
j
1
j
1
f
j
j
f
1
f
^f
f
j
/
j
i
I
f
/
~f^
J
J
f
/
/
j
f
i
f
f
i
j
i
}
j
I
f
1
/
J
1
/
i
C
4-
CO
1
90
f
A
/
/
f
1
/
/
j
/
/
/
r
f
j
/
/
J
j
/
/
80
j
f
f
f
i
j
j
*
j
1
f
f
/
/
j
j
j
/
f
f
f
/
f
/
t
f
f
A
/
I
j
f
/
/
/
i
I
J
/
1
f
/
f
I
T
'
f
J
y
J
I
/
J
^
f
)
f
j
1
f
/
/
*}
f
j
y
j
/
I
/
^^
/
i
/
J
/
/
/
/
f
/
/
/
i
I
J
f
J
/
/
/
Y
X
1
j
f
J
/
j
J
y
n I
1
f
/
/
f
/
f
f
/
/
J
/
j
/^
1 dead panel load in thousands of
60
f /
j
/
f
j
j
J
/
'<i
/
f
y
i
/
f
/
/
^^/
/
f
/
j
/
yf
r\f-
f
f
/
f
f
/
-/9/o
J
f
J
/
J*
/
O/Q
f*f
f
/
f
f
/
ToJ
T
->y
/
/
J
J
-/
^
J/
f
j
/
j
/
-fa
>>v
J7^~
1
^
f
(Si
f
y
f
^
if\
$
f
f
f
J
fkj.
y
j
f
/
<&-
f
-Q*
1 /
/
/
A
t
^
^
7
/
/
P^
Sfi
/
2
P>
f~
~X
-p
Y ,
y
/
V
/
4V
y^
f
y^
/*
y
.v^
s^L.
KX
f
-f
y
_ /:
1 '
>^
1*
f
y
j
/
f
/
y
jr
f f
f
y
yj
/
y
y
jf
A
/
f
/
f
J
f
j
/
J
/
j
f
J
/
f
3D
,/^
Xy
/
/
/
/
/
/
AO
7
J
-/
f
7
r
{ /
/
/
/
/
/
y
^x 1
/
f/ /
+
/
/
/
t
y
-v
y_
~~7T ^
f-
-/
-/
X-
^-
50
y^
~f~
-f~
--f-
/
-}
*
7*
;
' t
1
-
t /
/
/
y .
^~
/
'/"
y
/
I
;
s\
1*f
-y^
^
y?*
~^T~
f
^
^
./
t*t-
^
20
j->
^
"7^
-/
-/>
^^
-^^
^-
..
^^ ^
^ ^|
r
^^^f
^^*
^^
^f)
^^
^^r
^r
_^^
^
^r
^ ^
^
^^
^
pj ~.(
^
_^^
^*^
s^
^^^
^s^
^s
s
^r
^^^
.^
.
x^^
rfX
^
-]
10
*
t
2
$
s
K
(VJ
(VI
S3
s
10
OJ
s
l^
S
Column spacing in feet
197
COLUMNS
DIAGRAM 43
WEIGHT OF TYPICAL FLOOR PANEL OF FLAT SLAB CONSTRUCTION
DESIGNED IN ACCORDANCE WITH CHICAGO BUILDING CODE
(FOR ESTIMATING COLUMN LOADS)
Column spacing in feet
SECTION 8
BENDING AND DIRECT STRESS
Rectangular Sections
The following notation is used :
R = resultant thrust.
N = vertical component of R.
x = eccentricity of thrust.
t = thickness or depth of section.
6 = breadth of section.
d' = embedment of steel top and bottom.
As = area of steel on tension side.
A' = area of steel on compression side.
Ao = total area of steel = A a + A'.
p = total percentage of steel = r-r-
f c = maximum unit compression in concrete.
f a = maximum unit tension in steel.
// = maximum unit compression in steel.
Case I. Compression Over Whole Section (A' = A s }.
ir$
Diagrams 44 to 49 inclusive give values of K for various values of p , -~i and-,
and for both n = 12 and n = 15. For values of ~ beyond the termination of the
curves, tension occurs over part of the section and the diagrams for Case II should
be used.
Case n. Tension Over Part of Section (A' = A s ).
Diagrams 50, 51, 52, 54, 55 and 56 give values of k for various values of p , , and
y> and for both n = 12 and n = 15. Diagrams 53 and 57 give values of L.
The method of procedure in solving problems is as follows: (1) Determine k from
the proper diagram; (2) find L from Diagram 53 or 57; (3) solve equation (2) for/ c ;
(4) find unit stresses in the steel from the formulas
(3)
(4)
199
- BENDING AND DIRECT STRESS
Case III. Tension Over Part of Section (A' = 0). Notation is given on Dia-
grams 58 and 59.
k* -2pn(l - A;) = k*j d e , (5)
3 = 1- l Ak (6)
(8)
/ - /c (10)
Diagrams 58 and 59 may be used as shown in two of the examples which follow.
Examples for Rectangular Sections
A beam is 9 in. wide and 20 in. deep. The reinforcement both above and below
consists of one steel rod 1 in. in diameter embedded at a depth of 2 in. At a certain
section, the normal component of the resultant force is 60,000 lb., acting at a distance of 3 A
in. from the gravity axis. Assume n 15. Compute the maximum unit compressive
stress in the concrete.
A _ (2) (0.7854) _
__
Po ~ ~
bt ~ (9)(20
d r = O.lOi
For these values of p and , Diagram 48 gives K = 1.70 and shows that the
problem falls under Case I. Then by formula (1)
NK (60, 000) (1.70)
(9) (20) = 567 Ib. per sq. in.
Change the eccentricity of the preceding problem to 6 in. and solve.
/ , /v
For p, = 0.0087 and -r = 0.30, Diagram 48 shows that y is too great for the
problem to come under Case I. The method of procedure for Case II must then be
followed.
Diagram 55 gives k = 0.73 for the values of p and -y given above. With k =
0.73 and p = 0.0087, Diagram 57 shows L to be 0.123. Solving equation (2)
M (60,000;(6)
fc = LbT* = (0.123)(9)(20) = 815 lb ' Per Sq ' in '
Using formula (3)
/. - nf c (~- t - l) = (15) (815) (0-7320 - l ) = 283 lb - P er sq- in.
The stress /,' may be found by formula (4) but is always less than n X fc-
An arch is 20 in. deep and is reinforced with three rods % in. in diameter to each
foot of width, both above and below. If the rods are embedded to a depth of 2 in. and the
normal component of the resultant thrust on a section is 100,000 lb. for 1-ft. width of arch.
200
BENDING AND DIRECT STRESS
ivith an eccentricity of 3.4 in., determine the maximum intensity of compressive stress on
the concrete. Assume n 15.
(6) (0.4418)
Po= -
Diagram 48 gives K = 1.63 and the problem comes under" Case I. Then by
formula (1)
NK (100,000)(1.63) a _ nlu
'- !
The vertical wall of a cantilever retaining wall is subjected to an earth pressure of
2400 Ib. applied at a distance of 4.54 ft. above the top of footing. The weight of vertical
wall is 2200 Ib. which can be considered as applied 5 in. in front of the steel. Determine
the unit stresses f c andf s , assuming n = 15, p = 0.0077 and d = 10.5 in.
The moment at the top of footing
M = (2400) (4.54) (12) + (2200) (5) = 141,700 in. - Ib.
= _141,700_
(12)(10.5) 2
e^ 141,700
d (2200) (10.5)
Entering Diagram 59 with a value of p = 0.0077 on the lower right-hand margin
pt
and tracing vertically to a value of -r = 6.1, then horizontally to the left to a point
vertically above K = 107, we find /. = 14,000 and f c = 610.
Design the vertical watt of the retaining wall described in the preceding problem
so thatf f = 750 and /, = 16,000. Assume the weight. of wall to be 2000 Ib.
For these unit stresses the left-hand part of Diagram 59 shows K = 133.8. Then
d = V(133!s)(12) = 9 ' 4 ^ Say 9 ^ in '
: = _Hi,70o_
d (2000) (9.5)
Following across the diagram horizontally to the right to a value of -r = 7.45 and then
vertically downward to the lower right-hand margin, we find p = 0.0085.
Round Columns
Concrete outside of the hooping is neglected. The following notation is used:
P = direct load (compression).
e = eccentricity of load.
r = radius of column core.
p = total percentage of steel.
f e = maximum unit compression in concrete.
fc = minimum unit compression in concrete.
f s = maximum unit tension in steel.
/.' = maximum unit compression in steel.
Case I. Compression Over Whole Section. Diagram 60 gives values of
for various values of p and , and for both n = 12 and n = 15.
201
BENDING AND DIRECT STRESS
Case II. Tension Over Part of Section.
*-
r>
The right-hand side of Diagrams 61 and 62 gives values of 7- in formula (11) for
Jc
various values of p and , and the left-hand side of these diagrams gives values of ^ in
R
formula (12).
Case III. Bending Only.
*-
ff f?
Values of j and -7- in the preceding equations are given in Diagram 63. Diagram
J c J s
64 gives the concrete and steel stresses in solid circular sections in the same manner as
the familiar diagrams for rectangular sections with steel in tension side only. In the
present case the value of ; is used instead of T-TO'
irr 3 bd 2
Examples for Round Columns
Assuming a column with 2Q-in. core reinforced with ten l-in. square rods and sus-
taining a load of 200,000 Ib. applied 2 in. off center, determine the maximum unit stress
in the concrete, n = 15.
10 e 2
r = 10 in. - (angexioy = 0.0318 r = Fd - - 2
From Diagram 60
or
1.12P 224,000
~i^~ " "31TT6 = 712 lb ' PW * Sq " m -
Find the maximum unit stresses in the concrete and steel of the column in the preceding
problem if the eccentricity of the load is 8 in.
r = 10 in. p = 0.0318 - = = 1.25
8
From Diagram 62
? = 0.325
R - ^ - 1 > 600 > 000 - r )
" irr* ~ 3141.6
fc = ~ = 0^25 = 1)56
/, = 25R = (25) (509) = 12,720 lb. per sq. in.
f/ = nf c = 23,500 lb. per sq. in.
202
44
BENDING
AND
DIRECT STRESS
OCTANGULAR SECTIONS COMPRESSION OVER WHOLE SECTION
btf d'= 0.051
VALUES OF ^ n =12
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204
DIAGRAM 46
BENDING
AND
DIRECT STRESS
RECTANGULAR SECTIONS COMPRESSION OVER WHOLE SECTION
VALUES OF ~~
d'=0.15t
n=12
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:ssion Over Whole Section
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205
BENDING
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DIRECT STRESS
DIAGRAM 47
RECTANGULAR SECTIONS COMPRESSION OVER WHOLE SECTION
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BENDING
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RECTANGULAR SECTIONS COMPRESSION OVER WHOLE SECTIOI
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BENDING
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DIRECT STRESS
RECTANGULAR SECTIONS TENSION OVER PART OF SECTION
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VALUES OF k n = 12
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DIAGRAM 51
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VALUES OF k
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DIRECT STRESS
RECTANGULAR SECTIONS TENSION OVER PART OF SECTION
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211
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DIAGRAM 53
RECTANGULAR SECTIONS TENSION OVER PART OF SECTION
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DIAGRAM 54
BENDING
AND
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RECTANGULAR SECTIONS TENSION OVER PART OF SECTION
VALUES OF k d n=15 5t
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213
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DIAGRAM 55
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DIAGRAM 56
BENDING
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DIRECT STRESS
RECTANGULAR SECTIONS TENSION OVER PART OF SECTION
d
VALUES OF k
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n =15
BENDING
AND
DIRECT STRESS
DIAGRAM 57
RECTANGULAR SECTIONS TENSION OVER PART OF SECTION
M
DIAGRAM 58
BENDING
AND
DIRECT STRESS
RECTANGULAR SECTIONS TENSION OVER PART OF SECTION
STEEL IN TENSION FACE ONLY
VALUES OF f c , f, AND p
n = 12
A'=0
217
BENDING
AND
DIRECT STRESS
DIAGRAM 5!
RECTANGULAR SECTIONS TENSION OVER PART OF SECTION
STEEL IN TENSION FACE ONLY
VALUES OF f c , f s AND p
DIAGRAM 60
BENDING
AND
DIRECT STRESS
ROUND COLUMNS COMPRESSION OVER WHOLE SECTION
VALUES OF
n=12
n=15
219
BENDING
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DIAGRAM 61
ROUND COLUMNS TENSION OVER PART OF SECTION
n=12
VALUES OF AND-
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DIAGRAM 62
BENDING
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DIRECT STRESS
ROUND COLUMNS TENSION OVER PART OF SECTION
VALUES OF ^ AND 4
tc K
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BENDING
AND
DIRECT STRESS
DIAGRAM 63
ROUND COLUMNS BENDING ONLY
JJ =1 ,l VALUES OF k, ~, ~, AND p
n J.O i a f c
5 J/ y ^o sen]OA
1
<n
<& ^ 5 S 2
C 0" O C> <
vO 5* OJ O COI \O -d-
P o o P g g 8
o- o c> c> c>
O Q
- - N -- - -- -
:: 4H
>j ^0 S3
n|D A SOO
s ^ - - 1 - -
i:^:::: - 5
l!|j;;j|!ll!l|j||!l|jj|l 8 S
||
o
<=>
^ In
- S ^-- IBM
&OC
i ^\
\ s * 1
if} : : :.; ; ;
AM
\
\
1
>> II
::::::::::::^-:s^::::::
t :::::: ::
Cf
:::::::::::::V5s::::::F
s
\_
\
WW V
O^~
rii
- - ~:
^^ . ^ ^ 1 -JU |
-:: :::::: ^,5" ::^LfA:::::: ::
""""J^|H^~"" TW
^r^
; > ITKJ::::: ::
Hd+"J"
t^Y/"
1 Percentage of vertical
^*^
Mvl ^ S
- lyy
^3
Mr >\ s
UU ^cS-- --
rt^
hfft~t ^~ -
_S_
i*j
i - III
-i * 5
^ ^ r\fv/i
' + 5-
1 L i 1 J_
IT" " "
" " ~ * " CAn
(D - - -s - \
n
; ; " aC/v,
w " s
4 11
C I-5
S . --X-.
C TV
r-.
r- . -SI-
V
V> v
\ I
_L. .
D s
: ; :.: :;;_:: :__:
:._ :: ;
5' r
:
O- - ^
::5:::
< \ **> 1
OS
:_ .: :_i>:
::_:: lA^I^^ J^ :_:.:: _I
:i
i
. iijfci. { j. .'^
yt
-rr
s, r^_ ii i - 1 i
1
U :
i
r INI
111 L. ..
3
"s "S
ffi :: = ::::
-
_SI ^__
m
^ f ::
^lsS^- S s ::x
B!E!!
II
_ :iss : ::::S
ttf ====:==
Clj:
M^
ao'o
::: = -::::::- = ::::: = |
- 100
S J "^
^- 10 (vj
O 0]
oOOO
o
**/& j-o sanfDA
222
DIAGRAM 64
BENDING
AND
DIRECT STRESS
ROUND COLUMNS BENDING ONLY
VALUES OF R, f s , f e AND p
= 12
= 15
223
SECTION 9
FOOTINGS
Diagram 65 makes it possible to find readily the bending moments which occur at
each face of column for both square and rectangular footings. The illustrations
above this diagram show how the diagram is used. For example, suppose the bending
moment is required at the face of a 24-in. column supporting a load of 300,000 Ib.
and resting on a footing 9 ft. 2 in. square. From the upper part of Diagram 65, C\ =
6.2 and
M = (6.2) (300,000) = 1,860,000 in.-lb.
Tables 49, 50 and 51, based on the recommendations contained in Bulletin 67 of
the University of Illinois Engineering Experiment Station, give the design of square
reinforced footings for different loads, column sizes and soil pressure. These footings
are without offsets and for large footings it will usually be found more economical to
use one or two offsets.
These tables are computed for square columns. If round columns are used,
multiply the diameter by 0.7854 to get the size of square columns of equivalent
perimeter and enter the table with that size.
The recommendations in the bulletin mentioned above are as follows:
Width of Footing to Use in Flexure Computations for Two-way Reinforcement.
With two-way reinforcement evenly spaced over the footing, it seems that the tensile
stress is approximately the same in bars lying within a space somewhat greater than
the width of the pier and that there is also considerable stress in the bars which lie
near the edges of the footing. For intermediate bars stresses intermediate in amount
will be developed. For footings having two-way reinforcement spaced uniformly
over the footing, the method proposed for determining the maximum tensile stress in
the reinforcing bars, is to use in the calculation of resisting moment at a section at the
face of the pier the area of all the bars which lie within a width of footing equal to the
width of pier plus twice the thickness of footing, plus half the remaining distance on
each side to the edge of the footing. This method gives results in keeping with the
results of tests. When the spacing through the middle of the width of the footing is
closer, or even when the bars are concentrated in the middle portion, the same method
may be applied without serious error. Enough reinforcement should be placed in the
outer portion to prevent the concentration of tension cracks in the concrete and to
provide for other distribution of stress.
No failures of concrete have been observed in tests and none would be expected
with the low percentages of reinforcement used.
Bond Stresses. The method proposed for calculating maximum bond stress in
column footings having two-way reinforcement evenly spaced, or spaced as npted in the
preceding paragraph, is to use the ordinary bond stress formula, and to consider the
circumference of all the bars which were used in the calculation of tensile stress, and
to take for the external shear that amount of upward pressure or load which was used
hi the calculation of the bending moment at the given section.
Bond resistance is one of the most important features of strength of column
footings, and probably much more important than is appreciated by the average
225
FOOTINGS
designer. The calculations of bond stress in footings of ordinary dimensions- where
large reinforcing bars are used show that the bond stress may be the governing element
of strength. Tests show that in multiple-way reinforcement a special phenomenon
affects the problem and that lower bond resistance may be found in footings than in
beams. Longitudinal cracks form under and along the reinforcing bar due to the
stretch in the reinforcing bars which extend in another direction, and these cracks act
to reduce the bond resistance. The development of these cracks along the reinforcing
bars must be expected in service under high tensile stresses, and low working bond
stresses should be selected. An advantage will be found in placing under the bars a
thickness of concrete of 2 in., or better 3 in., for footings of the size ordinarily used in
buildings.
Difficulty may be found in providing the necessary bond resistance, and this points
to an advantage in the use of bars of small size, even if they must be closely spaced.
Generally speaking, bars of %-in. size or smaller will be found to serve the purpose of
footings of usual dimensions. The use of large bars, because of ease in placing, leads
to the construction of footings which are insecure in bond resistance. Column footings
reinforced with deformed bars develop high bond resistance. Curving the bar upward
and backward at the end increases the bond resistance, but this form is awkward in
construction. Reinforcement formed by bending long bars in a series of horizontal
loops covering the whole footing gives a footing with high bond resistance.
The use of short bars placed with their ends staggered increases the tendency to fail
by bond and cannot be considered as acceptable practice in footings of ordinary pro-
portions. In footings in which the projection is short in comparison with the depth,
the objection is very great.
Diagonal Tension. As a means of measuring resistance to diagonal tension failure,
the vertical shearing stress should be calculated by using the vertical sections formed
upon the square (assuming square column) which lies at a distance from the face of the
pier equal to the depth of the footing. This calculation gives values of the shearing
stress, for footings which failed by diagonal tension, which agree fairly closely with
the values which have been obtained in tests of simple beams. The formula used in
V
this calculation is v = rrj? where V is the total vertical shear at this section taken to
ojd'
be equal to the upward pressure on the area of the footing outside of the section con-
sidered, b is the total distance around the four sides of the section, and jd is the dis-
tance from the center of reinforcing bars to the center of the compressive stresses.
The working stress now frequently specified for this purpose in the design of beams,
40 Ib. per sq. in., for 1:2:4 concrete, may be applied to the design of footings.
226
DIAGRAM 65
BENDING MOMENTS FOR SINGLE COLUMN FOOTINGS
.- d
M=C,P
*.
EH
LJi
M-QdP
M=CjdP
Square footings with
square or round columns
M = C,P (in.-lh)
Length of footing, side (b) in feet
Rfictungjlar fbalrnqs-for
squan- or round cofumns
M-CjdP
far rectanular columns
Values of a /d (or
227
FOOTINGS
DESIGN OF SINGLE SQUARE FOOTINGS
Punching shear = 120
Bond stress =100
Tension in steel = 16, 000
2 TONS ON SOIL
TABLE 49
Squart column
Footing
size
b
Column
size
a
(in.)
Allowable
load
P
(thousands
of pounds)
Total
depth
(in.)
Steel
Volume
of
concrete
(cu. ft.)
Size
(in.)
No. rods each way
Weight of
sq. rods
Ub.)
(ft.)
(in.)
Square
Round
3
10
34.8
11
H
8
10
37.4
8.3
12
" 34.9
10
9
12
42.0
7.5
14
35.0
9
10
13
46.7
6.8
3
6
10
46.9
14
M
8
10
44.2
14.3
12
47.2
12
10
12
55.2
12.3
14
47.3
11
11
13
60.7
,11.3
4
10
60.6
17
H
8
10
51.0
22.7
12
61.2
14
10
13
63.7
18.7
14
61.4
13
11
14
70.1
17.3
16
61.6
12
12
15
76.5
16.0
4
6
10
75.9
20
H
8
10
57.7
33.8
12
76.7
17
10
12
72.2
28.7
14
77.2
15
12
15
86.6
25.3
16
77.7
13
14
18
101.0
22.0
5
10
92.7
23
H
8
10
64.6
47.9
12
93.7
20
10
12
80.7
41.7
14
94.4
18
11
14
88.8
37.5
16
95.0
16
13
16
105
33.4
18
95.6
14
16
20
129
29.2
5
6
10
110.8
27
2
8
10
71.4
68.0
12
112.8
23
10
12
89.2
58.0
14
113.4
20
12
15
107
50.4
16
114.2
18
13
17
116
45.4
18
114.6
17
14
18
125
42.8
6
10
130.1
31
H
7
9
68.4
93.0
12
131.8
27
9
11
88.0
81.0
14
133.2
24
11
14
108
72.0
16
134.5
21
13
16
127
63.0
18
135.4
19
15
19
147
57.0
20
22
136.3
136.8
17
16
&
17
18
22
23
166
176
51.0
48.0
6
6
10
150.5
35
M
8
10
85
123.0
12
153.1
30
10
12
106
106.0
14
154.7
27
11
14
117
95.0
16
156.3
24
13
16
138
84.5
18
157.3
22
14
18
149
77.5
20
158.4
20
16
20
170
70.4
22
158.9
19
17
21
181
67.2
228
TABLE 49
FOOTINGS
DESIGN OF SINGLE SQUARE FOOTINGS
2 TONS ON SOIL
Punching shear = 120
Bond stress =100
Tension in steel = 16,000
Footing
size
b
Column
size
a
(in.)
Allowable
load
P
(thousands
of pounds)
Total
depth
D
(in.)
Steel
Volume
of
concrete
(cu. ft.)
Size
(in.)
No. rods each way
Weight of
sq. rods
db.)
(ft.)
(in.)
Square
Round
7
12
175.1
34
H
10
12
115
139
14
177.6
30
12
15
138
123
16
179.5
27
13
17
149
110
18
181.3
24
14
18
161
98
20
182.5
22
17
21
195
90
22
183.1
21
17
22
195
86
24
184.4
19
. -
20
25
230
78
7
6
12
198.3
38
H
11
14
136
178
14
201.1
34
13
16
160
160
16
203.9
30
15
18
185
141
18
206.0
27
16
21
197
127
20
207.4
25
.
17
22
210
117
22
208.8
23
19
24
234
108
24
210.2
21
20
26
246
99
8
14
226.4
37
M
14
17
185
198
16
229.6
33
16
' 20
211
176
18
232.0
30
17
22
224
160
20
233.6 28
18 .
23
237
149
22
235.2
26
20
25
264
139
24
236.8
24
21
27
277
128
26
238.4
22
23
29
303
117
8
6
14
252.0
41
H
14
18
196
247
16
255.6
37
16
21
224
223
18
259.2
33
19
24
267
199
20
261.9
30
21
26
294
181
22
263.7
28
22
28
309
169
24
265.5
26
24
30
337
156
26
267.3
24
25
32
351
145
9
16
283.5
40
H
11
14
256
270
18
286.5
37
12
16
279
250
20
289.5
34
14
17
325
230
22
292.7
31
15
19
349
209
24
294.4
29
16
20
372
197
26
296.6
27
17
22
395
182
28
298.7
25
19
24
442
169
9
6
16
311.3
44
H
12
15
295
331
18
315.8
40
13
17
319
301
20
319.3
37
14
18
344
278
22
322.6
34
16
20
393
256
24
326.0
31
17
22
418
233
26
328.7
29
18
23
442
218
28
330.6
27
20
25
491
203
229
FOOTINGS
DESIGN OF SINGLE SQUARE FOOTINGS
2 TONS ON SOIL
Punching shear = 120
Bond stress =100
Tension in steel = 16,000
TABLE 49
Square column.
Footing
size
b
Column
size
a
vin.)
Allowable
load
P
(thousands
of pounds)
Total
depth
(in.)
Steel
Volume
of
concrete
(cu. ft.)
Size
(in.)
No. rods each way
Weight of
sq. rods
Ob.)
(ft.)
(in.)
Square
Round
10
16 340.0
48
%
12
16
310
400
18
346.3
43
14
18
362
358
20
349.9 40
15
19
388
334
22
353.8 37
17
21
440
308
24
357.4 34
18
23
466
284
26
360 . 32
19
25
492
267
28
362.5
30
20
26
518
250
30
365.0
28
22
28
565,
233
10
6
16
369.3
52
H
14
17
381
478
18
376.1
47
15
19
408
432
20
381.8
43
16
21
435
395
22
386.0
40
.
18
23
490
367
24
390.0
37
19
25
517
340
26
392.9
35
20
26
544
321
28
395.5
33
21
27
571
303
30
398.2
31
22
28
599
285
11
18
406.9
51
H
15
19
419
514
20
414.5
46
17
22
486
463
22
419.0
43
19
24
543
433
24
423.5
40
20
26
572
403
26
428.0
37
22
28
629
373
28
431.0
35
23
29
658
353
30
434.0
33
24
31
686
333
32
437.2
31
26
33
743
312
34
438.7
30
26
33
743
302
11
18
439.7
54
H
16
21
478
595
20
446.3
50
18
23
538
551
22
452.8
46
20
25
598
507
24
457.8
43
21
27
628
474
26
462.9
40
23
29
687
441
28
466.3
38
24
31
717
418
30
469.4
36
25
32
747
397
32
472.7
34
26
34
111
375
34
476.0
32
28
35
837
353
12
18
471.4
58
H
17
22
530
697
20
480.5
53
19
24
593
636
22
486.0
50
20
26
624
600
24
493.2
46
22
28
686
552
26 498.6
28 502 . 1
43
41
24
25
31
32
748
780
516
492
30
507.6
38
27
35
841
456
32
511.1
36
28
36
873
432
34
514.8
34
30
38
936
408
36
518.4
32
31
40
967
384
230
TABLE 50
FOOTINGS
DESIGN OF SINGLE SQUARE FOOTINGS
3 TONS ON SOIL
Punching shear = 120
Bond stress = 100
Tension in steel = 16,6
Footing
size
b
Column
size
(in.)
Allowable
load
P
(thousands
of pounds)
Total
depth
(in.)
Steel
Volume
of
concrete
(cu. ft.)
Size
(in.)
No. rods each way
Weight of
sq. rods
Ub.)
(ft.) ! (in.)
Square
Round
3
10
52.4
14
H
8
10
37.4
10.5
12
52.5
13
8
11
37.4
9.8
14
52.8
11
11
14
51.5
8.3
16
52.9
10
12
15
56.1
7.5
3
6
10
70.7
18
M
7
9
38.7
18.4
12
71.1
16
9
11
49.7
16.3
14
71.4
14
10
13
55.2
14.3
16
71.7
12
13
16
71.8
12.3
4
10
91.4
23
M
7
9
44.6
30.7
12
92.2
19
10
12
63.7
25.3
14
92.6
17
10
13
63.7
22.7
16
93.0
15
12
16
76.5
20.0
18
93.2
14
13
17
82.9
18.7
20
93.4
13
14
18
89.2
17.3
4
6
10
114.7
27
y*
7
9
50.6
45.6
12
115.7
23
9
11
65.0
38.8
14
116.2
21
10
13
72.2
35.5
16
116.9
18
12
16
86.7
30.4
18
117.2
17
13
16
94.0
28.7
20
117.7
15
15
19
108.0 25.3
5
12
141.2
28
H
8
11
64 . 6 58 . 3
14
142.2
25
10
12
80.7 i 52 1
J6
143.1
22
12
15
97.0 45.8
18
143.7
20
13
16
105 41.7
20
144.4
18
15
19
121 37.5
22
145.0
16
16
22
129 33.3
5
6
12
169.0
33
H
8
11
71.4
83.2
14
170.5
29
10
12
89.2
73.1
16
172.0
25
13
16
116.0
63
18
172.8
23
13
17
116
58.0
20
173.6
21
15
19
134
52 9
22
174.3
19
17
21
152
47.9
6
12 198.9
38
H
8
11
78.2 114.0
14 201.2
33
10
12
97.8 i 99.0
16 202.5
30
11
14
108 90 .
18
203.8
27
13
16
127
81.0
20
205.2
24
15
19
147
72.0
22
206.1
22
17
21
166
66.0
24
207 . .
20
19
24
186
60.0
26
207.4
19
20
25
195
57.0
6 6
12
230.8
43
M
9
11
95.7
152.0
14
233.5
38
10
12
106
134.0
16
235.6
34
11
14
117
120.0
18
237.7
30
13
17
138
106.0
20
238.7
28
14
18
149
98.5
22
240.3
25
17
21
181
88
24
241.4
23
18
23
192
81.0
26
241.9
22
19
24
202
77.4
231
FOOTINGS
Punching shear = 120
Bond stress =100
Tension in steel = 16,0
DESIGN OF SINGLE SQUARE FOOTINGS
3 TONS ON SOIL
Footing
size
Column
Allowable
i -_ j
Total
Steel
Volume
b
size
a
(in.)
load
P
(thousands
of uounds)
depth
(in.)
Size
(in.)
No. rods each way
Weight of
sq. rods
of
concrete
(cu. ft.)
(ft.)
(in.)
Square
Round
db.)
7
14 267.7
43
H
11
14
121 176
16 270.2
39
12
15
138 159
18 272.6
35
13
16
149 143
20 275.0
31
15
19
172
126
22
276.3
29
16
20
184
118
24
277.5
27
18
22
207
110
26
278.7
25
19
24
218
102
28
279.9
23
21
27
241
94
7 6
14
303.7
48
y*
12
.15
148
225
16
307.4
43
13
16
160
202
18
310.0
39
14
18
173
183
20
312.9
35
16
20
197
164
22
315.0
32
17
22
210
150
24
316.3
30
18
22
222
141
26
317.8
28
19
24
234
131
28
319.2
26
21
27
257
122
8
16
345.6
48
H
14
17
185
256
18 349.6
43
15
19
198
229
20
352.8
39
17
21 . 224
208
22
. 355.2
36
18
23 237 192
24
357.6
33
20
25 264 176
26
359 . 2
31
21
26 277 165
28
360.7
29
21
27 ! 277 155
30
362.4
27
23
29
303
144
8
6
16
386.6
53
y*
15
19
211
319
18
390.1
48
16
21
224
289
20
393.7
44
18
22 '
252
265
22 397.3
40
19
24
266
241
24 400 . 1
37
21
27
294
223
26
401.9
35
22
28
309
211
28
404.5
32
24
30
337
193
-
30
406.3
30
25
32
351
181
9
18
432.2
53
y%
.11
14
256
358
20
437.3
48
12
15
279
324
22
441.4
44
13
17
302
297
24
444.4
41
14
18
325
277
26
447.4
38
15
20
349
257
28
449.5
36
16
21
372
243
30
452.5
33
18
23
418
223
32
454.6
31
20
25
465
209
34
456.6
29
21
27
488
196
9
6
18
476.1
58
H
12
15
295
436
20
481.6
53
13
16
319
399
22
486.1
49
14
18
344
369
24
490.6
45
15
19
369
339
26
494.1
42
16
21
393
316
28
497.5
39
17
22
418
293
.-30 499.8 37
18
23
442
278
32 502 . 35
19
24
467
263
34 504.3 33
20
26
492
248
232
TABLE 50
FOOTINGS
DESIGN OF SINGLE SQUARE FOOTINGS
3 TONS ON SOIL
Punching shear = 120
Bond stress =100
Tension in steel = 16, 000
Footing
size
6
Column
size
a
(in.)
Allowable
load
P
(thousands
of pounds)
Total
depth
(in.)
Steel
Volume
of
concrete
(cu. ft.)
Size
(in.)
No. rods each way
Weight of
sq. rods
Ob.)
(ft.)
(in.)
Square
Round
10
18
521.3
63
H
13
16
336 525
20
527.5
58
14
17
362 483
22
533.7
53
15
19
388 442
24
538.9
49
16
20
414 408
26
542.5
46
17
22
440 383
28
546.3
43
18
23
465 358
30
550.0
40
19
25
492 333
32
552.5
38
20
25
518 317
34
555.0
36
21
27
544 300
36
557.5
34
22
28 569 283
10
6
18
566.3
69
K
14
17
381 634
20
574.5
63
15
18
408 , 579
22
581.5
58
16
20
435 533
24 . 587.1
54
17
21
463 496
26 593 . 2
50
18
23
490 456
28 596 . 6
47
19
24
517 432
30 600.8
44
20
26
544 404
32 604 . 9
41
22 28
599 377
34 608 . 8
39
23
29
626 358
36 610.5
37
23
30
626 340
38 613.2
35
24
31
653 322
11
20 623.2
68
M
15
20
458 686
22 630 . 8
63
17
21
486 635
24 638 . 3
58
18
22
515
585
26 644.4
54
19
24
543
544
28
648.9
51
20
25
582
514
30
653.4
48
21
27
600
484
32
657.9
45
23
29
658
454
34
662.5
42
24
31
686
423
36
665 .5
40
25
32
715
403
38
668.5
38
26
33
743
383
40
671.5
36
27
34
772
363
11
6
20
672.9
73
H
16
21
478
804
22
682.8
67
18
23
538
738
24
689.5
63
19
24
568
694
26 696.0
59
20
25
598
650
28 702 . 6
55
21
27
628
606
30 709 . 1
51
23
29
687
562
32 714.1
48
24
31
717
529
34 717.5
46
25
32
747
507
36 722.3
43
26
34
777
474
38 725 . 7
41
27
35
807
452
40 729 . 1
39
28
36
837
429
42 732.3
37
29
37
866
408
12
22 734.4
72
M
19
24
593
864
24
743.4
67
20
25
614
804
26
750 . 6 63
21
27
655
756
28
757 . 8 59
22
28
686
708
30
765.0 55
24
31
748
660
32
770.4 52
25
32
780
624
34
775.8 49
27
34
842
588
36
779.4 47
27
35
842
564
38 784.8 44
29
37
904
528
40 788 . 4 42
30
38
936
504
42 792 . 40
31
39
967
480
44 793.8
39
31
39
967
468
233
FOOTINGS
Square column
DESIGN OF SINGLE SQUARE FOOTINGS
A J
I ^
4 TONS ON SOIL
Punching shear = 120 m Iff
I
Bond stress =100 HfH
Q *
Tension in steel - 16,000 5 gFi
1
Footing
size
b
Column
size
a
(in.)
Allowable
load
P
(thousands
of pounds)
Total
depth
D
(in.)
Steel
Volume
of
concrete
(cu. ft.)
Size
(in.)
No. rods each way
Weight of
sq. rods
Ob.)
(ft.)
(in.)
Square
Round
3
10
70.0 18
H 7 9 32.8 13.5
70.3 15
9 11 42.0 11.3
14 70.5 13
10 13 46.7 9.8
16 70.6 12
11
14
51.5 9.0
18 70.8 11
12
15
56.1 8.3
3
6 10
94 . 5 23
M
7 9
38.7 23.5
12
94.9 20
8
10
44.2 20 4
14
95.4 17
10
12
55.2 17.4
16
95.7 15
11
15
60.7 15.3
18
95.9 14
12 15
66.3 14.3
20 96.2 ' 12
15
19
82.9 12.3
4
10
122.2 29
H
7
9
44 . 6 38 7
12
123.0 25
8
10
51.0 33 . 3
14
123.8
21
10
12
63.7
28.0
16
124.1
19
11
14
70.1
25.3
18
124.6 '
17
13
16
82.9
22.7
20
125.0
15
15
19
95.6
20.0
22
125.3
14
15
19
95.6
18.7
4
6
10
153.1
35
H
7
9
50 . 6 59 .
12
154.4
30
8
10
57 . 7 50 . 6
14
155.4
26
10
12
72 . 2 . 43 . 8
1
16
156.2
23
11
14
79.5
38.8
1
18
156.7
21
12
15
86.7
35.4
20
157.2
19
14
17
101.0
32.0
22
157.7
17
16
20
116.0 28.7
5
12
188.7
36
M
8
11
64.6
75.0
14
190.3
31
10
12
80.7
64.6
16
191.6
27
11
14
88.8
56.2
18
192.2
25
12
15
97.0
52.1
20
193 . 1
22
14
18
113
45.8
22
193.7
20
16
20
129
41.7
24
194.1
19
17
21
137
39.6
5
6
12
226.1
42
H
9
11
80.2
106.0
14
228.0
37
10
12
89.2
93.2
16
229.9
32
11
14
98.2
80.7
18
231 .0
29
13
16
116
73.1
20
232.2
26
14
18
125
65.5
22
232.9
24
15
19
134
60.5
24
233 . 7
22
17
22
152
55.4
26
234.4
20
19
24
170
50.4
6
14
268.6
43
H
9
12
88.0
129.0
16 270.6
38
11
14
108
116.0
18 272.7
34
12
16
117
102.0
20 274.0
31
14
17
137
93.0
22 275 . 4
28
15
19
147
84.0
24 276.3
26
17
21
166
78.0
26
277.2
24
18
23
176
72.0
28
278.1
22
20
26
195
66.0
6
6
14
312.1
49
y*
10
13
106
172.0
16
314.7
44
11
14
117
155.0
18
317.5
39
13
16
138
137.0
20
319.5
35
14
18
149
123.0
22
321.1
32
15
19
160
112.0
24
322.2
30
17
21
181
106.0
26
323 . 2
28
18
23
192
98.5
28
,", > 1 : . 3
26
i/
19
25
202
91 .5
30
325 . 3
24
21 27
223
84.5
234
TABLE 51
FOOTINGS
5quar<s column .
DESIGN OF SINGLE SQUARE FOOTINGS
4 TONS ON SOIL
Punching shear = 120
Bond stress =100
Tension in steel = 16,0
Footing
size
i
Column
size
a
(in.)
Allowable
load
P
(thousands
of pounds)
Total
depth
(in.)
Steel
Volume
of
concrete
(cu. ft.)
Size
(in.)
No. rods each way
Weight of
sq. rods
db.)
(ft.)
(in.)
Square
Round
7
16
361.4
50
H
12
15
138
204
18
364.4
45
13
16
149
184
20
367.5
40
14
18
161
163
22
369.3
37
15
19
172
151
24
371.1
34
17
21
195
139
26
372.4
32
18
22
207
131
28
374.2
29
20
25
230
118
30
375.4
27
22
27
252
110
32
376.7
25
25
30
287
102
7
6 16
410.6
55
H
13
16
160
263
18
414.2
51
14
17
173
239
20
417.7
46
15
19
185
215
22
420.4
42
16
20 197
197
24
422.5
39
16
21 197
183
26
424.7
36
18
22 222
168
28
426.8
33
20
25
246
155
30
428.2
31
21
27
259
145
32
429.6
29
23
29
284
136
34
431.0
27
25
31
308
126
8
18
466.4
57
H
15
19
198
304
20
471.2
51
16
21
211
272
22
474.3
47
17
22
224
251
24
477.6
43
18
23
237
229
26
480.0
40
19
24
250
213
28
482.4
37
20
25
264
197
30
484.0
35
21
26
277
187 '
32
485.6
33
22
28
290
176
34
487.2
31
24
30
316
165
36
488.8
29
26
32
343
155
8
6
18
521.0
63
H
16
20
224
380
20
526.5
57
17
22
238
343
22
531.0 52
19
24
266
313
24
534 . 6 48
20
25
281
289
26
537.3 45
21
26
294
271
28
540.0 42
21
27
294
253
30
542 . 7 39
22
28
309
235
32
545.4 .36
24
31
337
217
34
557.2
34
25
31
351
205
36
549.0
32
26
33
365
193
9
20
584.2
63
K
12
15
279
425
22
589.4
58
13
16
302
391
24
593.3
54
13
17
302 364
26
598.3
49
15
19
349
331
28
601.4
46
16
20
372
310
50
604.4
43
17
21
395
290
32
607.5
40
18
23
418 270
34
609.6
38
19
24
442 256
36
611.5
36
20
26
465 243
38
613.6
34
22
28
511 229
9
6 20
644.1
69
H
13
16
319 519
22
649.9
64
14
18
344 481
24
655.5
59
14
18
344 443
26
660.0
55
15
19
369 413
28
664.5
51
16
20
393 383
30
667.8
48
16
21
393 361
32
671.3
45
17
22
418 ' 338
34
674.6
42
19 . 24
467 316
36
676.8
40
20 26
491 301
38
679.1
38
21 27
516
286
40 681.3
36
23 29 565
271
235
FOOTINGS
TABLE 51
DESIGN OF SINGLE SQUARE FOOTINGS
Punching shear = 120
Bond stress =100
Tension in steel = 16, 000
4 TONS ON SOIL
Footing
size
b
Column
size
a
(in.)
Allowable
load
P
(thousands
of pounds)
Total
depth
(in.)
Steel
Volume
of
concrete
(cu. ft.)
Size
(in.)
No. rods each way
Weight of
sq. rods
Ob.)
(ft.)
(in.)
Square
Round
10
22 712.5
70 H
15
19
388 583
24 718.8
65
15
19
388
541
26 725.0
60
17
21
440-
500
28 730 .
56
17
22
440
467
30 735.0
52
18
23
466
4 33
32 738.8
49
19
24
492
408
34 742.5
46
20
25
518
383
36 745.0
44
20
25
518 367
38 748.7
41
22
28
569 342
40 751.2
39
23
29
595
325
42 753.8 37
24
31
620 308
10 6
22 777.3 76
H
16
20 435 698
j
24 785 . 5 70
17 21 462 i 643
26 792.5 65
18 22
490 . 597
|
28 797.9 61
18
23
490 561
30
803.3 57
19
24 517 524
1
32
807 . 7 54
20
25
544 496
|
34
811.6
51
20
26 544 469
36
815.9
48
21
27 571 441
38
820.0
45
'23
29
626 413
40
822.7
43
23
29
626 395
42
825.4
41
24
31
663
377
44
828.3
39
25
32
680
358
1 r
11
24
853.0 76 y*
18
22
515
766
26
860.6 71
19
24
543
716
| .
28
868.2 66
20
25
572
665
30
874 . 2 62
21
26
600
625
32 880.2 58
21
27
600
585
34 884 . 8 55
22
28
629
554
36 889.4 52
23
29
658
524
i
38 893 . 8 49
24
30
686
494
i
40 896.8 47
24
31
686
474
42
900.0
45
25
32
715
453
44
903 .
43
25
32
715
433
46
906.0
41
26
33
743
413
11 6
24 922.4
82 H 19
24
568
903
26 931.0
77
20
25
598
848
28 940.8
71
21
27
628
782
30
947.4 67
22
28
657
738
32
954.0
63
23
29
687
694
34
958.9
60
23
30
687
661
36
963.8
57
24
30
717
628
38
968.8
54
25
31
747
595
40
973.7
51
26
33
777
562
42
977.0
49
26
33
777
540
44
982.0
46
28
35
837
507
46
985.2
44
29
36
866
485
48
988.7
42
29
37
866
462
12
26
1002 . 7
83 H
21
26
655
996
28
1013.3
77
22
28
686
925
30
1022.2
72
23
29
717
865
32
1029.6
68
24
30
748
816
34
1036.8
64
25
32
780
768
36
1042.3
61
26
32
811
732
38
1047.5
58
26
34 811
697
40
1053.0
55
27
35
842
660
42
1058.4
52
29
36
905
624
44
1062.0
50
29
37 905
600
46
1065.6 48
30
38 936
576
48
1069.2 *6
30
39
936
552
50
1073 . 8 44
31
40
967
528
236
SECTION 10
MISCELLANEOUS
Estimates. Estimates of the cost of the concrete work for buildings and similar
structures can be easily made by applying current unit costs to the quantities ob-
tained from the tables and diagrams.
Diagram 66 gives the quantities of concrete, steel and forms for typical square
panels of a three beam* and girder floor system. Although the quantities of steel or
concrete may be somewhat affected by changing the proportions of beams or girders,
the total cost will vary only slightly. Quantities for flat slab floors may be found in
Section 2.
By means of Diagrams 42 and 43 of Section 7, which give weights of floor panels,
the column and footing loads can be quickly estimated and the quantities taken from
the column and footing tables.
Loads. Tables 52, 53 and 54, give the building code requirements for live load,
weights of contents of storage warehouses, and weights of building materials
respectively.
237
MISCELLANEOUS
DIAGRAM 66
APPROXIMATE QUANTITIES OF CONCRETE, STEEL AND FORMS FOR
TYPICAL SQUARE INTERIOR PANELS OF THREE BEAM AND GIRDER
FLOOR SYSTEM DESIGNED IN ACCORDANCE WITH JOINT
f c =650 COMMITTEE RECOMMENDATIONS
f s =16*000 (COLUMNS NOT INCLUDED)
4. 4.014 -DC aad cpuno
o o oo r: <o 10
o ol o ol c>
238
TABLE 52
MISCELLANEOUS
BUILDING CODE REQUIREMENTS FOR LIVE LOAD
Structure
i
Boston
Buffalo
Chicago
Cincinnati
Indianapolis
Milwaukee
Minneapolis
!
1
New York
Philadelphia
Pittsburgh
.2
1
San Francisco
A
1
Washington
\partments
60
50
70
40
40
50
30
50
40
70
50
60
40
50
100
100
70
75
100
100
100
125
125
100
120
150
100
Fxd seat auditoriums
75
100
50
75
75
Mov. seat auditoriums
Churches
125
100
100
1?5
80
50
75
125
100
75
Dance halls
?00
100
150
100
150
100
200
100
150
250
Theaters
100
100
100
125
50
100
75
75
Theater balconies
Theater stairways
80
100
Dwellings
60
50
40
40
40
50
30
50
40
40
70
70
50
60
40
50
Hospitals
70
50
50
30
50
70
50
60
50
Hotels
60
70
50
40
75
30
50
40
70
50
60
40
50
First floors
100
100
75
Corridors
125
100
75
Office rooms
50
75
Manufacturing ........
175
150
?00
150
200
150
250
Light manufacturing
Mercantile
125
m
125
?50
120
100
100
100
100
100
100
125
?00
120
100
150
125
125
Retail stores
Heavy storehouses
125
250
125
250
120
100
100
150
100
200
100
100
125
120
120
150
150
125
250
125
110
150
Warehouses . .
250
150
150
?00
200
150
200
150
250
150
Offices
75
100
70
50
50
75
40
75
70
60
100
60
60
50
75
First floor
150
100
150
80
100
100
125
Corridors
100
110
100
125
100
110
Schools class rooms
75
60
60
100
40
100
60
75
75
50
75
Assembly rooms ....
125
100
75
60
125
75
Corridors
60
125
100
Stairways
60
Sidewalks
?00
300
300
150
300
300
300
150
Stables, carriage houses,
garages
100
120
100
75
85
80
85
100
75
75
Stairways, general
70
100
80
60
70
100
Fire escapes . . .
70
70
100
Roofs slope under 20
Over 20 (hor. proj.)
Wind pressures
30
40
40
30
25
20
25
20
30
30
30
50
50
30
30
40
30
30
30
30
50
30
30
30
20
20
40
40
25
25
30
239
TABLE S3
MISCELLANEOUS
CONTENTS OF STORAGE WAREHOUSES
Material
Pounds
cubic foot
of space
Height
of pile,
feet
Pounds
per
square foot
of floor
Recommended
live loads,
pounds per
square foot
Produce, Grain, Fruit, Etc.
Grain, in bulk
Barley and corn
37
8
296 *
Oats
26
8
208
Rye and wheat
48
8
384
Fruit and vegetables, in bulk
Apples, pears, etc . . .
38
8
304
Potatoes, turnips, etc
Miscellaneous produce, packed
Beans, in bags ....
44
40
8
8
352
320
Corn, in bags
31
8
248
250 to 300
Cornmeal, in barrels
37
26
6H
240
234
Rice, in bags
Wheat, in bags
58
39
5
8
290
312
Wheat flour, in barrels
Hay, in bales, not compressed
Hay, in bales, compressed
Straw, in bales, compressed
Groceries
Miscellaneous articles, packed
40
14
24
19
7
9
9
9
280
126
216
171
Butter, lard, etc., in carrels
Canned goods, preserves, etc., in cases. .
Cheese
32
58
30
6
6
8 '--
192
348
240
Coffee, green, in bags
39
8
312
Coffee, roasted, in bags
33
8
264
Dates and figs, in cases, average
Meat, beef, pork* etc., in barrels
Molasses, in barrels
Salt, finely ground in sacks
65
37
48
60
5
5
5
5
325
185
240
300
250 to 300
Soap powder, in cases
Starch, in barrels
38
25
8
7
288
175
Sugar, in barrels
43
5
215
Tea, in chests
Wines, liquors, etc., in barrels
Dry Goods, Cotton, Wool, Etc.
Cotton, in bales, compressed, average. . . .
Cotton, unbleached goods, in bales
Cotton, tickings and duck, in bales
Cotton, printed goods, in bales
25
48
25
24
35
19
8
5
9
9
8
9
200
240
225
216
280
171
Cotton, printed goods, in cases
Cotton, quilts and flannels, in cases
31
16
8
9
248
144
Cotton, yarn, in cases
Hemp, in bales, compressed
Hemp, manila, in bales, compressed
Hemp, sisal, in bales, compressed
Hemp, tow, in bales, compressed.
Hemp, burlaps, in bales, compressed
25
22
26
24
29
43
41
8
8
9
9
9
6
6
200
176
234
216
261
258
246
200 to 250
Linen, bleached goods, in cases
35
7
245
Linen, damask goods, in cases . .
50
5
250
Wool, in bales, not compressed
13
9
117
Wool, in bales, compressed
Wool, dress goods, flannels, in cases
Wool, worsted goods, in cases
48
18
27
5
9
9
240
162
243
19
9
171
Excelsior, in bales, compressed
19
9
171
240
TABLE 63
MISCELLANEOUS
CONTENTS OF STORAGE WAREHOUSES
Material
Pounds
per
cubic foot
of space
Height
of pile,
feet
Pounds
per
square foot
of floor
Recommended
live loads,
pounds per
square foot
Drugs, Oils, Paints, Etc.
Chemicals:
Acids, muriatic and nitric, in carboys. . .
Acids, sulphuric, in carbovs. . .
45
60
m
75
100
Ammonia, in carboys . .
30
1?1
50
Alum, pearl alum, in barrels
Bleaching powder, in hogsheads
Copper sulphate, blue vitriol, in bbls. . .
Soda, caustic soda, in iron drums
Soda, soda ash, in hogsheads
33
31
45
88
62
7
I*
$
231
103
225
294
170
Soda crystals, sal soda, in barrels
Soda nitrate, niter, in barrels
Soda silicate, in barrels
30
45
53
5
5
5
150
225
265
Zinc sulphate, white vitriol, in barrels . .
Oils, fats, resins, etc.:
Glycerine, in cases
40
52
5
6
200
312
Oils, animal, lard, etc., in barrels. . .
34
6
204
200 to 250
Oils, vegetable, linseed, in barrels
Oils, mineral, lubricants, in barrels. . . .
Oils, petroleum, kerosene, in barrels. . . .
Oils, naphtha, gasolene, in barrels
Rosin, in barrels
36
35
33
28
48
6
6
6
6
216
210
198
168
288
Shellac gum in boxes . .
38
&
228
Tallow, in barrels
37
g
222
Dye stuffs, paints, etc.:
43
6
258
Logwood extract, in boxes
70
4H
315
Sumac, in boxes
39
5
195
Red lead, litharge, dry, in barrels
White lead, dry in barrels
132
86
3%
4%
495
409
White lead, paste, in cans
Building Materials
Cement, natural, in barrels
174
59
3>I
6
609
354
)
Cement, Portland, in barrels
Lime, quick lime, ground, in barrels. . . .
73
50
6
5
438
250
300 to 400
Plaster of Paris, ground, in barrels. .
53
5
265
1
Sheet Metal and Wire
Sheet tin, in boxes
278
1 LZ
417
Wire, insulated copper, in coils
63
5
315
Wire, galvanized iron in coils
74
414
333
300 to 400
Wire, magnet wire, on spools. . . .
75
g
450
Miscellaneous
Chinawarc, glassware, in crates
40
g
320
Chinaware, glassware, in casks .....
14
g
126
Glass, in boxes
69
g
360
Hardware, door and sash checks, in cases.
Hardware, hinges, in cases. .'..
46
64
6
g
276
384
Hardware, locks, in cases
31
6
186
Hardware, screws, in boxes
Hides, raw, not compressed, in bales
Hides, raw, conipressed, in bales
Leather in bales
101
13
23
16
4
10
10
10
404
130
230
160
300 to 400
Paper, calendered paper \
Paper, newspaper, manila, strawboards. . .
Paper writing paper
50
35
64
6
6
g
300
210
384
Rope in coils
42
g
252
241
MISCELLANEOUS
TABLE 54
WEIGHTS OF BUILDING MATERIALS
Kind
Weight in Ib.
per sq. ft.
FLOORS
. maple finish floor and %-in. spruce under floor on 2 X 4-in. sleepers, 16-in. centers, with
2-in. dry cinder concrete filling
Cinder concrete filling per inch of thickness
Cement finish per inch of thickness
Asphalt mastic flooring IJ-^ in. thick
3-in. creosoted wood blocks on H-in. mortar base
Solid flat tile on 1-in. mortar bed
CEILINGS
Plaster on tile or concrete
Suspended metal lath and plaster
ROOFS
Five-ply felt and gravel
Four-ply felt and gravel
Three-ply ready roofing
Cement tile
Slate, \i in. thick
Sheathing, 1 in. thick, yellow pine
2-in. book tile
3-in. book tile
Skylight with galvanized iron frame, 2s~i n - glass
18
7
12
18
21
1
16
J*
12
20
Kind
Weight in Ib. per sq. ft.
Unplastered
One side
plastered
Both sides
plastered
WALLS
9-in. brick wall
84
121
168
205
243
60
75
102
33
45
17
18
25
31
35
10
12
14
16
89
126
173
210
248
65
80
107
38
50
22
23
30
36
40
15
17
19
21
43
55
27
28
35
41
45
20
22
24
26
20
32
22
13-in. brick wall
18-in. brick wall
22-in. brick wall
26-in. brick wall
4-in brick 4-in tile backing
4-in. brick, 8-in. tile backing
9-in. brick, 4-in. tile backing
8-in. tile
12-in. tile
PARTITIONS
3-in. clay tile
4-in. clay tile
6-in. clay tile
8-in. clay tile
10-in. clay tile.
3-in. gypsum block
4-in. gypsum block
6-in. gypsum block
2-in. solid plaster
4-in. solid plaster
4-in. hollow plaster
Kind
Weight in Ib.
per cu. ft.
Kind
Weight in Ib.
per cu. ft.
Beech
Birch
Brickwork
Concrete, cinder, structural
42
42
120
108
Limestone
Maple
Marble
Oak
150
42
168
48
Concrete, cinder, floor filling
Concrete, stone
Concrete, stone, reinforced
Douglas fir .
96
144
150
36
Pine, southern yellow
Sandstone
Spruce
42
144
30
Granite
Granolithic surface
168
144
unfilled
72
120
242
APPENDIX
RULINGS PERTAINING TO DESIGN AND WORKING STRESSES
Joint Committee Recommendations*
Design
Massive Concrete. In the design of massive or plain concrete, no account should
be taken of the tensile strength of the material, and sections should usually be proportioned
so as to avoid tensile stresses except in slight amounts to resist indirect stresses. This will
generally be accomplished in the case of rectangular shapes if the line of pressure is kept
within the middle third of the section, but in very large structures, such as high masonry
dams, a more exact analysis may be required. Structures of massive concrete are able to
resist unbalanced lateral forces by reason of their weight; hence the element of weight
rather than strength often determines the design. A leaner and relatively cheap concrete,
therefore, will often be suitable for massive concrete structures.
It is desirable generally to provide joints at intervals to localize the effect of contraction.
Massive concrete is suitable for dams, retaining walls, and piers in which the ratio
of length to least width is relatively small. Under ordinary conditions this ratio should
not exceed four. It is also suitable for arches of moderate span.
Reinforced Concrete. The use of metal reinforcement is particularly advantageous
in members such as beams in which both tension and compression exist, and in columns
where the principal stresses are compressive and where there also may be cross-bending.
Therefore, the theory of design here presented relates mainly to the analysis of beams and
columns.
General Assumptions, (a) Loads. The forces to be resisted are those due to:
1. The dead load, which includes the weight of the structure and fixed loads and forces.
2. The live load, or the loads and forces which are variable. The dynamic effect of
the live load will often require consideration. Allowance for the lattter is preferably
made by a proportionate increase in either the live load or the live load stresses. The
working stresses hereinafter recommended are intended to apply to the equivalent static
stresses thus determined.
In the case of high buildings the live load on columns may be reduced in accordance with
the usual practice.
(6) Lengths of Beams and Columns. The span length for beams and slabs simply
supported should be taken as the distance from center to center of supports, but need
not be taken to exceed the clear span plus the depth of beam or slab. For continuous
or restrained beams built monolithically into supports the span length may be taken
as the clear distance between faces of supports. Brackets should not be considered as
reducing the clear span in the sense here intended, except that when brackets which make
an angle of 45 degrees or more with the axis of a restrained beam are built monolithically
with the beam, the span may be measured from the section where the combined depth
of beam and bracket is at least one-third more than the depth of the beam." Maximum
negative moments are to be considered as existing at the end of the span as here defined.
When the depth of a restrained beam is greater at its ends than at midspan and the
slope of the bottom of the beam at its ends makes an angle of not more than 15 degress
with the direction of the axis of the beam at midspan, the span length may be measured
from face to face of supports.
The length of columns should be taken as the maximum unstayed length.
(c) Stresses. The following assumptions are recommended as a basis for calculations:
1. Calculations will be made with reference to working stresses and safe loads rather
than with reference to ultimate strength and ultimate loads.
2. A plane section before bending remains plane after bending.
* From Final Report of the Special Committee on Concrete and Reinforced Concrete of the Ameri-
can Society of Civil Engineers, presented before the Society, Jan. 17, 1917.
243
3. The modulus of elasticity of concrete in compression is constant within the usual
limits of working stresses. The distribution of comprefisive stress inbeams is, therefore,
rectilinear.
4. In calculating the moment of resistance of beams the tensile stresses in the concrete
are neglected.
5. The adhesion between the concrete and the reinforcement is perfect. Under
compressive stress the two materials are, therefore, stressed in proportion to their moduli of
elasticity.
6. The ratio of the modulus of elasticity of steel to the modulus of elasticity of concrete
is taken at 15, except as modified in section on "Working Stresses."
7. Initial stress in the reinforcement due to contraction or expansion of the concrete
is neglected.
It is recognized that some of the assumptions given herein are not entirely borne out
by experimental data. They are given in the interest of simplicity and uniformity, and
variations from exact conditions are taken into account in the selection of formulas and
working stresses.
The deflection of a beam depends upon the strength and stiffness developed throughout
its length. For calculating deflection a value of 8 for the ratio of the moduli will give
results corresponding approximately with the actual conditions.
T-Beams. In beam and slab construction an effective bond should be provided at
the junction of the beam and slab. When the principal slab reinforcement is parallel
to the beam, transverse reinforcement should be used extending over the beam and well
into the slab.
The slab may be considered an integral part of the beam, when adequate bond and
shearing resistance between slab and web of beam is provided, but its effective width
shall be determined by the following rules:
(a) It shall not exceed one-fourth of the span length of the beam.
(6) Its overhanging width on either side of the web shall not exceed six times the
thickness of the slab.
In the design of continuous T-beams, due consideration should be given to the com-
pressive stress at the support.
Beams in which the T-form is used only for the purpose of providing additional com-
pression area of concrete should preferably have a width of flange not more than three
times the width of the stem and a thickness of flange not less than one-third of the depth
of the beam. Both in this form and in the beam and slab form the web stresses and the
limitations in placing and spacing the longitudinal reinforcement will probably be control-
ling factors in design.
Floor Slabs Supported Along Four Sides. Floor slabs having the supports extending
along the four sides should be designed and reinforced as continuous over the supports.
If -the length of the slab exceeds 1.5 times its width the entire load should be carried by
transverse reinforcement.
For uniformly distributed loads on square slabs, one-half the live and dead load may
be used in the calculations of moment to be resisted in each direction. For oblong slabs,
the length of which is not greater than one and one-half times their width, the moment to
be resisted by the transverse reinforcement may be found by using a proportion of the live
and dead load equal to that given by the formula r = r 0.5, where I = length and b =
breadth of slab. TJie longitudinal reinforcement should then be proportioned to carry
the remainder of the load.
In placing reinforcement in such slabs account may well be taken of the fact that
the bending moment is greater near the center of the slab than near the edges. For this
purpose two-thirds of the previously calculated moments may be assumed as carried by the
center half of the slab and one-third by the outside quarters.
Loads carried to beams by slabs which are reinforced in two directions will not be
uniformly distributed to the supporting beams and the distribution will depend on the
relative stiffness of the slab and the supporting beams. The distribution which may be
expected ordinarily is a variation of the load in the beam in accordance with the ordinates
of a parabola, having its vertex at the middle of the span. For any gn en design, the prob-
able distribution shlould be ascertained and the moments in the beam calculated accordingly.
Continuous Beams and Slabs. When the beam or slab is continuous over its supports,
reinforcement should be fully provided at points of negative moment; and the stresses in
concrete recommended in the section on "Working Stresses" should not be exceeded. In
computing the positive and negative moments in beams and slabs? continuous over several
supports, due to uniformly distributed loads, the following rules are recommended:
(a) For floor slabs the bending moments at center and at support should be taken
at jo" f r both dead and live loads, where w represents the load per linear unit and I the
span length.
244
(6) For beams the bending moment at center and at support for interior spans should
icl~ wl~
be taken at y^"' anc ^ f r en d spans it should be taken at -r/r for center and interior support,
for both dead and live loads.
(c) In the case of beams and slabs continuous for two spans only, with their ends re-
strained, the bending moment both at the central support and near the middle of the span
/2
should be taken at r-Tr*
(d) At the ends of continuous beams the amount of negative moment which will be
developed in the beam will depend on the condition of restraint or fixedness, and this
will depend on the form of construction used. In the ordinary cases a moment of may
10
be taken; for small beams running into heavy columns this should be increased, but not to
.wP
exceed--
For spans of unusual length, or for spans of materially unequal length, more exact
calculations should be made. Special consideration is also required in the case of con-
centrated loads.
Even if the center of the span is designed for a greater bending moment than is called
for by (a) or (6), the negative moment at the support should not be taken as less than the
values there given.
Where beams are reinforced on the compression side, the steel may be assumed to
carry its proportion of stress in accordance with the ratio of moduli of elasticity, as given
in the section on "Working Stresses." Reinforcing bars for compression in beams should
be straight and should be two diameters in the clear from the surface of the concrete.
For the positive bending moment, such reinforcement should not exceed one per cent of
the area of the concrete. In the case of cantile"\er and continuous beams, tensile and
compressive reinforcement over supports should extend sufficiently beyond the support
and beyond the point of inflection to develop the requisite bond strength.
In construction made continuous over supports it is important that ample foundations
should be provided; for unequal settlements are liable to produce unsightly, if not danger-
ous cracks. This effect is more likely to occur in low structures.
Girders, such as wall girders, which have beams framed into one side only, should
be designed to resist torsional moment arising from the negative moment at the end of the
beam.
Bond Strength and Spacing of Reinforcement. Adequate bond strength should
be provided. The formula hereinafter given for bond stresses in beams is for straight
longitudinal bars. In beams in which a portion of the reinforcement is bent up near the
end, the bond stress at places, in both the straight bars and the bent bars, will be consider-
ably greater than for all the bars straight, and the stress at some point may be several times
as much as that found by considering the stress to be uniformly distributed along the bar.
In restrained and cantilever beams full tensile stress exists in the reinforcing bars at the
point of support and the bars should be anchored in the support sufficiently to develop
this stress.
In case of anchorage of bars, an additional length of bar should be provided beyond
that found on the assumption of uniform bond stress, for the reason that before the bond
resistance at the end of the bar can be developed the bar may have begun to slip at another
point and "running" resistance is less than the resistance before slip begins.
Where high bond resistance is required, the deformed bar is a suitable means of supply-
ing the necessary strength. But it should be recognized that even with a deformed bar
initial slip occurs at early loads, and that the ultimate loads obtained in the usual tests
for bond resistance may be misleading. Adequate bond strength throughout the length
of a bar is preferable to end anchorage, but, as an additional safeguard, such anchorage may
properly be used in special cases. Anchorage furnished by short bends at a right angle is
less effective than by hooks consisting of turns through 180 degrees.
The lateral spacing of parallel bars should be not less than three diameters from center
to center, nor should the distance from the side of the beam to the center of the nearest
bar be less than two diameters. The clear spacing between two layers of bars should be not
less than one inch. The use of more than two layers is not recommended, unless the layers
are tied together by adequate metal connections, particularly at and near points where
bars are bent up or bent down. Where more than one layer is used, at least all bars above
the lower layer should be bent up and anchored beyond the edge of the support.
Diagonal Tension and Shear. When a reinforced concrete beam is subjected to flexural
action, diagonal tensile stresses are set up. A beam without web reinforcement will fail
if these stresses exceed the tensile strength of the concrete. When web reinforcement,
made up of stirrups or of diagonal bars secured to the longitudinal reinforcement, or of
longitudinal reinforcing bars bent up at several points, is used, new conditions prevail, but
245
even in this case at the beginning of loading the diagonal tension developed is taken princi-
pally by the concrete, the deformations which are developed in the concrete permitting
but little stress to be taken by the web reinforcement. When the resistance of the concrete
to the diagonal tension is overcome at any point in the depth of the beam, greater stress is
at once set up in the web reinforcement.
For homogeneous beams the analytical treatment of diagonal tension is not very
complex, the diagonal tensile stress is a function of the horizontal and vertical shear-
ing stresses and of the horizontal tensile stress at the point considered, an as the intensity
of these three stresses varies from the neutral axis to the remotest fibre, the intensity
of the diagonal tension will be different at different points in the section, and will change
with different proportionate dimensions of length to depth of beam. For the composite
structure of reinforced concrete beams, an analysis of the web stresses, and particularly
of the diagonal tensile stresses, is very complex; and when the variations due to a change
from no horizontal tensile stress in the concrete at remotest fibre to the presence of hori-
zontal tensile stress at some point below the neutral axis are considered, the problem
becomes more complex and indefinite. Under these circumstances, in designing recourse
is had to the use of the calculated vertical shearing stress as a means of comparing or
measuring the diagonal tensile stresses developed, it being understood that the vertical
shearing stress is not the numerical equivalent of the diagonal tensile stress, and that there
is not even a constant ratio between them. It is here recommended that the maximum
vertical shearing stress in a section be used as the means of comparison of the resistance to
diagonal tensile stress developed in the concrete in beams not having web reinforcement.
Even after the concrete has reached its limit of resistance to diagonal tension, if the
beam has web reinforcement, conditions of beam action will continue to prevail, at least
through the compression area, and the web reinforcement will be called on to resist only a
part of the web stresses. From experiments with beams it is concluded that it is safe
practice to use only two-thirds of the external vertical shear in making calculations of the
stresses that come on stirrups, diagonal web pieces, and bent-up bars, and it is here
recommended for calculations in designing that two-thirds of the external vertical shear
be taken as producing stresses in web reinforcement.
It is well established that vertical members attached to or looped about horizontal
members, inclined members secured to horizontal members in such a way as to insure
against slip, and the bending of a part of the longitudinal reinforcement at an angle,
will increase the strength of a beam against failure by diagonal tension, and that a well-
designed and well-distributed web reinforcement may under the best conditions increase
the total vertical shear carried to a value as much as three times that obtained when the
bars are all horizontal and no web reinforcement is used.
When web reinforcement comes into action as the principal tension web resistance,
the bond stresses between the longitudinal bars and the concrete are not distributed
as uniformly along the bars as they otherwise would be, but tend to be concentrated
at and near stirrups, and at and near the points where bars are bent up. When stirrups
are not rigidly attached to the longitudinal bars, and the proportioning of bars and stirrups
spacing is such that local slip of bars occurs at stirrups, the effectiveness of the stirrups
is impaired, though the presence of stirrups still gives an element of toughness against
diagonal tension failure.
Sufficient bond resistance 'between the concrete and the stirrups or diagonals must
be provided in the compressing area of the beam/
The longitudinal spacing of vertical stirrups should not exceed one-half the depth of
beam, and that of inclined members should not exceed three-fourths of the depth ef beam.
Bending of longitudinal reinforcing bars at an angle across the web of the beam may
be considered as adding to diagonal tension resistance for a horizontal distance from the
point of bending equal to three-fourths of the depth of beam. Where the bending is made
at two or more points, the distance between points of bending should not exceed three-
fourths of the depth of the beam. In the case of a restrained beam the effect of bending up
a bar at the bottom of the beam in resisting diagonal tension may not be taken as extending
beyond a section at the point of inflection, and the effect of bending down a bar in the
region of negative moment may be taken as extending from the point of bending down of
bar nearest the support to a section not more than three-fourths of the depth of beam beyond
the point of bending down of bar farthest from the support but not beyond the point of
inflection. In case stirrups are used in the beam away from the region in which the bent
bars are considered effective, a stirrup should be placed not farther than a distance equal
to one-fourth the depth of beam from the limiting sections defined above. In case the
web resistance required through the region of bent bars is greater than that furnished by
the bent bars, sufficient additional web reinforcement in the form of stirrups or attached
diagonals should be provided. The higher resistance to diagonal tension stresses given by
unit frames having the stirrups and bent-up bars securely connected together both longi-
tudinally and laterally is worthy of recognition. It is necessary that a limit be placed
246
on the amount of shear which may be allowed in a beam; for when web reinforcement
sufficiently efficient to give very high web resistance is used, at the higher stresses the
concrete in the beam becomes checked and cracked in such a way as to endanger its dura-
bility as well as its strength.
The section to be taken as the critical section in the calculation of shearing stresses
will generally be the one having the maximum vertical shear, though experiments show
that the section at which diagonal tension failures occur is not just at a support even though
the shear at the latter point be much greater.
In the case of restrained beams, the first stirrup or the point of bending down of bar
should be placed not farther than one-half of the depth of beam away from the face of the
support.
It is important that adequate bond strength or anchorage be provided to develop
fully the assumed strength of all web reinforcement.
Low bond stresses in the longitudinal bars are helpful in giving resistance against
diagonal tension failures and anchorage of longitudinal bars at the ends of the beams
or in the supports is advantageous.
It should be noted that it is on the tension side of a beam that diagonal tension develops
in a critical way, and that proper connection should always be made between stirrups or
other web reinforcement and the longitudinal tension reinforcement, whether the latter is
on the lower side of the beam or on its upper side. Where negative moment exists, as is
the case near the supports in a continuous beam, web reinforcement to be effective must be
looped over or wrapped around or be connected with the longitudinal tension reinforcing
bars at the top of the beam in the same way as is necessary at the bottom of the beam at
sections where the bending moment is positive.
Inasmuch as the smaller the longitudinal deformations in the horizontal reinforce-
ment are, the less the tendency for the formation of diagonal cracks, a beam will be strength-
ened against diagonal tension failure by so arranging and proportioning the horizontal
reinforcement that the unit stresses at points of large shear shall be relatively low.
It does not seem feasible to make a complete analysis of the action of web reinforce-
ment, and more or less empirical methods of calculation are therefore employed. Limiting
values of working stresses for different types of web reinforcement are given in the section
on "Working Stresses." The conditions apply to cases commonly met in design. It is
assumed that adequate bond resistance or anchorage of all web reinforcement will be
provided.
When a flat slab rests on a column, or a column bears on a footing, the vertical shearing
stresses in the slab or footing immediately adjacent to the column are termed punching
shearing stresses. The element of diagonal tension, being a function of the bending
moment as well as of shear, may be small in such cases, or may be otherwise provided for.
For this reason the permissible limit of stress for punching shear may be higher than the
allowable limit when the shearing stress is used as a means of comparing diagonal tensile
stress. The working values recommended are given in the section on "Working Stresses."
Columns. By columns are meant compression members of which the ratio of unsup-
ported length to least width exceeds about four, and which are provided with reinforcement
of one of the forms hereafter described.
It is recommended that the ratio of unsupported length of column to its least width be
limited to fifteen.
The effective area of hooped columns or columns reinforced with structural shapes
shall be taken as the area within the circle enclosing the spiral or the polygon enclosing the
structural shapes.
Columns may be reinforced by longitudinal bars; by bands, hoops, or spirals, together
with longitudinal bars; or by structural forms which are sufficiently rigid to have value in
themselves as columns. The general effect of closely spaced hooping is to greatly increase
the toughness of the column and to add to its ultimate strength, but hooping has little
effect on its behavior within the limit of elasticity. It thus renders the concrete a safer and
more reliable material, and should permit the use of a somewhat higher working stress.
The beneficial effects of toughening are adequately provided by a moderate amount of
hooping, a larger amount serving mainly to increase the ultimate strength and the deforma-
tion possible before ultimate failure.
Composite, columns of structural steel and concrete in which the steel forms a column
by itself should be designed with caution. To classify this type as a concrete column
reinforced with structural steel is hardly permissible, as the steel, generally, will take
the greater part of the load. When this type of column is used, the concrete should
be adequately tied together by tie plates or lattice bars, which, together with other details,
such as splices, etc., should be designed in conformity with standard practice for structural
steel. The concrete may exert a beneficial effect in restraining the steel from lateral
deflection and also in increasing the carrying capacity of the column. The proportion of
load to be carried by the concrete will depend on the form of the column and the method of
247
construction. Generally, for high percentages of steel, the concrete will develop relatively
low unit stresses, and caution should be used in placing dependence on the concrete.
The following recommendations are made for the relative working stresses in the
concrete for the several types of columns:
(a) Columns with longitudinal reinforcement to the extent of not less than 1 per cent
and not more than 4 per cent, and with lateral ties of not less than 34 inch in diameter
12 inches apart, nor more than 16 diameters of the longitudinal bar: the unit stress rec-
ommended for axial compression, on concrete piers having a length not more than four
diameters, in section on "Working Stresses."
(6) Columns reinforced with not less than 1 per cent and not more than 4 per cent
of longitudinal bars and with circular hoops or spirals not less than 1 per cent of the volume
of the concrete and as hereinafter specified : a unit stress 55 per cent higher than given for
(a), provided the ratio of unsupported length of column to diameter of the hooped core is
not more than 10.
The foregoing recommendations are based on the following conditions:
It is recommended that the minimum size of columns to which the working stresses
may be applied be 12 inches out to out.
In all cases longitudinal reinforcement is assumed to carry its proportion of stress in
accordance with (c) Stresses, page 243. The hoops or bands are not to be counted on
directly as adding to the strength of the column.
Longitudinal reinforcement bars should be maintained straight, and should have suffi-
cient lateral support to be securely held in place until the concrete has set.
Where hooping is used, the total amount of such reinforcement shall be not less than
1 per cent of the volume of the column, enclosed. The clear spacing of such hooping
shall not be greater than one-sixth the diameter of the enclosed column and preferably
not greater than one- tenth, and in no case more than 2% in. Hooping is to be circular
and the ends of bands must be united in such a way as to develop their full strength.
Adequate means must be provided to hold bands or hoops in place so as to form a column,
the core of which shall be straight and well centered. The strength of hooped columns
depends very much upon the ratio of length to diameter of hooped core, and the strength
due to hooping decreases rapidly as this ratio increases beyond five. The working stresses
recommended are for hooped columns with a length of not more than ten diameters of the
hooped core.
The Committee has no recommendation to make for a formula for working stresses
for columns longer than ten diameters.
Bending stresses due to eccentric loads, such as unequal spans of beams, and to lateral
forces, must be provided for by increasing the section until the maximum stress does
not exceed the values above specified. Where tension is possible in the longitudinal
bars of the columns, adequate connection between the ends of the bars must be provided
to take this tension.
Reinforcing for Shrinkage and Temperature Stresses. When areas of concrete too
large to expand and contract freely as a whole are exposed to atmospheric conditions,
the changes of form due to shrinkage and to action of temperature are such that cr cks may
occur in the mass unless precautions are taken to distribute the stresses so as to prevent the
cracks altogether or to render them very small. The distance apart of the cracks, and
consequently their size, will be directly proportional to the diameter of the reinforcement
and to the tensile strength of the concrete, and inversely proportional to the percentage of
reinforcement and also to its bond resistance per unit of surface area. To be most effective,
therefore, reinforcement (in amount generally not less than one-third of 1 per cent of the
gross area) of a form which \vill develop a high bond resistance should be placed near the
exposed surface and be well distributed. Where openings occur the area of cross-section of
the reinforcement should not be reduced. The allowable size and spacing of cracks depends
on various considerations, such as the necessity for water-tightness, the importance of
appearance of the surface, and the atmospheric changes.
The tendency of concrete to shrink makes it necessary, except where expansion is
- provided for, to thoroughly connect the component parts of the frame of articulated
structures, such as floor and wall members in buildings, by the use of suitable reinforcing
material. The amount of reinforcement for such connection should bear some relation to
the size of the members connected, larger and heavier members requiring stronger connec-
tions. The reinforcing bars should be extended beyond the critical section far enough, or
should be sufficiently anchored to develop their full tensile strength.
Flat Slab. The continuous flat slab reinforced in two or more directions and built
monolithically with the supporting columns (without beams or girders) is a type of construc-
tion which is now extensively used and which has recognized advantages for certain
types of structures as, for example, warehouses in which large, open floor space is desired.
In its construction, there is excellent opportunity for inspecting the position of the re-
inforcement, The conditions attending deposition and placing of concrete are favorable to
24S
securing uniformity and soundness in the concrete. The recommendations in the following
paragraphs relate to flat slabs extending over several rows of panels in 'each direction.
Necessarily the treatment is more or less empirical.
The co-efficients and moments given relate to uniformly distributed loads.
(a) Column Capital. It is usual in flat slab construction to enlarge the supporting
columns at their top, thus forming column capitals. The size and shape of the column
capital affect the strength of the structure in several ways. The moment of the external
forces which the slab is called upon to resist is dependent upon the size of the capital;
the section of the slab immediately above the upper periphery of the capital carries the
highest amount of punching shear; and the bending moment developed in the column
by an eccentric or unbalanced loading of the slab is greatest at the under surface of the
slab. Generally the horizontal section of the column capital should be round or square
with rounded corners. In oblong panels the section may be oval or oblong, with dimensions
proportional to the panel dimensions. For computation purposes, the diameter of the
column capital will be considered to be measured where its vertical thickness is at least
lj^ inches, provided the slope of the capital below this point nowhere makes an angle with
the vertical of more than 45 degrees. In case a cap is placed above the column capital,
the part of this cap within a cone made by extending the lines of the column capital upward
at the slope of 45 degrees to the bottom of the slab or dropped panel may be considered as
part of the column capital in determining the diameter for design purposes. Without
attempting to limit the size of the column capital for special cases, it is recommended that
the diameter of the column capital (or its dimensions parallel to the edge of the panel)
generally be made not less than one-fifth of the dimension of the panel from center to
center of adjacent columns. A diameter equal to 0.225 of the panel length has been used
quite widely and acceptably. For heavy loads or large panels especial attention should be
given to designing and reinforcing the column capital with respect to compressive stresses
and bending moments. In the case of heavy loads or large panels, and where the conditions
of the panel loading or variations in panel length or other conditions cause high bending
stresses in the column, and also for column capitals smaller than the size herein recom-
mended, especial attention should be given to designing and reinforcing the column capital
with respect to compression and to rigidity of connection to floor slab.
(6) Dropped Panel. In one type of construction the slab is thickened throughout
an area surrounding the column capital. The square or oblong of thickened slab thus
formed is called a dropped panel or a drop. The thickness and the width of the dropped
panel may be governed by the amount of resisting moment to be provided (the com-
pressive stress in the concrete being dependent upon both thickness and width), or its
thickness may be governed by the resistance to shear required at the edge of the column
capital and its width by the allowable compressive stresses and shearing stresses in the
thinner portion of the slab adjacent to the dropped panel. Generally, however, it is
recommended that the width of the dropped panel be at least four-tenths of the correspond-
ing side of the panel as measureU from center to center of columns, and that the offset in
thickness be not more than five- tenths of the thickness of the slab outside the dropped
panel.
(c) Slab Thickness. In the design of a slab, the resistance to bending and to shear-
ing forces will largely govern the thickness, and, in the case of large panels with light
loads, resistance to deflection may be a controlling factor. The following formulas for
minimum thicknesses are recommended as general rules of design when the diameter
of the column capital is not less than one^fifth of the dimension of the panel from center to
center of adjacent columns, the large dimension being used in the case of oblong panels.
For notation, let
t = total thickness of slab in inches.
L = panel length in feet.
w = sum of live load and dead load in pounds per square foot.
Then, for a slab without dropped panels, minimum t = 0.024L\/w -f 1^; for a slab
with dropped panels, minimum I = Q.Q2L'vw + 1; for a dropped panel whose width is
four- tenths of the panel length, minimum t = 0.03L\A0 + lM-
In no case should the slab thickness be made less than six inches, nor should the thick-
ness of a floor slab be made less than one-thirty-second of the panel length, nor the thick-
ness of a roof slab less than one-fortieth of the panel length.
(d) Bending and Resisting Moments in Slabs. If a vertical section of a slab be taken
across a panel along a line midway between columns, and if another section be taken
along an edge of the panel parallel to the first section, but skirting the part of the periphery
of the column capitals at the two corners of the panels, the moment of the couple formed by
the external load on the half panel, exclusive of that over the column capital (sum of dead
and live load) and the resultant of the external shear or reaction at the support at the
249
two column capitals (see Fig. 1), may be found by ordinary static analysis. It will be noted
that the edges of the area here considered are along lines of zero shear except around the
column capitals. This moment of the external forces acting on the half panel will be
resisted by the numerical sum of (a) the moment of the internal stresses at the section of
the panel midway between columns (positive resisting moment) and (b) the moment of the
internal stresses at the section referred to at the end of the panel (negative resisting
moment). In the curved portion of the end section (that skirting the column), the stresses
considered are the components which act parallel to the normal stresses on the straight
portion of the section. Analysis shows that, for a uniformly distributed load, and round
peripheries of -fin
column caprta/s
...7
section
section
FIG. 1.
FIG. 2.
columns, and square panels, the numerical sum of the positive moment and the negative
moment at the two sections named is given quite closely by the equation
In this formula and in those which follow relating to oblong panels:
w = sum of the live and dead load per unit of area.
I = side of a square panel measured from center to center of columns.
h = one side of the oblong panel measured from center to center of columns.
fa = other side of oblong panel measured in the same way.
c = diameter of the column capital.
M x = numerical sum of positive moment and negative moment in one direction.
My = numerical sum of positive moment and negative moment in the other direction.
(See paper and closure, Statical Limitations upon the Steel Requirement in Reinforced
Concrete Flat Slab Floors, by John R. Nichols, Jun. Am. Soc. C. E., Transactions Am. Soc.
C. E. Vol. LXXVII.)
For oblong panels, the equations for the numerical sums of the positive moment arid
the negative moment at the two sections named become
-! *(,.-!)'
Where M x is the numerical sum of the positive moment and the negative moment
for the sections parallel to the dimensions fa, and M y is the numerical sum of the positive
moment and the negative moment for the sections parallel to the dimensions h.
What proportion of the total resistance exists as positive moment and what as negative
moment is not readily determined. The amount of the positive moment and that of the
negative moment may be expected to vary somewhat with the design of the slab. It seems
proper, however, to make the division of total resisting moment in the ratio of three-eighths
for the positive moment to five-eighths for the negative moment.
With reference to variations in stress along the sections, it is evident from condi-
tions of flexure that the resisting moment is not distributed uniformly along either the
section of positive moment or that of negative moment. As the law of the distribution is
not known definitely, it will be necessary to make an empirical apportionment along the
sections; and it will be considered sufficiently accurate generally to divide the sections into
two parts and to use an average value over each part of the panel section.
The relatively largebreadth of structure in a flat slab makes the effect of local variations
in the concrete less than would be the case for narrow members like beams. The tensile
resistance of the concrete is less affected by cracks. Measurements of deformations in
250
buildings under heavy load indicate the presence of considerable tensile resistance in the
concrete, and the presence of this tensile resistance acts to decrease the intensity of the
compressive stresses. It is believed that the use of moment coefficients somewhat less
than those given in a preceding paragraph as derived by analysis is warranted, the calcula-
tions of resisting moment and stresses in concrete and reinforcement being made according
to the assumptions specified in this report and no change being made in the values of the
working stresses ordinarily used. Accordingly, the values of the moments which are
recommended for use are somewhat less than those derived by analysis. The values
given may be used when the column capitals are round, oval, square or oblong.
(e) Names for Moment Sections. For convenience, that portion of the section across
a panel along a line midway between columns which lies within the middle two quarters
of the width of the panel (HI, Fig. 2), will be called the inner section, and that portion in
the two outer quarters of the width of the panel (GH and IJ, Fig. 2) will be called the outer
sections. Of the section which follows a panel edge from column capital to column capital
and which includes the quarter peripheries of the edges of two column capitals, that portion
within the middle two quarters of the panel width (CD, Fig. 2) will be called the mid-
section, and the two remaining portions (ABC and DEF, Fig. 2), each having a projected
width equal to one-fourth of the panel width, will be called the column-head sections.
(/) Positive Moment. For a square interior panel, it is recommended that the positive
moment for a section in the middle of a panel extending across its width be taken
as wl[ I TT ) . Of this moment, at least 25 per cent should be provided for in the
25 \ 6 /
inner section; in the two outer sections of the panel at least 55 per cent of the specified
moment should be provided for in slabs not having dropped panels, and at least 60 per cent
in slabs having dropped panels, except that in calculations to determine necessary thickness
of slab away from the dropped panel at least 70 per cent of the positive moment should be
considered as acting in the two outer sections.
(Q) Negative Moment. For a square interior panel, it is recommended that the negative
moment for a section \\ hich follows a panel edge from column capital to column capital and
which includes the quarter peripheries of the edges of the two column capitals (the section
1 / 2c\ 2
altogether forming the projected width of the panel) be taken as u-ll I- \ . Of this
negative moment, at least 20 per cent should be provided for in the mid-section and at least
65 per cent in the two column-head sections of the panel, except that in slabs having dropped
panels at least 80 per cent of the specified negative moment should be provided for in the
two column-head sections of the panel.
(h) Moments for Oblong Panels. When the length of a panel does not exceed the breadth
by more than 5 per cent, computation may be made on the basis of a square panel with sides
equal to the mean of the length and the breadth.
When the long side of an interior oblong panel exceeds the short side by more than
one-twentieth and by not more than one-third of the short side, it is recommended that
the positive moment be taken as wlz l/i 5- J on a section parallel to the dimension
h, and wl\ (h TT ) on a section parallel to dimension Zi; and that the negative moment
25 V /
be taken as - wh [h ^ ) on a section at the edge of the panel corresponding to the
2c2
dimension h, and irli (h ^ 1 at a section in the other direction. The limitations of
the apportionment of moment between inner section and outer section and between mid-
section and column-head sections may be the same as for square panels.
(t) Watt Panels. The coefficient of negative moment at the first row of columns
away from the wall should be increased 20 per cent over that required for interior panels,
and likewise the coefficient of positive moment at the section halfway to the wall should
be increased by 20 per cent. If girders are not provided along the wall or the slab does not
project as a cantilever beyond the column line, the reinforcement parallel to the wall for the
negative moment in the column-head section and for the positive moment in the outer
section should be increased by 20 per cent. If the wall is carried by the slab this concen-
trated load should be provided for in the design of the slab. The coefficient of negative
moments at the wall to take bending in the direction perpendicular to the wall line may be
determined by the conditions of restraint and fixedness as found from the relative stiffness
of columns and slab, but in no case should it be taken as less than one-half of that for
interior panels.
0') Reinforcement. In the calculation of moments all the reinforcing bars which cross
the section under consideration and which fulfill the requirements given under paragraph
(I) of this chapter may be used. For a column-head section reinforcing bars parallel to the
251
straight portion of the section do not contribute to the negative resisting moment for the
column-head section in question. In the case of four-way reinforcement the sectional area
of the diagonal bars multiplied by the sine of the angle between the diagonal of the panel
and straight portion of the section under consideration may be taken to act as reinforcement
in a rectangular direction.
(k) Point of Inflection. For the purpose of making calculations of moments at sections
away from the sections of negative moment and positive moment already specified, the
point of inflection on any line parallel to a panel edge may be taken as one-fifth of the clear
distance on that line between the two sections of negative moment at the opposite ends of
the panel indicated in paragraph (e), of this chapter. For slabs having dropped panels the
coefficient of one-fourth should be used instead of one-fifth.
(1) * Arrangement of Reinforcement. The design should include adequate provision
for securing the reinforcement in place so as to take not only the maximum moments,
but the moments at intermediate sections. All bars in rectangular bands or diagonal bands
should extend on each side of a section of maximum moment, either positive or negative,
to points at least twenty diameters beyond the point of inflection as defined herein or be
hooked or anchored at the point of inflection. In addition to this provision bars in diagonal
bands used as reinforcement for negative moment should extend on each side of a line
drawn through the column center at right angles to the direction of the band at least a
distance equal to thirty-five one-hundredths of the panel length, and bars in diagonal bands
used as reinforcement for positive moment should extend on each side of a diagonal through
the center of the panel at least a distance equal to thirty-five one-hundredths of the panel
length; and no splice by lapping should be permitted at or near regions of maximum stress
except as just described. Continuity of reinforcing bars is considered to have advantages,
and it is recommended that not more than one-third of the reinforcing bars in any direction
be made of a length less than the distance center to center of columns in that direction.
Continuous bars should not all be bent up at the same point of their length, but the zone in
which this bending occurs should extend on each side of the assumed point of inflection, and
should cover a width of at least one-fifteenth of the panel length. Mere draping of the
bars should not be permitted. In four-way reinforcement the position of the bars in both
diagonal and rectangular directions may be considered in determining whether the width
of zone of bending is sufficient.
(ra) Reinforcement at Construction Joints. It is recommended that at construction
joints extra reinforcing bars equal in section to 20 per cent of the amount necessary to
meet the requirements for moments at the section where the joint is made be added to the
reinforcement, these bars to extend not less than 50 diameters beyond the joint on each
side.
(n) Tensile and Compressive Stresses. The usual method of calculating the tensile
and .compressive stresses in the concrete and in the reinforcement, based on the assump-
tions for internal stresses given in this chapter, should be followed. In the case of the
dropped panel the section of the slab and dropped panel may be considered to act integrally
for a width equal to the width of the column-head section.
(o) Provision for Diagonal Tension and Shear. In calculations for the shearing stress
which is to be used as the means of measuring the resistance to diagonal tension stress, it is
recommended that the total vertical shear on two column-head sections constituting a
width equal to one- half the lateral dimensions of the panel, for use in the formula for deter-
mining critical shearing stresses, be considered to be one-fourth of the total dead and live
load on a panel for a slab of uniform thickness, and to be three-tenths of the sum of the
dead and live loads on a panel for a slab with dropped panels. The formula for shearing
unit stress may then be written v = for slabs of uniform thickness, and v = ' .
bjd bjd
for slabs with dropped panels, where W is the sum of the dead and live load on a panel,
6 is half the lateral dimension of the panel measured from center to center of columns, and
jd is the lever arm of the resisting couple at the section.
The calculation of what is commonly called punching shear may be made on the assump-
tion of a uniform distribution over the section of the slab around the periphery of the
column capital and also of a uniform distribution over the section of the slab around the
periphery of the dropped panel, using in each case an amount of vertical shear greater by
25 per cent than the total vertical shear on the section under consideration.
The values of working stresses should be those recommended for diagonal tension
and shear in the section on "Working Stresses."
(p) Walls and Openings. Girders or beams should be constructed to carry walls and
other concentrated loads which are in excess of the working capacity of the lab. Beams
should also be provided in case openings in the floor reduce the working strength of the
slab below the required carrying capacity.
(q) Unusual Panels. The coefficients, apportionments, and thicknesses recom-
mended are for slabs which have several rows of panels in each direction, and in which
252
the size of the panels is approximately the same. For structures having a width of one,
two, or three panels, and also for slabs having panels of markedly different sizes, an analysis
should be made of the moments developed in both slab and columns, and the values given
herein modified accordingly. Slabs with paneled ceiling or with depressed paneling in the
floor are to be considered as coming under the recommendations herein given.
(r) Bending Moments in Columns. Provision should be made in both wall columns
and interior columns for the bending moment which will be developed by unequally loaded
panels, eccentric loading, or uneven spacing of columns. The amount of moment to be
taken by a column will depend upon the relative stiffness of columns and slab, and com-
putations may be made by rational methods, such as the principal of least work, or of slope
and deflection. Generally, the larger part of the unequalized negative moment will be
transmitted to the columns, and the column should be designed to resist this bending
moment. Especial attention should be given to wall columns .and corner columns.
Working Stresses
General Assumptions. The following working stresses are recommended for static
loads. Proper allowances for vibration and impact are to be added to live loads where
necessary to produce an equivalent static load before applying the unit stresses in propor-
tioning parts.
In selecting the permissible working stress on concrete, the designer should be guided
by the working stresses usually allowed for other materials of construction, so that all
structures of the same class composed of different materials may have approximately the
same degree of safety.
The following recommendations as to allowable stresses are given in the form of per-
centages of the ultimate strength of the particular concrete which is to be used ; this ultimate
strength is that developed at an age of twenty-eight days, in cylinders 8 inches in diameter
and 16 inches long, of proper consistency* made and stored under laboratory conditions.
In the absence of definite knowledge in advance of construction as to just what strength
may be expected, the committee submits the following values as those which should be
obtained with materials and workmanship in accordance with the recommendations of this
report.
Although occasional tests may show higher results than those here given, the Committee
recommends that these values should be the maximum used in design.
TABLE OF COMPRESSIVE STRENGTHS OF DIFFERENT MIXTURES OF CONCRETE
(In Pounds per Square Inch)
Aggregate
Granite trap rock
l:3t
3300
1 :4M t
2800
l:6f
2200
l:7Mt
1800
l:9t
1400
Gravel, hard limestone and hard sandstone . .
Soft limestone and sandstone
Cinders
3000
2200
800
2500
1800
700
2000
1500
600
1600
1200
500
1300
1000
400 .
NOTE. For variations in the moduli of elasticity see 254.
Bearing. When compression is applied to a surface of concrete of v at least twice the
loaded area, a stress of 35 per cent of the compressive strength may be allowed in the
area actually under load.
Axial Compression. For concentric compression on a plain concrete pier, the length
of.wnich does not exceed four diameters, or on a column reinforced with longitudinal bars
only, the length of which does not exceed 12 diameters, 22.5 per cent of the compressive
strength may be allowed.
For other forms of columns the stresses obtained from the ratios given in the preceding
section on " Design" may govern. .
Compression in Extreme Fiber. The extreme fiber stress of a beam, calculated on
the assumption of a constant modulus of elasticity for concrete under working stresses
may be allowed to reach 32.5 per cent of the compressive strength. Adjacent to the
support of continuous beams stresses 15 per cent higher may be used.
Shear and Diagonal Tension. In calculations on beams in which the maximum
shearing stress in a section is used as the means of measuring the resistance to diagonal
tension stress, the following allowable values for the maximum vertical shearing stress in
concrete, calculated by the method given in formula on page 4, v = J-TJ, are recommended:
* The materials should be mixed wet enough to produce a concrete of such a consistency as will flow
sluggishly into the forms and about the metal reinforcement, and which, at the same time, can be
conveyed from the mixer to the forms without separation of the coarse aggregate from the mortar.
The quantity of water is of the greatest importance in securing concrete of maximum strength and
density; too much water is as objectionable as too little.
t Combined volume fine and coarse aggregate measured separately.
253
(a) For beams with horizontal bars only and without web reinforcement, 2 per cent of
the compressive strength.
(6) For beams with web reinforcement consisting of vertical stirrups looped' about
the longitudinal reinforcing bars in the tension side of the beam and spaced horizontally
not more than one-half the depth of the beam; or for beams in which longitudinal bars are
bent up at an angle of not more than 45 degrees or less than 20 degrees with the axis of the
beam, and the points of bending are spaced horizontally not more than three-quarters of the
depth of the beam apart, not to exceed 4)^ per cent of the compressive strength.
(c) For a combination of bent bars and vertical stirrups looped about the reinforcing
bars in the tension side of the beam and spaced horizontally not more than one-half of the
depth of the beam, 5 per cent of the compressive strength.
(d) For beams with web reinforcement (either vertical or inclined) securely attached
to the longitudinal bars in the tension side of the beam in such a way as to prevent slipping
of bar past the stirrup, and spaced horizontally not more than one-half of the depth of the
beam in case of vertical stirrups and not more than three-fourths of the depth of the beam
in the case of inclined members, either with longitudinal bars bent up or not, 6 per cent of
the compressive strength.
The web reinforcement in case any is used should be proportioned by using two-thirds
of the external vertical shear in formulas (a) and (6) on page 4. The effect of longitu-
dinal bars bent up at an angle of from 20 to 45 degrees with the axis of the beam may
be taken at sections of the beam in which the bent up bars contribute to diagonal
tension resistance (see "Diagonal Tension and Shear," page 245) as reducing the
shearing stresses to be otherwise provided for. The amount of reduction of the shearing
stress by means of bent up bars will depend upon their capacity, but in no case should be
taken as greater than 4 % per cent of the compressive strength of the concrete over the
effective cross-section of the beam.* The limit of tensile stress in the bent up por-
tion of the bar calculated by formula (6) on page 4, using in this formula an amount of total
shear corresponding to the reduction in shearing stress assumed for the bent up bars,
may be taken as specified for the working stress of steel, but in the calculations the
stress in the bar due to its part as longitudinal reinforcement of the beam should be
considered. The stresses in stirrups and inclined members when combined with bent
up bars are to be determined by finding the amount of the total shear which may be
allowed by reason of the bent up bars, and subtracting this shear from the total external
vertical shear. Two-thirds of the remainder will be the shear to be carried by the stirrups,
using formulas (a) or (6) on page 4.
Where punching shear occurs, provided the diagonal tension requirements are met,
a shearing stress of 6 per cent of the compressive strength may be allowed.
Bond. The bond stress between concrete and plain reinforcing bars may be assumed
at 4 per cent of the compressive strength, or 2 per cent in the case of drawn wire. In the
best types of deformed bar the bond stress may be increased, but not to exceed 5 per cent of
the compressive strength of the concrete.
Reinforcement. The tensile or compressive stress in steel should not exceed 16,000
pounds per square inch.
In structural steel members the working stresses adopted by the American Railway
Engineering Association are recommended.
Modulus of Elasticity. The value of the modulus of elasticity of concrete has a wide
range, depending on the materials used, the age, the range of stresses between which it is
considered, as well as other conditions. It is recommended that in computations for the
position of the neutral axis, and for the resisting moment of beams and for compression
of concrete in columns, it be assumed as:
(a) One-fortieth that of steel, when the strength of the concrete is taken as not more
than 800 pounds per square inch.
(6) One-fifteenth that of steel, when the strength of the concrete is taken as greater
than 800 pounds per square inch.
(c) One-twelfth that of steel, when the strength of the concrete is taken as greater
than 2,200 pounds per square inch, and less than 2,900 pounds per square inch.
(d) One-tenth that of steel, when the strength of the concrete is taken as greater
than 2,900 pounds per square inch.
Although not rigorously accurate, these assumptions will give safe results. For the
deflection of beams which are free to move longitudinally at the supports, in using formulas
for deflection which do not take into account the tensile strength developed in the concrete,
a modulus of one-eighth of that of steel is recommended.
254
AMERICAN CONCRETE INSTITUTE RECOMMENDATIONS*
1. Conditions. All reinforced-concrete construction shall be designed to meet the
conditions of loading (including bending in columns) without stressing the materials used
beyond the safe working stresses specified.
2. Dead-Loads. The dead-loads shall be the weight of the permanent structure. The
weight of reinforced stone, gravel or slag concrete shall be taken as 144 Ib. per cu. ft.;
the weight of cinder concrete as 100 Ib. per cu. ft.
3. Live-Loads. The live-load shall be the working or variable load for which the
structure is designed.
4. Reduction of Loads. All parts of a structure shall be designed to carry safely the
entire combined dead- and live-loads with the exception that the loads on columns and
foundations may be reduced by considering that columns in top story carry the total live-
and dead-load above them; columns in next to top story carry the total dead-load and
eighty-five (85) per cent of the total live-load above; columns in the next lower story, the
total dead-load and eighty (80) per cent of the total live-load above: and thus on downward
reducing at each story the percentage of total live-loads carried, by 5, until a reduction of
fifty (50) per cent is reached. The columns in this and in every story below this point
shall be proportioned to carry the total dead-load and at least fifty (50) per cent of the
total live-load of all the floors and roofs above them.
For warehouses the increment of reduction per story shall be 2^ per cent instead of 5 per
cent.
5. General Assumptions. As a basis for calculations for the strength of reinforced-
concrete construction the following assumptions shall be made:
(a) Calculations shall be made with reference to working stresses and safe loads
rather than with reference to ultimate strength and ultimate loads.
(6) A plane section before bending remains plane after bending.
(c) The modulus of elasticity of concrete in compression within the usual limits of
working stresses is constant.
(d) In calculating the moment of resistance of beams, the tensile stresses in the
concrete are neglected.
(e) Perfect adhesion is assumed between concrete and reinforcement. Under
compressive stresses the two materials will, therefore, be stressed in proportion to their
moduli of elasticity.
(/) The ratio of the modulus of elasticity of concrete shall be taken as follows :
1. One-fortieth that of steel when the strength of the concrete is taken as not more
than eight hundred (800) Ib. per sq. in.
2 One-fifteenth that of steel when the strength of the concrete is taken as greater
than twelve hundred (1200) Ib. per sq. in. or less than twenty-two hundred
(2200) Ib. per sq. in.
3. One-twelfth that of steel when strength of the concrete is taken as greater than
twenty- two hundred (2200) Ib. per sq. in. or less than thirty- three hundred (3300)
Ib. per sq. in.
4. One-tenth that of steel when the strength of the concrete is taken as greater than
thirty-three hundred (3300) Ib. per sq. in.
6. Strength of Materials. The ultimate strength of concrete shall be that developed at
an age of 28 days, in cylinders 8 in. in diameter and 16 in. in length or 6 in. in diameter and
12 in. in length, of the consistency and proportions to be used in the work, made and stored
under laboratory conditions, but in no case shall the values exceed those allowed in the table
below. In the absence of definite knowledge in advance of construction as to just what
strength may be developed, the following values may be used:
* Passed by letter-ballot of the Institute, April 17, 1920.
' 255
TABLE OF STRENGTHS OF DIFFERENT MIXTURES
Proportion of cement to aggregate
Aggregate 1:3* 1:4> 2 * 1:6* 1:7^* 1:9*
For stone, gravel or slag with water-cement
ratiot of : 0.8 0.9 1.0 1.11 1.22
Strength of concrete 3000 2500 2000 1600 1300
Cinders SDO 700 600 500 400
7. Safe Working Stresses. Reinforced-concrete structures shall be so designed that the
stresses, figured in accordance with these regulations, in pounds per square inch, shall not
exceed the following:
(a) Extreme fiber stress in concrete in compression 37^ per cent of the compressive
strength specified in Section 6. Adjacent to the support of continuous members, 41 per
cent provided the member frames into a mass of concrete projecting at least 50 per cent
of the least dimension of the member on all sides of the compression area of the member.
(6) Concrete in direct compression 25 per cent of the compressive strength specified
in Section 6.
(c) Shearing stress in concrete when main steel is not bent and when steel is not
provided to resist diagonal tension, as specified in Section 10.
(d) Where punching shear occurs, provided the diagonal tension requirements are
met, a shearing stress as specified in Section 10 will be allowed.
(e) Vertical shearing stresses, as specified in Section 10.
(/) Bond stress between concrete and plain reinforcing bars 4 per cent of the
compressive strength.
(fir) Bond stress between concrete and approved deformed bars 5 per cent of the
compressive strength.
(ft) Compression applied to a surface of concrete of at least twice the loaded area,
a stress of 50 per cent of the compressive strength shall be allowd over the area actually
under load.
(?') Tensile stress in steel 16,000 Ib. per sq. in., except that for steel having an
elastic limit of at least 50,000 Ib., a working stress of 18,000 Ib. per sq. in. will be
allowed.
8. Girder, Beam, and Slab Construction. In determining the bending moment in
slabs, beams and girders, the load carried by the member shall include both the dead- and
the live-loads.
The span of the member shall be the distance center to center of supports, but not to
exceed the clear span plus the depth of the member, except that for continuous or fixed
members framing into other reinforced-concrete members the clear span may be used.
For continuous members supported upon brackets making an angle of not more than
45 degrees with the vertical, and having a width not less than the width of the member
supported, the span shall be the clear distance between brackets plus one-half the total
depth of the member.
If the brackets make a greater angle than 45 degrees with the vertical, only that portion
of the bracket within the 45 degrees slope shall be considered. Maximum negative mo-
ments are to be considered as existing at the end of the span as here defined.
~WJ
For members uniformly loaded the bending moment shall be assumed as -=r- > where
b
W = total load; L = span; and F = 8 for members simply supported, 10 for both
negative and positive bending moment for members restrained at one end and simply
supported or partially restrained at the other, and 12 for both negative and positive bend-
ing moment for members fixed or continuous at both supports. The above bending mo-
ments for continuous members apply only when adjacent spans are approximately equal.
A special condition of loading to be reduced to equivalent uniformly distributed loading
in accordance with approved engineering practice. For members having one end simply
supported or partially restrained, at least fifty (50) per cent of the tension reinforcement
required at center of span shall be bent up and adequately anchored to take bending moment
at exterior support.
At the ends of continuous beams, the amount of negative moment which will be devel-
oped in the beam will depend on the condition of restraint or fixedness, and this will depend
on the form of construction used. In the ordinary cases a moment of ,-- may be taken:
ID
for small beams running into heavy columns this should be increased but not to exceed ^
* Total volume of fine and coarse aggregate, measured separately,
t Water-Cement Ratio = Ratio of water to cement by volume.
256
9. Slabs. The main tensile reinforcement shall not be farther apart than two times
the thickness of the slab. For slabs designed to span one way, steel having an area of at
least two-tenths of one per cent (0.2 %) of section of slab shall be provided transverse to
main reinforcement, and this transverse reinforcement shall be further increased in the top
of the slab over girders to prevent cracking, and the main steel in slabs parallel and adjacent
to girders may be reduced accordingly. Where openings are left through slabs, extra
reinforcement shall be provided to prevent local cracks developing. This reinforcement
shall in no case be less than Y sq. in. in section and must be securely anchored at ends.
Floor finish when placed monolithic may be considered part of the structural section.
Where adequate bond and shearing resistance between slab and web of beam is provided,
the slab may be considered as an integral part of the beam, but its effective width shall not
exceed on either side of the beam one-sixth of the span length of the beam nor be greater
than six times the thickness of the slab on either side of the beam, nor greater than one-half
of the distance between beams on either side, the measurements being taken from edge of
web.
10. Shear and Diagonal Tension. (a) The notation used in this section is as follows:
V = total vertical shear at any section.
V = vertical shear carried by the web reinforcement.
v = V/bjd = Unit vertical shearing stress.
d = depth from compressive face to c. g. of tensile steel in inches.
b = breadth of beam.
b f = breadth of stem of T-beam or web of I-beam.
As = area of longitudinal steel.
A v = area of shear steel in section of beam considered.
j = ratio of lever arm of resistance couple to depth d.
p = Ag/bd = Longitudinal steel ratio.
r = A v /ba = Shear steel ratio.
a = spacing of shear steel measured perpendicular to its direction.
f e ' = ultimate strength of concrete cylinders at 28 days (or at time of test in considering
test data).
/ = tensile stress in web reinforcement.
Except where v is noted as the unit punching shearing stress, it is used as a shearing
stress index governing the v alue of the diagonal tension in the web as is the present common
practice.
(6) All allowances for design unit shearing stresses in the following sections are predicated
on proper design of the longitudinal reinforcement to effectively resist all positive and
negative moments, as prescribed in other sections of these standards. Wherever web
reinforcement is used it must be adequately anchored at both ends.
(c) Members with Web Reinforcement. When adequate mechanical anchorage of both
web and longitudinal rods is provided, the concrete may be figured to carry a unit vertical
shearing stress equal to 0.025/ c ' and the remainder of the shear shall be carried by web bars
designed according to the formula:
A - V ' a
~m
Properly anchored bent-up longitudinal bars may be considered as web reinforcement.
The maximum unit shearing stress shall not exceed 0.12/ c ' in any case.
(d) When adequate mechanical anchorage of the longitudinal rods as defined in the next
paragraph is not provided, the maximum unit shearing stress shall not exceed 0.06/ c ',
of which 0.02// may be considered to be taken by the concrete and the remainder of the
shear taken by the web bars designed as above. Web rods must be adequately anchored in
all cases.
(e) Adequate mechanical anchorage of the bottom longitudinal steel for positive
moments shall consist of carrying the reinforcement a sufficient distance beyond the point
of inflection to develop the assumed tension in the reinforcement at the point of inflection
by bond between the end of the bar and the point of inflection of the member (never to a
less distance than one inch from the center of the support or in case of wide supports to not
less than 12 in. of embedment in the support), or of bending the end of the bars over the
support to a half circle of diameter not less than 8 times the diameter of the bar, or by any
device that will transmit the tension on the bar to the concrete over the support at a
compressive stress of not over 0.50/ c '. The tension in the bar, at the point of inflection
to be resisted by the anchorage, shall be taken for this computation as not less than one-
third of the maximum safe tension in the bar. Reinforcement for negative moment shall
be thoroughly anchored at the support and extend into the span a sufficient distance to
adequately provide for negative tension by bond. Simply supported beams shall have the
longitudinal steel anchored by hooks of diameter specified above or by an equivalent anchor-
257
age, the tensile stress at the edge of the support being taken as one-third of the maximum
safe tension in the bar. (Figs. 1, 2 and 3.)
(/) Anchorage of the web steel shall consist of continuity of the web member with the
longitudinal member, or of carrying the web member about at least two sides of a longitudi-
nal bar at both ends, or of carrying the web member about at least two sides of a longitudinal
member at one end and making a half circular hook at the other end of a diameter not less
than eight times the diameter of the web rod. In all cases, the bent ends of web bars shall
extend at least eight diameters below or above the point of extreme height or depth of the
"^JT ^
_^L_
Steel from %&$('* Vertical stirrups
adjacent only
span not shown
FIG. 1,
Bent up rods i-j
and vertical stirrups
Steel from %
adjacent
span not shown
Bent up bars and inclined stirrups
FIG. 2.
Plate must be rigid-
ly connected to rod
FIG. 3.
:;* ; >'., : >>';
* ' ^ \
- $
po *
P5l
Hook must engage
a substantial block
of concrete
' . 4
_' A .
**Gd "'This dimension limited
by bond value unless wffb
* ^ ste*l is integral with
longitudinal steel
;:.?:
W
''' 4
FIG. 4.
on this section must not exceed .02 f,
unless steel is provided in top of beam at support
FIG. 5.
bar. In case the end anchorage is not in bearing on other reinforcing steel, the anchorage
shall be such as to engage an adequate amount of concrete to prevent the bar from pulling
off a portion of the concrete. In all cases the stirrups shall be carried as close to the upper
and lower surfaces as fireproofing requirements will permit. The size of web reinforcing
bars which are not either a part of the longitudinal steel or welded thereto shall be such that
not less than two-fifths of the maximum design tensile stress in the bar may be developed
at design bond stresses in a length of rod equal to 0.4d. This condition is satisfied for plain
258
round stirrups when the diameter of the bar does not exceed d/50. The balance of the
tensile stress in the bar may be considered as taken by adequate end anchorage as specified
above. (Fig. 4.)
(0) Beams in which no longitudinal reinforcement is provided in the upper portion of the
beam adjacent to the support and in which the ends of the beam are built monolithic with
other parts of the concrete structure, shall not carry a unit shearing stress in excess of
0.02//, regardless of amount of web reinforcement provided. (Fig. 5.)
(A) When the shear reinforcement consists of bars bent up at an angle so as to rein-
force all sections of the beam in which the unit shearing stress exceeds 0.02/ c ' the design
may be made as follows:
Atf v = V sec a.
Where A v = area of bent-up shear bars.
/ = stress in bent-up shear bars.
V' = total shear at end of span as prescribed for moment less the shearing
resistance of the concrete at a unit stress of 0.02/ c ' over the area b'jd.
a = angle between bent-up rod and the vertical. (F^g. 6.)
FIG. 6.
The maximum unit shearing stress shall not exceed 0.06 f c f with this arrangement of web
steel and the longitudinal steel shall be adequately anchored as defined above in all cases.
(i) In case the web reinforcement consists solely of inclined shear bars the first bent bar
shall bend downward from the plane of the upper reinforcement directly over or within the
edge of the support.
0') Where additional web reinforcement is provided the same may be figured in accord-
ance with Section 10 (c). The total shearing resistance of the beam shall be taken as the
sum of the resistances under Section 10 (c) and 10 (h).
(k) Beams without Web Reinforcement. When the longitudinal steel is not fully an-
chored, as prescribed above, the unit shearing stress shall not exceed 0.02//. When the
longitudinal steel is fully anchored, as prescribed above, the unit shearing stress shall not
exceed 0.03//.
(I) Critical Section for Shear in Beams. The critical section for shear as governing
diagonal tension shall be taken at a distance not greater than one-half the effective depth of
the beam O^d), from the end of the span as prescribed for moment.
C.G.
Shear governing diagonal tension
Critical sections (IJ following per-
iphery of drop panel, and (2) sur-
face of frustum of cone thru e>
of column capital; base
Punching shear:
- Critical section follows per-
iphery of column capital
The effective depth of the critical section for shear as governing diagonal tension shall
be taken as the depth jd of the beam in the plane of the critical section.
The breadth of the critical section shall be the full breadth of rectangular beams or the
breadth of the stem of T-beams or the thickness of the web in beams of I section.
(m) TUe and Concrete Joist Construction. The shearing stresses in tile and concrete
joist construction shall not exceed those in beams or slabs of similar reinforcement. The
breadth of the effective section for shear, as governing diagonal tension, may be taken as
the thickness of the concrete joist plus one-half the thickness of the vertical webs of the
tile, provided that the joints in one row come opposite the centers of tile in adjoining rows
on either side.
Where the tile joints are not staggered, only the concrete joists may be considered
effective in resisting shear.
259
(n) Flat-slab Construction. In flat-slab construction where a drop panel is used ad-
joining the column, the shearing stress, as governing diagonal tension, figured on the jd
depth on a vertical section along the periphery of the drop, shall not exceed 0.03/ c '. (See
Fig. 7.)
(o) In flat-slab construction, with or without drop panels, the shearing stress, as govern-
ing diagonal tension, figured between the compression face of the slab or drop and the level
of the center of gravity of the reinforcing steel, on the surface of the frustum of a cone or
pyramid passing through the periphery of the column capital and having a base angle of
45 degrees, shall not exceed 0.035/ c '.
(p) Footings. In footings carrying a single column or load, the shearing stress, as
governing diagonal tension, figured between the level of the centroid of the compressive
stresses and the level of the center of gravity of the reinforcing steel on the surface of the
frustum of a cone or pyramid passing through the base of the supported column or loaded
member and having a base angle of 45 degrees the unit stresses shall not exceed those in
beams without web reinforcement. Especial attention shall be given to bond in footings.
The total vertical shear on this section shall be taken as the upward pressure on the area
of the footing outside the base of this section.
(q) If adequate anchorage is provided for the tensile steel arid adequately anchored
web reinforcement is also provided such web reinforcement may be figured in accordance
with the formula given in Section 10 (c) above. Such calculations may be made for vertical
sections concentric with the supported column.
(r) For footings supporting two or more columns, the shearing stresses shall be figured
as for beams or slabs.
(s) Arrangement of Web Reinforcement. The spacing of web reinforcement as measured
perpendicular to their direction shall not exceed 3d/4 in any case where web reinforcement
is necessary. Where vertical stirrups or web members inclined less than 30 degrees to the
Shear governing diagonal tension :-} \ Punching shear :-
Critical section follows periphery-' ^- Critical 'section follows periphery
of supported portion at top of of supported portion,
footing; base angle 45
FIG. 8.
vertical are used, the spacing shall not exceed d/2. When the unit shearing stress exceeds
0.06/c' the spacing of the web reinforcement shall not exceed d/2 in any case, nor d/3 for
vertical stirrups or web steel inclined less than 30 degrees with the vertical.
The first vertical stirrup shall be placed not farther than d/2 from the face of the
support in any case. The first inclined stirrup or bent-up rod shall reach the level of the
upper longitudinal steel at a distance not greater than d/2 from the edge of the support if
the bottom longitudinal steel is adequately anchored and at the edge of the web support if
the longitudinal steel is not anchored. Web members may be placed at any angle between
and 60 degrees with the vertical, provided that, if inclined, they shall be inclined in the
proper direction to take tension, rather than compression, in the web.
(t) Punching Shear. Punching shear shall be figured on a vertical section through
the periphery of the smaller member. The unit shearing stress in punching shear, figured
on the full depth d to the center of gravity of the reinforcement, shall not exceed 0.1/ c '.
(u) When the depth of the supported or supporting member is less than one-fifteenth of
the span in the case of beams or slabs, or less than one-third of the overhang in the case of
cantilevers (including footings), the unit shearing stress in punching shear shall not exceed
0.06/c'.
11. Tile and Joist Floors. Wherever floors are built with a combination of tile or
other fillers between reinforced-concrete joists, the following rules regarding the dimensions
and methods of calculations of construction shall be observed:
(a) Wherever a portion of the slab above the fillers is considered as acting as a T-beam
section, the slab portion must be cast monolithic with the joist and have a minimum thick-
ness of two (2) inches.
(6) Wherever porous fillers are used which will absorb water from the concrete, oare
must be taken thoroughly to saturate same before concrete is placed.
260
(c) All regulations given above for beam and girder floors shall apply to tile and joist
floors.
(d) The sections of fillers shall be together and all joints reasonably tight before concrete
is placed.
12. Flat -slab or Girderless Floors, Continuous flat-slab floors, reinforced with steel
rods or mesh and supported on spaced columns in orderly arrangement, shall conform to the
following requirements:
FIG. 9.
(a) Notation and Nomenclature. In the formula let
w = total dead-and live-load in pounds per square foot of floors.
l\ ='span in feet center to center of columns parallel to sections on which moments
are considered.
lz = span in feet center to center of columns perpendicular to sections on which
moments are considered.
C = average diameter of column capital in feet at plane where its thickness is 1% in.
q = distance from center line of the capital to the center of gravity of the periphery
of the half capital divided by %c. For round capitals q may be considered
as two-thirds and for square capitals as three-quarters.
t = total slab thickness in inches.
L = average span in feet center to center of columns, but not less than 0.9 of the
greater span.
(a) Drop construction
(f>s Cop construct kjf >
7
\_i_/ i-
TF-- - -
(c) Poneifed ceiling consfPtocficn
FlG. 10.
The column head section, mid section, outer section, and inner section are located and
dimensioned as shown in Fig. 9. Corresponding moments shall be figured on similar
sections at right angles to those shown in Fig. 9.
(b) Structural Variations. Flat-slab floors may be built with or without caps, drops or
paneled ceilings. These terms are illustrated in Fig. 10.
Where caps are employed they shall be considered a part of the columns and the column
261
capital dimension c shall be found by extending the lines of the capital to an intersection
with the plane of the under surface of the slab as indicated in Fig. 10&. The cap shall be
large enough to enclose this extension of the capital lines.
The column capital profile shall not fall at any point inside an inverted cone drawn, as
shown in Fig. 10a, from the periphery of the designed capital of diameter c and with a base
angle of 45 degrees. The diameter of the designed capital c shall be taken where the verti-
cal thickness of the column capital is at least 1% in.
The drop, where used, shall not be less than 0.3 L in width.
Where paneled ceilings are used the paneling shall not exceed one-half of the slab
thickness in depth and the dimension of the paneling shall not exceed 0.8 of the panel dimen-
sion. (See Fig. lOo.)
(c) Slab Thickness. The slab thickness shall not be less than t = 0.02L ^/w + 1 in.
In no case shall the slab thickness be less than ^ 2-^ f r floor slabs nor less than Y oL for
roof slabs.
(d) Design Moments. The numerical sum of the positive and negative moments in foot
pounds shall not be less than 0.09wli(l gc) 2 . Of this total amount not less than 40
per cent shall be resisted in the column head sections. Where a drop is used, not less than
50 per cent shall be resisted in the column head sections.
Of the total amount not less than 10 per cent shall be resisted in the mid section.
Of the total amount not less than 18 per cent shall be resisted in the outer section.
Of the total amount not less than 12 per cent shall be resisted on the inner sections.
The balance of the moment shall be distributed between the various sections as required
by the physical details and dimensions of the particular design employed.
(c) Exterior Panels. The negative moments at the first interior row of columns and the
positive moments at the center of the exterior panel on sections parallel to the wall, shall
be increased 20 per cent o\er those specified above for interior panels. If girders are not
provided long the column line, the reinforcement parallel to the wall for negative moment in
the column head section and for positive moment in the outer section adjacent to the wall,
shall be altered in accordance with the change in the value of c. The negative moment on
sections at the wall and parallel thereto should be determined by the conditions of restraint,
but must never be taken less than 80 per cent of those for the interior panels.
(/) Reinforcement. In the calculation of moments all the reinforcing bars which cross
the section under consideration and which fulfill the requirements given under "Arrange-
ment of Reinforcement" may be used. For a column head section reinforcing bars parallel
to the straight portion of the section do not contribute to the negative resisting moment
for the column head section in question. The sectional area of bars, crossing the section
at an angle, multiplied by the sine of the angle between these bars and the straight portion
of the section under consideration may be taken to act as reinforcement in a rectangular
direction. Calculations for shearing stress shall be made in accordance with Section 10.
(g) Point of Inflection. For the purpose of making calculations of moment at sections
away from the sections of negative moment and positive moment already specified, the
point of inflection shall be taken at a distance from center line of columns equal to
/&(k ?c) + %qc. This becomes K(^2 + c) where capital is circular. For slabs having
drop panels the coefficient of Y should be used instead of Jo-
(h) Arrangement of Reinforcement. The design should include adequate provision for
securing the reinforcement in place so as to take not only the maximum moments but the
moments of intermediate sections. If bars are extended beyond the column capital and
are used to take the bending moment on the opposite side of the column, they must
extent to the point of inflection. Bars in diagonal bands used as reinforcement for negative
moment should extend on each side of the line drawn through the column center at right
angles to the direction of the band a distance equal to 0.35 of the panel length, and bars in
the diagonal bands used as reinforcement for positive moment, should extend on each side
of the diagonal through the center of the panel a distance equal to 0.35 of the panel length.
Bars spliced by lapping and counted as only one bar in tension shall be lapped not less than
80 diameters if splice is made at point of maximum stress and not more than 50 per cent
of the rods shall be so spliced at any point in any single band or in any single region of
tensile stress. Continuous bars shall not all be bent up at the same point of their length,
but the zone in which this bending occurs should extend on each side of the assumed point
of inflection.
(i) Tensile and Compressive Stresses. The usual method of calculating the tensile and
compressive stresses in the concrete and in the reinforcement, based on the assumptions
for internal stresses, should be followed. In the case of the drop panel, the section of the
slab and drop panel may be considered to act integrally for a width equal to a width of the
column head section. Within the column head section the allowable compression may be
increased as prescribed in Section 7 for continuous members.
0') Provision for Diagonal Tension and Shear. In calculations for the shearing stress
which is to be used as the means for measuring the resistance to diagonal tension stress, it
262
shall be assumed that the total vertical shear on a column head section constituting a
width equal to one-half the lateral dimension of the panel, for use in determining critical
shearing stresses, shall be considered to be one-fourth of the total dead- and live-load on a
panel for a slab of uniform thickness, and to be 0.3 of the sum of the dead- and live-loads on
a panel for a slab with drop panels.^ The formula for shearing unit stress shall be v =
f\ *) ^ TV 0^0 TV
' . for slabs of uniform thickness and v = ' , - for slabs with drop panels, where W is
bjd bja
the sum of the dead- and live-load on a panel, 6 is half the lateral dimension of the panel
measured from center to center of columns, and jd is the lever arm of the resisting couple
at the section.
The calculation for punching shear shall be made on the assumption of a uniform distri-
bution over the section of the slab around the periphery of the column capital and also of a
uniform distribution over the section of the slab around the periphery of the drop panel,
using in each case an amount of vertical shear greater by 25 per cent than the total vertical
shear on the section under consideration.
The values of working stresses should be those recommended for diagonal tension and
shear in Section 10.
(k) Walls and Openings. Additional slab thickness, girders, or beams shall be provided
to carry walls and other concentrated loads which are in excess of the working capacity of
the slab. Beams should also be provided in case openings in the floor reduce the working
strength of the slab below the required carrying capacity. Where lintels are used with
flat-slab construction the depth of the lintels being greater than the combined depth of
the slab and depressed panel, they shall be designed to carry a uniformly distributed
load equal to /- of the total panel load in addition to any other loads superimposed upon
the lintel and the dead weight of the lintel.
(1) Unusual Panels. The coefficients, steel distribution, and thicknesses recommended
are for slabs which have three or more rows of panels in each direction and in which the
sizes of the panels are approximately the same. For structures having a width of one or
two panels, and also for slabs having panels of markedly different sizes, an analysis should
be made of the moments developed in both slab and columns and the values given herein
modified accordingly.
(m) Oblong Panels. The requirements of design herein given for flat-slab floors do not
apply for oblong panels where the long side is more than four-thirds of the short side.
(n) Bending Moments in Columns. Provision shall be made in both wall columns and
interior columns for the bending moment which will be developed by unequally loaded
panels, eccentric loading, or uneven spacing of columns. The amount of moment to be
taken by a column will depend on the relative stiffness of columns and slab, and computa-
tions may be made by rational methods such as the principle of least work or of slope and
deflection. Generally the largest part of the unequalized negative moment will be trans-
mitted to the columns and the columns shall be designed to resist this bending moment.
Especial attention shall be given to wall columns and corner columns. Column capitals
shall be designed, and reinforced where necessary, with these conditions in mind.
The resistance of any wall column to bending in a direction perpendicular to the wall
shall be not less than 0.04 ivl\(li gc) 2 in which h is the panel dimension perpendicular to
the wall. The moment in such wall column may be reduced by the balancing moment
of the weight of the structure which projects beyond the center line of the supporting
wall column.
Where the column extends through the story above, the resisting moment shall be
divided between the upper and the lower columns in proportion to their stiffness. Calcu-
lated combined stresses due to bending and direct load shall not exceed by more than 50
per cent the stresses allowed for direct load.
13. Columns General. Reinforced-concrete columns, for the working stresses here-
inafter specified, shall have a gross width or diameter not less than one-fifteenth of the
unsupported height nor less than twelve (12) in. All vertical reinforcement shall be
secured against lateral displacement by steel ties not less than j in. in diameter, placed
not farther apart than 15 diameters of the vertical rods or more than 12 in.
For columns supporting flat-slab floors or roofs, the diameter shall be not less than
one-thirteenth of the distance between columns.
The length of columns shall be taken as the maximum unstayed length.
14. Columns with Longitudinal Reinforcement. For columns having not less than
0.5 per cent nor more than 4 per cent of vertical reinforcement, the allowable working unit
stress for the net section of the concrete shall be 25 per cent of the compressive strength
specified in Section 6, and the working unit stress for the steel shall be based upon the
ratio of the moduli of elasticity of the concrete and steel. Concrete to a depth of 1 3^ in.
shall be considered as protective covering and not a part of the net section.
15. Columns with Longitudinal and Lateral Reinforcement. Columns, having not less
than 1 per cent nor more than 4 per cent of vertical reinforcement and not less than 0.5 per
263
cent nor more than 2 per cent of lateral reinforcement in the form of hoops or spirals spaced
not farther apart than one-sixth of the outside diameter of the hoops or spirals nor more
than 3 in. shall have an allowable working unit stress for the concrete within the outside
diameter of the hoops or spirals equal to 25 per cent of the compressive strength of the
concrete, as given in Section 6, and a working unit stress on the vertical reinforcement equal
to the working value of the concrete multiplied by the ratio of the specified moduli of
elasticity of the steel and concrete, and a working load for the hoops or spirals determined
by considering the steel in hoops or spirals as four times as effective as longitudinal rein-
forcing steel of equal volume. The percentage of lateral reinforcement shall be taken as
the volume of the hoops or spirals divided by the volume of the enclosed concrete in a unit
length of column. The hoops or spirals shall be rigidly secured at each intersection to at
least four (4) verticals to insure uniform spacing. The percentage of longitudinal reinforce-
ment used shall be not less than the percentage of the lateral reinforcement. Spirals shall
be manufactured of steel having a yield point of not less than 50,000 Ib. per square inch.
16. For steel columns filled with concrete and encased in a shell of concrete at least
3 in. thick, where the steel is calculated to carry the entire load, the allowable stress per
square inch shall be determined by the following formula: 18,000 70^, but shall not
exceed 16,000 Ib. where L = unsupported length in inches and R = least radius of
gyration of steel section in inches. The concrete shell shall be reinforced with wire mesh or
hoop weighing at least 0.2 Ib. per square foot of surface of shell.
When the details of the structural steel are such as to fully enclose or encase the concrete,
or where a spiral of not less than one-half of 1 per cent of the core area, and with a pitch of
not more than 3 in., is provided for this purpose, the concrete inside the column core
or spiral may be loaded to not more than 25 per cent of the ultimate strength specified in
Section 6, in addition to the load on the steel column figured as above.
Composite columns having a cast iron core or center surrounded by concrete which is
enclosed in a spiral of not less than one-half of 1 per cent of the core area, and with a pitch
of not more than 3 in. may be figured for a stress of 12,000 60L/R, but not over 10,000
Ib. per square inch on the cast iron section and of not more than 25 per cent of the com-
pressive strength specified in Section 6 on the concrete within the spiral or core. The
diameter of the cast iron core shall not exceed one-half of the diameter of the spiral.
17. Footings General. Symmetrical, concentric column footings shall be designed for
punching shear, diagonal tension, and bending moment.
18. Punching Shear in Footings. Punching shear shall be figured in accordance with
Section 10.
19. Diagonal Tension in Footings. Shearing stresses shall be figured in accordance
with Section 10.
20. Bending Moment in Footings. The bending moment in isolated column footings
at a section taken at edge of pier or column shall be determined by multiplying the load on
the quarter footing (after deducting the quarter pier or column area) by six-tenths of the
distance from the edge of pier or column to the edge of footing. The effective area of
concrete and steel to resist bending moment shall be considered as that within a width
extending both sides of pier or column, a distance equal to depth of footing plus one-half
the remaining distance to edge of footing, except that reinforcing steel crossing the section
other than at right angles, shall be considered to have an effective area determined by
multiplying the section area by the line of the angle between the bar and the plane of
section.
21. Bond Stresses in Footings. In designing footings, careful consideration must be
given to the bond stresses which will occur between the reinforcing steel and the concrete.
22. Walls General. Walls shall be reinforced by steel rods running horizontally and
vertically. Walls having an unsupported height not exceeding fifteen times the thickness
may be figured the same as columns. Walls having an unsupported height not more than
twenty-five times the thickness may be figured to carry safely a working stress of 12% per
cent of the compressive strength specified in Section 6.
23. Exterior Walls. Exterior walls shall be designed to withstand wind loads or loads
from backfill. The thickness of wall shall in no case be less than 4 in.
24. Protection. The reinforcement in columns and girders shall be protected by
minimum thickness of 2 in. of concrete; in beams and walls by a minimum of lj^ in.
in floor slabs by a minimum of Y in. ; in footings by a minimum of 3 in.
264
NEW YORK BUILDING CODE REQUIREMENTS
Working Stresses. Reinforced concrete structures shall be so designated that the
stresses in pounds per square inch shall not exceed the following:
Extreme fibre stress on concrete in compression 650
Concrete in direct compression 500
Shearing stress in concrete when all diagonal tension is resisted by
steel 150
Shearing stress in concrete when diagonal tension is not resisted by
steel 40
Bond stress between concrete and plain reinforcement 80
Bond stress between concrete and approved deformed bars 100
Tensile stress in steel reinforcement 16,000
Tensile stress in cold drawn steel wire or fabric, 35 per cent of the
elastic limit but not more than 20,000
In continuous beams the extreme fiber stress on concrete in compression may be in-
creased 15 per cent, adjacent to supports.
The ratio of the moduli of elasticity of 1 : 2 : 4 stone or gravel concrete and steel shall be
taken as one to fifteen. The ratio of the moduli of elasticity of 1 : 1^ : 3 stone or gravel
concrete and steel shall be taken 'as one to twelve.
Slabs and Beams, (a) Thickness. Slabs shall not be less than 4 in. in thickness for
floors and 3% in. for roofs.
(b) Tee-Beams. Where adequate bond between slab and web of beam is provided, the
slab may be considered as an integral part of the beam provided its effective width shall
not exceed on either side of the beam one-sixth of the span length of the beam, nor be
greater than six times the thickness of the slab on either side of the beam, the measure-
ments being taken from edge of web.
(c) Placing of Reinforcement. All reinforcement shall be accurately located and secured
against displacement. The reinforcement for slabs shall not be spaced farther apart than
two and one- half times the 'thickness of the slab.
(d) Web Reinforcement. Members of web reinforcement shall be so designed as ade-
quately to take up throughout their length all stresses not taken up by the concrete. They
shall not be spaced to exceed three-fourths of the depth of the beam in that portion where
the web stresses exceed the allowable value of concrete in shear. Web reinforcement,
unless rigidly attached, shall be placed at right angles to the axis of the beam and carried
around the tension members.
Use of Fillers in Floor Construction. When hollow tile, concrete blocks or other
acceptable fillers are used in any reinforced concrete floor construction, the reinforced con-
crete members of such floor construction shall be designed in accordance with the provisions
of this article to take the entire loads, provided, however, that when the fillers do not exceed
60 per cent of the construction, not more than 2^ in. of concrete shall be required over
the fillers.
Columns, (a) With Longitudinal Reinforcements Only. In concrete columns, having
not less than one-half nor more than 4 per cent of vertical reinforcement secured against
displacement by 24-in. steel ties placed not farther apart than 15 diameters of the verti-
cal rods nor more than 12 in., the allowable load shall be 500 lb. per square inch on the
concrete, plus 7,500 lb. on the vertical reinforcement.
(6) With Longitudinal and Lateral Reinforcement. In concrete columns, having not less
than one-half nor more than 2 per cent of hoops or spirals spaced not farther apart than
one-sixth of the diameter of the enclosed column nor more than 3 in., and having not less
than 1 nor more than 4 per cent of vertical reinforcement, the allowable load shall be 500
lb. per square inch on the effective area of the concrete, plus 7,500 lb. per square inch on
the vertical reinforcement, plus a load per square inch on the effective area of the concrete
equal to two times the percentage of lateral reinforcement multiplied by the tensile stress in
the lateral reinforcement prescribed under " Working Stresses," the percentage of lateral
reinforcement being the volume of the hoops or spirals divided by the volume of the en-
265
closed concrete in a unit length of column. The hoops or spirals shall be rigidly secured
to at least four verticals to insure uniform spacing.
(c) Structural Steel and Concrete. In columns of structural steel, thoroughly encased in
concrete not less than 4 in. thick and reinforced with not less than 1 per cent of steel, the
allowable load shall be 16,000 lb. per square inch on the structural steel, the percentage of
reinforcement being the volume of the reinforcing steel divided by the volume of the con-
crete enclosed by the reinforcing steel. Not more than one-half of the reinforcing steel
shall be placed vertically. The reinforcing steel shall not be placed nearer than 1 in. to
the structural steel or to the outer surface of the concrete. The ratio\>f length to least radius
of gyration of structural steel section shall not exceed one hundred and twenty.
(d) When Richer Concrete is Used. In concrete columns the compression on the concrete
may be increased 20 per cent when the fine and coarse aggregates are carefully selected
and the proportion of cement to total aggregate is increased to one part of cement to not
more than four and one-half parts of aggregate, fine and coarse, either in the proportion
of one part of cement, one and one-half parts of fine aggregate and three parts of coarse
aggregate*, or in such proportion as will secure the maximum density. In such cases,
however, the compressive stress in the vertical steel shall not exceed 7,200 lb. per square
inch.
(e) Eccentric Loads. Bending stresses due to eccentric loads shall be provided for by
increasing the section of concrete or steel until the maximum stress shall not exceed the
allowable working stress.
(/) Length. In columns, the ratio of length to least side or diameter shall not exceed
fifteen, but in no case shall the least side or diameter be less than 12 in.
Walls. Enclosure walls of reinforced concrete shall be securely anchored at all floors.
The thickness shall not be less than one-twenty-fifth of the unsupported height, but in no
case less than 8 in. The steel reinforcement, running both horizontally and vertically,
shall be placed near both faces of the wall; the total weight of such reinforcement shall be
not less than }4, lb. per square foot of wall.
Protection of Reinforcement. The reinforcement in columns and girders shall be
protected by a minimum of 2 in. of concrete; in beams and walls by a minimum of 1^ in.;
in floor slabs by a minimum of 1 in.; and in footings by a minimum of 4 in. of concrete.
Flat Slabs*
Application. The rules governing the design of reinforced concrete flat slabs shall apply
to such floors and roofs, consisting of three or more rows of slabs, without beams or girders,
supported on columns, the construction being continuous over the columns and forming
with them a monolithic structure.
Compliance with Building Code. In the design of reinforced concrete flat slabs, the
provisions of the preceding articles of the building code shall govern with respect to such
matters as are specified therein.
Assumptions. In calculations for the strength of reinforced concrete flat slabs, the
following assumptions shall be made:
(a) A plane section before bending remains plane after bending.
(6) The modulus of elasticity of concrete in compression within the allowable working
stresses is constant.
(c) The adhesion between concrete and reinforcement is perfect.
(d) The tensile strength of concrete is nil.
(e) Initial stress in the reinforcement due to contraction or expansion in the concrete is
negligible.
Stresses. (a) The allowable unit shear in reinforced concrete flat slabs on the bd
section around the perimeter of the column capital shall not exceed 120 lb. per square inch;
and the allowable unit shearing stress on the bjd section around the perimeter of the drop
shall not exceed (60) lb. per square inch, provided that the reinforcement is so arranged or
anchored that the stress may be fully developed for both positive and negative moments.
The extreme fibre stresses to be used in concrete in compression at the column head
section shall not exceed 750 lb. per square inch.
Columns. For columns supporting reinforced concrete flat slabs, the least dimension of
any column shall be not less than one-fifteenth of the average span of any slabs supported
by the columns; but in no case shall such least dimension of any interior column supporting
a floor or roof be less than 16 in. when round, nor 14 in. when square; nor shall the least
dimension of any exterior column be less than 14 in.
Column Capital. Every reinforced concrete column supporting a flat slab shall be
provided with a capital whose diameter is not less than 0.225 of the average span of any
slabs supported by it. Such diameter shall be measured where the vertical thickness of the
capital is at least 1^ in., and shall be the diameter of the inscribed circle in that horizontal
* Adopted July 8, 1920.
266
plane. The slope of the capital considered effective below the point where its diameter is
measured shall nowhere make an angle with vertical of more than 45. In case a cap of less
dimensions than hereinafter described as a drop, is placed above the column capital, the
part of this cap enclosed within the lines of the column capital extended upwards to the
bottom of the slab or drop at the slope of 45 may be considered as part of the column
capital in determining the diameter for design purposes.
Drop. When a reinforced concrete flat slab is thicker in that portion adjacent to or
surrounding the column, the thickened portion shall be known as a drop. The width of
such drop when used, shall be determined by the shearing stress in the slab around the
perimeter of the drop, but in no case shall the width be less than 0.33 of the average span of
any slabs of which it forms a part. In computing the thickness of drop required by the
negative moment on the column head section, the width of the drop only shall be considered
as effective in resisting the compressive stress, but in no case shall the thickness of such
drops be less than 0.33 of the thickness of the slab. Where drops are used over interior
columns, corresponding drops shall be employed over exterior columns and shall extend to
the one-sixth point of panel from the center of the column.
Slab Thickness. The thickness of a reinforced concrete flat slab shall be not less than
that derived by the formulae t = 0.024Z/\/w + I'M f r slabs without drops, and t = 0.02
L\A0 + 1 for slabs with drops, in which t is the thickness of the slab in inches, L is the
average span of the slab in feet, and w is the total live- and dead-load in pounds per square
foot; but in no case shall this thickness be less than one-thirty-second of the average span
of the slab for floors, nor less than one-fortieth of the average span of the slab for roofs, nor
less than 6 in. for floors nor less than 5 in. for roofs.
Reinforcement. (a) In the calculation of moments at any section, all the reinforcing
bars which cross that section may be used, provided that such bars extend far enough
on each side of such section to develop the full amount of the stress at that section. The
effective area of the reinforcement at any moment section shall be the sectional area of the
bars crossing such section multiplied by the sine of the angle of such bars with the plane of
the section. The distribution of the reinforcement of the several bands shall be arranged to
fully provide for the intermediate moments at any section.
(fe) Splices in bars may be made wherever convenient but preferably at points of mini-
mum stress. The length of any splice shall be not less than 80 bar diameters and in no case
less than 2 ft. The splicing of adjacent bars shall be avoided as far as possible. Slab bars
which are lapped over the column, the sectional area of both being included in the calcula-
tion for negative moment, shall extend to the lines of inflection beyond the column center.
(c) When the reinforcement is arranged in bands, at least 50 per cent of the bars in any
band shall be of a length not less than the distance center to center of columns measured
rectangularly and diagonally; no bars used as positive reinforcement shall be of a length less
than half the panel length plus 40 bar diameters for cross bands, or less than seven-tenths
of the panel length plus 40 bar diameters for diagonal bands and no bars used as negative
reinforcement shall be of a length less than half the panel length. All reinforcement
framing perpendicular to the wall in exterior panels shall extend to the outer edge of the
panel and shall be hooked or otherwise anchored.
(d~) Adequate means shall be provided for properly maintaining all slab reinforcement in
the position assumed by the computations.
Line of Inflection. In the design of reinforced concrete flat slab construction, for the
purpose of making calculations of the bending moments at sections other than defined in
these rules, the line of inflection shall be considered as being located one-quarter the
distance, center to center, of columns, rectangularly and diagonally, from center of columns
for panels without drops, and three-tenths of such distance for panels with drops.
Moment Sections. For the purpose of design of reinforced concrete flat slabs, that
portion of the section across a panel, along a line midway between columns, which lies
within the middle two quarters of the width of the panel shall be known as the inner section,
and those portions of the section in the two outer quarters of the width of the panel shall be
known as the outer sections. Of the section which follows a panel edge from column to
column and which includes the quarter perimeters of the edges of the column capitals, that
portion within the middle two quarters of the panel width shall be known as the mid section
and the two remaining portions, each having a projected width equal to one-quarter of the
panel width shall be known as the column head sections.
Bending Moments. In the design of reinforced concrete flat slabs the following provi-
sions with respect to bending moments shall be observed. In the moment expressions
used:
W is the total dead- and live-load on the panel under consideration, including the weight
of drop whether a square, rectangle or parallelogram.
Wi is the total live-load on the panel under consideration.
L is the length of side of a square panel center to center of columns; or the average span
of a rectangular panel which is the mean length of the two sides.
267
n is the ratio of the greater to the less dimension of the panel.
h is the unsupported length of a column in inches, measured from top of slab to base of
capital.
/ is the moment of inertia of the reinforced concrete column section.
A. Interior Square Panels. The numerical sum of the positive and negative moments
shall be not less than Y\ 7 WL. A variation of plus or minus 5 per cent shall be permitted
in the expression for the moment on any section, but in no case shall the sum of the negative
moments be less than 66 per cent of the total moment, nor the sum of the positive moments
be less than 34 per cent of the total moment for slabs with drops; nor shall the sum of the
negative moments be less than 60 per cent of the total moment, nor the sum of the positive
moments be less than 40 per cent of the total moment for slabs without drops.
In two-way systems, for slabs with drops, the negative moment resisted on two column
head sections shall be^2^L; the negative moment on the mid section shall be Ms3
WL; the positive moment on the two outer sections shall be + %oWL and the positive
moment on the inner section shall be + Mss^FL; and for slabs without drops, the negative
moment resisted on two column head sections shall be %sWL, the negative moment on
the mid section shall be ^33 WL, the positive moment on the two outer sections shall
be + }^^WL and the positive moment on the inner section shall be + M.ssWL,
In four- way systems, the negative moments shall be as specified for two-way systems;
the positive moment on Ijie two outer sections shall be + HooWL, and the positive
moment on the inner section shall be + ^looWL for slab with drops; and the positive
moment on the two outer sections shall be + ^j.^WL, and the positive moment on the
inner section shall be + ^ooWL, for slabs without drops.
In three-way systems, the negative moment on the column head and mid sections and
the positive moment on the two outer sections, shall be as specified for four-way systems.
In the expression for the bending moments on the various sections, the length L shall be
assumed as the distance center to center of columns, and the load W as the load on the
panel parallelogram.
B. Interior Rectangular Panels. When the ratio n does not exceed 1.1, all computa-
tions shall be based on a square panel of a length equal to the average span, and the rein-
forcement shall be equally distributed in the short and long directions according to the
bending moment coefficients specified for interior square panels.
When the ratio n lies between 1.1 and 1.33, the bending moment coefficients specified
for interior square panels shall be applied in the following manner:
(a) In two-way systems, the negative moments on the two column head sections and the
mid section and the positive moment on the two outer sections and the inner section at right
angles to the long direction shall be determined as for a square panel of a length equal to the
greater dimension of the rectangular panel; and the corresponding moments on the sections
at right angles to the short direction shall be determined as for a square panel of a length
equal to the lesser dimension of the rectangular panel. In no case shall the amount of
reinforcement in the short direction be less than two-thirds of that in the long direction.
The load W shall be taken as the load on the rectangular panel under consideration.
(6) In four-way systems, for the rectangular bands, the negative moment on the column
head sections and the positive moment on the outer sections shall be determined in the same
manner as indicated for the two-way systems.
For the diagonal bands, the negative moments on the column head and mid sections and
the positive moment on the inner section shall be determined as for a square panel of a length
equal to the average span of the rectangle. The load W shall be taken as the load on the
rectangular panel under consideration.
(c) In three-way systems, the negative and positive moments on the bands running
parallel to the long direction shall be determined as for a square whose side is equal to
the greater dimension; and the moments on the bands running parallel to the short direc-
tion shall be determined as for a square whose side is equal to the lesser dimension. The
load W shall be taken as the load on the parallelogram panel under consideration.
C. Exterior Panels. The negative moments at the first interior row of columns and
the positive moments at the center of the exterior panels on moment sections parallel to
the wall, shall be increased 20 per cent over those specified above for interior panels.
The negative moment on moment sections at the wall and parallel thereto shall be deter-
mined by the conditions of restraint, but the negative moment on the mid section shall
never be considered less than 50 per cent and the negative moment on the column head
section never less than 80 per cent of the corresponding moments at the first interior row of
columns.
D. Interior columns shall be designed for the bending moments developed by un-
equally loaded panels, eccentric loading or uneven spacing of columns. The bending
moment resulting from unequally loaded panels shall be considered as YW\L, and shall
be resisted by the columns immediately above and below the floor line under consideration
in direct proportion to the values of their ratios of I /h.
E. Wall columns shall be designed to resist bending in the same manner as interior
268
columns, except that W shall be substituted for Wi in the formula for the moment. The
moment so computed may be reduced by the counter moment of the weight of the structure
which projects beyond the center line of the wall columns.
F. Roof columns shall be designed to resist the total moment resulting from unequally
loaded panels, as expressed by the formulae in paragraphs (D) and (E) of this rule.
Walls and Openings. In the 'design and construction of reinforced concrete flat slabs,
additional slab thickness, girders or beams shall be provided to carry any walls or concen-
trated loads in addition to the specified uniform live- and dead-loads. Such girders or
beams shall be assumed to carry 20 per cent of the total live and dead panel load in addition
to the wall load. Beams shall also be provided in case openings in the floor reduce the
working strength of the slab below the presciibed carrying capacity.
Special Panels. For structures having a width of less than three rows of slabs, or in
which exterior drops, capitals or columns are omitted, or in which irregular or special
panels are used, and for which the rules relating to the design of reinforced flat slabs do
not directly apply, the computations in the analysis of the design of such panels, shall,
when so required, be filed with the superintendent of buildings.
269
CHICAGO BUILDING CODE REQUIREMENTS
Ratio of Moduli of Elasticity Adhesion Bond, (a) The calculations for the strength
of reinforced concrete shall be based on the assumed ultimate compressive strength per
square inch designated by the letter " C7" given in the table below for the mixture to be
used.
(b) The ratio designated by the letter "#" of the modulus of elasticity of steel to that
of the different grades of concrete shall be taken in accordance with the following table:
Mixture U R
cement, 1 sand, 2 broken stone, gravel or slag 2,900 10
cement, 1% sand, 3 broken stone, gravel or slag 2,400 12
cement, 2 sand, 4 broken stone, gravel or slag 2,000 15
cement, 2^ sand, 5 broken stone, gravel or slag 1,750 18
cement, 3 sand, 7 broken stone, gravel or slag 1,500 20
Unit Stresses for Steel and Concrete, (a) The stresses in the concrete and the steel
shall not exceed the following limits:
(6) Tensile stress in steel shall not exceed one-third of its elastic limits and shall not
exceed 18,000 Ib. per square inch.
(c) Shearing stress in steel shall not exceed 12,000 Ib. per square inch.
(d) The compressive stress in steel shall not exceed the product of the compressive
stress in the concrete multiplied by the elastic modulus of the steel and divided by the
elastic modulus of the concrete.
(e) Direct compression in concrete shall be one-fifth of its ultimate strength. Bending
in extreme fiber of concrete shall be thirty-five one-hundredths of the ultimate strength.
(/) Tension in concrete on diagonal plane shall be one-fiftieth of the ultimate compres-
sive strength.
((/) For a concrete composed of one part of cement, two parts of sand and four parts of
broken stone, the allowable unit stress for adhesion per square inch of surface of imbedment
shall not exceed the following:
Pounds per
sq. in.
On plain round or square bars of structural steel 70
On plain round or square bars of high carbon steel 50
On plain flat bars in which the ratio of the sides is not more than 2 to 1 . . 50
On twisted bars when the twisting is not less than one complete twist in
8 diameters 100
(h) For specially formed bars, the allowable unit stress for bond shall not exceed one-
fourth of the ultimate bond strength of such bars without appreciable slip which shall
be determined by tests made by the person, firm or corporation to the satisfaction of the
Commissioner of Buildings, but provided that in no case shall such allowable unit stress
exceed 100 Ib. per square inch of the specially formed bars.
Design for Slabs, Beams and Girders. Reinforced concrete slabs, beams and girders
shall be designed in accordance with the following assumptions and requirements.
(a) The common theory of flexure shall be applied to beams and members resisting
bending.
(b) The adhesion between the concrete and the steel shall be sufficient to make the two
materials act together.
(c) The steel to take all the direct tensile stresses.
(d) The stress strain curve of concrete in compression is a straight line.
(e) The ratio of the moduli of elasticity of concrete to steel shall be as specified in the
table in preceding article.
Moments of External Forces, (a) Beams, girders, floor or roof slabs and joists shall be
calculated as supported, or with fixed ends, or with partly fixed ends, in accordance with the
actual end conditions, the number of spans and the design.
(b) When calculated for ends partly fixed for intermediate spans with an equally distri-
buted load where the adjacent spans are of approximately equal lengths:
270
Bending moment at center of spans shall not be less than that expressed in the formula
-TO~ for intermediate spans and -^ for end spans.
WL*
(c) The moment over supports shall not be less than the formula =- and the sum of
lo
the moments over one support and at the center of span shall be taken not less than the
. WL*
formula 5
o
In the formula hereinabove given "TF" is the load per lineal foot and "L" the length
of span in feet.
(d) In case of concentrated or special loads the calculations shall be based on the critical
condition of loading.
(e) For fully supported slabs, the free opening plus the depth, for continuous slabs, the
distance between centers of supports, is to be taken as the span.
(/) Where the vertical shear, measured on the section of a beam or girder between the
centers of action of the horizontal stresses, exceeds one-fiftieth of the ultimate direct
compressive stress per square inch, web reinforcement shall be supplied sufficient to carry
the excess. The web reinforcement shall extend from top to bottom of beam, and loop or
connect to the horizontal reinforcement. The horizontal reinforcement carrying the direct
stresses shall not be considered as web reinforcement.
(0) In no case, however, shall the vertical shear, measured as stated above, exceed one-
fifteenth of the ultimate compression strength of the concrete.
(h) For T-beams the width of the stem only shall be used in calculating the above shear.
(t) When steel is used in the compression side of beams and girders, the rods shall be tied
in accordance with- requirements of vertical reinforced columns with stirrups connecting
with the tension rods of the beams or girders.
0') All reinforcing steel shall be accurately located in the forms and secured against
displacement; and inspected by the representative of the architect or engineer in charge
before any surrounding concrete be put in place. It shall be afterwards completely in-
closed by the concrete, and such steel shall nowhere be nearer the surface of the concrete
than \}^ inches for columns, lj^ inches for beams and girders, and } inch, but not less
than the diameter of the bar, for slabs.
(fc) The longitudinal steel in beams and girders shall be so disposed that there shall be a
a thickness of concrete between the separate pieces of steel of not less than one and one-half
times the maximum sectional dimension of the steel.
(1) For square slabs with two-way reinforcements the bending moment at the center of
WL 2
the slab shall be not less than that expressed in the formula - (> -.~ for intermediate spans, and
.
tor end spans.
W7.2
(ra) The moment over supports shall not be less than the formula -^- and the sum of
OO
the moments over one support and at the center of the span shall be taken not less than the
WL*
formula -TO--
In which above formula " TF" is the load per lineal foot and "L" the length of the span.
(n) For square or rectangular slabs, the distribution of the loads in the two directions,
shall be inversely as the cubes of the two dimensions.
(o) Exposed metal of any kind will not be considered a factor in the strength of any part
of any concrete structure, and the plaster finish applied over the metal shall not be deemed
sufficient protection unless applied of sufficient thickness and so secured as to meet the
approval of the Commissioner of Buildings.
(p) Shrinkage and thermal stresses shall be provided for by introduction of steel.
Limiting Width of Flange in "T" Beams. (a) In the calculation of ribs, a portion of
the floor slab may be assumed as acting in flexure in combination with the rib. The width
of the slab so acting in flexure is to be governed by the shearing resistance between rib and
slab, but limited to a width equal to one-third of the span length of the ribs between sup-
ports and also limited to a width of three-quarters of the distance from center to center
between ribs.
(6) No part of the slab shall be considered as a portion of the rib, unless the slab and
rib are cast at the same time.
(c) Where reinforced concrete girders support reinforced concrete beams, the portion of
floor slab acting as flange to the girder must be reinforced with rods near the top, at right
angles to the girder, to enable it to transmit local loads directly to the girder and not through
the beams.
Reinforced Concrete Columns Limit of Length Per cent of Reinforcement Bending
Moment in Columns Tying Vertical Rods. (a) Reinforced concrete may be used for
271
columns in which the concrete shall not be leaner than a 1:2:4 mixture and in which the
ratio of length to least side or diameter does not exceed twelve, but in no case shall the
cross section of the column be less than 64 sq. in. Longitudinal reinforcing rods
must be tied together to effectively resist outward flexure at intervals of not more than
twelve times least diameter of rod and not more than 18 in. When compression
rods are not required, reinforcing rods shall be used, equivalent to not less than one-half of
1 per cent (0.005) of the cross sectional area of the column; provided, however, that the
total sectional area of the reinforcing steel shall not be less than 1 sq. in., and that
no rod or bar be of smaller diameter or least dimensions than /^-in. The area of rein-
forcing compression rods shall be limited to 3 per cent of cross sectional area of the
column. Vertical reinforcing rods shall extend upward or downward into the column,
above or below, lapping the reinforcement above or below enough to develop the stress in
rod by the allowable unit for adhesion. When beams or girders are made monolithic with
or rigidly attached to reinforced concrete columns, the latter shall be designed to resist a
bending moment equal to the greatest possible unbalanced moment in the beams or girders
at the columns, in addition to the direct loads for which the columns are designed.
(6) When the reinforcement consists of vertical bars and spiral hooping, the concrete may
be stressed to one-fourth of its ultimate strength as given on page 270, provided, that the
amount of vertical reinforcement be not less than the amount of the spiral reinforcement,
nor greater than 8 per cent of the area within the hooping; that the percentage of spiral
hooping be not less than one-half of 1 per cent nor greater than 1.5 per cent; that the
pitch of the spiral hooping be uniform and not greater than one-tenth of the diameter
of the column, nor greater than 3 in.; that the spiral be secured to the verticals at every
intersection in such a manner as to insure the maintaining of its form and position, that
the verticals be spaced so that their distance apart, measured on the circumference be
not greater than 9 in., nor one-eighth the circumference of the column within the
hooping. In such columns, the action of the hooping may be assumed to increase the
resistance of the concrete equivalent to two and one-half times the amount of the spiral
hooping figured as vertical reinforcement. No part of the concrete outside of the hooping
shall be considered as a part of the effective column section.
Structural Steel Columns. When the vertical reinforcement consists of a structural
steel column of box shape, with lattice or batten plates of such a form as to permit its being
filled with concrete, the concrete may be stressed to one-fourth of its ultimate strength as
given in table on page 270, provided that no shape of less than 1 sq. in. section be
used and that the spacing of the lacing or battens be not greater than the least width of the
columns.
Curtain Walls in Skeleton Construction Buildings. Buildings having a complete
skeleton construction of steel or of reinforced concrete construction, or a combination of
both, may have exterior walls of reinforced concrete 8 in. thick; provided, however,
that such walls shall support only their own weight and that such walls shall have steel
reinforcement of not less -than three-tenths of 1 per cent in each direction, vertically and
horizontally, the rods spaced not more than 12-in. centers and wired to each other at
each intersection. All bars shall be lapped for a length sufficient to develop their full
stress for the allowable unit stress for adhesion. Additional bars shall be set around open-
ings, the verticals wired to the nearest horizontal bars, and the horizontal bars at top and
bottom of openings shall be wired to the nearest vertical bars. The steel rods shall be
combined with the concrete and placed where the combination will develop the greatest
strength, and the rods shall be staggered or placed and secured so as to resist a pressure of
30 Ib. per square foot, either from the exterior or from the interior on each and every
square foot of each wall panel.
Flat Slabs*
1. Definitions. Flat slabs as understood by this ruling are reinforced concrete slabs,
supported directly on reinforced columns with or without plates or capitals at the top, the
whole construction being hingeless and monolithic without any visible beams or girders.
The construction may be such as to admit the use of hollow panels in the ceiling or smooth
ceiling with depressed panels in the floor.
2. The column capital shall be defined as the gradual flaring out of the top of the column
without any marked offset.
3. The drop panel shall be defined as a square or rectangular depression around the
column capital extending below the slab adjacent to it.
4. The panel length shall be defined as the distance c. to c. of columns of the side of a
square panel, or the average distance c. to c. of columns of the long and short sides of a
rectangular panel.
5. Columns. The least dimension of any concrete column shall be not less than one-
twelfth the panel length, nor one-twelfth the clear height of the column.
* Went into effect Mar. 1, 1918.
272
6. Slab Thickness. The minimum total thickness of the slab in inches shall be deter-
mined by the formula: t = W /44( = square root of W divided by 44), where t = total
thickness of slab in inches, W = total live-load and dead-load in pounds on the panel,
measured c. to c. of columns.
7. In no case shall the thickness be less than >^ 2 of the panel length (L/32) for floors,
nor VIQ of the panel length (Z//40) for roofs (L being the distance c. to c. of columns).
8. In no case shall the thickness of slab be less than 6 in. for floors or roofs.
9. Column Capital. When used the diameter of the column capital shall be measured
where its vertical thickness is at least 1)^ in. and shall be at least 0.225 of the panel length.
The slope of the column capital shall nowhere make an angle with the vertical of more
than 45 deg. Special attention shall be given to the design of the column capital in con-
sidering eccentric loads, and the effect of wind upon the structure.
10. Drop Panel. When used, the drop panel shall be square or circular for square
panels and rectangular or elliptical for oblong panels.
11. The length of the drop shall not be less than one-third of the panel length (Z//3)
if square, and not less than one-third of the long or short side of the panel respectively, if
rectangular.
12. The depth of the drop panel shall be determined by computing it as a beam, using
the negative moment over the column capital specified elsewhere in this ruling.
13. In no case, however, shall the dimensions of the drop panel be less than required for
punching shear along its perimeter, using the allowable unit shearing stresses specified below.
14. Shearing Stresses. The allowable unit punching shear on the perimeter of the
column capital shall be ^oo f the ultimate compressive strength of the concrete as given
on page 270. The allowable unit shear on the perimeter of the drop panel shall be 0.03
of the ultimate compressive strength of the concrete. In computing shearing stress for
the purpose of determining the resistance to diagonal tension the method specified by the
ordinance shall be used.
15. Panel Strips. For the purpose of establishing the bending moments and the
resisting moments of a square panel, the panel shall be divided into strips known as strip
A and strip B. Strip A shall include the reinforcement and slab in a width extending from
the center line of the columns for a distance each side of this center line equal to one-
quarter of the panel length. Strip B shall include the reinforcement and slab in the half
width remaining in the center of the panel. At right angles to these strips, the panel shall
lie divided into similar strips A and B, having the same widths and relations to the center
line of the columns as the above strips. These strips shall be for designing purposes only,
and are not intended as the boundary lines of any bands of steel used.
16. These strips shall apply to the system of reinforcement in which the reinforcing bars
are placed parallel and at right angles to the center line of the columns, hereinafter known
as the two-way system, and also to the system of reinforcement in which the reinforcing
bars are placed parallel, at right angles to and diagonal to the center line of the columns
hereinafter known as the four-way system.
17. Any other system of reinforcement in which the reinforcing bars are placed in cir-
cular, concentric rings and radial bars, or systems with steel rods arranged in any manner
whatsoever, shall comply with the requirements of either the two-way or the four-way .
system herein specified.
18. Bending Moment Coefficients, Interior Panel, Two-way System. In panels where
standard drops and column capitals are used as above specified, the negative bending
moment, taken at a cross-section of each strip A at the edge of the column capital or over
it, shall be taken as TTL/30.
19. The positive bending moment taken at a cross-section of each strip A midway
between column centers shall be taken as WL/60.
20. The positive bending moment taken at a cross-section of each strip B in the middle
of the panel shall be taken as WL/12Q.
21. The negative bending moment taken at a cross-section of each strip B on the center
line of the columns shall be taken as WL/12Q.
22. In the formulas hereinabove given W = total live- and dead-load on the whole panel
in pounds, L = panel length, c. to c. of columns.
23. Bending Moment Coefficients, Interior Panel, Four-way System. In panels where
standard drops and column capitals are used as above specified, the negative bending
moment, taken at a cross-section of each strip A at the edge of column capital or over it,
shall be taken as WL/30.
24. The positive bending moment, taken at a cross-section of each strip A, midway
between column centers, shall be taken as WL/8O.
25. The positive bending moment, taken at a cross-section of each strip B, taken in the
middle of the panel, shall be taken as TFL/120.
26. The negative bending moment, taken at a cross-section of each strip B on the center
line of the columns, shall be taken as JFL/120.
273
27. Bending Moment Coefficients, Wall Panels. Where wall panels with standard
drops and capitals are carried by columns and girders built in walls, as in skeleton con-
struction, the same coefficients shall be used as for an interior panel, except as follows:
The positive bending moments on strips A and B midway between wall and first line of
columns shall be increased 25 per cent.
28. Where wall panels are carried on new brick walls, these shall be laid in Portland
cement mortar and shall be stiffened with pilasters as follows: If a 16-in. wall is used, it
shall have a 4-in. pilaster. If a 12-in. wall is used, it shall have an 8-in. pilaster. The length
of pilasters shall be not less than the diameter of the column, nor less than one-eighth of
the distance between pilasters. The pilasters shall be located opposite the columns as
nearly as practicable, and shall be corbeled out 4 in. at the top, starting at the level of the
base of the column capital. Not less than 8-in. bearing shall be provided for the slab, the
full length of wall.
The coefficients of bending moments required for these panels shall be the same as those
for the interior panels except as provided herewith: The positive bending moments on
strips A and B midway between the wall and first line of columns shall be increased 50
per cent.
29. Where wall panels are supported on old brick walls, there shall be columns with
standard drops and capitals built against the wall, which shall be tied to the same in an
approved manner, and at least an 8-in. bearing provided for the slab, the full length.
Where this is impracticable, there shall be built a beam on the underside of slab adjacent to
the wall between columns, strong enough to carry 25 per cent of the panel load.
The coefficients of bending moments for the two cases of slab support herein described
shall be the same as those specified in Sect. 27 and Sect. 28 for skeleton and wall bearing
condition, respectively.
30. Nothing specified above shall be construed as applying to a case of slabs merely
resting on walls or ledges, without any condition of restraint. These shall be figured as in
ordinary beam-and-girder construction specified in the ordinances.
31. Bending Moment Coefficients, Wall and Interior Columns. Wall columns in
skeleton construction shall be designed to resist a bending moment of TFL/60 at floors and
TFL/30 at roof. The amount ot steel required for this moment shall be independent
of that required to carry the direct load. It shall be placed as near the surfaces
of the column as practicable on the tension sides, and the rods shall be con-
tinuous in crossing from one side to another. The length of rods below the base of the
capital and above the floor line shall be sufficient to develop their strength through bond,
but not less than 40 diameters, nor less than one-third the clear height between the floor
line and the base of the column capital.
32. The interior columns must be analyzed for the worst condition of unbalanced
loading. It is the intention of this ruling to cover ordinary cases of eccentric loads on the
columns by the requirement of Sect. 5. W T here the minimum size of column therein
specified is found insufficient, however, the effect of the resulting bending moment shall
be properly divided between the adjoining slab and the columns above and below according
to best principles of engineering, and the columns enlarged sufficiently to carry the load
safely.
33. Bending Moment Coefficients, Panels Without Drops, or Capitals, or Both. In
square panels where no column capital or no depressions are used, the sum total of positive
and negative bending moments shall be equal to that computed by the following formula:
B.M. = (TFL/8)(1.53 - 4k + 4.18A; 3 )
where B.M . = numerical sum of positive and negative bending moments, regardless of
algebraic signs.
W = total live- and dead-load on the whole panel.
L = length of side of a square panel, c. to c. of columns.
k = ratio of the radius of the column or column capital to panel length, L.
This total bending moment shall be divided between the positive and the negative
moments in the same proportion as in the typical square panels for two-way or four-way
systems specified above for interior and wall panels respectively.
34. Point of Inflection. For the purpose of making the calculations of the bending
moment at the sections away from the column capital, the point of inflection shall be
considered as being one-quarter the distance c. to c. of columns, both crosswise and
diagonally, from the center of the column.
35. Tensile Stress in Steel and Compressive Stress in Concrete. The tensile stress in
steel and the compressive stress in the concrete to resist the bending moment shall be
calculated on the basis of the reinforcement and slab in the width included in a given strip,
and according to the assumptions and requirements given in the first three articles on
274
page 270. The steel shall be considered as being concentrated at the center of gravity of
all the bands of steel in a given strip.
36. For the four-way system of reinforcement the amount of steel to resist the negative
bending moment over the support in each strip A shall be taken as the sum of the areas of
steel in one cross band and one diagonal band. The amount of steel to resist the positive
bending moment of each strip B shall be considered as the area of the steel in a diagonal
band. The amount of steel to resist the positive bending moment in each strip A shall
be considered as the area of the steel in a cross band, and the amount of steel to resist
the negative moment in each strip B shall be the steel included in the width of strip B.
37. For the two-way system of reinforcement the amount of steel to resist the bending
moment in any strip shall be considered as the area of steel included in the width of the
strip.
38. In both systems of reinforcement the compressive stress in the concrete in any
strip shall be calculated by taking the area of steel considered for each strip and applying
it in a beam formula based on the principles given in the article on "Design for Slabs,
Beams and Girders" on page 270.
39. Where drop panels are used, the width of beam assumed to resist the compressive
stresses over the column capital shall be the width of the drop.
40. The width of beam, where no drop panels are used, shall be the width of steel bands.
Where this is found insufficient, the area shall be increased by introducing compression
steel in the bottom of slab.
41. Rectangular Panels. When the length of panel in either two-way or four-way
system does not exceed the breadth by more than 5 per cent, all computations shall be
based on a square panel whose side equals the mean of the length and breadth, and the
steel equally distributed among the strips according to the coefficients above specified.
42. In no rectangular panel shall the length exceed the breadth by more than one-third
of the latter.
43. Rectangular Panels, Four-way System. In the four-way system of reinforcement,
where length exceeds breadth by more than 5 per cent, the amount of steel required in strip
A, long direction, both positive and negative, shall be the same as that required for the
same strip in a square panel whose length is equal to the long side of the rectangular panel.
44. The amount of steel, strip A, short direction, positive and negative, shall be the
same as that required for the same strip in a square panel, whose length is equal to the
short side of the rectangular panel.
45. The amount of steel in strip B, positive and negative, shall be the same as that
required for similar strip in a square panel whose length is equal to the mean of the long
and the short side of the rectangular panel.
46. In no case shall the amount of steel in the short side be less than two-thirds of that
required for the long side.
47. Rectangular Panels, Two-way System. In the two-way system of reinforcement
the amount of steel required for the positive and the negative moment of each strip A shall
be determined in the same manner as indicated for the four-way system above.
48. The amount of steel in strip B, positive and negative, running in short direction,
shall be equal to that required for the same strip in a square panel whose length equals the
long side of the rectangular panel.
49. The amount of steel in strip B, long direction, positive and negative, shall be equal
to that required for the same strip in a square panel, whose length equals the short side of
the rectangular panel.
50. In no case shall the amount of steel in strip B, long direction, be less than two-thirds
of that in the short direction.
51. Walls and Openings. Girders and beams shall be constructed under walls, around
openings and to carry concentrated loads.
52. Spandrel Beams. The spandrel beams or girders shall, in addition to their own
weight and the weight of the spandrel wall, be assumed to carry 20 per cent of the wall
panel load uniformly distributed upon them.
53. Placing of Steel. In order that the slab bars shall be maintained in the position
shown in the design during the work of pouring the slab, spacers and supports shall be
provided satisfactory to the Commissioner of Buildings. All bars shall be secured in place
at intersections by wire or other metal fastenings. In no case shall the spacing of the bars
exceed 9 in. The steel to resist the negative moment in each strip B shall extend one-
quarter of the panel length beyond the center line of the columns in both directions.
54. Splices in bars may be made wherever convenient, but preferably at points of
minimum stress. The length of splice beyond the center point, in each direction, shall not
be less than 40 diameters of the bars, nor less than 2 ft. The splicing of adjacent bars shall
be avoided as far as possible.
55. Slab bars which are lapped over the column, the sectional area of both being in-
cluded in the calculations for negative moment, shall extend not less than 0.25 of the panel
length for cross bands and 0.35 of the panel length for diagonal bands, beyond the column
center.
275
56. Computations. Complete computations of interior and wall panels and such other
portions of the building as may be required by the Commissioner of Buildings shall be
left in the office of the Commissioner of Buildings when plans are presented for approval.
57. Test of Workmanship. The Commissioner of Buildings or his representative may
choose any two adjacent panels in the building for the purpose of ascertaining the character
of workmanship. The test shall not be made sooner than the time required for the cement
to set thoroughly, nor less than 6 weeks after the concrete had been poured.
58. All deflections under test load shall be taken at the center of the slab, and shall be
measured from the normal unloaded position of the slab. The two panels selected shall be
uniformly loaded over their entire area with a load equal to the dead-load plus twice the
live-load, thus obtaining twice the total design load. The load shall remain in place not
less than 24 hr. If the total deflection in the center of the panel under the test load does
not exceed 3^ o f the panel length, the slab may be placarded to carry the full design live-
load. If it exceeds this amount of deflection, and recovers not less than 80 per cent of the
total deflection within 7 days after the load is removed, the slab may be placarded to carry
the full design live-load. If the deflection exceeds the allowable amount above specified,
and the recovery is less than 80 per cent in 7 days after the removal of the test load, other
tests shall be made on the same or other panels, the results of which will determine the
amount of live-load the slabs will be permitted to carry.
59. General. The design and the execution of the work shall conform to the general
provisions and the spirit of the Chicago Building Ordinances in points not covered by this
Ruling and to the best engineering practice in general.
276
r.N
OK IS DUE ON THE LAST DA 1
STAMPED BELOW
AN INITIAL FINE OP 25 CENTS
WILL BE ASSESSED FOR FAILURE TO RETURN
THIS BOOK ON THE DATE DUE. THE PENALTY
WILL INCREASE TO SO CENTS ON THE FOURTH
DAY AND TO $1.OO ON THE SEVENTH DAY
OVERDUE.
....
APR 24 1941
ADD H 4 4rt4)
Arn 11 1942
APR 18 1943
APR -Jr,
* 1&1943
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UNIVERSITY OF CALIFORNIA LIBRARY