or THE UNIVERSITY or Showing Method of Determining Elastic Behavior of Concrete Bars, 6x6-Inches in Cross- Section. Specimen, with Electric Extensometer Attached, Mounted for Compression in the 150,000 Pound Emery Testing Machine of Columbia University. CEMENTS, MORTARS AND CONCRETES THEIR PHYSICAL PROPERTIES MYRON S. FALK, PH. D., > i INSTRUCTOR IN CIVIL ENGINEERING IN COLUMBIA UNIVERSITY IN THE CITY OF NEW YORK. UNIVERSITY OF NEW YORK M. C. CLARK 1904 GENERAL Copyright, 1904, BY MYRON S, FALK. INTRODUCTION. The purpose of this treatise has been to set forth as concisely as possible the physical properties of cement and cement mix- tures, with principal reference to those properties which concern the engineer. The results of investigations made upon these ma- terials have been examined with great care. Engineers desiring such data on cements, mortars and concretes, have hitherto been obliged to refer to numerous scattered articles and books. It has been the author's object to abstract, classify and summarize all the reliable data extant, filling in certain gaps with data of his own. The following headings outline, for the greater part, the scope of the work: General Physical Properties : Changes in Volume When Setting. Coefficient of Expansion Due to Temperature Changes. The Action of Sea Water and Salt. Porosity and Impermeability. Effect of Freezing. Adhesion of Iron Rods to Cement Mixtures. Fatigue of Cement Mixtures. General Elastic Properties : Tensile and Compressive Properties. Coefficient of Elasticity, Elastic Limit. Ultimate Resistance. Flexural Properties. Coefficient of Elasticity. Modulus of Rupture. Shearing Resistance. The sources from which the experimental data have been ob- tained are furnished, in every instance, with those data; it is 1 26223 iv INTRODUCTION. therefore unnecessary to give separate credit to the various ex- perimeriters at/this point. It is proper to say, however, that use has beenrrratfe only of those results which gave evidence of care- ful work, so that no conclusions might be invalidated by reason of the unreliability of the experiments. Free use has been made of the Annual Reports of the Watertown, Mass., Arsenal, of the Transactions of the American Society of Civil Engineers, and of the Proceedings of the Institution of Civil Engineers of Great Britain. The experiments, not previously published, made under the author's direction in the laboratories of Columbia University, have also been included. It is believed that the results obtained relating to the elastic properties of the material, such as the values of the coefficients of elasticity .and the ultimate strengths, have been so analyzed that these values may be determined in advance, for any mix- ture, within small limits of error; but future experiments and future improvement in the manufacture of cement mixtures may cause considerable changes in these figures. In order that a cement's physical peculiarities may be more clearly comprehended, it has been thought advisable to consider as a preliminary some of the chemical characteristics of cements. In connection with the discussion of chemical compositions, the theories of the setting of cements have therefore been analyzed, and it has been possible to abstract, in an appendix, Mr; Clif- ford Richardson's theory as to the constitution of Portland cements. In addition, a chapter, together with an appendix, treating briefly of the ordinary commercial tests has been in- cluded. M. S. F. August 22, 1904. CONTENTS. CHAPTER I. CHEMICAL PROPERTIES OF CEMENT. ART. ^ PAGE 1 . Theories of Setting I 2. Chemical Analyses 3 Portland Cements > Natural Cements 6 CHAPTER II. PHYSICAL TESTS OF CEMENT. 3. Commercial Physical Tests 9 4- Specific Gravity Tests 10 5. Fineness Test II 6. Test for Time of Setting 13 Action of Plaster of Paris 14 Temperature Affects Time of Setting 16 Retarding the Set 17 Temperature Changes During Setting 18 7. Tests of Tensile Strength 19 8. Ratio of Compressive and Tensile Strengths 26 9. Variations in the Making of Tensile Tests 29 10. Variations of Sands in Tensile Tests 30 Effect of Clay in Sand 34 1 1. Test of Constancy of Volume 39 CHAPTER III. GENERAL PHYSICAL PROPERTIES. 12. Variation in Volume of Cement Mortars in Air and Water 40 13- The Coefficient of Expansion Due to Temperature Changes 43 14- The Action of Sea Water on Cements 45 Strength in Sea Water 47 Gauging with Salt Water 50 15- Porosity and Permeability 51 Feret' s Conclusions 52 16. The Effect of Freezing on Cement Mixtures 55 17. Adhesion of Iron in Concrete 61 18. The Fatigue of Cement Mixtures 66 vi CONTENTS. CHAPTER IV. ELASTIC PROPERTIES IN GENERAL. 19. Treatment of Stress-Strain Curves ............................... 70 CHAPTER V. TENSILE PROPERTIES. 20. Coefficient of Elasticity and Ultimate Resistance .................. 75 Conclusions ..................................... ............. 97 CHAPTER VI. COMPRESSIVE PROPERTIES. 21. Coefficient of Elasticity and Ultimate Resistance .................. 99 22. Ultimate Compressive Resistance ................................ 121 Setting Under Water .......................................... 130 Wet or Dry Concretes .......................................... 130 High Temperatures ............................................ 132 23. Conclusions .................................................... 132 CHAPTER VII. FLEXURAL PROPERTIES. 24. The Theory of Flexure as Applied to Concrete .................... 142 25. Flexural Coefficient of Elasticity ................................ 144 26. Modulus of Rupture in Bending .................................. 149 27. Shearing Resistance and Conclusion ............................. 157 APPENDIX I. Report on Uniform Tests of Cement by the .Special Committee of the American Society of Civil Engineers ........................... 159 Sampling, 159; Chemical Analysis, 159; Specific Gravity, 160; Fineness, 161; Normal Consistency, 162; Time of Setting, 163; Standard Sand, 164; Form of Briquette, 164; Moulds, 164; Mixing, 165; Moulding, 165; Storage of the Test Pieces, 166; Tensile Strength, 166; Constancy of Volume, 1 67. APPENDIX II. Constitution of Cement ............................................ 169 Authors' Index ..................................................... 175 CHAPTER I. CHEMICAL PROPERTIES OF CEMENT. Definition Cement is a material which has the property of set- ting and hardening under water, and is composed principally of lime, silica and alumina. Two forms of cement are commonly recognized, natural and Portland, and to these the following pages will be entirely restricted. The difference between these forms is principally one of manufacture; the basic principles in both varieties are the same. Article i Theories of Setting. The proper chemical constitution of cements involves the con- sideration of the theory of the setting and hardening of cements, the reasoning concerning which is, at the present time, not unani- mous. Chemists have not definitely determined the chemical changes that occur when water is added to dry cement; but the conclusions reached by Le Chatelier in 1887 and by the New- berry s in 1897 have been accorded more weight than those of others. Le Chatelier'' s Theory ( Annales des Mines, 1887, p. 345). Le Chatelier considers that when the raw materials of a cement have been burned two different sets of compounds possessing the property of setting and hardening upon the addition of water may be formed. In the first case he considers that the finished material contains lime (CaO) just sufficient in amount to combine with the silica (SiO 2 ) and alumina (A1 2 O S ) to form tricalcic silicate (3CaO.SiO_>) and tricalcic aluminate (3CaO.Al 2 O 3 ). These compounds, upon hydration, set and harden. He finds it unnecessary to provide lime to react on the sesquioxide of iron which may be present in the 2 CHEMICAL PROPERTIES OF CEMENT. [Ch. I. mixture, since the calcic ferrites that might form fall to powder upon the addition of water. Magnesia (MgO) and lime he con- siders as possessing equivalent properties, and, therefore, inter- changeable. In this case, then, no multiple silicates of alumina and lime are formed; and in order that the finished cement may have no free lime existing in it, Le Chatelier states that the pro- portion of lime and magnesia to silica and alumina should be subject to the following conditions: CaO+MgO < The objection to the presence of free lime or magnesia is due to the fact that they blow or expand in volume when acted upon by water ; disintegration of the -cement follows and it becomes unfit for use. For the second condition Le Chatelier believes that only tri- calcic aluminate and a silico-aluminate of lime, represented by 2SiO 2 .Al 2 O 3 .3CaO, are formed, and that the Fe 2 O 3 acts similarly to A1 2 O 3 in the case of multiple silicates and need not be sepa- rated from it. For this case Le Chatelier states the condition of the propor- tions of the constituents as follows: Ca O+MgO > The Newberrys' Theory (J. Soc. Chem. Ind., 1897, p. 889). The conclusions reached by Spencer B. and W. B. Newberry are quite different; it is their belief that the compounds that harden, upon hydration, are tricalcic silicate and dicalcic alumi- nate, and not tricalcic aluminate. Tricalcium silicate requires 2.8 parts of weight of lime to i part of silica, and dicalcic aluminate requires i.i parts of lime to I of alumina. The Newberry formula for a theoretically perfect ce- ment is therefore: 2.8 Silica+i.i Alumina Lime In this equation the materials represent percentages of weight in the cement. Art. 2.1 CHEMICAL ANALYSES. 3 The Newberrys also conclude that Fe 2 O 3 acts similarly to A1 2 O 3 , but should not be allowed in excess of 5 per cent. In this they differ from Le Chatelier. Again, Le Chatelier's for- mula places magnesia and lime of equivalent value in a cement; the Newberrys, on the contrary, consider magnesia inactive, and to perform no useful function. One general opinion concerning the magnesian compounds in cement is that they cause the first or preliminary setting of the cement, but that they expand and crack after aging. In all cases the calcic compounds are considered to be the ones which harden with age, and they are the compounds which cause ultimate strength. On account of this possibility of blowing, it is there- fore the common practice at present to limit the presence of mag- nesia to 5 per cent. Cements containing up to this limit have not been shown to be inferior. Another theory as to the first or quick setting properties of cement attributes these properties to the presence of calcium- aluminate, and the final or ultimate strength to the calcium- silicate only. It is difficult to reconcile these conflicting opinions. Other chemical elements which appear in a cement are be- lieved to be of no practical importance, and none other will be considered, except plaster of Paris or sulphate of lime, CaSO 4 , which is added in percentage never exceeding 2 per cent., for the purpose of causing a slower setting of the cement. This is a common practice, and its effect on the strength of the cement will be considered later. Art. 2. Chemical Analyses. It will be interesting to examine the different chemical com- positions of cement as they have been recorded by different analysts. It will be found that the variations of the different constituents, on the whole, are very slight. Portland Cements Table I. exhibits the values of analyses as taken from the report of the Watertown Arsenal "Test of Metals, etc.," for 1901. CHEMICAL PROPERTIES OF CEMENT. [Ch. I. TABLE I. PORTLAND CEMENTS. Brand Location of Works | CO "o V 3 G X Oi Alumina j Hi Magnesia t. 4> 3 -0 as & Carbon Dioxide SiO 2 Fe 2 3 A1 2 O 3 CaO MgO SO 3 CO 2 Alpha Easton, Pa Northampton, Pa . . WestCoplay, Pa-- Siegfried, Pa Akron NY 20.60 18.32 23.84 22.00 22.45 22.94 20.30 20.42 20.04 22.92 2.91 3.36 1.30 2.50 2.53 2.90 2.95 2.10 3.95 2.46 11.20 11.22 8.12 9.00 9.27 6.30 10.87 11.00 7.48 7.98 59.00 60.00 61.58 59.90 60.27 43-74 62.15 57.50 63.02 63.39 3-25 3.78 2.48 3.50 3.59 *20.72 2.51 2.53 1.23 Trace 1.40 1.40 1.60 1.98 0.60 2.83 1. 10 2.26 1.62 1.28 .34 .92 .08 0.75 .00 .00 0.12 4-19 3.00 1.97 Atlas Lehigh Star (with plaster) . . Star (without " ) Whitehall Cementon, Pa- . . Germany Alsen Dyckerhoff Josson Belgium 21.38 2.70 9. 23 \ 60. 76 2.54 I.6I 1.64 ' : Not included in average. TABLE II. PORTLAND CEMENTS. Brand Location of Works Si0 2 AloO 3 FeoOs CaO MgO S0 3 Alpha 22.62 21.96 19-92 22.68 21.08 22.04 21.86 21.8 23.08 20.95 22.93 8.76 8.29 9.83 6.71 7.86 6.45 7.17 7.95 6.16 9.74 ^10 2.66 2.67 2.63 2.35 2.48 3-41 3.73 4.95 2.9 3.12 .33-^ 61.46 60.66 60.32 62.3 63.68 60.92 61.14 61.9 62.38 63.17 64.67 2.92 3.43 3.12 3.14 2.62 3.53 2.34 1.64 I.2I .75 .94 .53 .43 .13 .88 .25 2.73 1.94 .79 1.66 .86 1.05 Atlas Giant Saylors Vulcanite Empire Jordan NY Coplay Pa Vulcanite N. J Warner N.Y Diamond Sandusky Bronson Whitecliffs-.-. Middlebranch, Ohio Bronson, Mich Whitecliff, Ark Average . . 21.90 7.89 3.09 62.04 2.33 1.49 TABLE III. EUROPEAN PORTLAND CEMENTS. Brand SiO 2 A1 2 3 Fe 2 3 CaO MgO SO* White label, Alsen 20 48 7 28 3.88 64 3 1.76 2 46 Dyckerhoff 20 64 7 15 ? 69 63 06 2 33 39 Germania 22 08 6 84 3 36 63 72 32 82 Hemmoor 21 14 5 95 4 oi 63 24 44 47 Lagerdorfer 23 55 7 47 2 4 61 99 42 07 Brook, Shoobridge & Co 22 2 7 3") 4 77 61 46 35 87 22 18 8 48 5 08 61 44 34 56 Condor 23 87 6 91 2 27 64 49 04 88 Candlot Prench 22 3 85 "3. \ 62 8 45 7 Boulogne French 22 3 7 2 *) 64 62 I 04 75 Average 22 07 7 OQ KT 63 12 I 3*1 I 40 Art. 2.] CHEMICAL ANALYSES. Table II. shows similar quantities obtained from analyses of American cements, compiled by Ries & Eckels, in "Lime and Cement Industries of New York," 1901, page 705. Table III. is taken from the same book and exhibits the com- position of some European Portland cements. TABLE IV. CaO Si0 2 A1 2 3 FeaOs MgO SO 3 60.94 23.23 7.75 3.04 2.14 1.56 Table IV. shows the average results of chemical analyses made on thirty-eight samples of cement used in submarine work on the Charlestown bridge, Boston, by the Boston Transit Commission, as published in their report for 1900. Finally, owing to the interest which has been aroused by the novel conditions of manufacture, Table V., containing an analysis of the Edison Portland Cement Company's cement, is given. The analysis is taken from a reported test by Lathbury & Spack- man, Incorp., of Philadelphia, and was published in the "Engi- neering Record" December 26, 1903. TABLE V. CaO SiO 2 A1 2 O 3 Fe 2 3 MgO 62.71 20.14 7.51 3.33 2.34 These tables show very uniform results; in general, the per- centages of the constituents are as follows : CaO MgO SiO 2 A1 2 3 Fe 9 O, averages 62% 2% 22% 8% 3% Inserting these values in the Newberry formula, the result ob- tained is CHEMICAL PROPERTIES OF CEMENT. [Ch. I. 2.8X22+i.iX8 =i 62 or an error of 14 per cent, as compared with a theoretically per- fect cement. By substitution the first of Le Chatelier's formulas reduces to 62+2 and the second to 22+8 62+2 =2.13; -5-82 2283 These values are respectively smaller and greater than 3, as they should be; but they give no indication of the standard of ex- cellence obtained. Natural Cements The following tables show the average an- alyses of both European and American natural cements : Table VI. is taken from the Watertown Arsenal report on "Test of Metals" for 1901; Table VII. from U. Cummings's TABLE VI. NATURAL CEMENTS. Brand Location of Works SiO 2 Fe 2 O 3 AloO 3 CaO MgO SO 3 C0 2 Akron Star Akron, N.Y Mankato, Minn. Siegfried, Pa. ... Rosendale, N. Y. Mankato, Minn. . Whiteport, N.Y.. Binne water, N.Y. Akron, N.Y..... 20.40 19.02 30.40 25.00 27.70 28.71 26.66 23.70 32.00 2.56 1.24 2.60 2.27 1.86 3.60 3.02 3.30 2.70 6.22 8.96 10.36 8.93 7.06 5.88 11.48 16.70 8.79 40.64 41.18 52.12 39.30 37.00 27.00 38.33 37.00 33-89 25.80 26.58 0.21 16.18 22.63 30.00 16.41 15.30 18.10 2.91 .27 .24 .40 .23 .30 .35 .98 .31 1.47 1.75 3.07 2.66 2.46 3.52 2.75 2.00 3.20 Austin Bonneville Improved. . Hoffman* Newark & Rosendale. . Norton. . Obelisk Potomac 25.95 2.57 9.37 38.49 19.02 1.55 2.54 ^Contains 4.26 per cent, of Oxides of Sodium and Potassium. "American Cements," and Table VIII. from analyses, reported by D. J. Whittemore, in the Transactions of the American Society of Civil Engineers, 1880. The American natural cements of Table VII. cover a wide range of territory. Art. 2.] CHEMICAL ANALYSES. TABLE VII. NATURAL CEMENTS.* Brand and Location of Works. SiO-2 Alo0 3 Fe 2 O 3 CaO MgO Buffalo Hydraulic Cement ; Buffalo, N. Y Utica HI 24.3 34.66 23.16 26.4 25.28 30.5 29.98 30.84 27.3 27.98 28.38 19.9 22.62 26.69 24-34 23.32 27.6 33.42 22.58 22.44 28.43 22.21 32.06 28.45 18.59 28.02 25-15 2.61 5.1 6.33 6.28 7.85 6.84 6.88 7.75 7.14 7.28 11.71 5-92 7.44 7.21 8.56 6.99 10.6 10.04 7.23 6.7 6.71 16.48 21.27 2.24 9.14 10.2 8. 6.2 1. 71 1.43 2.42 2.5 2. 1 1 1.8 1.7 2.29 1. 14 1.4 1.3 2.08 5.97 .8 6. 3.35 2. 1.94 1.67 2. 1 1 2. I. 8.8 3.28 39.45 30.24 36.08 45.22 44.65 34.38 33.23 34.49 35.98 37.59 43.97 46.75 40.68 43.12 61.62 53.96 33.04 32.79 48.18 32.73 36.31 39.64 35-56 56. 40.7 44.48 49-53 6.16 18. 20.38 9. 9.5 18. 17.8 17.77 18. 15. 2.21 16. 22. 19.55 .4 7.76 7.26 9.59 15. .67 23.89 17.5 7. 10. 27. 13.78 Milwaukee Wis N L &C Co Rosendale N Y Rocklock* Rosendale N Y N Y to R Ro?>ndnle N Y Hoffman* Rr<;c>ndale NY Norton High Falls* Rosendale NY Brockett; Ft. Scott Hydraulic, Kansas City, Mo ITtim Rrnnd' Utirn 111 ^honhc>rH^trwn W^ Va Hydraulic Cem Rock* Platte River Neb St. Louis Hydraulic Cement, near E. Carondelet, 111. Warnock Ohio Round Top Cement* Hancock Md 26.40 8.17 2.55 41.12 12.97 "From "American Cements," by U. Cummings TABLE VIII. NATURAL CEMENTS. Cement No. CaO MgO SiO 2 A1 2 3 Fe 2 3 j 45 17 16.52 23.40 8.07 2.45 2 ... 36.32 14.47 24.50 14-32 2.93 3 33.97 15.21 28.04 12.82 4.60 4 40.75 25.25 22.22 8.68 1. 18 Average. . 39.05 15.36 24.54 10.97 2.79 The results show that CaO MgO SiO 2 A1 2 O 8 Fe 2 3 averages 40 % 15 % 26 % 8 CHEMICAL PROPERTIES OF CEMENT. [Ch. I. It will be seen that the greatest difference between the natural and Portland cement is in the varying proportions of the lime and magnesia contents; the other constituents remain about the same. Using the average figures of the natural cements given on the preceding page, the Newberry formula becomes 2.8X26+i.iX8j = 40 the first of Le Chatelier's formulas becomes 4I5 =I . 6 26+8| and the second, =3.67 3 7 None of these formulas furnishes results comparable with theo- retic requirements, in the case of the Newberry formula probably on account of the neglect of the magnesia. As a conclusion it is evident that a chemical analysis may give no final indication of the quality of the cement. Adulteration of the cement with inert material, such as slag, may be discovered. Certain materials, such as magnesia or plaster of Paris, may be found present in too large quantities; but it seems evident that a poor cement may be due more to imperfect manufacture than to the use of improper constituents. CHAPTER II. PHYSICAL TESTS OF CEMENTS. The mechanical operations attending the manufacture of ce- ment, such as the mixing, burning and grinding of the raw ma- terials, bear intimate relation to the final physical properties of the cement, and should be analyzed just as closely as the chemical compositions; but in this treatise it is out of place to discuss manufacturing operations. The manufacture of a cement is therefore to be assumed correct if a sample of it passes those physical tests which are made for the purpose of determining its acceptance or rejectance for use. These tests are of such a char- acter that the results of all experimenters are comparable; but it is not necessary, although it is desirable, that these tests should furnish values of the strength of the material, values which might be used in designing engineering work. Art. 3 Commercial Physical Tests. The phys.ical tests require but brief explanation, and only those tests which are practiced in the United States need consideration. They are five in number: 1. Specific gravity, 2. Fineness, 3. The time of setting, 4. The tensile strength, and 5. The constancy of volume. They are fully explained in the reports presented on January 21, 1903, and on January 20, 1904, to the American Society of Civil Engineers by its Committee on "Uniform Tests of Ce- ments." A copy of these reports is given in the appendix. Experience has shown that good cements furnish certain re- 10 PHYSICAL TESTS OF CEMENTS. [Ch. II. suits in these standard tests, and it is to be expected that, if new cements fulfill the same conditions, their behavior in construction work will be the same. Art. 4 Specific Gravity Tests. As stated in the first of the two reports mentioned above, the specific gravity of a cement is lowered by underburning, adul- teration and hydration ; but the adulteration must be in consider- able quantity to affect the result appreciably. When properly made, this test affords a quick check for underburning or adul- teration. Table I. exhibits the values of the specific gravity of repre- sentative Portland and natural cements, and is taken from the Watertown Arsenal Report on "Tests of Metals" for 1901. The determinations were made with a Schumann volumeter, benzine being the liquid employed. Brand TABLE I. g^# Alpha Portland Cement 3- 1 1 Atlas Portland 3-09 Storm King Portland 3.07 Whitehall Portland (14 days after grinding) 3.13 Alsen Portland 3-08 Dyckerhoff Portland 3. 1 1 Josson Portland 3.04 Bonneville Improved Natural Cement 2.85 Hoffman Natural 3.06 Norton Natural 3-03 Austin Natural 3-15 Mankato Natural 2.93 Newark & Rosendale Natural (12 days after grinding) . . 3.06 Obelisk Natural 3. 12 Potomac Natural 2.94 It will be seen that Portland cements give uniform results, the average of seven cements being 3.09. The specific gravity of the above cements after they had set was obtained in various ways. Table II. shows the specific gravity of the reground material after the cement had set for a period of three days. Different Art. 4.] SPECIFIC GRAVITY TESTS. 11 percentages of water were used, as indicated. It will be seen that in general the larger amount of water reduces the specific gravity. TABLE II. Brand Specific Gravity. Material mixed with percentages of water of 5% 10% 15% 20% 30% 40% Alpha Portland 2.94 2.69 2.83 2.88 2.73 2.80 2.69 2.82 2.73 2.77 2.75 2.77 2.59 2.73 2.77 2.67 Lyckerhoff Portland Bonneville Improved Nat'l Mankato Natural The specific gravity of the hydrated material in a cake of cement was also determined, as shown in Table III. The ma- terial was weighed both in air and in water by means of a chemi- cal balance, account being taken of the water absorbed when the cement was immersed, thus making the necessary correction for voids. The cakes of material in this case were halves of tensile briquettes, but the report does not give the age of the briquettes; there seems to be no difference in the values of those briquettes which set in air or in water. TABLE III. Brand Specific Gravity of Briquettes Which Set In Air Water Alpha Portland 2.23 2. 1 1 1.65 1.79 1.65 2.29 2.07 1.66 1.77 1.66 1.92 to 2.17 Dyckerhoff Portland Atlas Portland (Material from 12 inch Cubes). . (it will be seen that the specific gravity of the cement after set- ting is considerably less than the cement before the addition of water./ Article 5. Fineness Test. The fineness of a cement indicates to a great degree the pro- portion of inert material in it. Until lately it has been thought sufficient to measure the fineness of a cement with a No. 100 sieve, but it is now becoming the practice to use a No. 200 sieve. 12 PHYSICAL TESTS OF CEMENTS. [Ch. II. As recommended by the American Society of Civil Engineers, these sieves should be made of woven cloth of brass wire which has the following diameters : No. 100 0.0045 inches No. 200 0.0024 inches The mesh should be regular in spacing and be within the follow- ing limits: No. 100 96 to 100 meshes to the linear inch No. 200 188 to 200 meshes to the linear inch The sifting is continued upon a sample until not more than one-tenth of i per cent, passes through after one minute of con- tinuous sifting. The percentage sifting through is found by weighing the residue and subtracting from the original quantity. There is naturally a commercial limit to the fineness of grind- ing of a cement; the following tables show characteristic results obtained from various well known brands of Portland and natural cements. Table I. is taken from the Report of the Watertown Arsenal ''Test of Metals," etc., 1901 ; chemical analyses made on the dif- ferent sized particles of these brands show substantially the same composition which was found in the material taken from the barrels. TABLE I. Size of Grain Brand of Cement Greater Than .0058 Inch .0050 .0034 .0027 Smaller Than .0027 Corresponding to Sieve Having Meshes 98 x 100 112x118 155x170 188x198 Atlas Portland II. 2 12.9 19.3 14. 1 33.6 12.5 3.8 4-7 5-7 1.9 9.1 10.4 7.9 6.4 6.6 II. 4 8.2 12.5 23.8 17.5 69.3 60.6 58.9 65.1 42.6 70.0 Star Portland Alsen Portland Hoffman Natural Mankato Natural Norton Natural Table II. is taken from Vol. VI. of covers Portland cements only. 'Mineral Industry," and Art. 5.] FINENESS TEST. 13 TABLE II. Brand. Percentage Passing Sieve- No. 50 No. 100 No. 200 100 99 99.5 99.7 99.6 99.6 98.8 99.7 100 99.6 96.4 94.9 92.7 94.8 95.3 92.8 88.3 92.4 99.6 88.5 68.4 72.0 Giant Atlas Alpha Brooks Shoobrid^c & Co. ...... Alsen Aalborg As a matter of present day interest, the following test of the Edison Portland Cement Company's cement, from the same re- port previously mentioned, may be noted: Passed No. 100 sieve 99.8$ Passed No. 200 sieve 91.6$ Although two cements may furnish the same degree of fine- ness as to a No. 100 sieve, finer sieves may show different results. German experimenters have therefore employed the velocities and carrying capacities of liquids as a measure of fineness, but such refinement in testing is unnecessary. The No. 200 sieve furnishes a sufficient test. The tests which have been made upon cements to prove the superiority of fine grinding are not of great importance, and even in, some cases show contradictory results. These are, however, easily explained. Neat unsifted cement, for instance, may show greater strength than the finely sifted, because the grains in the mixture may be better balanced, or because the coarser material, which is the harder burned, and usually the better, has been ex- cluded from the sifted. In the case of mortars the proportions and balancing of the sand greatly outweigh any results that may be obtained due to the sifting of the cement itself. The reader is, however, referred to experiments by Grant, Vol. XXL, Proc. Inst. Civ. Eng., and to Clarke, Trans. Am. Soc. C. E., Vol. XIV. Art. 6. Test for Time of Setting. Two periods are noted in determining the time of setting of a cement: the initial setting, when the material first begins to set, 14 PHYSICAL TESTS OF CEMENTS. [Ch. II. and the final setting, when the material has acquired a certain degree of hardness. The former period determines the begin- ning of the process of crystallization, and is important to deter- mine, as a disturbance of the cement after the time of this initial setting produces loss of strength; but the time of setting never furnishes a gauge as to the ultimate strength of a cement. It is unnecessary to describe the apparatus used in this test; the report of the Committee of the American Society of Civil Engineers records in detail the methods of operation. Table I., taken from the Watertown Arsenal Report, 1901, shows some characteristic results of the time of setting of some standard American cements, when gauged with different per- centages of water; the tests were made according to both Ameri- can and German standards. The differences for the varying per- centages of water are quite marked, the time of set increasing with the amount of water. There is also considerable difference in the results of the two methods of test. In general, it may be said that natural cements set faster than Portland. TABLE I. Brand Water Gillmore's Method German Method Per Cent. Initial Set Final Set Initial Set Final Set Alpha (Portland) \ Atlas (Portland) I Hoffman (Natural). . . . < Newark and Roscndale J (Natural) 1 20 25 30 20 25 30 30 35 40 35 40 45 H. M. 2 20 3 20 5 40 4 05 5 10 7 00 2 15 2 55 3 43 37 47 I 08 H. M. 5 00 7 30 H. M. 35 2 50 4 40 2 45 3 35 5 30 I 25 2 20 2 48 32 40 48 H. M. 4 25 6 35 8 40 6 10 7 05 7 10 8 05 3 25 5 40 2 55 4 10 I 17 3 44 4 18 I 07 2 19 3 33 Action of Plaster of Paris The time of setting of a cement may be delayed by the addition of a small percentage of plaster of Paris. The action in that case is merely mechanical. The plaster of Paris dissolves in the water and forms a protecting covering about the cement particles; at the same time it hardens Art. 6.] TEST FOR TIME OF SETTING. 15 and prevents action of the water on the cement. In small per- centages, plaster of Paris is found to increase the strength of ce- ments, but in large quantities expansion or blowing of the cement is likely to occur. The action in that case is similar to that of sea-water on cement. E. S. Wheeler, on page 2938 of the Report of the Chief of Engineers, U. S. Army, for 1895, records numerous tests show- ing the effect of plaster of Paris on the time of setting. An ad- dition up to 2 per cent, increases both the periods of initial and final set, but an addition of more than 2 and up to 10 per cent, decreases this period. It is not necessary to give the detailed figures of these experiments. Table II. is taken from the Report of the Chief of Engineers, U. S. Army, for 1896, p. 2832, and shows the varying values of TABLE II. Tensile Strength of Portland Cement with Varying Percentages of Plaster of Paris. The sand is natural Point aux Pins. Each result is an average of five specimens. Plaster of Paris to Total Cement Ratio of Cement to Sand Strength in Lbs. Per Sq. Inch at Age of i 7 Days 6 Months 1 Year per cent :0 :0 :0 :0 :0 :2 ;2 :2 :2 1:2 487 626 600 519 380 323 388 360 289 192 743 746 754 742 660 492 530 547 607 663 487 515 610 588 647 3 per cent 6 per cent the tensile strength of a Portland cement with the addition of various percentages of plaster of Paris. It will be seen in gen- eral that an addition of plaster of Paris up to 2 per cent, has no weakening effect. This is shown both for neat cement and for a cement mortar of I part of cement to 2 of sand. Again, it will be seen that the mortar in which the cement contained a large amount of plaster of Paris attained considerable strength at the age of one year. The report noted records tests on three brands of Portland cements and on some natural cements; the results 16 PHYSICAL TESTS OF CEMENTS. [Ch. II. are similar to those in the table; but many of the natural cements checked and disintegrated before the time of testing. The effect of the addition is seen to give very variable results, but a safe limit is 2 per cent. The time of setting of a cement depends also on its chemical composition and on the character of its burning. In general, a lightly burned cement sets quicker, as does also a freshly burned cement; but there are frequent exceptions. The quantity of water used in gauging the cement, the temperature of the water and the temperature of the air all affect the time of setting. A rise of temperature follows the setting of all cements, and this rise increases very rapidly for fast setting cements. The time of setting is also affected by the volume of cement mixed. TABLE III. Compressive Strength in Pounds per Square Inch when regauged after an interval of Brand Alpha Portland Dyckerhoff Portland Star Portland Storm King Portland 1 -> 1 |l 3 < Bonneville Natural Norton Natural Hours After First Mixing 7279 3549 3667 3412 3402 2686 2439 2312 1893 1745 1758 1666 1690 3489 3737 3753 3903 3889 1792 1599 1495 II5I 3328 3498 3827 3696 719 724 895 387 388 *425 713 443 340 424 378 2 6169 7146 6774 6539 i 4 340 276 6 8 10 12 16 1Q 20 *After seven hours. Temperature Affects Setting Gen. Gillmore, in his Treatise on Limes, Mortars and Cements, page 83, shows some interesting results as to the variations in time of setting due to changes of temperature of water used in mixing. It is unnecessary to re- produce here his results, but he shows that invariably high tem- peratures increase the rapidity of setting. There may be marked differences in the variations for different cements, but the state- Art. 6.1 TEST FOR TIME OF SETTING. 17 ment is true of all. Exactly similar results are recorded by E. S. Wheeler in the Report of the Chief of Engineers, U. S. Army, 1895, page 2936. Retarding the Set If agitated sufficiently, it is possible to pre- vent a cement from setting at all; if disturbed after the final set- ting has commenced, its strength is greatly decreased, and since natural cements, as a class, reach their final set in periods of time considerably less than Portland cements, it may be expected that the effect of regauging the natural cements is of greater conse- quence. This is clearly shown by Table III., which is taken TABLE IV. Ult. Compressive Strength in Pounds per Square Inch after elapse of X hours be- tween initial mixing and placing of material in moulds Brand of Cement Ult. Compressive Strength in Pounds per Square Inch after elapse of X hours be- tween initial mixing and placing of material in moulds Brand of Cement CO 0.2 ga- =j= * S V) Star Portland Without Plaster Star Portland With Plaster Star Portland Without Plaster Hours Hours o 5467 4665 6421 5470 2718 2662 2387 2160 2214 2154 1901 2414 2594 2561 2167 2282 2021 1842 1541 1242 1426 1499 24 1669 1442 1279 1132 1 168 1150 1 00 1 763 723 681 1462 1216 IIOI 1 143 1069 IIIO 849 834 782 737 I 30 2 36 4 . . . 42 . 6 ")0 . . 8 60 10 70 12 80 14 90 16 100 20 from the Watertown Arsenal Report for 1901, and exhibits the results obtained in retarding the setting of cements which, after having been mixed with water, were left undisturbed until each of the periods shown, when a sample from the main batch was extracted. The majority of these specimens were 6 inch cubes, although some were smaller sized cubes. Many of the results obtained were averages of two or more samples, and the average age of the specimens was about thirty days. In this set of experiments the main batch of the cement was left undisturbed until the sam- 18 PHYSICAL TESTS OF CEMENTS. [Ch. II. pies were extracted, when the entire mass w r as again gauged with water; the sample was then tamped into a mould and allowed to set without further interference. Table IV. shows the compressive strengths attained when the main batch of the cement was not left undisturbed after the initial mixing, but kept in a continual state of agitation in the mixing bed. In this test the two kinds of cement used were both Star Portland, but one contained plaster of Paris, as a restrainer to control the time of setting, while the other contained no plaster. The effect of the restrainer is clearly shown. TABLE V. Brand of Cement Percentage of Water Maximum Temperature in Degrees Centigrade Ultimate Compressive Resistance in Pounds per Sq. Inch Age in Days Weight per Cu. Ft. in Lbs. Alpha Portland 26.2 95- 5706* 9 133 4 Star Portland 26.5 76. Storm King Portland. . Whitehall Portland 27.0 OK o 42.5 ino t Dyckcrhoff Portland . . 25.0 oq 7 63. (;i 1547 13 130.9 Atlas Portland Bonnevillc Natural. . . . Obelisk Natural. ...... 22.7 37.6 35 81.5 39-5 37 5 4872 840 9 13 137.5 116 7 36 5 74 o 740 g 1 15 I Austin Natural 40.0 44 6 35-0 40 Norton Natural 41.8 39.0 *Not ruptured. Temperature Changes During Setting Table V. shows the temperatures acquired by cements during setting; these values have been abstracted from the Watertown Arsenal Report for 1901. Experiments were made on 1 2-inch cubes, the upper sur- face being exposed to the air. The thermometer bulbs reached to the centre of the cubes. It is interesting to note that the highest temperatures were reached by Portland cements as a class, in some cases exceeding the boiling point of water. A number of hours elapsed before the maximum temperature was obtained, generally six to twelve hours for a neat Portland ce- ment, while a 1:1 mortar required about eighteen hours. At the end of one and one-half days the Portland cements still remained Art. 7.] TESTS OF TENSILE STRENGTH. 19 above the temperature of the room, but the natural cements had nearly returned to the temperature of the room. The .cements which reached the highest temperatures almost invariably showed the sharpest crests in the curves which were plotted with the times and temperatures as ordinates. It is probably merely a matter of coincidence that the highest temperatures belonged to cements showing the highest ultimate compressive resistance, but it may be interesting to investigate this point more fully at some future time. The difference be- tween the Portland and natural cements is very marked, but may be due partly to the excess of water used in mixing the samples. Temperature changes are naturally less marked when a cement is mixed with sand and stone than when neat, but they are still very noticeable. Experiments regarding these changes are now in progress on some large pieces of concrete work, but the results are not yet public. Art. 7 Tests of Tensile Strength. The test of the tensile strength of a cement is the decisive test in regard to its acceptance for use, even though in the majority of building operations it is not the tensile strength, but the crushing strength of the material, which is desired. It may be shown, however, that these two resistances bear an almost fixed ratio to one another, and since the tensile tests are more easily made and require less expensive apparatus, they have practically displaced the crushing tests. The tests are made on small briquettes of standard form whose minimum area of cross-section is one square inch; these bri- quettes are formed both from the neat cement and from mixtures of the cement with various percentages of standard or normal sand, and they are tested at stated periods after making. The periods are usually one, seven and twenty-eight days. The tests which are made to determine the tensile strength of cement have often been criticised on account of the poor form of cross-section of the briquette, and on account of the use of a class of sand which is never employed in practice. Although errone- ous values of the actual strength of the cement in working prac- 20 PHYSICAL TESTS OF CEMENTS. [Ch. II. tice are thus found, a standard of comparison between different cements is still obtained. It is unnecessary to describe* any of the apparatus or any de- tails of the methods of operation. The following figures and tables are of interest as showing characteristic results of tests made on the tensile strength of various kinds of cement, and are given for the purpose of determining a point in the life of a cement when its strength ceases to show an increase at an ap- preciable rate. TABLE I. TENSION EXPERIMENTS Age 1 Cement OSand 1 Cement OSand 1 Cement 3 Sand 1 Cement 3 Sand 1 Cement 5 Sand 1 Cement 5 Sand Immersed Not Immersed Immersed Not Immersed Immersed Not Immersed Ultimate Resistance in Pounds per Square Foot. 7 days 515 6^8 697 814 765 838 642 651 600 638 575 507 277 350 457 487 550 503 301 438 538 605 703 650 127 180 233 281 271 270 131 247 335 410 442 408 28 days 84 days I year 2 years Gauged with . . . 23 % 10. 1 % 9.5^ water COMPRESSION EXPERIMENTS 6320 6200 2570 2930 1210 1260 28 days 8400 8050 3520 4360 1560 I960 84 days 1 1 200 9700 5100 5750 1910 57 JO 13000 12200 5280 6160 2150 3200 I year I4I80 14200 6520 7720 2150 3560 2 years 14700 14800 6000 7100 2450 3500 Table I. shows the results of two sets of experiments made at the Laboratory de 1'Ecole des Fonts et Chaussees, under date of February 6, 1896, and published by Berger & Guillerme in "Ci- rri ent Arme." The values given are all the mean of five or six specimens. In the first series of experiments the briquettes were exposed to damp air for twenty-four hours and then immersed in fresh water; in the second series there was no immersion. The cross- *See Appendix. or THE I'NHVERSITY C'f H Art. 7.] OF TENSILE STRENGH. 21 section qf the specimens varied from 0.78 to 1.2 square inches. The lower part of the table is inserted to show the ratio between tensile and compressive stresses for mixtures of the same kind. Figure i was plotted from results published by E. C. Clarke, in Vol. XIV., 1885, of the Transactions of the American Society of Civil Engineers, and shows the strength obtained by Portland and natural cement and mortar briquettes whose minimum area of cross-section was 2j square inches. Twenty different brands 12 Months Age FIG. l.-CLARKE'S TESTS. of cement were used, and the figure represents 25,000 breakings. The ordinary cement briquette has a minimum area of I square inch, but comparative tests made at the time showed little dif- ference in result between cross-sections of i and 2j square inches. Figure 2 shows the results obtained in tensile tests on four brands of Portland cement, as published in the report for 1895 of M. L. Holman, Water Commissioner of St. Louis; each plotted point represents an average of ten briquettes. The briquettes were all i cement to 3 normal sand and were left one day in air 22 PHYSICAL TESTS OF CEMENTS. [Ch. II. and the remainder of the time in water. The figure shows a continual increase in the strength of the briquettes for the period 6 Months l Year 2 Years 3 Years 3fc Years Age of Specimens. FIG. 2. HOLMAN'S TESTS. of 3J years shown; but a similar series of tests made upon neat cement briquettes showed a slight decrease after the end of one 500 iOO 100 1:4 1:6 1 Month i Year Age of Specimens. FIG. 3. CLARKE'S TESTS. 8 Years year, the greatest decrease, as compared to the maximum strength obtained, being about 20 per cent. It is only proper to note that Art. 7.] TESTS OF TENSILE STRENGTH. 23 FIG. 4,-RAFTER'S TESTS. briquettes, when one year old or over, become very brittle and may show erratic results in the testing machine. Figure 3 shows the results ob- tained by E. C. Clarke, as part of the same experiments mentioned pre- viously, in which he found the varia- tion in the strength of cements when mixed with increased proportions of sand. These tests were all made on one single brand of cement and rep- resented 500 breakings*. Figure 4 shows the strength at- tained by a Portland cement both at various ages and when mixed with different volumes of sand. Each point marked on the curves repre- sents an average of five briquettes. These tests were made by Mr. .900, 800 600 500 100 IT* 100 200 300 400 Age in Days. FIG. 5. 24 PHYSICAL TESTS OF CEMENTS. [Ch. II. George W. Rafter and are published in the annual report of the "State Engineer of New York" for 1894. Figure 5 is taken from Johnson's "Materials of Construction," page 575, and shows the average tensile strength acquired at various ages by many samples of one brand of American Port- land cement, as reported by Messrs. R. W. Hunt & Co. R. W. Lesley published in the Journal of the Association of Engineering Societies, 1895, the results of long time tests made on samples of cement representing 300,000 barrels of the Giant 2 Years 3 i Age of Specimen in Years FIG. 6,-LESLEY'S TESTS. Portland brand of cement. Figure 6 is plotted from these results, and represents a series of tests made on 50,000 barrels of cement used on the Sodom and Bog Brook dams of the New York aque- duct. The results there shown are characteristic of the entire series. Each point plotted is an average of 1,000 to 1,300 bri- quettes. Taking only the tests made on briquettes of one cement to three sand, it will be seen that the strength at three months and six months, as compared to five years, are respectively 60 per Art. 7.] TESTS OF TENSILE STRENGTH. 25 cent, and 73 per cent.; and for three months and six months, as compared to one year, respectively 82 per cent, and 100 per cent. Figure 7 shows the results of experiments recorded by J. Grant in the Proceedings of the Institution of Civil Engineers, Vol. XXXI I. , page 280, and shows the variation in the tensile strength of Portland cement briquettes from observations extend- ing over a considerable number of years. The form of specimen used was not the standard form as used to-day, the minimum area of cross-section being 2\ square inches. The specimens were all kept in water from the time of making until the time of testing, and ten specimens were tested at each age. It will be fi-S a ^ ' I Portland Cement Neat / *** 1 : Th lines \ Jand 1 ; f 1200 800 Age in Years FIG. 7. GRANT'S TESTS. seen that there is no increase of strength after two years. For neat specimens the percentage of increase gained after three months' age is 20 per cent., as compared to the final strength; and for the one cement to one sand mortar the corresponding percentage is 33. Similarly, comparing the increase in strength after six months to the final strength, these percentages become respectively 1 1 and 22. The following table shows the tensile strength of the Edison Portland Cement Company's cement, and is inserted as a matter of interest as giving the tensile resistance of the latest cement on the American market; the tests are taken from the report already mentioned. Neat, I day =325 Ibs. per sq. in. Average of 5 specimens. Neat, 7 days=676 Ibs. per sq. in. 1:3, 7 days=255 Ibs. per sq. in. 1:3, 28 days=33I Ibs. per sq. in. 26 PHYSICAL TESTS OF CEMENTS. [Ch. II. In all these figures it is seen that cement and the cement mix- tures attain a strength not differing greatly from the ultimate strength within a period of three months from the time of set- ting, and practically that within a month or so after this period no appreciable change in the strength takes place. It is important to recognize this fact in order to appreciate that it will make no sensible difference in tests of cement mix- tures when the age of the specimen is in the neighborhood of three months. The results so obtained need no correction for age and will all be comparable. It is of interest to record the following empirical formula which has been proposed by W. C. Unwin (Proc. Inst. Civ. Eng., Vol. LXXXIV.) for determining the tensile strength of a briquette within two years after making; he derived it by analyzing the re- sults of tests by Bauschinger, Grant, Clarke and others. If y is the strength of a cement or mortar at x weeks after mix- ing, and # the strength of the same in pounds per square inch at seven days, then y=a-\-b (x i) n The constant n has values which can be assigned beforehand, and the constant b is determined by experiment on pieces more than one week old. Unwin, assuming for the case of tension n to be J, finds that b varies within rather narrow limits. Art. 8. Ratio of Compressive and Tensile Strengths. The ratio of compressive and tensile strength is not a constant quantity for all ages of a mortar, since, in general, compressive strength increases faster than the tensile strength; but experi- ments show that the variation of this ratio is not very great. J. B. Johnson in "Materials of Construction" analyzes the re- sults of numerous experiments on a mortar of one cement to three sand, which were recorded by Tetmajer in his "Communi- cations," Vol. VI., and expresses the ratio between these strengths by the following equation : R=8.64+i.8 log A where R represents the ratio between the compressive strength Art. 8.] RATIO OF COMPRESSION TO TENSION. 27 and the tensile strength, and A is the age of the cement mortar in months. Busing and Schumann, in "Der Portland Cement," 1899, pre- sent in Table I. results which furnish the relations between these two kinds of stress. The specimens were made with ordinary sand and gauged with different percentages of water, and were TABLE I. Age in Days. 10 Per Cent. Water 1 2 per Cent. Water 15 per Cent. Water Pounds per Sq. In. Ratio Pounds per Sq. In. Ratio Pounds per Sq. In. Ratio Tension Com- pression Tension Com- pression Tension Com- pression 7 28 284 370 407 456 2860 4050 5050 5400 10. 1 10.9 12.4 II. 8 196 326 366 380 1550 2270 2940 3200 7.8 7.0 8.0 8.4 143 260 328 321 781 1420 2130 2410 5.4 5-5 6.5 7.5 90 180 tested at various ages. It is to be noted that with the increase of water the compression decreases faster than the tension, and that with the increase of age the compression tends to resume its former relations. TABLE II. Age in Weeks Mixture Tension Compression Bending Shear Ult. Resistance Pounds per Square Inch Ult. Resistance Pounds per Square Inch Extreme Fibre Stress in Lbs. per Sq. Inch Ult. Resistance Pounds per Square Inch Specimens Hardened in Air Water Air Water Air Water Air Water { I :0 :3 :5 :0 :3 :5 :0 :3 :5 231 106 68 266 148 119 257 244 177 224 95 64 294 169 103 292 272 232 I860 920 543 2460 1500 962 3400 2080 1510 1910 880 537 2490 1040 977 4680 3340 2960 695 273 168 860 392 284 1010 748 545 625 247 158 887 381 276 1350 973 810 276 109 81 316 182 136 388 294 248 271 116 77 346 181 131 415 375 364 I 104 to 113. | An exceedingly interesting set of experiments was published as long ago as 1879, by Bauschinger, in the Proceedings of the Munich Technical Institute, Bauschinger experimented on mor- tar specimens of I cement to o sand, I cement to 3 sand, and I ce- 28 PHYSICAL TESTS OF CEMENTS. [Ch. II. ment to 5 sand. His tension specimens had a cross-section of 2.4X4-8 ins. = 11. i sq. ins. The compression specimens were cubes 4.8 inches on the side, and his flexure tests were made on specimens 2.4X4.8X12 inches long, tested with a span of 10 inches. The 4.8 inch side was vertical. Tests of the shearing resistance were made on the flexure specimens. Table II. shows results of all these tests, each value shown being an average of 9. The extreme limits of the ratio of compression and tension will be found between 13.2 and 8.00 for dry specimens, and 16.02 to 7.35 fcr the wet. It is to be noted, however, that this value of 16.02 was exceptional, the next highest ratio being 12.76. The limits of the ratios of the ultimate fibre stress in flexure to maximum tensile stress were 3.93 to 2.46 for the dry, and 4.65 to 2.25 for the wet. The limits of the ratios between shear and ten- sion were 1.51 to 1.03 and 1.57 to I.Q7 for the dry and wet re- spectively. TABLE III. Gauged with Gauged with Gauged with 20 per Cent. Water 22 per Cent. Water 25 per Cent. Water Age in J5 c w c c W J3 c 12$ e d- 1.8 5 C 9 ~ C CT c a || I 6 *> ||| Ratio III ill Ratio If! 2 u co s5 Ratio Air. Water. Days. Days. 8l5 B fl JS Hcfl-J U 015 4 082 021 13 ... 104 024 26 125 028 39 139 030 52 146 O"^ M. Gary records in the Trans. Am. Soc. Civ. Eng. for October, 1893, the results of some tests by Dr. Tornei, manager of the Stern Portland cement factory; the size of specimen was the same as used by Bauschinger. Table III. is an abstract, being the average of the first six cements there shown. TABLE III. Mixture Age in Days Percentage of Contraction, Hardening in Air Percentage of Expansion, Hardening Under Water r 7 .064 .014 Neat < 28 129 026 90 .181 .021 I Cement \ 3 Sand.. / " '1 7 28 90 .018 .053 .089 .Oil .018 .028 Considere has stated that the shrinkage of cement in air may vary from 0.15 to 0.2 per cent, for neat cement, and from 0.03 to 0.05 per cent, for mortar poor in cement; and, similarly, he has found that pure cement swells under water from o.i to 0.2 per cent., and that concrete poor in cement swells from 0.02 to 0.05 Art. I3-] THERMAL LINEAR EXPANSION. 43 per cent. These figures show accordance with the preceding re- sults and may be adopted for use. The report of the Boston Transit Commission for the year ending August 15, 1901, records some measurements made by H. S. R. McCurdy on the shrinkage taking place in concrete after it has set. Two beams were used; the one kept in air was 8 inches square and 8.9 feet long, and the other, whose size is not given, was kept in water. The conclusions reached were that the concrete hardened in air would shrink .028 per cent, in twelve weeks, and that the concrete in water would shrink two- thirds of this. The latter conclusion does not agree with results obtained by other experimenters, and probably little reliance should be placed upon these figures, since the apparatus used was crude and the number of tests was small. Art. 13 The Coefficient of Expansion Due to Temperature Changes. The earliest work recorded concerning the linear thermic ex- pansion of concrete is due to Bouniceau, who published his re- sults in the "Annales des Fonts et Chaussees," 1863, page 178. His work was performed on rectangular prisms 65 to 94 inches long and about 7 inches on each side, the blocks being placed in water whose temperature varied from 10 to 95 degrees C. The apparatus used was checked by measuring the determined co- efficient of expansion for other materials. Bouniceau tested altogether ten blocks, either of solid stone, concrete, mortar or neat cement, the latter being in all cases Portland; the following are the results obtained on the cement mixtures: Neat Portland cement 00000594 per degree F. One cement to two silicious sand 00000655 " " " Concrete (proportions not given) (stone being silicious gravel) 00000795 " " " Professor W. D. Pence of Purdue University has made a series of investigations, the results of which are given in a paper of the Western Society of Engineers, November, 1901. He 44 GENERAL PHYSICAL PROPERTIES. [Ch. III. made experiments on Portland cement concretes of the composi- tions shown in the following table. The values there given show the coefficient of linear expansion per degree Fahrenheit. TABLE I. Kind of Concrete Coefficient of Expansion I Cement .. ^ 2 Sand I 0000055 I . \ 2 Sand . ( .0000054 4 Gravel J . | } .0000053 The method of conducting these experiments involved the comparison of the concrete bars with metal bars, and the results obtained may perhaps be regarded with some suspicion on this account. Busing and Schumann, in "Portland Cement," page 77, quote Meier as giving the coefficient of expansion of neat cement between 5 to -f- 2 5 degrees C. as being the same as for iron. Similarly, Christophe, in "Le Beton Arme," page 706, quotes Bouniceau, Meier, Bauschinger, Adie and Durand-Claye in stating that the coefficient may vary from .00000667 to .00000805 per degree F., and that it is essentially constant even with varying percentages of mixture. Berger and Guillerme, in "Ciment Arme," page 84, quote Durand-Claye as giving the coefficient of expansion but little different from .0000075 per degree F. In the early part of 1902 tests were made by Messrs. J. G. Rae and R. E. Dougherty, graduating students in Civil Engineering at Columbia University, on one bar of 1:3:5 gravel Portland ce- ment concrete and one 1 :2 mortar bar, the bars being four inches by four inches in cross-section and about three feet long, with an age of about five and one-half years. The results found are as follows : Mixture Coefficient of Expansion per Degree Fahrenheit 1:3:5 1:2 .00000655 .00000561 Art. 14.] THE ACTION OF SEA WATER ON CEMENTS. 45 The tests were made under the direction of Professor W. Hal- lock of the Department of Physics of Columbia University, and the results are believed to be accurate. It appears therefore that the thermal linear expansion of ce- ment mixtures does not differ materially from that of iron. Art. 14. The Action of Sea Water on Cements. The prevention of the disintegration of cement mixtures by sea water or by water containing solutions of salts has long been a question of dispute among chemists, although the reasons for its occurrence are fairly established. Sea water contains small percentages of magnesium-sulphate and magnesium-chloride, in addition to the ordinary salt, sodium chloride. The magnesium- sulphate and magnesium-chloride react either on the hardened cement or on the hydrated lime which is present in the cement and form calcium-sulphate and calcium-chloride. The calcium- sulphate crystallizes and expands, and therefore disintegrates the mass, but the .calcium-chloride is soluble and simply deposits inert magnesia. Dr. Michaelis believes that this chemical action can be an- nulled by adding to the cement some pozzalana, which, in com- bination with lime, has of itself the property of hardening under water. The lime which is needed must separate from the cement, since pozzalana does not harden by itself. Candlot and others think, however, that the difficulty is more easily solved by mak- ing the cement mixture impermeable to the water, and that, in order to avoid disintegration, it is simply necessary to prevent the sea water from attacking the interior of the mass. They be- lieve, then, that if the addition of pozzalana is of value, it is only so because it provides a denser mixture. Le Chatelier has formulated a new opinion on this question and attributes the disintegration, in large manner, to the pres- ence of alumina. In that case the sulphates in the water attack the aluminate of lime and form sulpho-aluminate of. lime, which swells and expands. Under those conditions Le Chatelier con- siders it advantageous to have as little alumina as possible in the 46 GENERAL PHYSICAL PROPERTIES. [Ch. III. cement, or to replace it as far as possible by iron oxides. No ex- tended tests have as yet been applied to this theory. A complete discussion concerning the first two opinions may be found in Vol. XXXVII. of the Transactions of the American Society of Civil Engineers, including also a final statement of the Association of German Portland Cement Manufacturers upon the proposition of Dr. Michaelis. In this particular instance it is declared that cement mixtures for use in sea water are not im- proved by the addition of pozzalana or trass. R. Feret has presented a paper, in Vol. IV., 1901, of the "An- nales des Fonts et Chaussees," concerning the effect of the addi- tion of pozzalana to Portland cements which are to be used in sea water. In the paper are recorded tests made upon several specially manufactured cements, marked G, R, T and A, which were afterward used in actual construction work in harbors. The G cements consisted of equal weights of good Portland cement and of lightly burned gaize*; the R cements consisted of equal weights of good Portland cement and Roman pozzalana; the T cements, of equal weights of good Portland cement and trass, and the A cements were manufactured from pastes containing about 23 per cent, of clay. The results obtained from these ce- ments were compared to Portland cements of various brands, manufactured from a paste containing about 21 per cent, of clay. Tests were made in the waters of the harbors of Boulogne, Calais, Havre, La Rochelle and Bordeaux. The longest tests extended over a period of three and one-half years; and although the re- sults obtained were not in all respects harmonious, it was found that the mortars made of the specially prepared cements were, in general, stronger and showed less signs of disintegration than the mortars made from the ordinary Portland cements. This was found to hold true, however, only when the mixtures were deposited under water. When the mixtures were allowed to harden in air it was found that the specially prepared cements possessed little strength, even after an interval of two years. The ordinary cements naturally attained their usual strength. Feret *Gaize A light, porous stone of variable degree of hardness, resulting from the silification of certain clays. Art. 14.] THE ACTION OF SEA WATER ON CEMENTS. 47 finally concludes that the most useful mixture, as well as the most economic, is made by grinding together two parts, by weight, of Portland cement to one of gaize. Such a cement has. been specially made, and is now being subjected to tests in the harbors of Bordeaux and Boulogne. There are two ways of depositing concrete in sea water- either as blocks, which have already set in air, or by depositing the plastic concrete, by means of buckets, under the water. These two methods admit still of two other variations. Concrete may be mixed either with fresh water or with salt or brackish water. There is at present a lack of reliable 'information as to the final resistance of concrete prepared in any of these ways, although the question is being studied with great care by the So- ciety of German Portland Cement Manufacturers, who estab- TABLE I. Mixture Ratio in Percentages of Tensile Strength of Sea Water vs. Fresh Water Hardening Age in Weeks 1 4 26 52 104 I Cement, I Cement, I Cement, I Cement, I Cement, I Sand 92.0 89.3 92.6 99.4 91.5 93.7 92.2 92.7 88.8 67.7 93.3 90.0 77.5 87.1 76.3 89.6 90.5 78.6 74.3 77.6 92.6 88.2 80.5 87.7 74.0 2 Sand 4 Sand 4 Sand, ^ HydratLime. I Sand, l / 2 HydratLime. lished, in 1894, with the aid of the Prussian government, an ex- periment station on the island of Sylt, in the North Sea. It is there also that it is proposed to determine finally the soundness of the theory advanced by Dr. Michaelis concerning the admix- ture of pozzalana in concrete which is to remain in sea water. Strength in Sea Water The strength of cement mixtures does not increase as rapidly in salt water as in fresh. Experiments set forth by Dyckerhoff in the Proceedings of the Association of German Portland Cement Manufacturers, 1896, are shown in Table I., in which are given the ratios in percentages of tensile strengths of mortars hardening in salt and fresh water. The table shows some irregularities in regard to the mixtures includ- ing lime, the older mixtures of which, although furnishing high 48 GENERAL PHYSICAL PROPERTIES. [Ch. III. resistance at the time of setting, also showed marked signs of disintegration. Table II. furnishes very similar results, and is taken from Busing and Schumann's "Portland Cements," page 128, from experiments made by Sympher on the crushing resistance of mortars when deposited in weak sea water. The relations be- tween results of the fresh and sea water specimens is very satis- factory, although in the last case shown the specimens were at- tacked and partially destroyed in the sea water. Table III. is taken from the Report of the Boston Transit Commission for the year ending June 30, 1902, and shows the effect of keeping briquettes in compressed air, in fresh water and TABLE II. Mixture Hardening in Ultimate Crushing Resistance in Lbs. per Sq. In. at the Age of 4 Weeks 52 Weeks 104 Weeks Remarks I Cement, I Sand. . < ' \ I Cement, 3 Sand. . / % Hydrat Lime , I Cement, 4 Sand. . f Yz Hydrat Lime. . . - \ FreshWater. Sea Water. . . FreshWater'. Sea Water. . . ! Fresh Water. Sea Water. . . 4230 3440 3640 3530 2840 2340 2210 2110 6330 4340 5000 4320 3560 3400 2640 2340 6880 5420 5300 4590 4190 3820 2880 2340 Edges broken off; disin- tegration in sea water in sea water. The briquettes were of the usual type used in tensile testing, the mixture used being i part of cement, 2,\ parts of fine crushed stone, ranging in size from an impalpable powder to -J inch in diameter, and 4 parts of coarse crushed stone, J to i inch in size. All the briquettes were kept in air at 60 to 80 de- grees Fahr. for the first twenty-four hours after making, and then in compressed air at a pressure of 18 to 25 pounds per square inch for thirteen days; they were then divided into three lots and placed as shown in the table. Each figure is a mean of three briquettes. The results shown belong to Vulcanite cement only, but other brands acted similarly. It will be seen that the briquettes kept in compressed air were always the strongest, and that up to the age of four months there was no practical difference between those kept in fresh water and Art. 14.] THE ACTION OF SEA WATER ON CEMENTS. 49 in sea water ; but at nine months the sea water briquettes did de- preciate considerably in strength. R. Feret has recorded in Vol. CVII. of the Proceedings of the Institution of Civil Engineers, page 163, some very interesting TABLE III. Place of Keeping the Briquettes Average Tensile Strength in Lbs. per Square Inch at 1 Month 4 Months 9 Months Compressed Air (18-25 Pounds Pressure). Fresh Water (Changed Each Day) 440 460 420 617 501 533 866 662 543 Sea Water (Under the Harbor) experiments on the hardening of cement mortars in fresh and sea water. Table IV. is an abstract of these tests. Each result shown is a mean of six tensile briquettes of .775 square inch cross-section and of two compressive cubes whose area of cross- section was 7f square inches. TABLE IV. Ultimate Resistance in Lbs. per Square Inch Neat Cement a * '5 l5 Mortars Composed of 1 Cement, 3 Fine Gravel by Weight, Mixed with Trowel to Plastic Consistency l|l s-a Mixed With and Mixed With and Mixed With and Mixed With Fresh Immersed in Immersed in Immersed in Water and Kept Sea Water SeaX 7ater Fresh Water in Air Ace Ten- Ten- Ten- Com- Ten- Com- Ten- Com- sion sion sion pression sion pression sion pression 4 Weeks... 422 149 95 T T C 327 71 QQ 469 70 77 426 I Year 736 275 1 \") 179 540 146 731 173 838 It will be seen that the tension and compression tests do not furnish uniform results; the tension specimens hardening in sea water are stronger than those hardening in fresh water. This is not true of the compressive specimens, whose crushing resist- ance, moreover, is exceptionally low. The cement used in these 50 GENERAL PHYSICAL PROPERTIES. [Ch. III. tests had the following fineness : 50 per cent, passed a sieve hav- ing 32,300 meshes per square inch; 31 per cent, passed a sieve of 5,800 meshes per square inch, but was retained by previous sieves, and the remaining cement was retained on the 5,800 mesh screen. It may then be concluded that, unless mixtures fail by disin- tegration, their strength under sea water approximates that at- tained under normal conditions, but is never greater. And, finally, disintegration may be avoided, either by making the mixture impermeable or by adding some substance such as poz-- zalana. Gauging with Salt Water The action of ordinary salt solu- tions on the strength of cement mixtures still remains to be con- sidered. Figure i is taken from tests reported by A. Noble in Vol. XVL, 1887, of the Transactions of the American Society of Civil Engineers. The figure shows the effect on the tensile strength of one cement to one sand mortar briquettes when mixed with water containing various percentages of salt, it will be seen that there is but very little loss in strength when the water contains small per- centages of salt, and not much more loss even when the percentages rise to 1 6. E. C. Clarke records very similar experiments in Vol. XIV. of the same Transactions; in this case briquettes were gauged with fresh water and with salt water, and were also immersed in both fresh and salt water; the results show no great variations in strength. Clarke states that the time of setting is somewhat retarded; in this he is corroborated by Heath, page 83, of his Manual of Limes, Cements and Mortars. C. S. Gowen records in a paper read before the American So- 18 Months Months Age of Specimens, FIG. 1. NOBLE'S TESTS. Zi Months Art I5-] POROSITY AND PERMEABILITY. ciety of Testing Materials, July 3, 1903, results of tensile tests made on the usual standard briquettes as to the effect of salt water in gauging mortar under normal laboratory temperature conditions; the briquettes were composed of one part of cement and two and three parts of quartz sand. It will be seen (Table V.) that at the end of a year there is no appreciable difference in strength between the specimens which were gauged with fresh water or salt water. The salt water was about a 10 per cent, solution; each result shown is an average of ten breakings. It may therefore be defi- nitely stated that gauging cement mixtures with salt water does not affect the ultimate strength injuriously. TABLE V. Age 1:2 Briquettes 1:3 Briquettes Tensile Strength in Lbs. per Square Inch, Gauged with Fresh Water Salt Water Fresh Water Salt Water 7 Davs 236 289 414 549 554 572 126 231 294 424 452 576 112 183 268 335 351 458 68 131 215 266 301 413 I Month 3 Months 9 Months 12 Months Art. 15. Porosity and Permeability. Porosity and permeability are terms often confused in meaning when applied to cement mixtures; but they apply to entirely dif- ferent properties. Porosity is a measure of the voids and gives no indication .of the connection of these voids with one another. Permeability, on the other hand, implies paths from one void to another. The question of porosity is not of the greatest impor- tance, except as giving indication of the denseness of a mixture and perhaps, indirectly, an indication of its ultimate strength. Due to the fineness of grinding and to the uniformity of grain, it is to be expected that neat cements should be more porous than mixtures of sand and cement. This is perhaps the more evident when neat cement is compared to concrete, since in the latter possibly 50 per cent, of the mass consists of large pieces of dense stone. However, in the case of concrete, it is clear that paths between the voids are more likely to exist than 52 GENERAL PHYSICAL PROPERTIES. [Ch. III. in the case of neat cement, and that, therefore, the concrete may be the more permeable. R. Feret, in a very valuable paper* published in Vol. IV., 1892, of the "Annales des Fonts et Chaussees," discusses fully the po- rosity and permeability of various kinds of cement mortars, and shows that the actual solid contents of a mixture are clearly indi- cated by the amount of water absorbed. He states that a mix- ture in which the fine sands predominate is always the more porous; the permeability, however, varies inversely to the po- rosity. Feret's experiments were carried on with three sizes of sand grains; a coarse sand, which would correspond to a sand passed by a No. 5 sieve and retained on a No. 12 sieve; a medium sand, which would correspond to a sand retained between a No. 12 and a No. 50 sieve, and a fine sand, all of which would pass a No. 50 sieve. Feret's Conclusions It is perhaps best to quote Feret's con- clusions directly :f (a) The permeability of a mortar depends less on the total vol- ume of the voids than on their individual dimensions. (b) The continuous passage of water through mortars dimin- ishes the permeability very rapidly. (c) The filtration of sea water through mortars often results in their more or less rapid disintegration. (d) All other things being equal at the beginning of filtration, plastic mixtures are less permeable than dry; after some time this difference disappears, and it appears that, in the case of sea water, disintegration is not more rapid for one than for the other. (e) In general mortars made with the same sand are the less permeable, as they contain the more cement. (f) Mortars of the same richness, but of different granulometric sand composition, are disintegrated by the passage of sea water as rapidly as in proportion to the fine grains in the sand. The ef- *Sur la Compacite des Mortiers Hydr antiques. }Page 143 of Feret's paper. Art. I5-] POROSITY AND PERMEABILITY. fects may not be the same for mortars which are simply placed in water. A very full discussion on impervious concrete is also recorded in the Transactions of the American Society of Civil Engineers, December, 1903, and the work of various experimenters is cited. The general conclusion, there summarized by R. W. Lesley, is as follows: That neat cement mortars show the least permea- bility; that mortars with fine sand are less permeable than those mortars with coarse sand, and that the lessening of the per- meability is due to the closing of the pores by lime, which is car- ried in suspension, in the process of filtration, through the mass, and which ultimately forms a coating on the surface of the ma- sonry. In almost all cement mixtures, even if permeability does exist in the beginning, it decreases very fast as the mixture ages, provided disintegration does not take place. This is very clearly shown by experiments reported in Vol. CVIL, page 95, of the Proceedings of the Institution of Civil Engineers. Figure i is taken from that report and shows the filtration of sea water under a head of twenty-four feet, through one cubic foot of Portland cement concrete of the pro- portions indicated, three months old. It is seen how rapidly the amount of water which passes through the mass decreases with the time, even for widely varying proportioned mixtures. Figures 2 and 3 are taken from Feret's paper, already noted. Figure 2 shows the initial permeability of two series of mortars, mixed with different proportions of sand and gauged with dif- ferent percentages of water. The size of the specimens and the 10 15 Age in Days FIG. 1. 54 GENERAL PHYSICAL PROPERTIES. [Ch. III. surface through which the water passed are not given ; the speci- mens set in air two weeks before being tested. The small initial permeability of the richer mixtures is immediately noted. 7060 3530 Initial Permeability of 2 Series of Mortars of different Consistencies \ 7.3 Sand 4.9 Sand 3.6 Sand \ 1 Cement 1 Cement _ 1 Cement Parts of Sand to Cement FIG. 2.-FERET'S TESTS. Figure 3 shows the variation in the permeability of three mor- tars during the two first days of filtration; the experiments were continued for one year, and at the end of that time it was found that the percolation through the lean mixture had ceased, but 81180 Variation of Permeability Of 3 Mortars during the first days of flltratioa 6 12 84 3& 4& Bonra Time Elapsed from Beginning of Filtration. FIG. 3. FERET'S TESTS. that the other richer mixtures had been slightly attacked by sea water and were passing very small quantities of water. Feret notes that tEe permeability decreases the more rapidly as the first filtration is the more abundant, and that the amount Art. 16.] EFFECT OF FREEZING ON CEMENT MIXTURES. 55 passed is independent of the nature of the liquid (fresh or sea water). In conclusion, inspection of existing concrete work is sufficient to show that almost any well balanced mixture can be made im- pervious to the passage of liquids; the greatest care in mixing, due to the non-homogeneity of the ingredients, must be observed. Where concrete masses do pass water, the permeability will in general be found to be due, not to some defect in the concrete itself, but to open cracks which may have been caused from one of various reasons, such as improper joining of work laid at dif- ferent times, settlement of foundations or temperature changes. The addition of salts or soaps to cement mixtures to cause im- permeability has not been considered by the author; although many experiments have been made along such lines, the results are not in such form as to warrant the drawing of definite con- clusions, the more so when it seems possible to make cement mixtures impervious without such aid. Art. 1 6. The Effect of Freezing on Cement Mixtures. The effect of cold temperatures on the setting and hardening of cements has been much discussed, but appears at present to be very simple. It is now the opinion that the hardening properties of frozen cement are not impaired, if the freezing has taken place before the initial setting of the cement has begun. Under those conditions the physical action of the changing of the water into globules of ice has prevented the chemical action of the crystalliz- ing of the cement particles ; crystallization cannot take place until the ice globules return to the liquid form. No damage will then have been done, if freezing does not again take place before the cement has set; but if continued thawing and freezing take place, allowing an intermittent action of setting, it is very likely, under those conditions, that the cement will be injured. Many large pieces of concrete work have been built in freezing weather and have remained for long periods of time in a frozen condition, but, after thawing, have shown no evil effects. It is only necessary to bear in mind that the physical action of freezing must so far pre- cede the beginning of the chemical action as to preclude the lat- 56 GENERAL PHYSICAL PROPERTIES. [Ch. III. ter's taking place. The use of salt, glycerine or other substances in the water used for laying cements at cold temperatures seems, therefore, unnecessary, more particularly as there is always the possibility that these admixtures may prove injurious. The percentage of injury done by the addition of salt sub- stances may not be very great, and may often be nil, but it is probable that the use of these adulterants will cease. Laboratory experiments made to determine the change in strength of mixtures gauged with salt water must be treated with some caution, since in the laboratory the experiments are made under normal temperature conditions, whereas in practice salt is added to cement mixtures only during freezing weather; the hardening of a cement under the latter condition may be very different. It has already been shown in a preceding article that, in the case of laboratory experiments, there is but little, if any, decrease in the strength of the mixture, even when a 16 per cent, salt solu- tion is used. Experiments made with salt mixtures during freez- ing weather have shown very similar results; but it seems un- necessary at the present time to record such experiments in any detail, since, as has already been stated, concrete mixed with fresh water is now laid at almost any temperature, and is found to suffer no ill effects, if alternate freezing and thawing do not take place. For such experiments with salt mixtures the reader is referred to tests made by E. S. Wheeler and recorded by him in the Report of the Chief of Engineers, U. S. Army, for 1895, page 2968 and following. The following experiments, made at the Watertown, Mass., Arsenal on frozen cement mixtures, gauged with fresh water, are of exceeding value. Table I. is taken from the Watertown Arsenal Report for 1901, and shows the crushing strength of two-inch cubes which were left for various intervals of time in a temperature of o degrees and were then exposed to a temperature of 70 degrees Fahr. It will be seen that the compressive strength did not vary to any considerable degree, no matter how long the specimen had been exposed to the freezing temperature, if it had been exposed Art. 16.] EFFECT OF FREEZING ON CEMENT MIXTURES. 57 the same number of days at the 70 degree temperature. It is clear that no setting action takes place when the water in the mixture is frozen. The results of tests on three brands of cements only is ab- stracted, since these are characteristic examples. Tables II. and III. show the ultimate compressive resistance of two-inch cubes composed of neat Portland and natural ce- ments and of 1:1 mortars subjected to low temperatures at the times of making. These experiments are also recorded in the Report of the Watertown Arsenal for 1901. TABLE I. Brand Length of Time at F. Subsequent Length of Time at 70 F. Compressjve Strength in Lbs. per Sq. In. Months Days Days *) 7 846 14 7 1000 Star I : I Mortar - Portland Cement 2 21 31 7 7 7 1010 981 981 3 7 1010 7 7 1470 14 7 1230 Josson 1:1 Mortar...' 21 7 1240 Portland Cement 29 7 1430 3 7 1520 { 6 14 540 15 14 527 Hoffman 1:1 Mortar. < 20 14 624 Natural Cement 28 14 561 1 3 14 579 In Table II. there were three general groups of specimens; one was allowed to set in the open air of the testing laboratory at the ordinary atmospheric temperature, given in the report as 70 degrees Fahr. The specimens belonging to the other two groups were placed in a cold storage warehouse, where they re- mained different intervals of time. One group was placed in a room whose temperature was maintained at about 39 degrees, and the other group in a room whose temperature was in the vicinity of o degrees. Specimens intended for this last room were mixed on cold days, with the thermometer in the neighbor- hood of 15 to 20 degrees Fahr., and it was intended to freeze the 58 GENERAL PHYSICAL PROPERTIES. [Ch. -III. material as soon as practicable after mixing and use mixtures as wet as ordinarily employed in construction. The table shows clearly the lengths of time the various specimens were left under these varying temperature conditions and the length of time at which the frozen specimens were allowed to thaw under normal conditions. Careful examination will show that the frozen speci- TABLE II. Compressive Strength in Lbs. per Square Inch Brand Specimens Set in Air at F., and Then Placed in Air at 70 F. Specimens Only in Air at 70 F. Specimens in Air at 39 F., and Then Placed in Air at 70 F. Star Portland 3 Mos. and 30 Days 362ft 30 Days 4^70 Alsen Portland 2520 3900 Star Portland 1 Mo. and 30 Days 346ft 30 Days 4^70 Star I * I Mortar 1400 I960 Storm KinjJ Portland 1680 2520 3 Mos. and 14 Days TO rr\ 14 Days IQ7ft Alsen Portland 04^0 3780 64ft 1 1 60 1020 800 S7Q 808 A39 744 Star 3 Mos. and 14 Days 4410 3 Mos. and 14 Days 42ftft Storm Kinj( 4 Months 2380 3 Mos. and 1 Month 2700 jc;i(-) 64ftft 3 Months 31 10 3 Mos. and 8 Days 4970 3 Mos. and 15 Days 580 3 Mos. and 15 Days I4ftft 3 Months 1720 3 Mos. and 13 Days 906ft Norton 4 Months Qtf) 3 Mos. and 14 Days mens exhibited practically no deterioration in strength, if the time allowed them under normal temperature conditions was equal to that of the specimens of the same mixture to which they could be compared. The specimens noted in Table III. were treated a little differ- ently;, the frozen specimens were kept frozen for various inter- Art. 16.] EFFECT OF FREEZING ON CEMENT MIXTURES. 59 vals of time up to one year and then allowed to set for one day only under normal temperature conditions. It will be seen that the strength of the frozen material increased to some extent, showing some faint chemical action; but in no case did a frozen specimen one year old attain, even approximately, the strength of a normal specimen one month old. C. S. Gowen presented a paper before the American Society of Testing Materials, July 3, 1903, in which are also recorded some tests on Portland cement mortar exposed to various cold temperatures. The tests were made on the standard form of TABLE III. Brand Compressive Strength in Lbs. per Square Inch Specimens Set in Air at Temperature F. (One Day in Air at 70 F. Before Testing) Specimens Set in Air at 70 F. 1 Month 3 Months 1 Year 1 Month 3 Months Star Portland 1350 383 749 986 347 238 411 206 341 225 1720 497 703 1210 624 241 478 276 347 274 2724 864 1370 1580 802 333 428 680 358 4350 2520 3900 3970 724 1 140 1 140 1000 1560 4400 2430 4040 3110 661 1720 1070 1090 1240 Star I * I Mortar Storm King Portland Obelisk Natural 534 637 1015 2256 2085 tensile briquettes, composed of one part Giant Portland cement and two parts of crushed quartz sand. Table IV. shows the re- sults obtained under normal temperature conditions; Table V., results obtained under freezing temperature. In the latter table each figure is an average of eight tests. It should be noted that the results recorded for the six months freezing temperature are subject to an error, due to the fact that the briquettes were con- tinually in air up to that time and were probably dried out. The briquettes of nine and twelve months, made under the same con- ditions, were placed in water at the end of six months, and showed uniform increase in strength over the strength of one and three months. 60 GENERAL PHYSICAL PROPERTIES. [Ch. III. TABLE IV. Tensile Strength of 1:2 Mortar Briquettes Age Number of Specimens Broken Average Tensile Strength in Lbs. per Sq. In. 28 Days 690 441 3 Months 215 563 185 657 9 Months I*)*) 671 12 Months . 165 663 TABLE V. Tensile Strength of 1:2 Mortar Briquettes Tensile Strength in Lbs. per Square Inch at Age of oenes 28 Days 3 Months 6 M nths 9 Months 12 Months A 370 474 366 553 553 B 458 455 347 381 586 c 371 413 314 452 510 D 272 360 287 567 602 E 255 246 300 437 512 Series A. Placed in cold air, 24-32 deg. F., immediately after mixing; fresh water used. Series B. Placed in cold air, 24-10 deg. F., immediately after mixing; fresh water used. Series C. Placed in cold air, 24-32 deg. F., after taking heavy Gillmore needle ; fresh water used. Series D. Placed in cold air, 20-10 deg. F., immediately after mixing; brine* used. Series E. Placed in cold air, 20-10 deg. F., immediately after mixing; fresh water used. J. S. Costigan records in the Transactions of the Canadian Society of Civil Engineers, 1903, some interesting tests on the effects of freezing neat cements, in which various briquettes were moulded under a pressure of twenty pounds per square inch. When these briquettes were twenty-four hours old they were all placed in water and allowed to remain there until they were seven days old, with the exception of some twenty-four hours during this period, when they were exposed to the action of * About 10 % by weight, solution. Art. 17.] ADHESION OF IRON IN CONCRETE. 61 frost for twenty-four or forty-eight hours. The results show al- most a uniform ultimate resistance, no matter at what period after making the specimens they were subjected to the freezing conditions. Reviewing these recorded experiments, it may be seen that no fear need be apprehended if specimens are frozen once only and then thawed out. The ultimate strength attained under those conditions is not appreciably lower than that attained under nor- mal conditions. Art. 17 Adhesion of Iron in Concrete. Table I. shows the adhesion of iron rods in concrete, as found by E. Morsch and reported by him in "Beton und Eisen," Part III., 1903. It will be seen that the adhesion varies not only with the richness of the cement mixtures, but also with the per- centage of water used in gauging. TABLE I. Percentage of Water Adhesion in Lbs. per Square Inch , Richness of Mixture 1:1 1:2 1:3 1:4 1:5 1:6 1:7 1:8 10 Per Cent 15 Per Cent 20 Per Cent 213 655 398 313 270 696 398 427 270 569 356 328 370 540 356 342 427 299 171 114 384 270 171 170 237 213 156 128 171 142 100 100 25 Per Cent The table exhibits no positive fact, although, in general, the richer mixture furnishes the greater adhesion. Neither too little nor too much water is to be used in the mixing, since some in- termediate percentage furnishes the greatest adhesion. Professor Charles Spofford made a series of tests upon the hold- ing power of different types of rods, which are reported in the same number of the publication. The concrete used was a Portland cement concrete of 1 13 :6, the stone used being a mix- ture of two parts of one-inch trap and one part of one-half-inch trap. The concrete was wet sufficiently so that when tamped into the moulds water flushed to the surface. The rods were all thoroughly cleaned by a sand blast before the concrete speci- mens were made. Several types of rods were used the Ran- 62 GENERAL PHYSICAL PROPERTIES. [Ch. III. some rod, which is a square rod, but twisted through an angle of 20 degrees ; the Thacher rod and the Johnson rod (the two latter TABLE II. Type of Rod Cross Sec- tion of Rod in Inches Mean Area of Cross Sec- tion of Rodin Sq. Inches Cross Sec- tion of Con- crete Block in Inches Length of Rod Imbedded in Inches Greatest Adhesion in Lbs. per Sq. In. I Remarks Ransome 1 A X l / 2 0.25 6x6 12 454 > 16 228 o t4 44 44 44 26 291 I 44 44 44 8x8 12 310 I 44 44 44 16 396 8 4 " 44 44 " 26 260 # ,, % x # 0.56 44 20 388 Cfl"-' .4 44 24 399 Iff 4, 44 44 44 36 305 2 44 i l A x iyi 1.27 10 X 10 27 245 Sg. 44 37 HI w 8: .3 44 44 44 50 138 L o J 2: Thacher Yz x y> 0.18 6x6 12 222 Sn 16 282 1* ,, 44 44 44 26 223 . 82 4. V x % 0.39 8x8 20 402 LftJ ,4 24 290 < V 44 44 44 44 36 250 &l 44 l*/8 X l l /8 1.03 10 x 10 27 238 8. ,, 37 304 Is 44 44 44 // 50 268 " Johnson. . Yz x y* 0.19 6x6 12 508 0. 16 410 5" 44 44 44 44 26 264 &> ,, % x K 0.37 8x8 20 461 H 44 24 347 3- 44 44 44 36 259 5 tl I \ X \\i 1. 17 10 x 10 27 313 e ., 37 252 i t , 44 44 // 50 242 ^ Plain ... 3/ round 0.44 8x8 24 271 ] 31 255 ,4 44 44 44 36 219 44 % x # 0.56 44 24 274 44 44 31 243 ,, 44 44 36 221 M 4, i*A x y* 44 44 24 159 1 44 44 44 31 201 1, C 44 44 44 44 36 185 o 44 l*A x 3 A .4 44 24 226 1 ,, 44 44 31 188 ,, 44 44 44 36 164 ,, 1}i x \i 44 44 24 42 .. 44 44 31 165 44 44 44 44 36 145 Art. 17.] ADHESION OF IRON IN CONCRETE. 63 being well known forms of specially rolled rods), and also plain round, square and flat rods. All tests were made twenty-eight days after mixing of the concrete. Table II. shows the value of the adhesion in pounds per square inch obtained by these different bars. Of the various plain forms, it will be seen that the round bars show the greatest adhesion and the flat bars the least. In general the adhesion de- creased as the depth to which the rods were imbedded was in- creased, but no conclusive superiority of one kind of bar as com- pared to another can be shown; moreover, in many cases the rods did not pull out at failure, but the blocks were split. The true adhesion was not found in those cases. Table III. shows the values of adhesion of round iron rods, de- termined by Professor W. K. Hatt and reported by him before the American Section, International Association for Testing Ma- terials, at its annual meeting of 1902. The table gives averages of three tests each, the concrete being a mixture of 1:2:4 and its age about thirty-two days. TABLE III. Size of Rod Depth of Rod in Concrete in Inches Ultimate Adhesion in Lbs. per Sq. In. of Rod Surface 7-16 Inch 6 636 5-8 Inch 6.4 7^6 E. S. Wheeler records, on page 2940 of the Report of the Chief of Engineers, U. S. Army, for 1895, a considerable number of tests made upon the adhesion of iron bars in cement mixtures. In the first set of experiments, shown in Table IV., the mixture was composed of one part, by weight, of Portland cement to two parts of sand, the latter being limestone screenings passing f-inch slits; the age of the mortar was one month. The bars were im- bedded to depths varying from 8 to 10 inches; they were in the form of bolts, being cut from bar iron, and were without fox wedges. The twisted bolts were formed by twisting a piece of one-inch square bar iron, the length of the twisted portion being 8 inches. The periphery of a twisted bolt was taken to be the circumference of a circle whose diameter was the distance be- 64 GENERAL PHYSICAL PROPERTIES. [Ch. III. tween opposite corners of the bolt after twisting; a core of mortar of this diameter was torn from the bar in pulling. It is seen that the increase in resistance of the -twisted to the plain bar is not very great. The tests shown in Table V. differ only in that ordinary river sand was used, the mixtures used being neat, 1 :2 and 1 14. The bolts were imbedded 2 to 10 inches. TABLE IV. Description of Bolt Mortar Number of Bars Tested Average Adhe- sion in Lbs. per Sq. Inch Plain Vz In Diameter, Round I Cei nent, 1 S and 3 3 3 3 4 3 3 3 3 447 556 524 543 562 434 608 516 561 Plain, 1% In. Diameter, Round Plain I In Square . ...... Plain \% In Square I In. Sq., Twisted I Turn in 8 Ins.. I In. Sq., Twisted 1 Turns in 8 Ins. I In. Sq., Twisted 3 Turns in 8 Ins. In the Watertown Arsenal Report for 1901 are reported vari- ous tests made on the adhesive resistance of JxJ inch steel bars imbedded in Portland cement concrete prisms 6x6x18 inches long. The age of the prisms was about thirty days and their average crushing resistance about 2,278 pounds per square inch. It was found that the adhesion of the rods per square inch aver- TABLE V. Mortar No. of Bars Tested Average Adhesion in Lbs. per Sq. In. 5 7T7 11 264 10 III All bolts were plain, 1 inch in diameter, and round. aged 204 pounds per square inch of surface, with a maximum value of 296 pounds and a minimum of 77 pounds per square inch. Three other prisms, whose crushing resistance was 4,210 pounds per square inch, gave an average adhesion of 297 pounds per square inch. The rods were imbedded various lengths from 2 to 12 inches. Art. 17.] ADHESION OF IRON IN CONCRETE. 65 Considere has made some experiments upon the adhesion of iron rods in concrete in a different way from other experiment- ers; and since his values are calculated upon an assumed condi- tion of internal stress, too much weight should not be placed on these results. His values for iron wire of .17 inch diameter, whose surface was perfectly clean, shining, and possibly some- what greasy, were found to vary from 70 to 170 pounds per square inch of surface, for concrete kept in the air. The re- sistance to sliding increased to 256 pounds for prisms of the same concrete, reinforced by larger rolled iron rods .24 inch in diameter, and in other experiments, in which the surface of the .17 inch diameter iron wires was slightly rusted, the sliding re- sistance varied from 330 to 500 pounds per square inch. In these last tests the specimens were kept under water. He found TABLE VI. Diameter of Wire in Inches Condition of Wire Surface Resistance per Sq. In. of Surface at Cessa- tion of Adherence in Lbs. Resistance per Sq. In. of Wire Rod at Ces- sation of Adher- ence in Lbs. 0.14 0.12 0.10 41 Smooth Barbed, with Split Ends Smooth Barbed, with Split Ends Smooth Barbed, with Split Ends 502 493 442 423 286 356 33500 33100 35200 34000 27400 34100 that the resistance to sliding bore some relation to the amount of water used; for instance, in three prisms made alike and in which the first had an excess of water, the second was normal concrete and the third was too dry, the resistances were respect- ively 155, 170 and 70 pounds per square inch. De Joly records in Vol. III., 1898, of "Annales des Fonts et Chaussees," some very interesting experiments which he made on the adhesion of anchor rods fastened by means of neat Port- land cement in holes drilled in granite blocks. Three sizes of round iron rods were used .14, .12 and .10 inches in diameter. The depth of the holes in the granite blocks was 23.6 inches. The cement was allowed to harden one month in air. De Joly comes to this very interesting conclusion : That the ultimate ad- 66 GENERAL PHYSICAL PROPERTIES. [Ch. III. hesive resistance does not depend on the surface of contact be- tween the two materials, but on the elastic limit of the inserted iron rod. Table VI., which is characteristic of several series of experi- ments, shows how the adhesive resistance per square inch of contact surface varies at the cessation of adherence between the two materials from 286 to 502 pounds per square inch ; but if the adhesive resistance is expressed in pounds per square inch of the rod cross-section the values so obtained show no very great variation for the different sizes of rods. Experiments are recorded by De Joly for various qualities of iron rods and show very uniform results, according to this method of reasoning, which is correct, when the length of bar imbedded is so great that the ultimate resistance developed by the adhesion is greater than the resistance of the imbedded bar at its elastic limit. In conclusion, it seems proper to take the ultimate adhesive resistance of iron rods in concrete as between 250 and 400 pounds per square inch of surface. Art. 1 8. The Fatigue of Cement Mixtures. The question of the fatigue of cement mixtures has lately re- ceived some discussion, although the matter is probably not of the very greatest importance. Professor J. L. Van Ornum has presented in the Transactions of the American Society of Civil Engineers, December, 1903, a paper in which he records com- pressive tests made upon neat Portland cement cubes two inches on the side, which were crushed when four weeks old. The ulti- mate strength was determined in the usual way with one con- tinuous application of the load, and, in addition, similar blocks were subjected to repeated loadings of certain percentages of the ultimate strength, varying from 95 to 55 per cent, of the same. In the latter case the load was applied and removed repeatedly until failure occurred. Figure I shows the results obtained from ninety-two tested blocks. The same subject has also been considered by De Joly, who has recorded the results of his experiments in "Annales des Art. 18.] THE FATIGUE OF CEMENT MIXTURES. 67 S g 8 3 8 *. **. ^ 'a^. ercentage of Load applied \ X. =- =; Fonts et Chaussees," Vol. III., 1898. He experimented on the usual type of tensile briquette, whose ultimate tensile resistance for one application of a load was first found. Similar specimens of the same age were then tested under re- peated applications of a stress considerably lower than the ultimate, and it was found that the speci- mens broke under a vary- ing number of repetitions. This number of repetitions increased rapidly with the age of the specimens. In Table I., which is characteristic of a series, De Joly shows, for instance, that a specimen which broke under a tensile load of 187 pounds at the end of two days could naturally not sustain a load of 200 pounds per square inch, but that at the end of three days, when one application of 276 pounds caused failure, it required TABLE I. 3000 Number of Repetitions producing failure FIG. 1. Brand of Cement Age of Specimen in Days Average Ultimate Tensile Resist, in Lbs. per Sq. In. One Application of Load No. of Application of Ten- sile Stress of 200 Lbs. per Sq. In. Before Rupture Candlot 2 187 o 3 276 18 4 390 346 tj 405 2815 6 505 ^>2I720 Demarle 17 3 665 212 105600 5 347 97 7 420 ^5000 eighteen applications of 200 pounds per square inch to cause rupture. The table is otherwise self-explanatory. De Joly's ex- periments were performed so that the time of application of each load was almost instantaneous, being approximately i-io of a second. In order to determine the effect of a slower application of a load, De Joly made a series of experiments, the results of which 68 GENERAL PHYSICAL PROPERTIES. [Ch. III. are shown in Table II. In this case the rapidity of the applica- tions varied from 92 to 26 per minute, and it will be seen how TABLE II. Age of Specimens in Days Ultimate Tensile Resistance in Lbs. S;r Sq. In., with ne Application of Load Number of Applications of a Load, Intensity of 200 Lbs. per Square Inch Before Rupture Rate of Application 92 per Minute 52 per Minute 26 per Minute 4 5 6 7 271 328 361 364 7 36 16 2 34 174 173 75 398 More than 2300 None less than 3000 very rapidly the number of applications increased as the time be- tween applications increased. Table I. seems to indicate that there might be a limit of fatigue to a material, so that a load, if TABLE III. Brand of Cement Age of Briquette Number of Applications pf Tensile Load of 200 Lbs. per Sq. In. Ult. Resistance in Lbs. per Sq. In. Remarks After One Appli- cation of Load After Treatment as in Column 3 Ten- sion Com- pression Ten- sion Com- pression Demarle . 12 days 5000 558 4800 507 4900 (No rest after \ repeated load- (ing. Demarle . 14 " " 525 5380 521 5070 (Tested 24 hrs { after repeated (loading. Demarle . 7 " 6500 421 3600 400 3620 UK hrs' rest < after repeated (loading. Demarle . 15 " 20000 560 6400 545 6170 !No rest after repeated load- Demarle . 20 " * 573 6900 523 6950 ing. (48 hrs' rest \ after repeated (loading. Demarle . \Yz years 857 14800 834 13450 (48 hrs' rest < after repeated (loading. Candlot. . 7 days 40000 552 5350 490 5420 ( No rest after j repeated load- Candlot. . II " ,, 576 7300 545 7100 ( Av'ge 12 hrs' jrest after re- ( peated load'g Sollier. . . 4X nionths " 681 9470 618 9860 (No rest after ] repeated load- (ing. Sollier. . . 5 " 708 10200 666 10300 (48 hrs' rest j after repeated (loading Demarle . 1^ years " 848 14400 826 I4IOO (48 hrs' rest \ after repeated (loading. Art. 18.] THE FATIGUE OF CEMENT MIXTURES. 69 applied sufficiently, although below the rupture point, might finally cause failure. Table II. shows, however, that, given suffi- cient time between applications, the material may not sustain any injury. Table III. is also abstracted from De Joly's paper; it shows the ultimate tensile and crushing resistance of a cement of vari- ous ages, first, when subjected to only one application of the final load, and also, of similar specimens, after the elapse of various periods of time after having been subjected to repeated applications of a tensile stress of 200 pounds per square inch. Each result shown is an average of three tests, the specimens used being the French type of tensile briquette. It will be seen in this case that, although the final tensile re- sistance is slightly lowered, no appreciable change occurs in the compression pieces. It will require many experiments of a character similar to these quoted to determine definitely whether there is in concrete, as there is in steel, a critical point above which the material should never be stressed if it is never to fail at loads below the usual ultimate resistance. CHAPTER IV. ELASTIC PROPERTIES IN GENERAL. Art. 19. Treatment of Stress-Strain Curve. The deformation that appears in a material which is subjected to any form of stress determines, in connection with the stress, its elastic properties. A diagram which shows the stress-strain relations throughout the entire range of stress is, therefore, of great assistance in showing clearly the elastic properties of any material. In direct tension and compression tests this diagram consists of a curve which shows the relative elongation or shortening of the specimen for each intensity of stress; in flexure tests the curve illustrates the ratio between deflections and the loads ap- plied, and in torsion tests the ratio between the twist and the ap- plied moment. In this treatise, however, torsion stresses will not be considered. The stress-strain curve for tension and compression speci- mens needs no explanation, but it will be well to consider its algebraic equivalent. The general designation of this relation is the coefficient or modulus of elasticity. It is usually denoted by E and expresses the ratio for any stress between the unit stress / and the unit strain /; that is, This ratio E does not possess a constant value for any ma- terial between a point of no stress and the ultimate; that is, the ratio is never represented by a straight line between the origin of co-ordinates and the point representing the breaking load. The curve is, indeed, very complex for the majority of materials used in construction; but it is a straight line from the zero stress to a Art. 19.] TREATMENT OF STRESS-STRAIN CURVE. 71 point called the elastic limit, the latter point being, in fact, that point where E changes in value. In the case of some materials it has been found that every stress, however small, causes a permanent strain or set to remain in the specimen after the removal of the stress. This involves slightly the proper method of calculating E. It may be deter- mined by dividing the unit stress either by the total unit strain in the specimen or by the elastic unit strain, which, is the total unit strain less the unit set. In the opinion of the author, the proper method to employ is the second, which determines what will be called hereafter the ''elastic" coefficient of elasticity. 2000 1900 1300 1700 1600 1500 SfliOO Il300 3 1200 B 1100 fUN 3 900 . xx 1 / / / // / x X // 1-5 J y v > //: Q 2 4& ,*?*? P r Z3 ^r Cylindrical Specimen of Neat Cement Height 39.4 Inches 1 Diameter 9t8 Inches ) 89 Days Old Reported by Bach. Zeitsch. Ver.Deutsh.Iiig. Nov. 28, 1896 r% I2g^ 800 |TOO I 600 500 100 300. 200 100; 5 gin B ^ r /? i 3 2*4 Cinder 9 558 600 *J'J ACtZ, 4 2:4 Cinder. . 9 553 000 5Qt 5 :2:4 Cinder. . 7 630 000 JJJ 416 6 6 2 088 000 I I A^ composed of I part Peninsular Portland cement and 2 parts of clean, sharp pit sand, of which 84 per cent, was retained on a Xo. 30 sieve, and 4 parts of broken limestone, all of which passed through a one-inch sieve and of which 75 per cent, was retained on a ^-inch sieve. The coefficient of elasticity was computed with regard to the 84 TENSILE PROPERTIES. [Ch. V. set experienced after previous loads; in other words, it is the "elastic" modulus of elasticity. Table VI. furnishes values of the compressive coefficient of elasticity for concrete cylinders 12 inches high and 8 inches in diameter, also reported by Professor Hatt in the same paper. In addition to the concrete mixture noted above, tests were made on a 1:2:4 cinder concrete and a 1 15 gravel concrete, the gravel being a good quality of coarse gravel. The intensity of stress at which the compressive coefficient of elasticity was com- puted is shown in the table. These experiments show the coefficient for compression to be considerably larger than for tension, but Professor Hatt has lately (Western Society of Engineers, 1904,) published the re- sults of a greater number of tests, and he states definitely that he finds no appreciable difference between the two moduli. Table VII., taken from the latter paper, is otherwise self-explanatory; TABLE VII. Kind of Concrete. Parts of Age in Days Coefficient of Elasticity in Lbs. per Sq In. Ultimate Strength in Lbs. per Sq. In. Cement Sand Broken Stone Gravel Com- pression Tension Com- pression Tension I I I I 2 in in 5 90 28 90 28 4,610,000 3,350,000 4,800,000 4,130,000 5,460,000 3,800,000 4,510,000 4,320,000 2413 2290 2804 2405 359 237 290 253 the results being averages of thirty-seven compression and twen- ty-seven tension specimens; the broken stone was limestone, being the product of the crusher below i inch, and the gravel ex- cellent pit gravel, including sand and pebbles. The concrete was mixed medium wet. The following tests on the tensile strength and the tensile co- efficient of elasticity of concrete were made in the Mechanical Laboratory of the Department of Civil Engineering of Columbia University under the author's supervision by Walter T. Derleth and John Hawkesworth, graduating students of the fourth class in civil engineering. The work was begun early in 1903 and lasted until the first part of June, 1904. The cement which was Art. 20.] COEFFICIENT OF ELASTICITY AND RESISTANCE. 85 used was Atlas Portland, upon which the usual acceptance tests were made. As determined by the Gillmore needle, the initial set took place in i hour and 45 minutes, and the final set in 3 hours and 50 minutes. The strength of the neat cement briquettes, gauged with 13 per cent, of water, averaged 508 pounds per square inch at the end of 48 hours, 595 pounds per square inch at the end of 7 days, and 849 pounds per square inch at the end of 28 days. Mortar briquettes of one cement to one normal sand, gauged with 11.3 per cent, of water, averaged 583 pounds per square inch at the end of 7 days and 671 pounds per square inch at the end of 28 days. Mortar briquettes, one cement to three normal sand, gauged with about 8 per cent, of water, averaged 148 pounds per square inch at the end of 7 days and 203 pounds per square inch at the end of 28 days. The sand which was used in making the concrete was Cow Bay, and was clean and sharp. Its fineness, as tested by stand- ard sieves, was as follows: Retained by No. 2 sieve 0.49% * " 3 " 1.15% " " 4 " 6.68% " " 20 " 9.52% " " 30 " 15-55% " " 50 " 38.90% Passed " " 50 " 27.7% The percentage of voids in the sand was determined to be 40.5 per cent. The stone which was used for the concrete was a blue limestone, broken into sharp, angular pieces, varying in dimen- sions from 3 inches to J inch. The percentage of voids, deter- mined by an average of two tests, was 48.1 per cent. All the concrete for the tests was composed of one part of cement to three parts of sand and five parts of broken stone, by volume; and these ratios by volume correspond very closely to the actual weights of the different constituents used in the mixture. Each specimen or bar contained about ij cubic feet of concrete, and each was prepared separately from a batch of the materials 86 TENSILE PROPERTIES. [Ch. V. which averaged about ij cubic feet. The sand and cement were first thoroughly mixed dry and then the moistened broken stone was added, the whole being turned several times before the ad- dition of water. Water was then slowly added while the ma- terial was being turned over by shovels until its consistency was very plastic. The concrete was then deposited in the wooden moulds and lightly rammed into place with a wooden rod. After the first five bars had been moulded, it was found better to make the mixture so fluid that very little tamping was necessary; its consistency was then what is known as "very wet concrete." The moulds were always well moistened, and also greased with soft soap, before depositing the concrete, and no trouble was experienced in removing the bars from the moulds. The pins were covered with paraffined paper, so that they were easily withdrawn after the specimen had set. It was found imprac- ticable to remove the specimens from the moulds before four or five days. Specimens Nos. 2, 3 and 4 broke during the manu- facture, due to improper handling or too early removal from the moulds. In order to strengthen the heads of the specimens in the neighborhood of the pins through which the tensile pressure was later applied looped pieces of iron telegraph wire or heavy- weight picture wire were inserted. The shape of the specimens is clearly shown in the following figure, the cross section of each piece being 6x6 inches and the diameter of the pin hole through the head being if inches. Pin hole 1^diain. FIG. 3. For the purpose of measuring the stretch or decrease in length of these specimens, upon the application of loads, it was neces- sary to have built a special extensometer. This piece of appara- tus was made by T. Olsen & Co. of Philadelphia, and consisted of two frames which inclosed the specimen and which were firmly fastened to it at a distance apart of 25 inches ; on opposite Showing Method of Determining the Elastic Behavior of Concrete Bars, 6x6-Inches in Cross-Section, the Specimens, with Electric Extensometer Attached, being Mounted for Tension Experiments in the 150,000 Pound Emery Testing Machine of Columbia University. In the Photographs, as Shown, the Test-Pieces Are Blocked Up with Wooden Wedges. The First Specimens Tested Were Hung from Heavy Steel Cables, with Looped Eyes, but a Second, and Better Method of Attachment, by Means of Parallel Side Plates, is Shown in the Right-Hand Figure. Enlarged Views of the Heads of the Specimens Are Shown Opposite Page 120. Art. 20.] COEFFICIENT OF ELASTICITY AND RESISTANCE. 87 sides of the tipper frame were fastened two brass rods held in ball-and-socket joints; by means of micrometer screws these made electrical contact with two contact plates, which were in turn fastenend to the lower frame. Two rods, one on each side of the specimen, were used in order to guard against errors of observation and to eliminate errors due to bending cf the speci- men. The micrometer screws had a pitch of 1-40 of an inch, and \ H t FIG. 4. the micrometer head was divided into 250 parts, so that each division of the head represented .0001 of an inch. It was found impracticable to measure smaller parts than one division of the head. The accuracy of the screws was tested by means, of a dividing engine in the laboratory of the Physics Department of Columbia University, and was found to be exact for the range of testing for which the instrument was designed. Tests were also made upon concrete bars of the same form which were reinforced by wrought-iron bars, and it will be con- v-enient to record at this point the results of tests made upon these wrought-iron bars. Three bars were tested one f of an inch square, which de- veloped an ultimate resistance of 48,700 pounds per square inch, with a coefficient of elasticity of 29,620,000; one bar ^ inch square showed an ultimate resistance of 54,800 pounds per square inch and a coefficient of elasticity of 29,900,000, and one bar f of an inch square had an ultimate resistance of 52,275 pounds per square inch and a coefficient of elasticity of 27,- 590,000. Failure of the specimens, in the tensile tests, occurred in ail cases but two, in the head, on each side of the pin hole. The wires imbedded in the head were not broken, but had slipped 88 TENSILE PROPERTIES. [Ch. V, in the concrete. The ultimate tensile resistances are therefore not of any value; the stress conditions at the pins in members of this shape are so peculiar that in future it will be well to devise some other method of applying the stress than the one which was used. In the compression tests none of the specimens was Load pe: in Ibs. sq.in. c A H J fl 1 "* -^4 i 1 | /1 50 J |ioo Sp< Ag ciinei : 138 c No. 5 ays. Pla Lengt Sectio n Con i :6 jrete / 1150 Area Areas tPuy-32 4 /5 G/ ' f 200 Ult Rests ., Boc Pin y 876 Ibs.per sq.in. 1000 " I L Elastic L Load Ibs.per sq.in 0-300 300 - 500 unit \ \ J " a o g . Coel icient|of Elasticity 2860000 Ibs. per sq.ir 2665000 u m 350 500-60 i 25000 00 << J/ll i 400 X !" 1 450 / 1 1 500 / / 8 1 550 / 1 / 600 FIG. 5. stressed to such an extent as to cause failure in the body of the bar; failure occurred generally by crushing or shearing at the heads or at the pin holes, but was usually accompanied by fine cracks appearing generally over the entire surface, so that the Art. 20.] COEFFICIENT OF ELASTICITY AND RESISTANCE. 89 FIG. 6. ultimate resistance was very nearly developed. None of these considerations concerning methods of failure disturbs, however, the measurements of the elastic deformations. It should be 90 TENSILE PROPERTIES. [Ch. V. Load per in Ibs. sq.in. Age: 125 da -s. 50 Coeffi Ult.K cient i esist., a f Bias Body t Pin ticity 33 lbs.per sq.in, 1154000 Ibs. per sq.in 40 j 30 1 / / J 6 H 20 t 7 10 ll\ / i 1 | i 1 I 1 i i \P/ Id d j\5Q ^ i. i I I 1 p jioo i Sp Ag ^cimei 1 i: 133 e No. 8 ays. Plain Con Length Section crete w; 6x65 i" / !*> Area Area at Pin 37 H a" 32V S Q// / Ll 200 Ult.B E esist., astic i Body tPin Jmit 686 Ibs. per sq.in. '785 " 450 < / > / / s / 350 I J It U / j 7 400 5 // s/ PI It | 450 .// / ^7 / // 500 * / / / / I 550 X / / / / / 600 FIG. 7. noted, however, that both kinds of stress, tension and compres- sion, were applied, in the order named, to every individual speci- men. This was done in order to eliminate from the results any Art. 20.] COEFFICIENT OF ELASTICITY AND RESISTANCE. 91 possibility of differences in the method of manufacture of the specimens, and that the elastic properties of the two kinds of stress might be directly compared. An objection might there- fore be lodged against the compression tests, since these suc- ceeded the tension tests; but, in the opinion of the author, none of the specimens was injuriously affected by the previous tests, principally because the tension tests failed at such low intensities. Table VIII. , page 95, records the results of these experiments. After each whole specimen had been subjected to the com- pression test, parts of the same were then subjected to crushing Ult Resis Age: e: 124 days. Specimen No. 9 31 daj s. Ult.Resist., Elastic Linlit n Ibs. per sq.in. ., Body 29 lbs.per_sq.in. at Pin 33 . f Elasticity 13150001 Length Section Aitaa at I Body: Pin Load|lbs.p.sq.in. 0- 200 I Concr !te per sq.in. Icient of 1800000 *l Elasticity Lbs.per sq.i FIG. 8. and to shearing tests. The manner of loading in the latter case is shown in Figure 4, page 87. It is the opinion of the author that the size of broken stone used in these tests was too large. In bars 6x6 inches in section 3 inch stone is too large; it would have been preferable if 2, inch stone had been the limiting size. The stress-strain curves for specimens Nos. 5, 6, 8, 9, n, 22 92 TENSILE PROPERTIES. [Ch. V. and 23 are shown in Figures 5 to 1 1 respectively ; it will be seen that the curves for tension and compression are very nearly straight lines, with equal inclinations. Table IX., page 96, shows the results of tests made in the Laboratory of the Technical Institute of Vienna during 1891 and 1892, and are recorded in the Transactions of the Austrian Soci- ety of Civil Engineers for 1895. 1 Load per in Ibs. sq.in. 10 U ge: 120|days. It.Resikt., Bi >dy 33 in 38 Ibs. per. sq.in. 30 s C( efficie it of E astic ty 133 WOO Ib s. per s a.m. M \ , 1 I / 2 3 H 10 ' / /// I 1 | 1 i I I 1 1 Jd I'S /l * i i 1 i 1 Sp< Agt cimen : 123 ds No. 1 ys. PI, Leng Sect! ,in Coi ;h t>n crete 25;; 6x6: " /i- i Area! Area kit Pin 36% " 32k,o=' I 150 Ult.R esist., 3ody Pin 728 Ibs 832 - per sq. n. / / / / 'I 200 1 Ibs Load per sq. In. Coefl icient )f Elai ticity a 1 250 5 0- 300 1666000 / i i / 350 FIG. 9. The batch numbers marked Wa were left in water three months from the day of making, being removed three days be- fore the test; batch numbers marked Wb were left in water the entire time. The table gives the ultimate compressive resistance of 4 inch cubes and of 3^x3^x10 inch prisms. The strains experienced by the latter were also measured, so that it was possible to obtain values of the coefficient of elasticity. The table also gives values Art. 20.] COEFFICIENT OF ELASTICITY AND RESISTANCE. 93 Load per in Ibs. sq.in. Age: 111 da r s. 50 1 Ult.Resist., Body Pin 43 Ibs.] 19 _ jer sq.ii ? 40 / / 2 3 Coeffi cient jrf Elas ticity 8800001 bs. per sq.in. 30 / / / / X 1 20 i // / 5 10 //; / s~ PI 1 i i I i 1 i i w a* 5 i I i Sp Ag jciiner i: 117 d .No. 2 ays. 2 Plain Co Length Section acrete 25// 6x6! (" / 100 Area | Area at Pin 38M^' 32H y/ / 150 UU.B E esist., astic Body Pin Limit 537 Ibs. per sq.in, 612 " 400 " 200 , Lo Ibspei id- sq.in; Coef icient of Ela iticity / 260 0- 300- 300 500 1390000 lbs.per sq.in. / 1258000 / , / / 300 s '/ // / 350 1 o. / , / / 100 x x / / / / y : 150 / X / / x / / 500 "^ / / 560 600 FIG. 10. of the ultimate resistance and the coefficient of elasticity of con- crete and mortar specimens in tension. It was found that the concrete prisms had permanent sets at relatively low stresses. 94 TENSILE PROPERTIES. [Ch. V. p \ Load in Lbs. r_sq._iij Age: Ult. I 112 days lesist.,|Body 59 Ib 67 17 ICO s.per sq.in. 1 y Coeffi cient ( )f.Elas ticity 1)0 Ibs.j >er sq. n. 10 ' f /f n a 0) // Jc l ill i i | ! i i 1 I ! i : i 1 1 1 I / 100 / .. - Specmen -Age-:-l-).S- l 23 P ainCc ncrett ! 200 Length 25 Ins. Section 6?x 6%" Area 38M = " // Ulll Resii t., Bo ly 561 651 325 Area, bs.per Pin 3 sq.in. */ J/ /L Elastic Limit Load / / 350 O I Ibs.per sq.in. Coefficient of Elasticity / 0-300 1800000'lbs.per'Sq.In.X ^ / f i Uoo 3 o 300-50JO 910000 /* 7 / / L ^^Z. ^ ^ ,. / / L ^" 550 600 FIG. 11. The report states that the total strain in both tension and com- pression was nearly always proportional to the loadings, but that this cannot be set down as a rule. Nor could the tests decide Art. 20.] COEFFICIENT OF ELASTICITY AND RESISTANCE. 95 ko ko ko I-H OJkOH-ii-.O ? ? ? nnn n : o : o o o CL CL D. d. 3 K D /=0 : a vjvjj'-'Oo I oo oo ko I cr\ a>M ? 5'S) S la^t-ga 5tsrI 3 S n O ^o o^ ui 00 oo CD vj oo -fk CT\ 00 OJ rf Slo 00 1-1 U* O O O VJT ji. I 00 I 1 i. ' kO <-> kJ Oi VO \Q ^Q -> ON OS I OB vjn - oo >-| kO I kO 4XI-. 1-1 \Q \Q 00 i i ^jt i i v<3 oo vj P C^ >* H-I 00 O O O O O O HI 1-1 i-. kO kO ) >vO O CD > o o o wo >-. \> ,-, O H-I >- O VO O O O O O O O O O O o o o o o P 00 K-l H-< kO p p u> o o o o o o 000 ko v>o i i <-> 00 ^o ^o p c> o o o o o o Of 6 Inch Cube in Lbs. per Sq. Inch I I I I I i I I At Age of Days _ _ _ ^0 Ut 00 CN ' 00 ' vJCN4^ In Lbs. per Sq.In. I I I I I I I I I I . . ko ko vji oo oo ' ' -i M . M ^ M M { At Age of 2?. si 5 96 TENSILE PROPERTIES. [Ch. V. , ui *b jad -sqq A-JIDIJSB[3JOJU3IO !JJ 3O D 33J3Ay lil 11 i II ii o 55 55 ui 'b J3d -sqq Ul 30UBJSIS3JI JJQ 33BJ3AV t^* ^" O ^N 00 ^" ^- * r^ "^ C^N vTN u H sqjuow ui 33y === u -- -- SU3UIp3d - - i 1 .c ui 'bg J3d -sqq A"JIOIJSB[3 JOJU3IO ooo o o oo oo ^" co 1^ O CO t^ tx *"- \& C o X ui "bg J3d 'sqq UI 30UBJSIS3JI JIQ 33BJ3AV 00'^"'' con ir\O G^ CO r\fS ir> co co oo co in r% in cs ^ t^ ootx v^oo i>in oo^ oo > i COCSCN i i COCO CSCO C^CO no X , v "^f ^ -^- coco co coco coco O CO , S o"^ N S cococo - -> r- r*- TTCO M flu XJIABJQ oijioads ^\OOO JNCO OcO CS^* i ii i (NCS c Q> U J3 U C sqjuoiv ui 33y f "* ^f coco coco coco -co 1 (A FSSS& - - - * r* *O o **<, -== -f -f -f -5 oO S - co c o .\BKAtfy- OF THE UNIVERSITY Art. 20.] COEFFICIENT OF ELASTICITY AND RESISTANCE. 97 definitely whether the coefficient of elasticity for tension or com- pression differed. It will be seen in these experiments that the values of the coefficients of elasticity decrease as the proportions of other materials to sand increase, and that as the ultimate strength of the mixture increases so does the coefficient of elas- ticity. It is not clearly stated whether the values are the elastic values of the coefficients; it must be so inferred. Tensile Properties. Conclusions. From the foregoing experiments it is possible to draw the fol- lowing conclusions : First. Concrete in tension appears to possess no point which might be termed the elastic limit; in other words, the coefficient of elasticity is a constant quantity from a condition of no stress to the point of rupture. Second. The coefficient of elasticity appears to increase with the ultimate tensile strength of the material, but, due to the great difficulty in determining the actual breaking loads of concrete bars in tension, it seems impossible to connect in any rational manner the coefficients with the breaking loads. Third. The ultimate tensile resistance varies in some manner with the richness of the mixture and with the age of the speci- men, but it appears impossible to determine any expression which will present rationally the relation of these quantities to one another. It is only possible to say that the value of the elastic or true coefficient of elasticity has been found to vary between 1,000,000 and 5,000,000 pounds per square inch, and that the ultimate ten- sile resistance varies from 100 to 500 pounds per square inch. It will be seen later that it appears possible to connect the ultimate crushing resistance of concrete with the compressive co- efficient of elasticity, and since it has previously been shown that the ratio between ultimate tensile and compressive resistance is about as 1:10, it may be possible to transpose to tension the empiric relations deduced in the compression experiments by in- 98 TENSILE PROPERTIES. [Ch. V. serting in those expressions, in the proper manner, the ratio of i to 10. From the experiments that have been recorded so far, and from those which will be shown for compression, it may be said without much error that the coefficients for both tension and compression for any one mixture may always be taken equal. This will indicate the manner in which the ratio of i to 10 must be used. CHAPTER VI. COMPRESSIVE PROPERTIES. Art. 21. Coefficient of Elasticity and Ultimate Resistance. Professor C. Bach of Stuttgart has made perhaps the most in- teresting and most reliable of experiments on the compressive elasticity of cement and cement mixtures. His experiments on the elasticity of concrete have been published in the "Zeitschrift des Vereines Deutscher Ingenieure" for April 27, 1895, and No- vember 28, 1896. The experiments recorded in the first issue mentioned were made by Professor Bach in July, 1894, on 32 cylinders with a circular cross section having a diameter of 9.9 inches and a height of 39.4 inches. Six different proportions of ingredients were used, and in general six specimens were made of each mix- ture, three with one brand of cement and three with another brand. The following table shows the mixtures employed, the parts being expressed by volume: I. i cement, 2.\ Neckar sand, 5 Neckar gravel. II. cement, 2.\ Neckar sand, 5 limestone shingle. III. cement, 7J natural gravel and sand mixed. IV. cement, 3 Neckar sand, 6 Neckar gravel. V. cement, 3 Neckar sand, 6 limestone shingle. VI. cement, 9 natural gravel and sand mixed. The ends of the specimens were plastered with a layer of neat cement in order to facilitate planing. The specimens were taken from the moulds at the end of one day, and were then covered with bagging, which was kept moistened, for 28 days. At the time of testing the age of the specimens varied from 76 to 97 days. 100 COMPRESSIVE PROPERTIES. [Ch. VI. The deformations were measured by means of a specially de- signed instrument reading directly to .00013 inch, on a meas- ured length of about 29 inches. The load was applied to the specimens at a steady rate, from o to the point desired, in i-J- min- utes, and the removal of the load was accomplished at the same rate. In all of Professor Bach's experiments the loads were added and removed until it was found that there was no change in the TABLE I. Composition in Parts by Volume Cement Used Brand "B" Cement Used Brand "L" tx 0) . | M "tl TJ ^ Coefficient of 2~* fe Coefficient of 1 1 1 1 CO JS 1 Elasticity Between Inten- ll CO .C C 1 Elasticity Between In- C 3 e 1 "^ g 1> C O sities of Stress ^k _0 O tensities of U co M O & * o G of and 113 Lbs. in Lbs t/; * and 113 Lbs. in Lbs. g 1 u & s" & 1 per Sq. In." 13 a 1 per Sq. In. P W & C .-; . u C? J 55 oi < M 5.5 < CO 55 2^ 5 2^ 2.37 4,340,000 1370 2Yz 2.33 3,410,000 880 2/-2 5 2^2 2.42 4,670,000 1780 iy 2 2.44 5,160,000 1520 2^2 5 2*4 2.42 5,340,000 1980 3 2.46 4,950,000 1580 2]/2 5 2]/z 2.43 4,730,000 1800 3 2.45 4,760,000 1615 7/2 2)4 2.39 4,870,000 1 865 2^2 2.33 3,820,000 1230 7/2 3 2.42 4,970,000 2000 3 2.34 3,450,000 1200 7/2 3 2.40 4,480,000 2090 3 2.35 3,480,000 1280 3 6 2^ 2.39 4,470,000 1640 1]/2 2.37 3,920,000 1090 3 6 2^ 2.39 4,200,000 1560 3 2.38 3,680,000 1000 3 6 3 2.39 4,180,000 1700 3 2.38 3,910,000 1080 3 6 2J!^ 2.43 4,910,000 1680 2]/2 2.46 4,170,000 1240 3 6 2]/z 2.43 4,640,000 1720 2^ 2.43 4,190,000 1360 3 6 3 2.42 4,470,000 1640 3 2.45 4,170,000 1230 9 2/^ 2.42 4,270,000 1510 2^2 2.34 3,610,000 960 9 3 2.40 4,530,000 1660 3 2.33 3,250,000 908 I 9 3 2.41 5,170,000 I960 3 2.34 3,220,000 915 deformation as found by a previous reading. This required, in general, when the applied load was less than 570 pounds per square inch, four to eight repetitions; but with higher intensities of stress the deformations of the specimen were found to be also dependent on the time which the load remained on the specimen ; that is, the strain was a function of both the load and the length of time the load was applied. This agrees with experiments made on some other materials, more notably those made by Pro- Art. 21.] COEFFICIENT OF ELASTICITY AND RESISTANCE. X X X X 1 1 VjO >wO WJ ^C kO kO -i ~ ^^ 1*1 I O I .1 *al lovl iv*l I M I 5 2 o 5" 13 ^> vr ^ ^ 00 kO VJ 00 kO W* GN ^ CD ^J VS vo.t.(jNkOkO O O O 00000 tO kO kO kO kOkOkOkOkOkOkOtOtOkOtOkOkOkOkOtO 'kOkOtO *-o kO vjo to _t. tO *- O kO O O O O 00 88 . 580^ ^. ys to to tO ^ vj "Jo So o 8 p 8 tOitOi-i kO^kOtO tOkO ^kOtO>-kOUOtO W \Q CD O 4x 4i- ^5 OJ O O O O ^ -t*- ^>^ ^ ^J^ kO i i ^ji to vj (7\ (T\ * O O O O O O Number of Speci- mens Tested Cement Sand from Danube Sand Egginger Gravel from Danube Broken Limestone Shingle f 3- SSL Ultimate Resistance to Crushing in Lbs. per Sq. In. Specific Gravity 0-112 bs. per Sq r cr P a o o o o o o 80 o o o o o o o . -U o i v^o to o -&. CD kO VI M \Q O O o o o o o o o o o o 888 Coeffi fo t of Elasticity in Lbs. per Sq Compressive Stress Between the Limits of 102 COMPRESSIVE PROPERTIES. [Ch. VI. fessor Thurston. This question is of the greatest interest in con- nection with the fatigue of materials. Table I. shows the results obtained. The second set of experiments, which were recorded by Pro- fessor Bach in the issue of the 28th of November, 1896, were made on two sizes of round cylindrical specimens, the first being 39.4 inches high, with a diameter of 9.9 inches, and a consequent cross section of 77^ square inches; the second being cylinders of the same cross section, but only 9.9 inches high. The experi- ments on the elasticity of the material were made only on the larger specimens, the deformations being measured on a length of about 29^ inches, by the same instrument noted before, read- ing directly to .00013 inch. Loads were applied at intervals of 112 pounds per square inch. The average age of the speci- mens at the time of testing was about three months. The con- crete was prepared as nearly as possible in the same way as in the case of actual construction work; water was added in such quantities that by ramming the whole mass appeared very plastic. Table II. shows in detail the proportions of the mixtures em- ployed and the number of specimens tested, the total number being 102. The sand marked "Egginger" was quartz sand with a little feldspar, while the "Danube" sand was river sand. It will be seen that in almost all cases the concrete in which the stone was a limestone attained a higher ultimate resistance to crushing. It would seem, then, that the gravel concrete should be the more elastic ; that is to say, it should yield more under stress than the limestone concrete; the table shows this to be so. Table II. also shows clearly the increase and decrease in the coefficient of elas- ticity with the variation of cement in the mixtures. Figure i is plotted from the results of the table and shows the variation in the coefficient of elasticity with varying proportions of cement to other aggregates. In the case of mortar, it will be seen that the coefficient rises from the neat cement to a mortar of one cement to one sand, and then slowly drops until, with a mix- ture of one cement to three and one-half sand, it is about the same as that for neat cement. The results as plotted for the Art. 21.] COEFFICIENT OF ELASTICITY AND RESISTANCE. 103 *>"". 4,000 0(K I J 3,000 00( limestone and gravel concretes show a steady decrease in the co- efficients as the ratio between cement to aggregate increases. The latter results in the case of the concretes are perhaps to be expected, since it seems rea- sonable to suppose that a ma- terial whose strength depends on cement will be yielding in I* proportion to the quantity of P j cement in it. |-~ 2,000 Professor Bach quotes ex- periments by Hartig, in "Civil Ingenieur," 1893, page 467, and Baker, in "Civil Inge- nieur," 1894, page 718, as fur- nishing results corroborating the variation of the elasticity as found by him. The coincidence in the rise of the values of the coefficient of Elastic 1:2 1:4 1:6 1.8 1:10 1:12 1:U Proportion of Cement to Aggregate FIG. 1. BACH'S TESTS. Failec at 1960-1 bs. s ^ ^*~~ M- ,^--' 1000 / ^ ^^ a !500 laOO / ^ t /* *. h 14W J z / o5 f / A S d uo , T? I ^1 / ce qoo I $V i 1 Cement Concrete] Q ^ n Mortar VI* 1 :2^ :5 Concrete VIII* 1:3:6 Concrete XVI* ....1:5:10 Concrete Vllf I:2>:5 Concrete IXt .1:3:6 Concrete XVIIt 1 :5:IO Concrete *Gravel Concrete. tLimestone Concrete. Stress-Strain Relation, Expressed in Lbs. per Sq. In., from Equation 3 556000 ji.ii 5,050,000 = pi. 4,480,000 = -y p ^.n 3, 270,000 = ~- ,1.14 4,230,000 = -y pi.u 3,980,000 = 1.16 3, 080, 000 = -y- P\M 6,500,000 = ^- 5,400,000 = - - 5,210,000 = - Art. 21.] COEFFICIENT OF ELASTICITY AND RESISTANCE. 1 05 As shown, the value of the constant E in the Bach equation in- creases over that calculated in Table II. in the same sense as the exponent n\ that is, if n increases, so does the value of E, as compared to its value when n equals one. It seems to the author that Bach's refinement is unnecessary. It has never been found necessary to express the stress-strain relation of a material like steel by an algebraic expression covering the entire range of stress, and it will be shown that concrete possesses an elastic TABLE III. COMPRESSIVE STRENGTH OF NEAT DYCKERHOFF CEMENT. Size of Specimen Crushing Load in Lbs. per Sq. In. Average Modulus of Elasticity in Lbs. per Sq. In. I In 2 3 4 5 6 7 8 9 10 II 12 4x 4x 4x 8x 8 x 8x 8x 8x 12 x 12 x 12 x 12 x ch Cu 4x I 4x2 4x3 8x2 8x3 8x4 8x5 8x6 12 x 2 12 x 4 12x6 12x8 be 5896 7094 5937 4847 4610 4283 4987 5007 4754 4761 5374 5291 1 647 1 6370 6003 10664 7186 5952 6019 5771 1 Tested in built-up I piers, set dry. Re- f suits not compara- 1 ble. 1,358,774 1,421,111 1,510,416 1,703,877 1,635,107 limit, although not a precise one, below which the stress-strain relation may be expressed by a constant. General Q. A. Gillmore treats very extensively of the com- pressive resistance and elasticity of Portland and natural cement mixtures in his book, "Notes on the Compressive Resistance of Free Stone," etc., published in 1888. The accuracy of the tests appears to be insured, since they were all made at the Water- town Arsenal. 106 COMPRESSIVE PROPERTIES. [Ch. VI. In the case of the neat cement experiments, abstracted in Table III., a series of cubes and prisms was made of Dyckerhott Portland cement, the average age of the specimens at the time of testing being one year, ten and one-half months. The cubes varied in sizes, by increments of one inch, from one to twelve inches on the side, there being six samples of each size. The ma- jority of the specimens which were tested, including both the cubes and prisms, had plastered faces, the exceptions being a few of the 2, 3, 4, 5, 6, 7, 8, 9, 10 and n inch cubes. It should be noted that plastering the compressed surfaces uniformly increases the ultimate resistance. It will be seen that in the case of the cubes the smaller cubes gave slightly higher crushing resistances than the others ; that in the case of the prisms the very flat prisms furnished extremely high values. This is to be expected. It will be seen that the average value is about 5,000 pounds per square inch. The co- efficient of elasticity was determined for the larger cubes, and in calculating these values General Gillmore divided the unit stress at a point which he names the elastic limit by the unit deforma- tion, no deduction being made for permanent set; these coeffi- cients, therefore, are not the true elastic coefficients; they would be greater than given in the table. Figure 3 shows the stress-strain curve determined for one 10- inch cube, and also for one 1 2-inch cube. The curves are char- acteristic of all the tests, although some show a slight convexity to a horizontal line at the origin. This may possibly be due to the squeezing out of the plaster between the specimen and the bed plate, since it seems that the deformations were measured between the heads of the testing machine. The majority of the curves shown by General Gillmore are, however, very similar to Figure 3. The elastic limit might be placed at .6 to .75 of the ultimate resistance. Table IV. gives the values of the ultimate resistance obtained by General Gillmore for mortar and concrete cubes mixed with three different brands of cement two natural and one Portland. Each result shown is an average of two specimens, the beds of all specimens being plastered before being tested. Some of the Art. 21.] COEFFICIENT OF ELASTICITY AND RESISTANCE. 1 07 k** p OQ pi Tf fl fs I f o Total Load on Specimen in Pounds 1 I I i I i i I i i I I 1 1 108 COMPRESSIVE PROPERTIES. [Ch. VI. cubes were, in addition, placed between wooden pine cushions, but it was invariably found that the use of these wooden cushions did not develop the full possible strength of the material. In the table as given no distinction has been made between specimens, whether they were provided with such cushions or not. The coefficient of elasticity could only be determined for .02 .03 .(it- Decrease in Total Length in Inches FIG. 4. FROM GILLMORE'S TESTS. those specimens in which no wooden blocks were used, because the deformations were measured directly between the heads of the testing machine and the concrete was forced rather deeply into the wooden cushions. The values shown have this peculiarity: that the concretes seem to possess, on the whole, a greater strength than the mor- tars, which is rather exceptional, and can perhaps be explained only by the fact that the mixtures were better balanced. Table V. shows the values of the coefficients of elasticity of the larger size cubes, determined in the same manner as in the Art. 21.] COEFFICIENT OF ELASTICITY AND RESISTANCE. 109 Total Compressive Load in Pounds tO G* rf* O' CT- ~J II S 8 1 8 1 I I 1 1 110 COMPRESSIVE PROPERTIES. [Ch. VI. case of the neat specimens of Table III. The intensity of stress for which these coefficients are calculated is shown. Figures 4 and 5 are characteristic stress-strain curves of all the mortar and concrete tests. It will be seen that there is a point which might be called the elastic limit, although all the TABLE IV. Brand of Cement Composition of Specimen Parts by Volume Size of Specimen Cubes 2 In. 4 In. 6 In. 8 In. 10 In. 12 In. 14 In. 16 In. 18 In. Cement g & u 1 B 11 Ultimate Compressive Resistance in Lbs. per Sq. In. A.. B." C." I (DryMeas.) I (Paste) 3 3 IK 3 IK 3 3 3 2 4 6 6 6 1429 758 1032 2042 1324 2322 1633 3450 4014 800 1 127 1340 750 963 1000 2655 2629 707 1035 1746 790 1434 861 2469 3025 945 1 167 685 972 1346 688 1560 765 2434 2690 715 723 612 856 1247 718 1447 843 2519 2978 941 A Newark Co.'s Rosendale; tested at age of about 22 months. B Norton's Natural; tested at age of about 3 years and 10 months. C National Portland; tested at age of about 3 years and 10 months. specimens show considerable permanent deformations at fairly low stresses. This elastic limit might be taken between two- thirds and three-quarters of the ultimate resistance. None of TABLE V. Brand of Cement Composition of Specimens Size of Specimen lliJ Cement o w Stone Cube Sin. 10 In. 12 In. 16 In. 18 In. Q " J Coefficient of Elasticity in Lbs. per Sq. In. Newark ) Rosendale ) Norton's Nat. . National Port. 1 1 1 1 1 1 1 3 3 3 2 3 3 (2 Gravel) 1 4 Stone j 6 6 6 1,092,000 1,076,000 549,000 465,000 614,000 573,000 708,000 702,000 1,606,000 1,350,000 572,000 655,000 484,000 778,000 530,000 1,864,000 1,732,000 567,000 650 750 410 800 500 1800 1500 the curves show the coefficient to be a constant quantity, and not much error is introduced if it is taken constant below the assumed elastic limit. Art. 21.] COEFFICIENT OF ELASTICITY AND RESISTANCE. 11 Table VI. gives the results of Henby's compression tests on stone concrete and cinder concrete, these tests having been made at the same time and in the same manner as the tension tests noted in Art. 20. TABLE VI. COMPRESSION TESTS STONE CONCRETE. 1) H 09 Composition- Parts of cS JS-g i Modulus M.5 4> c of cm/? u Q c Treat- ment .5 Elasticity Lbs. per VJC/J k C ~ Con- sistency Remarks a S o c C g 8 ^U Sq. In. 3 2 M u at S C/5 OQU N O Ss M 220 90 2 4 A 2 Air dry 140 4,421,000 1243 Dry 221 90 2 4 4i 2 44 144 5,792,000 982 ii 80 2 5 44 2 44 146 3,927,000 726 44 272 60 3 6 2 Air 2,886,000 413 Very dry 225 30 2 4 156 44 160 7,171,000 3020 Plastic 226 30 2 4 Water 152^ 4,625 000 2610 76 9 2 5 \% Air 152 4,930,000 423 44 248 32 2 5 \y z 44 151 5,055,000 2097 4 249 32 2 5 \ l /i Water 154^ 7,292,000 2830 4 250 34 3 6 1/2 Air 143 5,104,000 1310 4 251 39 3 6 15 44 146 7,520,000 1733 4 252 39 3 6 14 \YZ Water 152 6,646,000 2242 4 253 38 4 8 44 \% 44 143 4,560,000 1282 4 291 90 i M 44 136 6,578,000 5280 4 \ Sudden 292 90 i Air 129 3,940,000 4580 4 ) Failure 254 38 i 4 8 A i^ 44 139 2,446,000 617 Excess 255 38 i 4 8 151 138 2,247,000 797 CINDER CONCRETE. 49 50 2 4 48 152 30 2 154 tt 189 30 2 190 138 60 2 139 tt 140 60 216 217 60 3 193 30 218 3/t> AAtlas Cement ; M Medusa Cement. It will be seen that the ultimate compressive resistance de- creases very uniformly as the percentage of materials other than cement in the mixture increases, and, also, that the modulus of elasticity increases with the ultimate resistance. The compress- ive resistance of the neat cement cubes is about 5,000 pounds per 112 COMPRESSIVE PROPERTIES. [Ch. VI. square inch and reduces to about 1,000 pounds for a 1:4:8 mix- ture. These compressive resistances have been plotted in the usual manner in Figure 6 and the results averaged by means of 4800 S 400 "**.,, $* No S 01 Lot *T JW L ^ 9 J> We rag eN 0.0 sts j U, x S 2 X, s^ 1 '2 < S^e C {tltf ^ C ** ^ X "^**^. <) -. *: ** X x 1 I 2 1 i i 2 1 3 ] i 1 5 1 6 1 7 1 Parts of other Material to Cement FIG. 6. FROM HENRY'S TESTS. a straight line, which may be expressed algebraically by the fol- lowing equation: *=4350 2587 (i) For Eq. (i), then, it will be seen that a neat cement mixture 1100 1000 4*900 't 800 700 400 200 .0001 .0004 .001 Proportionate Deformation FIG. 7. FROM HENRY'S TESTS. .0018 Art. 21.] COEFFICIENT OF ELASTICITY AND RESISTANCE. 1 1 3 will have an ultimate resistance of 4,350 pounds, and that a mor- tar of i cement to i6J parts of other materials will have no strength at all. Table VI. also furnishes results of ultimate compressive re- sistances and coefficients of elasticity for the cinder specimens, and the results of these tests are also plotted in Figure 6; but it has not been thought proper to express these results by means of an equation. Figure 7 shows some stress-strain curves of compression tests made on the cinder concrete. In this case the elastic limit might be considered to be one-half of the ultimate resistance. From an examination of the coefficients of elasticity deter- mined by Henby it is impossible to check Bach's proposition that there is some mixture which attains the highest value of the coefficient, and that mixtures either leaner or richer have de- TABLE VII. Brand of Cement Mixture Average Com- pressive Strength, Lbs. per Sq. In. Coefficient of Elasticity in Lbs. per Sq. In. Between Loads of 100 and 600 Lbs. per Sq. In. I '3 2001 2*3 16^4 ,, ,, 2-4 TQoe; ,, ,, :2:5 1084 " - :3:6 788 Alpha Portland.... :I:3 2834 2,500,000 " " :2:5 1600 1,279,000 Atlas " :I:3 2414 3,125,000 " " :2:5 1223 1,138,000 creasing values. In these experiments the value of the coeffi- cient decreases rather uniformly as the mixtures become more lean. Table VII. is taken from the Watertown Arsenal Report for 1898, and shows results of tests made on cinder concretes for the Eastern Expanded Metal Company of Boston. In all 84 twelve- inch cubes of various ages, made with different brands of ce- ment, were tested. Only the results of the better known brands are here abstracted, and only those which reached the age of about three months. Each result shown is an average of three tests. The cinder used was in the condition in which it came 114 COMPRESSIVE PROPERTIES. [Ch. VI. from the furnace; it was not sifted, and only the larger clinkers were broken. In the same Watertown Arsenal Report for 1898 are also re- corded results of tests on 95 cubes and prisms which were manu- factured at the Arsenal. Only those specimens in which Alpha cement was used are shown in Table VIII., the mixtures being 1:1:3. The sand was bank sand, the pebbles were from the Ar- TABLE VIII. 12-INCH CUBES 1:1:3 ALPHA CEMENT. Kind of Stone Ultimate Compressive Resistance in Lbs. per Sq. In. at Age of Coefficient of Elasticity in Lbs. per Sq. In. Bet Loads of 100 and 600 Lbs. per Sq. In. at Age of About 1 Month About 2 Months About 1 Month About 2 Months Trap Yz Inch 2800 3200 4917 4349 4800 2992 5024 3817 3800 3000 4140 2700 2190 3800 3572 4400 5551* 5021 3,571,000 8,333,000 6,250,000 8,333,000 8,333,000 4,167,000 6,250,000 4,167,000 4,167,000 3,125,000 5,000,000 4,167,000 3,125,000 4,062,000 5,208,000 5,000,000 5,000,000 4,167,000 8,333,000 6,250,000 8,333,000 3,125,000 12,500,000 2,778,000 5,000,000 3,125,000 12,500,000 " 3/ " 14 T H 5272 4544 5542* 3870 4700 4018 3490 3800 4523 /Trap y 2 Inch I Part \ \ " V/2 " --I Parts] f " 2> " .... I Part -^ { :: '* : ::::! : } Pebbles Y% Inch f Trap 2^ Inch 2 Parts \ \ Gravel l /& Inch. . . I Part J Pebbles \Yt Inch f Pebbles # " . . I Part \ \ " \Y 2 " ..2 Parts/ f Gravel l /& Inch.... I Part) \ " X " ...-I " \ \ Pebbles \% Inch.. I " J Trap iy 2 Inch ( Trap 1V 2 Inch I Part) { Pebbles # Inch... I " V 1 Gravel % Inch. . . . I " J Mixture 1:3:6 of I In. Trap. . Pc>hKlc><; I l /> In to 1 In Trap I ^ Inch I ' I Mortar 4800 6,250,000 *Not fractured. senal grounds and the rock was broken trap of different sizes from Waltham, Mass. The f inch stone all passed a f inch sieve and was all retained on the next smaller size, viz., J inch. The other graded sizes were obtained in a similar manner. The ages of the specimens varied from 7 to 76 days; only those having an Art. 2 1 . ] COEFFICIENT OF ELASTICITY AND RESISTANCE. 115 age of 30 to 70 days need be discussed, since the others are of no practical importance. As shown, the results are for one speci- TABLE IX. Brand of Cement Approx mate Composition by Parts Modulus of Elasticity in Lbs. per Sq. In. Between Loads per Sq. In. of SjJd 3 .2J5 08 a* .< Z M o u 5.sg Cement Sand Stone 100-600 100-1000 Gcncsce I I I I 2 3 4 *) 6 2 3 4 2 3 4 5 I 2 3 4 5 2 3 4 2 3 4 2 3 4 2 3 4 2 3 I 2 3 5 7 9 12 15 16 4 6 8 II 5 7 9^ 12^ 15 4K 6^ 8 II 12 7K 10 15 6*/ 2 8^ II 7 10 13 6^ 8 10/2 5 7 9 4 5^ 8 2,428,000 2,619,000 2,108,000 1,403,000 1,370,000 1,087,000 1,628,000 2,263,000 1,745,000 1,801,000 1,822,000 2,314,000 2,018,000 1,528,000 1,427,000 3,072,000 2,285,000 1,845,000 1,449,000 1,318,000 2,518,000 1,752,000 1,408,000 3,273,000 2,168,000 1,792,000 2,874,000 2,292,000 1,608,000 2,685,000 2,609,000 2,081,000 2,781,000 2,609,000 1,528,000 2,780,000 2,516,000 1,602,000 2,113,000 2,748,000 1,974,000 1,382,000 1,300,000 4080 3291 2930 2226 1842 1365 3330 2519 2567 2094 4165 3221 2311 1851 1713 4031 3465 2230 1843 1723 2852 1927 1665 3678 2296 1880 3521 2460 1774 3579 2545 1899 2928 2459 1495 3127 2377 1393 ,, ,, ,, ti 44 1,508,000 2,081,000 1,580,000 1,499,000 1,749,000 2,002,000 1,721,000 1,432,000 1,273,000 2,265,000 1,991,000 1,555,000 1,218,000 1,100,000 2,295,000 1,227,000 tt .t ,, Wayland ,, tl tl ,, " tt 2,937,000 1,757,000 1,468,000 2,505,000 1,890,000 1,266,000 2,446,000 2,176,000 1,622,000 2,253,000 2,207,000 1,046,000 2,571,000 2,228,000 lt Empire .. 4, 44 lt Champion tt ,< 44 44 men only. It will be seen that the values of the coefficient of elasticity are very high. This may be explained by the density of the specimens, which averaged about 150 pounds per cubic 116 COMPRESSIVE PROPERTIES. [Ch. VI. foot; whereas, in the tests made by Rafter, and to be noted later, the average weight was only about 140 pounds per cubic foot. Table IX. is taken from the Watertown Arsenal Report for 1898 and records ex- periments made for Mr. George W. Rafter on twelve-inch cubes of concrete made with various brands of ce- ment. Mr. Rafter's tests are explained in greater detail on page 121 et seq. ; here are only given the experiments concerning the elasticity. The average age of the specimens was about one year, seven and one-half months. The majority of results are aver- .001 .006 .01 .015 Deformations in Gauged Length in Inches. FIG. 8. .017 .005 .01 .015 Deformations in Gauged Length in Inches. FIG. 9. ages of tests made on two to four specimens ; n o distinction has been drawn between dry, plastic or excess. The gauged length on which the elastic properties were measured was five inches. The experi- ments are tabulated in - * the order of the richness of the various mixtures. It will be seen, in general, that the values of the modulus of elas- ticity decrease with the leanness of the mixture. The ultimate crushing resistance also decreases .001 ,001 .007 .01 .015 Deformations in Gauged Lengthjn.lnches. FIG. 10, Art. 21.] COEFFICIENT OF ELASTICITY AND RESISTANCE. 17 3000 Composition: Wayland Cement 1 ) _J Saud 1 t Broken Stone 6.43/ Consistency of Mortar, Plastic Age, 1 Year, 3 Mos.. 20 Days Ironclad Cement 1 "\ Sand 1 [ Broken Stone 7.76) | Age, 1 Year. 7 Mos., 15 Days Wayland Cement 1 \ 3 Broken Stone 8.29'- Age, 1 Year, 8 Mos., 17 Days Empire Cement 1 Sand 2 Broken Stone 7.5 Age. 1 Year, 8 Mos., It Days Mortar Empire Cement I \ Sand 4) Age, 1 Year, 7' Mos., 22 Days Mortar Empire Cement 1} Sand 2J Age, 1 Year, 7' Mos., 18 Days Mortar Empire dementi Age, 1 Year, 7 Mos., 18 Days Mortar Prism 6"x6"xl8" - Alpha Cement 1 > Fine Sand 1 ) Age. as Days Mortar Prism 6"x6"xl8" Age, 38 Days 1 Day in Mold ) 37 Day s in. Water) Gaugeu Jjcnfrth 10 35 Days in Wate Gauged Length 10 .03 .04 .01 .02 .03 .04 Deformations in Gauged Length of 5 Inches. FIG. 11. .03 118 COMPRESS1VE PROPERTIES. [Ch. VI. with the leanness of the mixture; in other word's, the modulus of elasticity is some function of the ultimate crushing resistance. Table IX. also shows that the modulus is not a constant quan- tity for any one specimen. The values given are calculated be- tween two increments of stress, from 100 to 600 pounds and from 100 to 1,000 pounds per square inch. In every instance the val- ues for the second increment of stress are smaller. Figures 8 to 12 are all abstracted from the Watertown Ar- senal Report for 1898 and 1901, and show clearly the elastic be- havior of some of the mixtures which have been tabulated on the Specimen same as below Age,l Year, 6 Mos., K Das Set in Mold, 23 Hours ) Cool Cellar; 1 Year, 5 Mos., 28 Das. f la Air. 27 Das. ) 1 Genesee Cemen 1 Sand 4. 71 Broken. Stone Set in Mold, ,23 hours 17 Das. 10 Das. Consistency of Mortar, Dry ige, 1 Year, 9 Months, 5 Days Wt. per Cu.Ft. = 147.16 Ibs Specimen 12" Cube Gauge Length =-5 Ins. .001 .01 .015 Deformation in Gauged Length in Inches FIG. 12. preceding pages. Two curves are shown, the one to the right being the curve of total deformation and the other the curve of sets. The curves are characteristic of all the tests made, and in- spection tends to confirm the opinion that concrete mixtures in compression have a point which might be called the elastic limit, at about 5-10 or 6-10 of the ultimate crushing resistance. In the case of the neat cements or mortars, this elastic limit approaches more closely to the ultimate resistance, having a value of perhaps 8- 1 oof it. Professor E. J. McCaustland records in the Transactions of Art. 21.] COEFFICIENT OF ELASTICITY AND RESISTANCE. 1 1 9 the American Society of Civil Engineers, 1903, some experi- ments which he made on concrete and mortar columns of various compositions and of various ages, and for which he determined the true coefficient of elasticity at 500 pounds per square inch. Table X. shows the results of his tests on these columns, which were circular, 10 inches in diameter and 40 inches long. It will be seen that the coefficients varied, although not uniformly, with the variation in the ultimate compressive resistance, and, from the stress-strain curves which are shown in the original paper, the material might be said to have an elastic limit of 5-10 to 6-10 of the ultimate resistance. TABLE X. Proportions Age in Months Coefficient of Elasticity in Lbs. per Sq. In. Ultimate Crushing Strength Lbs. per Sq. In. Cement Sand Broken Stone 2 3 14 ,050,000 1000 N 2 2 3 3 II 13 ,530,000 ,060,000 1752 1215 1654 2 3 14 ,010,000 2650 3 4 10 ,100,000 1484 3 3 4 4 II 14 ,380,000 ,425,000 1382 1230 141 1 3 4 II ,441,000 1550 3 5 14 ,450,000 1550 3 3 5 5 14 14 ,531,000 1500 1792 1504 3 5 14 ,050,000 1 170 2 5 15 840,000 10451 2 2 5 5 15 14 ,510,000 ,372,500 1955 i 1532 1450 f l 2 5 23 1680 J 4 23 2,775,000 2660 I 2 23 4,625,000 3410 I 3 23 3,700,000 2250 Figure 13 presents the results of compressive experiments re- ported by Professor Edgar Marburg to the American Society for Testing Materials, at its annual meeting, 1904. These stress- strain diagrams represent tests on four 6x6-inch prisms, 24 inches long; the deformations were measured on a gauge length of 18.5 inches. The concrete was composed of i part of Delaware River bar sand, to 2 parts of Atlas Portland Cement, to 4 parts of J-inch broken trap rock ; the materials were mixed rather wet. The age 120 COMPRESSiVE PROPERTIES. [Ch. VI. of the specimens, all being stored in air, was 30 days, and the average weight 154 pounds per cubic foot. ::: - 1 ^-^i^^^-^^ 1 j EHEE L r ___-, __j_|_,-. 7^~~ T]3 "r5~ - ' . . ..'",.!, ,,r ~~* -fi ~ Til' --; Jr xT^ BffrFFrW :: 1 :: +f-^-+y-+rr j p ; IT q i y a. i / L 5 z: 1 l ' vf i i 1 1-^- 1 [ y - Material, 1 :i! :4 Concrete. Age 30 daya s GLength 34" measured between ved to Specimen 18" Specimens 6 i i/* f J . T~_ ' f . ,,i ~ -^ " -T- r>H H~i~i 4 ' r H: i 7' 1 i 1 -Jf _!_ f : j i 4- ' -- ! !-r- -i- r*- (Eh - :! * -*-. r- 1 H r"n~i r |||' 1 | i 1 J- -L -a- I | si . . 4- 1 :E ] ! i ^G: i i n~i i ! - - "i ~ ' i i nc i i O^'OOOO O."0005 O."0010 O."0000 O."0005 Ol'OO O."0005 O."0000 Compression per inch length 0.0005 FIG. 13. MARBURG'S TESTS. The figure shows the stress-strain curve to be sensibly a straight line to a point about one-half the ultimate resistance. The values of the compressive coefficient of elasticity, calcu- lated without reference to any permanent set occurring in con- nection with the applied stresses, are given in the following table; the specimens in the figure are numbered from left to right : TABLE XI. Specimen No. Ultimate Compressive Resistance in Lbs. per Sq. In. Coefficient of Elasticity in Lbs. per Sq. In. Determined for Stresses of 1 1 166 2 000 000 'SOO I h<; rtpr Sn In 2 .... 1154 2 000 000 500 " " 3 4 1277 1316 2,300,000 2,700,000 0500 600 It is seen that the coefficient increases with the ultimate re- sistance. Professor Marburg also furnishes the average ultimate com- pressive resistance of nineteen 6-inch cubes of the same materials and same age, but taken from batches mixed at various times. The value given is 1643 pounds per square inch. Two specimens, Enlarged Views of Figures Opposite Page 86. The Location of the Points of Fracture, as Well as Details of the Extensometer, Are Clearly Shown. Art. 22.] ULTIMATE COMPRESSIVE RESISTANCE. 1 2 \ mixed with less water and thoroughly rammed, developed resist- ances, however, greater than the ioo,ooo-pound capacity of the machine used. Art. 22. - Ultimate Compressive Resistance. George W. Rafter has recorded in the Report of the State Engineer of New York for 1897 results of compression tests made on 544 twelve-inch cubes whose age at the time of testing averaged about 600 days. The concrete was prepared in three different ways in dry blocks, in which the mortar was only a little more moist than damp earth; in plastic blocks, in which the mortar was like that used by masons; and im blocks, in which the water was in excess, so that the concrete quaked like liver under moderate ramming. From every batch mixed in one of these ways four specimens were prepared and stored differently. One block was placed in water from the time of making (sum- mer of 1896) until December i, 1896, then buried in sand until January 10, 1898, when it was shipped from the place of manu- facture to the Watertown Arsenal in Massachusetts. The sec- ond block stood in a cool cellar until shipment; the third block was exposed to the weather, and the fourth block was covered with burlap and was wet with water several times a day until November i, 1896, after which it took the weather as it came until the day of shipment. The tests were made with Portland cement only. The sand was hand-broken Portage sandstone passing through a two-inch ring. Examination of these detailed experiments shows that the four specimens of any one series treated to the various conditions of weather gave rather uniform results; at least, it cannot be no- ticed that any one condition shows radically worse effects than any other. In further considering these experiments, therefore, the average of the four specimens prepared at any one time will be used. Mr. Rafter does not express the ingredients of a concrete mix- ture in the usual way, such as one part of cement to three of sand, to three of stone, either by weight or measure; but he ex- presses the relations, in percentages, between a definite mortar, 122 COMPRESSIVE PROPERTIES. [Ch. VI. say, 1 13, to a unit weight of stone. In order to make his results comparable to others the following table has been prepared, which expresses roughly Mr. Rafter's nomenclature in the more Percentage of Mortar Ratio of Cement to Sand in the Mortar 1:1 1:2 1:3 1:4 1:5 1:6 33 1:1:3 1:1:4 1:2:7 1:2:6 1:3:9/2 1:3:8 1:4:12 1:4:10^ 1:5:15 1:5:12 1:6:16^ 40 usual terms. Two percentages of mortar to stone were used, 33 per cent, and 40 per cent., and six different mortars, varying from i : I to 1 :6. TABLE I. Consistency of Mortar Parts of Cement to Sand Percentage of Mortar to Stone Ultimate Crushing Strength in Lbs. per Sq. In. Average of 4 Specimens Excess of Water. . . . Drv ] ] ] ] ] 1 1 4 ] :2 :3 :4 :5 :I :2 :3 :4 :5 :I :2 :3 :4 :3 :I :2 :3 :4 :5 :I :2 :3 :4 :5 :I :2 :3 :4 :5 3? 4 % % 3764 2847 1723 1767 1441 4267 2888 2056 1810 1537 4072 2777 2207 1600 1586 3256 3168 2016 1670 1400 3966 3404 2179 1671 1559 4123 2960 2027 1750 1465 ,, ,, ,, Plastic ,, tl ,, Excess of Water 41 it 44 44 Drv. . tl ,, Plastic . . . tt 4, .4 It will be seen, for instance, that the concrete known as I .-3 niortar, 40 per cent, may be expressed as a 1:3:8 concrete. Art. 22.] ULTIMATE COMPRESSIVE RESISTANCE. 123 Table I. is characteristic and shows the results obtained for Wayland Portland cements only, being the tests numbered 29 to 58 in the Report. The results obtained from the other brands of cements will be discussed, but need not be given here in de- tail, since they show but little variation. In the Transactions of the American Society of Civil Engi- neers, December, 1899, Professor I. O. Baker has tabulated and arranged very concisely all of Mr. Rafter's experiments, and the following tables are taken from his discussion of the experiments : TABLE II. Plasticity of Mortar Amount of Mortar Strength of the 40% Concrete in Terms of That of the 33% 33% 40% Crushing Strength in Lbs. per Sq. In. D rv . 2408 2259 2133 2532 2329 2227 105 % 103% 104% Plastic . . . Mean 2267 2363 104% It will be seen, therefore, that the effect of plasticity is not of great importance; in practice, what little gain in strength the dry mixed specimens may show is negligible in the face of other considerations, the principal one being the increased cost of TABLE III. Proportions in the Mortar Amount of Mortar Strength of the 40% Concrete in Terms of That of the 33% 33% | 40% Crushing Strength in Lbs. per Sq. In. I Cement' 2 Sand 2640 1893 1684 2820 1905 1689 107% 102% 100% I Cement'. 3 Sand I Cement" 4 Sand manufacture of dry over the wet concretes. This is due to the extra cost of the ramming required. Table III. shows that there is but very little increase in strength of the 40 per cent, concretes as compared to the 33 per cent. This may possibly be explained by the fact that in the 33 per cent, specimens the mortar did not entirely fill the voids in the stone; the stones therefore had direct bearing on each other, while in the 124 COMPRESSIVE PROPERTIES. [Ch. VI. 40 per cent, concrete the voids were just about rilled; the strength of the mortar itself in that case had less influence than the direct bearing of the stones on each other in the first instance. Mr. Rafter's method of determining the proportions of the in- gredients in the mixture is open to criticism. The densest con- crete is formed when the sand grains fill as many voids as pos- sible in the stone, and the cement grains then fill as many as possible of the remaining voids in the stone-sand mixture. This is different from first filling the voids in the sand with cement and then the voids in the stone with mortar. In the latter case TABLE IV. Brand of Cement Cement to Sand by Measure Percentage of Mixed Mortar to Broken Stone Ultimate Crushing Strength in Lbs. per Sq. In. Waj Say rland Portland :2 :3 :4 :6 :2 :I :2 :3 :4 :5 :6 :2 33^ 42 % 41% 41% W% 41% 41% 41% 41% 41% 41% 3154 2454 1720 1363 143 1 4381 2409 2978 1890 1542 1132 1087 729 2550 or's Natural the voids in the sand will usually be found to be greater than the sum of the voids in the stone-sand mixture. Table IV. is taken from the Report of the State Engineer of New York for 1894, and records experiments which were made by Mr. George W. Rafter previous to those just tabulated. These tests were made on 174 concrete cubes of one cubic foot each whose average age was three months. The stone which was used was hard quarry stone, broken to pass a two-inch ring and was washed clean. Each result shown is an average obtained from two to six specimens. Some of the blocks were placed in water after the final set had taken place. The result obtained from such blocks was averaged in with others in the table, it being found almost uniformly, however, that the ones which Art. 22.] ULTIMATE COMPRESSIVE RESISTANCE. 125 hardened in water, as compared to those which set in air, were very slightly stronger. In these experiments Mr. Rafter also expressed the ratios between the materials by a relation between the broken stone and the mixed mortar, having in mind that the mortar should more than fill the voids in the stone; this explains column three of the table. Table V. is taken from the Watertown Arsenal Report for TABLE V. Composition Ult. Strength in Lbs. per Sq. In. at the Age of Cement Sand Gravel Stone 30 Days 7 Months 1 Year I IX 4 1448 2213 2917 I 3 ? 1 A 1024 1987 2076 I 2 3 4 1096 2180 2094 I 2 7 746 1633 1792 I 2^ 8 739 1540 1448 1901, and shows the ultimate compressive resistance, at various ages, of 12-inch concrete cubes made from one brand of cement. Each result shown is an average of three tests. It will be seen that this concrete did not gain in strength after seven months. Tables VI. and VII. are taken from the same Report; the for- mer shows the ultimate crushing strength of concrete prisms TABLE VI. Composition Number of Ultimate Crushing Specimens Tested Strength in Lbs. per Sq. In. Cement Sand Stone I 2^ /4 l /2 In. to 2 In. Diam. 1 1 Pebbles / 8 2326 I 1 l /z f 4 % In. to iy z In. Diam. "1 1 Gravel J 6 3363 I V/2 f 41 In. to 2^ In. Diam. \ \ Hard Trap Rock J 6 3886 6x6x36 inches in length, pressed on their ends, the average age being about 33 days. The results show that the same ratio of cement to aggregate, but with different sizes of stone, may fur- nish entirely different balancing of the mixture, and may thus affect directly the ultimate crushing strength. Table VII. shows the ultimate crushing resistance of 2-inch 126 COMPRESS1VE PROPERTIES. [Ch. VI. cubes made of various brands of neat cement tested at various ages. Each value is a mean of from five to six specimens, all of which set and hardened in the air. The following series of compression tests (Table VIII.) on cement and mortar bricks, 9 inches x 4^ inches x 3 inches, is re- TABLE VII. Age in Days Ultimate Compressive Strength in Lbs. per Sq. In. Storm King Portland Alsen Portland Lehigh Portland Hoffman Rosendale Norton Rosendale Potomac Rosendale 7 I4-... 30.... 577 1400 1820 2160 1140 3980 3830 4170 4540 5210 5760 261 543 676 1010 225 476 609 878 145 403 590 1010 corded by John Grant in the Proceedings of the Institution of Civil Engineers, Vol. XXXII. , page 288. Ten specimens were prepared from each mixture, the composition being as shown in the table; five were allowed to harden in air and five in water, the age when tested being one year. The results as published are expressed in tons, and in reducing the figures it was assumed TABLE VIII. Crushing Resistance in Lbs. per Sq. In. Left in Cement : Sand Air Water N eat 5370 7350 !! 4580 4620 I2 .... 3880 3170 1-3 2980 1470 1.4 2420 1 160 !* 2070 835 1-6 1680 622 1 .7 .... 1600 584 j.g 1070 453 I.Q. . 970 412 T.fO 855 312 that the ton of 2,240 pounds was meant. The specimens were either rammed or pressed by hydraulic press at the time of making. Grant also made a series of tests (Table IX.) on concrete blocks, some of which set in air and were so kept for one year, Art. 22.] ULTIMATE COMPRESSIVE RESISTANCE. 127 and some of which set and were kept in water for the same period of time. The blocks were either 12 or 6 inch cubes, but only TABLE IX. Proportions of Cement to Sand 12-Inch Cubes 6-Inch Cubes Crushing Resistance in Lbs. per Sq. In. Kept in Air Kept in Water Kept in Air Kept in Water i 2660 2490 1800 1690 1550 1420 1250 1 180 1060 745 2360 2680 1870 1870 1520 1270 1030 840 750 625 2080 2150 2210 1740 2210 1220 990 840 680 625 2 2320 1760 1600 1380 1250 1160 950 840 760 3 4 ...... 5 . . 6 .7 8 j.q iio those cubes in which the material was pressed or rammed in the moulds are here considered. It appears that each figure is the average of two tests, but the TABLE X. Brand of Cement Composition Age Ult. Resist, in Lbs. per Sq. In. Cement Sand Broken Stone Years Months Alpha Portland ! 2* 4906 " " .... I 2 4 ^ In. Trap 3187 " .... I 3 6 2070 " " .... I 4 8 1499 " " .... I 5 10 949 " " .... I 6 12 791 " " .... I 2 1 Trap / 2 2789 I 2 4 < r > 2 2549 " I 2 |_ i rap J 4 iy z In. Trap 2 2466 " " .... I 2 7 I 2 2406 I 2 f I*/* to 3 In.l 4 1 Pebbles / I 2 3589 " " .... I 2 4 { Brok'nB 2 rickJ I 2 3241 " " .... I 3 6 I I 2545 " .... I 4 I I 1446 *Granite dust. composition of the concrete is not clearly explained; the aggre- gate is called ballast and sand. The tables are inserted on ac- 128 COMPRESSIVE PROPERTIES. [Ch. VI. count of the interest attached to them, for the experiments were made in 1867. Table X. is taken from the Watertown Arsenal Report for the TABLE XI. Parts by Weight of Sand to Cement Ultimate Crushing Resistance per Sq. In. 1:1 l:l 1:2 I:2 1:3 l:3 1:4 II330 10390 9520 8110 6140 6280 5230 year 1901, and shows the ultimate crushing resistance of 12 inch cubes, composed of various proportions of cement, sand and broken stone. TABLE XII. Brand of Cement Percentage of Water Compressive Strength in Lbs. per Sq. In. at an Age of 7 Days 1 Month 3 Months Alpha Portland- ... 25 25 26.8 18 22^ 25 30 25 29.2 26.7 26.7 18 28^ 18 35.4 38.7 36.2 41.2 38.7 39.6 35-8 39.2 6010 3490 4280 5780 4620 5560 5030 5630 3510 2750 2110 3860 1300 3050 356 620 464 566 407 472 750 423 7340 5370 5590 5990 5180 5980 5620 6640 4940 4030 2970 3970 1790 3470 1090 1130 790 1020 1090 880 1360 840 8580 5870 6310 6980 5930 7730 6810 7630 5510 4660 3430 4490 2110 4470 1530 1560 1230 1420 1440 1570 2220 mo Atlas " Lehigh " Star Portland a a Whitehall Portland Alsen " Silica Cement Bonneville Improved Natural Newark & Rosendale Natural Obelisk " Potomac " Table XL gives the values of the compressive resistance of ce- ment mortar cubes; the tests were made for the United States Engineering Corps and are recorded in the Watertown Arsenal Art. 22.] ULTIMATE COMPRESSOR RESISTANCE. 129 Report for 1902. The cubes were six-inch, of Atlas Portland cement, and the sand used was natural, 43.62 per cent, passing the No. 30 sieve. The cubes were each kept three months in dry air, fifteen days in water at 65 degrees Fahr., and then in air until the date of crushing, almost two and a half years after making. The compressed surfaces were faced with plaster of Paris. The rapid decrease in the ultimate crushing resistance as the per- centage of sand in the mixture increases is worthy of note. These tests are inserted on account of the extraordinary com- pressive strengths attained. The age of the specimens hardly accounts for this. Table XII., which is taken from the same re- port, shows the ultimate crushing strength of four-inch cubes of neat cement with various brands of Portland and natural cements. Each result is a mean of from four to five speci- TABLE XIII. Ultimate Crushing Strength in Lbs. per Sq. In. With Fine Sand With Coarse, Sharp Sand 1595 1 185 985 1825 2145 1 102 Selected Stone, Containing Some Mica. . mens. All the specimens set in air. In not one of these tests did the ultimate crushing resistance approach that shown in Table XL Table XIII. gives the crushing strength of concrete composed of one part Portland cement, three parts sand and five parts stone, in eight-inch cubes, as reported by T. S. Clark in Engi- neering News of July 24, 1902. The table is given for the pur- pose of showing that different crushing strengths may be attained by concrete with different classes of stone. The cubes were kept in air twenty-four hours and in water five months before being tested. The three kinds of stone used were standard limestone, a stone containing a large amount of mica and which had been rejected for use, and a better quality of this rejected stone con- taining less mica. It will be seen that the quality of both the sand and the stone bears intimate relation to the final crushing 130 COMPRESSIVE PROPERTIES. [Ch. VI. strength, and the rather vague opinion that a calcareous stone is better than other kinds is to a certain extent corroborated. Setting Under Water Table XIV. is taken from the Report of the Watertown Arsenal for 1902, and furnishes comparative crushing tests on mortars which were allowed to set both in air and in water. The majority of the specimens were two-inch cubes; larger size cubes are noted. The specimens which were placed in water were allowed to set first one day in air, and each result is an average of from four to five specimens. It will be seen that almost uniformly those specimens which set under water attained the greater compressive strength. The table only shows results for one brand of cement, but in all seven brands TABLE XIV. Brand of Cement Composition Age in Days Compress- ive Strength in Lbs. per Sq. In. Remarks Cement Sand Water Per Ct. Air Water Atlas I I I I I I I I I I I 32.0 32.0 32.0 32.0 32.0 32.0 32.0 32.0 33.7 33.7 33.7 33.7 32.0 32.0 7 I 30 I 92 I 93 I 92 I 92 I 183 I 6 29 2540 2580 3010 3470 3390 4550 4100 6590 3555 5000 3805 5630 3370 4800 3 In. Cubes 1 3 In. Cubes 4 In. Cubes 4 In. Cubes 6 In. Cubes 6 In. Cubes to W %* B z -ill 38 38.- 3T 91 92 91 91 182 were tested, for neat, 1:1 and 1:3 mixtures. All the tests furnish similar results. These results do not corroborate those of Grant, previously recorded, in which the specimens under water were almost in- variably weaker. Table XIV., taken in connection with Mr. Rafter's tests, indicates, however, that mortars and concretes kept damp or under water are in general the stronger. The latter is the author's opinion. Wet or Dry Concretes Table XV. shows results obtained from experiments made as thesis work by J. W. Sussex, published Art. 22.] ULTIMATE COMPRESS1VE RESISTANCE. 131 in the "Technograph" of the University of Illinois for 1903. The experiments were made to determine the relative strength of wet and dry concretes. The tests were made on forty-five six-inch cubes mixed with three different percentages of water and broken at the ages of seven days, one month and three months. The concrete was composed of one volume of Portland cement, three TABLE XV. Age Crushing Strength in Lbs. per Sq. In. Dry Medium Wet Lightly Tamped Heavily Tamped Lightly Tamped Heavily Tamped 7 Days 1200 1750 2500 1340 I960 2600 2280 2290 2150 1330 2560 2590 1040 2230 3040 I Month 3 Months volumes of sand containing a small percentage of fine gravel and six volumes of crushed limestone. Tests were made with th^ three degrees of plasticity noted, and also with two degrees of tamping light and hard. Each result shown is an average of three tests. At the end of three months it will be seen that the wet concretes furnished the greatest ultimate resistance, although TABLE XVI. Kind of Cement and Sand Age in Days Ultimate Compressive Resistance in Lbs. per Sq. In. When Mixed Dry Medium Wet Portland ; Natural ; Portland ; Natural ; Bar Sand 7 7 7 7 28 28 28 28 1330 1650 258 427 2560 2360 481 708 1230 1500 292 253 1890 2470 507 470 1245 1450 328 138 1320 1540 334 282 White Bar White Bar White Bar .... White at the end of seven days and one month the medium specimens furnished the highest ultimate resistance, whether tamped lightly or hard. T. L. Doyle and E. R. Justice record in "Engineering News" for July 30, 1903, the ultimate compressive resistances of six-inch cubes made with both Alpha Portland and Hoffman natural ce- 132 COMPRESSIVE PROPERTIES. [Ch. VI. ments and mixed to three different consistencies. Two kinds of sand, white sand and bar sand, were used, and the stone was one- inch trap rock. The ages of the specimens were seven and twenty-eight days. Table XVI. shows the results obtained, each figure being an average of five tests. It will be seen that in all cases the dry specimens furnished higher ultimate resistances than either of the Other two kinds. The age of the specimens is not sufficient to show whether the wet mixtures would not ulti- mately be stronger than the dry. High Temperatures The effect of high temperatures on ce- ment mixtures has not been studied to any extent as yet, but Table XVIL, which is taken from the Watertown Arsenal Re- port for 1902, shows the variation in the ultimate crushing strength of four-inch cubes after they had been heated to differ- ent temperatures. The age of the cubes was, in most cases, TABLE XVII. Composition Ultimate Crushing Strength in Lbs. per Sq. In. After Heating to Cement Sand Not Heated 200 F. 300 F. 400 F. 500 F. 600 F. 700 F. 800 F. 900 F. 1 Alpha* 1 1 9167 12480 5017 1867 3873 538 2170 8830 14447 1657 4043 491 2067 7920 13853 1876 3523 432 1953 9190 13767 1966 3810 9400 13910 1603 4133 471 2063 9333 12787 4313 1453 4013 8217 12130 3483 1496 3957 381 2240 8060 9985 4280 1400 3900 6060 1185 2990 317 1767 1 Alphat 1 Dyckerhoff* 1 Mankato* 1 " t 1 " * 1 " t *Cubes set in air before heating. tCubes set in water before heating. slightly over one year, and they were tested, usually, about thirty days after having been heated. Each result is an average of three tests. It will be seen that there is practically no decrease in strength, even up to a temperature of 600 degrees Fahr., but a decrease is shown for higher temperatures. Art. 23. Compressive Properties. Conclusions. It has seemed to the author that the graphical method used in determining the straight-line formula for long columns was the most rational way to combine the experiments which have been recorded in the preceding pages. Two sets of straight-line dia- Art. 23.] ULTIMATE COMPRESSIVE RESISTANCE. 133 grams have, therefore, been prepared, one showing the relation between ultimate compressive stress and the compressive coeffi- cient of elasticity, and the other showing the relation between ultimate compressive resistance and the parts of cement to aggre- gate in the mixture. The question of age has been entirely ex- cluded, since very little material under three months of age was used, and it has previously been shown that mixtures do not gain appreciably in strength after that period. The figures otherwise f / g ^ 1 * /" 3 ^ "/ M ? "/"'' 1 03 / ^ / z< a ^ - X /- ^ 7 B A 1 , 1 / -3 ^ *o Q 000 000 y 1 6 i 10 IX) 2( 100 3000 Ultimate Crushing Resistance Lbs. per Sq. In. FIG. l.-FROM BACH'S TESTS. TABLE I., ART. 21. need but little explanation ; each represents graphically one of the tables which have been recorded in the previous pages. Tables III., IV., V. and VI. of Art. 21 have not been included, since the values there shown are not the true or elastic coefficients ; Table VII. has not been included on account of the limited number of tests. There has also been included in Figure 8 a summary of the tests made at the Watertown Arsenal in 1899 on twelve-inch con- crete cubes varying in age from one to six months. The tests 134 COMPRESSIVE PROPERTIES. [Ch. VI. were made with five well known brands of Portland cement, with various mixtures of sand and stone. The tests made by Messrs. Derleth and Hawkesworth were not sufficient in number to enable their results to be included in a figure. : 1,000,000 * g 8,000,000 z 1000 2000 Ultimate Crushing Resistance Lbs. per sq. in. FIG. 2. FROM BACH'S TESTS. TABLE II., ART. 21. Figures i to 9 represent the variation of the coefficient of elas- ticity with the variation of the ultimate compressive resistance. The equations of the lines there shown are as follows, / represent- ing the ultimate compressive resistance: Ei, 520,000+ 1 cjoo/ (Bach) Fig. I. E o +1820^ (Bach) Fig. 2. = o -\-iooop Fig. 3. = o +I090/ Fig. 4. E o +i6oo/ (Hatt) Fig. 5. E o +i 57o/ (Austrian) Fig. 6. = 62,000-j- 794/ (Rafter) Fig. 7. E o +1150^ Fig. 8. E= o +IOOO/. . . . (McCaustland) Fig. 9. Art. 23.] ULTIMATE COMPRESSIVE RESISTANCE. 135 Averaging the nine different numerical expressions which these figures furnish, it will be found that an average value of the compressive coefficient of elasticity may be expressed by the equation ^=175,000+1325^, in which p represents the ultimate compressive resistance. The constant quantity, 175,000, is negligible in relation to the other and may be neglected with very little error, so that a simpler form of expression is the fol- lowing: Coefficient of Elasticity in Lbs. per sq. ii i ! i / w fyr / / X 2000 3000 TJlt. Comp. Strength in Lbs. per sq. in. FIG. 3.-EASTERN EXPANDED METAL CO.'S TESTS. FROM TABLE VII., ART. 21. The constant 175,000 may be neglected with all the more safety since it depends mainly on one series of experiments, viz., Professor Bach's, and in these experiments the coeffi- cients are undoubtedly higher than in other cases, on account of the repeated application of every load. In a similar way, Figures 10 to 15 represent the variation of the ultimate crushing resistance with the variation in the ratio of the cement to aggregate; the following equations are then ob- tained: /=475O 250 m ................ (Bach) Fig. 10. ^=5140 2380* ............... (Rafter) Fig. n. /=4578 289 m ............... (Rafter) Fig. 12. ^=3835 2070*. .(Watertown, Table V.) Fig. 13. ^=3440 280 m ......... (McCaustland) Fig. 14. ^=5035 2i^m ...... (Watertown, 1899) Fig. 15. Henby's tests (page 112) in addition furnish an equation of ^=4350 258^. The average of all these equations furnishes /=4449 2470*, in which / equals the ultimate crushing resistance and m the 136 COMPRESSIVE PROPERTIES. [Ch. VI. 9,000,000 * X X x. C 7,OW,WU t X XV ,5 6,000,000 a / / -s & / - *V7 / 1,000,000 / 1000 2000 3000 4000 6000 6000 Ult. Comp. Strength in Lbs. per sq. in. FIG. 4. WATERTOWN, 1898, TESTS. TABLE VIII., ART. 21. 5,000,000 5,000,000 ? J 4,000,000 .3 | 3,000,000 1 P o 2,000,000 ^ 3 i 01,000,000 / :/ / 3 /:' / / / 1000 2000 3000 1000 Ult. Comp. Strength in Lbs. per sq. in. FIG. 5. HATT'S TESTS.-TABLES VI. AND VII., PAGES 83 AND 84. .55,000,000 g I 4,000,000 3 B X / M / /x X 1 2 33,000,000 22,000,000 B .2 i 1,000,000 I , ? y // y / / / 1000 2000 TJlt. Comp. Strength Lbs. per sq. in. FIG. 6. AUSTRIAN SOCIETY'S TESTS.-TABLE IX. PAGE 96. Art. 23.] ULTIMATE COMPRESS1VE RESISTANCE. 137 teriiiined for Intensities of Stress 100-GOO Lbs. per Sq. In. Coefficient of Elasticity in Ibs. per sq. in. 1 X 3,W 10,00 1 ^ / X X s * f ' x - / JJ 4 i> t I 10 1000 2000 3000 iUOO \ \L Ult. Comp. Strength in Lbs. per sq. in. FIG. 9. McCAUSTLAND'S TESTS. FROM TABLE X., ART. 21. 1UOU 2000 3000 1000 Ult. Crush. Resist, in Lbs. per sq. in. FIG. lO.-BACH'S 1896 TESTS, ON 10-IN. CYLINDERS, 10 INS. HIGH. TABLE II., ART. 21. the relation between the cement to the aggregate. Another method of dealing with this question has, however, been studied by R. Feret in Europe, and is being studied by William B. Fuller in America; the latter's results are not yet published. This ' Parts of Aggregate to 1 of Cement otow-o OCCIOH^ o So < X> x . > \* ^ f V S -J> <: x \ ^! \ \ X S ^v s ) 1000 2000 3000 1000 5000 Ult. Crush. Resist, in Lbs. per Sq.In. Approximately: Parts of (Sand + Stone) to Cement 0. S 5 > s *X, fix, N^ \T \ x FIG. 11. RAFTER'S TESTS. FROM TABLE I., ART. 22. 1000 2000 3000 loo Ult. Crush. Resist, in Lbs. per sq. in. FIG. 12. RAFTER'S TESTS. FROM TABLE IV., ART. 22. method considers not merely the relation between the cement and the aggregate, but also the balancing of the entire mixture. Art. 23.] ULTIMATE COMPRESSIVE RESISTANCE. 139 R. Feret, for instance, has shown that the ultimate resistance to compression of 1 13 mortar blocks, in which the sand was com- posed of varying proportions of the three graded sizes of sand which have been previously noted in some of his tests, varies from some minimum value to a value perhaps three times as large, depending merely on the proportions of the various sizes 1000 2000 3000 Ult. Crush. Resist, in Lbs. per sq. in. FiG. 13. WATERTOWN TESTS. FROM TABLE V., ART. 22. 1000 2000 3000 MM Ult. Crush. Strength in Lbs. per sq. in. FIG 14. McCAUSTLAND'S TESTS. FROM TABLE X., ART. 21. of sand. This variation in strength is in proportion to the varia- tion of the solid material in the mass, the maximum value being obtained when the medium sized grains are eliminated. This was found to hold true no matter under what conditions the mor- Parts of Sand and Stone to Cement e o c, S gfj v^ Alsen "^-, ^ l^*^ >< Say or's Gei man ia-^ ^^^ v; ^"^, ^^_ / = 5 035- 14 n - ^ ^ ^; ^ as x ^ ^ ^C r AH ha ""^-^ fe Si" -x ^ ^ : ^-. .^ -*- -K 00 2000 3000 1000 6000 Crushing Resistance in Lbs. per sq. in. FIG. 15. WATERTOWN, 1899, TESTS ON FIVE WELL-KNOWN BRANDS OF PORTLAND CEMENTS. tars were allowed to set and harden. Feret cites numerous ex- amples, but Figures 16 and 17 are characteristic of all his experi- ments. In this case the percentages of the various sizes of sand grains are represented on the perpendiculars erected on the sides 140 COMPRESSIVE PROPERTIES. [Ch. VI. of an equilateral triangle, a system of co-ordination which is familiar. The ultimate crushing resistance of the various mor- tars is marked at the proper points within the triangle ; with these points as guides, contour lines, representing mixtures having an equal ultimate resistance, are then drawn. Figure 16 shows very clearly how the strength of the mixture increases as the medium sized grains are eliminated. Figure 17 was drawn in a similar manner, but represents the relation of solid matter to the total cubic contents in a freshly mixed mortar. The close similarity between these two figures 1:3 Mortar, 9 months in air, 3 months in sea water. 1:3 Mortar (freshly mixed) 1420 2130 FIG. 17. G 4400 F Note: The letters G, M, F, indicate large, medium and fine grains of sand. FIG - 16 - Showing Proportion of Solid Matter to Total Cubic Showing the Ultimate Compressive Resistances, Contents of Mortars Mixed with Differing Per- in Lbs. per Sq. In., of Mortars, Mixed with centages of Various Sized Sand. Differing Percentages of Various Sized Sand. is noticeable and checks Feret's conclusion that the .ultimate compressive resistance varies in proportion to the solid matter in a specimen. It will require much work of this character in order that some definite conclusions may be obtained. Considering in general all the tests which have been tabulated, it may be concluded : First That concretes in compression have a point that may be termed the elastic limit, and its value is between one-half and two-thirds of the ultimate resistance. Second That up to this elastic limit the compressive coeffi- cient of elasticity may have in general a value of 1325 times the ultimate crushing resistance. Art. 23.] ULTIMATE COMPRESSIVE RESISTANCE. 1 4 1 Third That, within certain limits, the ultimate crushing re- sistance for cement mixtures over three months old may be ex- pressed by the equation ^-4449 247 m, in which / represents the ultimate crushing intensity and m the number of parts of aggregate to one part of cement. Fourth That concretes mixed dry and thoroughly tamped are slightly stronger than those mixed wet; but in actual construc- tion work other considerations besides the slight increase in strength may offset this advantage which appears in favor of the dry concretes. Fifth That concretes hardening under water attain slightly greater ultimate resistance than the same mixtures hardening in air. Sixth That temperatures below 600 degrees Fahr. do not af- fect adversely the strength of concretes. It has been shown that there is no appreciable increase in strength after the material is three months old. Therefore, if it is desired that a concrete should possess ultimately a high value of the coefficient of elasticity, it is possible to obtain it only by using richer mixtures. And, finally, it appears that the values of the coefficients of elasticity for tension and compression are practically equal. CHAPTER VII. FLEXURAL PROPERTIES. Art. 24. The Theory of Flexure as Applied to Concrete. Careful consideration must be given to the theory of flexure in connection with concrete beams in flexure. In determining the coefficient of elasticity for flexure two conditions in the theory of flexure are usually assumed, viz., that the coefficients of elasticity for direct tension and direct compression are equal, and that they are constant. This is rarely, if ever, the case ; but in order to de- termine the deflections of beams it is necessary to make these as- sumptions in order to determine the empirical value for the flex- ural coefficient of elasticity. It has been shown that neither of these assumptions holds precisely for concrete, and that, therefore, FIG. 1. the value of the coefficient of elasticity which may be deduced for bending has no reasonable basis; but it seems to be perfectly proper to determine it as an empirical quantity, since it is a pos- sible way in which to determine in advance the deflection of these concrete beams. The quantity, which is usually called the modulus of rupture, or the extreme fib're stress at rupture, is probably as correct a quantity for concrete as in the case of any other material, even such as steel or wrought iron. This modulus of rupture is de- . Art. 24.] THE THEORY OF FLEXURE. 143 termined from the theory of flexure, on the assumption that the stress in any fibre at a section of the beam varies directly as the distance from the neutral axis of the beam. At the time of rup- ture this does not hold true for steel, for wood, for concrete or for any substance whatsoever. This value, therefore, is not cor- rect for any material, but it is of the greatest value in the design of beams. The writer has discussed the analytic treatment of concrete beams fully in another place,* and it is therefore unnecessary to repeat that treatment here ; but the following analysis for finding the deflection of a beam composed of a material having unequal coefficients of elasticity for tension and compression is of con- siderable interest on account of the simplicity of the final equa- tions. Let Figure i represent the cross section of a beam of such a material, NN representing the neutral axis as determined in some possible way. The following notation will be used : /=intensity of stress at units distance from NN; 2=the distance of any elementary area dA, from NN; =the unit strain corresponding to/; EI and .fic^the coefficients of elasticity of the materials for ten- sion and compression respectively; A t and ^4 C the areas at any section which carry tension and compression respectively; It and / c =the moments of inertia of A t and A c respectively about NN as an axis. From the general theory of flexure, the moment of the stress acting on the differential area dA, distant z from NN, about that axis is : z . p . dA . z=fji . z*. dA. The differential internal moment, integrated over the entire section, becomes equal to M, the external moment: /d, /~fy ^i z\dA c +E t .p\ z\dA t . . . (i) fj / O /.f* . ..... (2) * Trans. Am. Soc. C. ., Dec., 1903. 144 FLEXURAL PROPERTIES. [Ch. VII. But ft=z =: , if p represents the radius of curvature of the P do? neutral axis; therefore dx i M or, - - ....... (3) do? E c l c +E t l t If c=t, then -- = where / represents the moment of do? El inertia of the entire section about NN. By the aid of Eq. 3, it would be possible to determine both E t and EC, by means of the deflections found under two different loads, provided the position of the neutral axis could be deter- mined. To determine the neutral axis it becomes necessary to know in advance, or to assume, both Et and E c . If assumed, the correctness of these values must then afterward be checked by means of the deflections. To pass through such a procedure becomes a tedious task, more especially, as has been shown, that E t and E c for concrete do not differ greatly, if at all. In all his work the author there- fore has calculated the apparent flexural coefficient of elasticity, assuming E t equal to E c . Since concrete beams show permanent deflections under com- paratively light loads, it also becomes necessary, as in the case of pure compression, to distinguish between the elastic coefficient and one calculated from the total strains only. Art. 25. Flexural Coefficient of Elasticity. Table I. and Figure i are taken from a paper by the author and recorded in the Transactions of the American Society of Civil En- gineers, 1903. The table shows the values of the flexural coeffi- cient of elasticity and of the extreme fibre stress for concrete beams 4x4 inches X36 inches span, tested to destruction by a centre load. The table is of interest on account of the age of the specimens tested, which was seven and one-third years. The mixtures used are given in the table; the sand was Cow Bay, L. I., Art. 25.] FLEXURAL COEFFICIENT OF ELASTICITY. 145 and the gravel was rounded, varying in diameter from \ to 2.\ inches ; it was well washed before being used. Figure i shows the deflections at the centres of the different specimens. The deflections of each bar are represented by two Load at Center, in Pounds Load at Center, in Pounds iiiiiiiiiiiiiliil 111111111 \ 600 500 400 300 200 100 1100 1000 900) 800 700 600 500 400 :',00 200 100 F "'i RESULTS OF TESTS OF CONCRETE AND MORTAR BEAMS Corapositiou of Bars or Beams. A = 1 Aalborg cement, 2 sand and 4 gravel B = 1 Atlas cement and 3 sand. C^= 1 Alsen cement, 3 sand and 5 gravel. D = 1 Alsen cement and 2 sand. The subscript figures refer to the tests in Table No.l. B '/ \ r i / / / /> J q / / /* / / ^ ^ ^ All Bars 4.12 ins. high and 4.06 ins. *ide. Span for = 36 ins. Span for Cj= 16 ina. Span for Oi= 16 ins. / i // /' *w. / / ; I , ; I I / / 1 1 / / 2 / H / j 3 2 r/ 3 1 / ? / a // ? j > 1 / 1 y // if 1 X J / l / ' / t / x' I / / // s* ^ i , / { ^ & k '/ ^ / z. All B, ai 1 rs 4.12 ina. high d 4 ins. wide. Q for B = 30 ins. nforB^lCins. n-teBgieisfe. 1 I* & 2 * All Bars 4. 10 ins. high and 4.15 'ins. wide. Span for D= 36 Ins. Span for D!=-- 16 ins. Span for D?= 16 ins. k X ^ ^ : i ^ 1 1 1 0.006 0.010 0.014 0.018 0.022 Deflection at Center, in Inches FIG. 1. 0.002 O.OOG 0.010 0.011 0.018 Deflection at Center, in Inches curves lettered with the same subscript. The curve to the left shows the set when the load at that given point was entirely re- moved. It was found that the true or elastic coefficients of elas- 146 FLEXURAL PROPERTIES. [Ch.VII. ticity, calculated in the way which has already been explained, gave constant values for the coefficient for any one specimen al- most up to the breaking load. The table shows that neither the coefficient nor the ultimate strength shows any remarkable in- TABLE I. Bar Age in Years Span in Inches Section of Bar in Inches Coefficient of Elasticity in Lbs. per Sq. In. Extreme Fibre Stress in Lbs. per Sq. In. Depth Width A 7 4 Of. 419 A Ofi A,.... 7.4 16 4.12 4.06 1,591,000 278 A,.... 7.4 16 4.12 4.06 1,102,000 315 B 7 36 4 12 4 00 2 122 000 606- B!,... 7 16 4.12 4.00 2,440,000 636 B ? .... 7 16 4.12 4.00 1,220,000 530 C.... 7 36 4.12 4.05 1,315,000 247 C,.... 7 16 4.12 4.05 387,000 229 c ? .... 7 16 4.12 4.05 1,023,000 208 D.... 7.3 36 4.10 4.15 1,165,000 294 D,.... 7.3 16 4.10 4.15 597,000 415 D 2 .... 7.3 16 4.10 4.15 597,000 346 Bars A=l Aalborg cement, 2 sand and 4 gravel. " B=l Atlas cement and 3 sand. " C=l Alsen cement, 3 sand and 5 gravel. " D=l Alsen cement and 2 sand. crease for very old specimens. They may increase for beams less than one year old, but for bars of the age shown in the table neither of the constants shows any material increase. In discussing these experiments Professor E. J. McCaustland TABLE II. Specimen No. Brand Coefficient of Elasticity in Lbs. per Sq. In. Extreme Fibre Stress in Lbs. per Sq. In. C" * \ \s 571 357 238 190 623 618 452 2 1,384,000 600,000 460,000 1,219,000 1,582,000 920,000 7 < ,, 4 . . < tt ^ . . Empire Portland- . . 6 7 records in the same Transactions some experiments made by him on neat cement beams 2x2f inches deep X24 inches span, one year old, tested by centre loads. Table II. shows results of the constants determined in the same Art. 25.] FLEXURAL COEFFICIENT OF ELASTICITY. 147 manner as in the preceding table. It is to be noted that the co- efficient of elasticity increases with the increase of the extreme fibre stress. The stress-strain curves shown by Professor Mc- Caustland are exactly similar to those of Figure I and need not be reproduced. In the same discussion Professor G. Lanza records results of experiments on one plain and twenty-six reinforced concrete beams 8x12 inches xn foot span. At this point it is only necessary to introduce the results of the neat specimen, since the others must be analyzed by a theory of flexure, which is not a part of the present discussion. For the plain concrete beam, whose age was forty days, the value of the extreme fibre stress was found to be 170 pounds per square inch, the composition of the concrete being one part Port- land cement, three parts sand, four parts of trap rock passing a one-inch ring sieve, and two parts 01 the same rock passing a -J- inch ring sieve, all proportions being measured by volume. Jules A. Coelos and R. A. W. Carleton, graduating students of the Civil Engineering course at Columbia University, 1904, per- formed during the winter of 1903-04 an extended series of tests on plain and reinforced concrete beams 6x6 inches in cross sec- tion, tested on a span of 36 inches. The materials which were used were exactly the same as those used in the direct tension and compression tests recorded previously on page 84 in the ex- periments of Messrs. Derleth and Hawkesworth, and need no further explanation. The loading was either a single centre loading or was placed at two points symmetrically distant from the centre of the span. The deflections were read in the centre of the beam in the same manner as the tests which were recorded in Table L, and the co- efficient of elasticity was calculated as the true coefficient. Only the plain concrete beams are given in Table III. Tests of the ultimate shearing resistance of the bars were made after they had been broken, and these values are also given in the table. W. L. Brown has recorded in the Proceedings of the Institu- tion of Civil Engineers, 1898-1899, a series of tests on cross 148 FLEXURAL PROPERTIES. [Ch.VII. bending of neat cement and mortar mixtures. The size of the specimens was always 2 inches deep by i inch wide by 30 inches span. Three kinds of sand were used a good ordinary coarse red sand, well washed; a poor argillaceous fine sand, unwashed, and a fine Laxey gravel, which was really a very coarse sand. Two sets of experiments were made, using two brands of ce- ment. The deflections were measured at the centre of the beams, the loads being placed at the same points. The coefficients of elasticity were determined from the formula of the common the- ory of flexure and calculated between the extreme limits of stress obtained. The breaking load varied from a centre load of 5 to 35 TABLE III. FLEXURAL TESTS ON 1:3:5 PORTLAND CEMENT CONCRETE BEAMS, 6x6x36 INCH SPAN. No. Age in Days Loading Coefficient of Elasticity in Lbs. per Sq. In. Net Fibre Stress Lbs. per Sq. In. Shearing Tests Shearing Intensity in Lbs. per Sq. In. At First Crack At Failure I 127 128 128 125 141 121 At 2 Points At Centre 1,118,900 1,002,300 1,440,900 2,161,500 1,012,500 1,205,500 170 218 189 225 148 223 180 / 118 1153 101 167 f 97 I 86 1256 1 196 1 178 1 180 f 168 1255 214 /330 1226 2 5 . 7 8 21 pounds. On account of the small sizes of the specimens and on account of some ambiguity in the methods of calculation, it has been thought better not to give here in detail the experiments themselves, but merely Mr. Brown's general conclusions: That E is greater for neat cements than for mortars; that E varies inversely with the amount of sand in a specimen; that the quality of sand affects E, but not considerably, but that age does increase E to a measurable extent. Some experiments on the coefficient of elasticity of concrete beams have been recorded by Durand-Claye in "Annales des Fonts et Chaussees," 1888, and are here shown in Table IV. Tests were made on seven bars; six were neat Portland cement II 3 Z S s 5 a Art. 26.] MODULUS OF RUPTURE IN BENDING. 149 and one was 1:2 mortar. The prisms were approximately 1.2 inches square, tested on a span of 39.4 inches; it does not appear that the sets remaining after the loads were removed were meas- ured, so that the values given in the table are not the elastic coefficients. It is seen, therefore, that the coefficient increases with the value of the extreme fibre stress, and acts, therefore, similarly to TABLE III. Composition in Parts by Weight Age When Tested How Kept Coefficient of Elasticity in Lbs. per Sq. In. Extreme Fibre Stress in Lbs. per Sq, In. Net Tensile Resistance of Similar Specimens in Lbs. per Sq. In. Cement Sand Neat I 5 to 6 Weeks 6 Months 2 Under Water In Air 3,380,000 3,370,000 2,810,000 3,410,000 3,340,000 3,860,000 3,410,000 1000 950 781 1020 923 1090 370 880 823 667 824 780 950 270 2 pure tension or compression; its value does not appear to differ greatly from that found in those cases. Art. 26. Modulus of Rupture in Bending. Table I. gives the results of flexural tests on in concrete beams, as reported by E. S. Wheeler in the Report of the Chief of Engineers, U. S. Army, for 1895, p. 2922. The specimens were all 10 inches square and 4^ feet long, broken on a 4- foot span, with a centre load. In general the bars were kept covered with moist earth, awaiting the time of breaking. The age of the beams was between six months and two years. It will be seen that there is considerable difference in the strength of those beams when the stone used was sandstone or limestone. In almost every case the limestone furnished higher values of the modulus of rupture. The tests included beams mixed with both Portland and natural cements. Figs, i and 2 are plotted from the table, the ordinates being the extreme fibre stresses of the beams and the abscissae being the ratios by volume of the aggregate (the sand and stone) to the cement. No attention was paid in 150 FLEXURAL PROPERTIES. [Ch.VII. the figures to the difference in age of the various specimens, but tests Nos. 98 to in were not plotted. A straight line was drawn 20 ; V x x * J! \ *x, N % x^ x X ^ ^ x x 2 , X X X -V ,v x * if ,?- ^^ ^ l! ^- S^ xX ' 1 \ ' ' O ri X ^ x. ^ X 5 a- x ^ ^ x 3 s " \ > X x x S a i X) 20 L-.( X) 1C 10 5( )() 00 71 K) 7 30 Extreme Fiber Stress in Ifts. per sq. in. FIG. 1. TESTS ON PORTLAND CEMENT BEAMS BY E. S. WHEELER. to average as nearly as possible the results as plotted; the equa- tion of the lines for Portland cement mixtures was found to be : * 840 37.67 and for natural cements ^=526 42.67. Using these lines as a basis, it will be seen that the greatest pos- sible modulus of rupture which can be obtained is for the neat B , x E < , 11 v s > K ~ % >. "^ = 5 ! ^ -v. si ; ^-1 "-5 Vf- Srr ' V* * * ^ y^ f\\ 2 B y ^ ^ X = ^0 v 3 oo o X x >~ * 1 ^0 100 200 300 400 500 ^ Extreme Fiber Stress in Ibs. per sq. in. FIG. 2. TESTS ON NATURAL CEMENT BEAMS BY E. S. WHEELER. cement, and is respectively 840 and 526 Ibs. per square inch for the Portland and natural. These values decrease steadily as the Art. 26.] MODULUS OF RUPTURE IN BENDING. 151 TABLE I. Proportionate Parts by Volume Kind of Stone Age When Broken Wt. per Cu. Ft. of Con- crete When Broken Extreme Fibre Stress in Lbs. per Sq. In. Cement Sand Gravel 22 1 Portland 1.24 3.0 Limestone 2 Years 153 597 23 1.67 4.0 155 551 24- ... " 1.67 4.0 ** 6 Months 155 465 25 1 Natural 1.78 4.18 Sandstone lYear 136 124 26 1.78 4.18 Limestone 148 150 27 " 1.78 4.18 " " 140 242 28 ' 2.16 4.18 Sandstone " 140 94 29 -.-. " 2.16 4.18 Limestone " 141 96 30 " 2.16 4.18 " 139 204 31 1 Portland 3.14 7.61 Sandstone and Gravel " 144 219 32 " 3.14 7.61 Limestone and Gravel " 151 239 33 " 3.14 7.61 Gravel " 150 192 34 " 3.14 7.61 Limestone and Gravel " 143 185 35 " 3.12 9.52 Gravel " 139 139 36 H 3.12 9.52 Limestone " 141 169 37 " 3.07 9.52 " " 144 283 38 " 3.08 7.61 " 148 422 39 " 3.08 6.34 M " 148 374 40 " 3.07 9.52 H " 143 285 41 " 3.08 7.61 M " 139 279 42 " 3.18 11.42 (( " 145 247 43 " 3.18 6.34 " " 140 319 44 45 1 Natural 3.18 2.30 11.42 8.23 Limestone with Screenings Gravel M 141 150 298 120 46 2.27 6.86 " 151 74 47 " 2.25 10.17 " " 146 110 '48 " 2.27 6.86 Sandstone " 146 123 49 " 2.25 10.17 " 131 74 50 " 1.87 5.33 " " 138 181 51 " 1.87 5.33 H " 139 214 52 " 1.87 5.33 " " 138 175 53 1 Portland 4.16 13.9 M 133 177 54 4.16 13.9 " " 132 213 55 " 4.16 13.9 " " 132 204 56 57 1 Natural 1.50 1.50 5.38 5.38 M (( " 140 136 194 210 58-. -. M 1.50 5.38 " 59 60 1 Portland 5.2 5.2 13.2 13.2 M H 135 141 193 221 61 5.2 13.2 " 62 1 Natural 1.12 4.15 " " 140 275 63 1.12 4.15 M M 137 306 64--.- " 1.12 4.15 M " 65 1 Portland 2.1 11.1 ii " 132 255 66 " 2.1 11.1 " " 134 269 67 " 2.1 11.1 " " 68 " 4.16 12.4 " 20 Months 357 69 " 4.16 12.4 " " . 288 70 " 3.12 12.4 " " 297 71 " 3.12 12.4 u " 351 72 " 2.08 12.4 " " 326 73 " 2.08 12.4 " " 345 74 " 1.04 12.4 " " 310 75 " 1.04 12.4 " " 288 76 " 0.00 2.09 " 19 Months 582 77 " 0.00 2.09 " 605 78 " 1.04 3.76 " " 652 79 " 1.04 3.76 " H 727 80 " 2.08 5.57 " " 488 81 " 2.08 5.57 II " 588 82 " 3.12 7.71 " " 513 83 " 3.12 7.71 " " 465 84 " 4.16 9.86 " " 376 85 " 4.16 9.86 " " 382 152 FLEXURAL PROPERTIES. [Ch. VII. TABLE \. Continued. Proportionate Parts by Volume Kind of Stone Age When Broken Wt, per Cu. Ft. of Con- crete When Broken $ c o fc EW:T j=co * Cement Sand Gravel 86.. . 1 Portland 5.20 11.93 Sandstone 19 Months 285 87.- 5.20 11.93 ** 283 88-. " 6.24 13.80 " " 288 89-- JSg Days o 1 3 wQ O 81 CQcfl II Max. Mean Min. .2 1.8 30 4 640 525 442 Kept in ground. .2 .8 30 7 634 571 341 Kept in ground; 26 in. span. .2 .8 30 5 805 651 522 Kept in ground; 30 in. span. .2 .8 136 3 1249 993 730 Kept in ground all winter. .2 .8 30 14 913 689 444 T 9 Of) 00 T 19 T 700 A&n 1 . A 1.7 2.75 .5" 30 JJ 12 1 i A i 999 /OJ 851 ^DU 677 (24 hours in compressed air (at 712 Ibs. per sq. in. 1.9 2.6 30 50 924 850 590 (24 hours in compressed air (at 12 18 Ibs. per sq. in. 2. 2.4 30 30 904 731 622 (48 hours in compressed air \at 18 25 Ibs. per sq. in. 2. 2.4 30 100 900 728 523 | 2830 days in compressed (air at 2025 Ibs. per sq. in. 2.5 4. 3Yrs. 2 972 849 726 Buried in sand under sea water. 2.5 4. " I 809 Buried in fresh earth. an impalpable powder to -J inch in diameter. It will be seen that the beams mixed with stone dust give higher results than those mixed with sand. Table IV. is an abstract from the Report of the Boston Transit TABLE IV. No. of Modulus of Rupture in Lbs. Average Remarks Beams Dimension - per Sq. In. Days in Tested Max'm Mean Minimum Ground Ingredients ( Cement; 4.... 6x6x30 In. 640 525 442 28 { Coarse, clean and sharp sand; ( Gravel. 7 5.... 6x6x26 In. 6x6x30 In. 634 805 571 651 341 522 28 28 ( Cement; j Coarse, clean and sharp sand; (Trap rock, 1 in. to 2% in. f Cement; 3-... " 1249 993 730 135 j Coarse, clean and sharp sand; (Trap rock, 1 in. to 2 l /z in. (Cement; I4-... " 913 683 444 28 Coarse, clean and sharp sand; (Trap rock, 1 in. to 2^ in. 33.-.. " II2I 777 460 <2g i (Same as above, but stone dust i \ instead of sand. Commission for 1901, and records the results of tests made on concrete beams 6x6x about 30 inches in length. The propor- Art. 26.] MODULUS OF RUPTURE IN BENDING. 155 tions of the ingredients of the concrete were I Vulcanite cement, 2 sand and 4 broken stone of the character as shown in the col- umn headed "Remarks." Table V. is taken from results recorded by E. C. Clarke in Vol. XIV. of the Transactions of the American Society of Civil Engineers, and shows the modulus of rupture obtained for beams 10 inches square and about 6 feet long, which were buried in a TABLE V. Materials Modulus of Rupture in Lbs. per Sq. In. I Natural Cement : 2 Sand : *} Stone I3'7 67 176 1-4-9 146 I'6'I I 112 pit and tested when six months old. The stone used was screened pebbles, an inch or less in diameter. The modulus of rupture as calculated includes the weight of the beams. Table VI. is taken from the Report of the Boston Transit Commission for the year ending June 30, 1902, and gives values of the ultimate fibre stress of concrete beams in flexure. The cement was Vulcanite Portland. The mixing was done by hand and the beams were kept the first twenty-four hours in air and TABLE VI. CONCRETE BEAMS 6x6x30 IN., 30 DAYS OLD. Composition by Volume (Approx.) No. of Tests Size of Stone Dust Ultimate Fibre Stress in Lbs. per Sq. In. Cement Sand Stone Dust Broken Stone Max. Mean Min. I I .9 1.6 .9 2 .9 .9 2.4 2.7 3 2.7 4 4 4 4 Medium Coarse 947 846 773 862 848 784 711 806 760 704 656 759 then twenty-nine days in damp earth. The results are of interest as showing the comparative strength of mixtures with stone dust and with sand. It will be seen that those beams in which the stone dust replaced the sand were the stronger and that in no case did the use of stone dust weaken the mixture. Table VII. is taken from some tests reported by T. S. Clark, in Engineering News of July 24, 1902, and shows the relation 156 FLEXURAL PROPERTIES. [Ch. VII. between the tensile strength of ordinary tensile briquettes and the extreme fibre stress of small concrete beams 1x1x8 inches. The same cement and aggregate were used for both kinds of tests and subjected to exactly the same treatment at the time of mixing. Each result shown is an average of from two to twelve specimens. All the mixtures were kept twenty-four hours in air, and the rest of the time presumably in water, although it is not so specifically stated. It will be seen that the ratio between the ultimate fibre stress in flexure as compared to the tensile strength varies from 1.32 to 1.66. TABLE VIL Compos! ion of Sp ;cimen in Parts of Age Ult. Tensile Extreme Fibre Ratio of Cement Sand Stone Cinder in Days Strength in Lbs. per Sq. In. Stress in Lbs. per Sq. In. Tension to Bending Neat 30 809 1242 53 " 112 932 1406 .50 2^ 30 376 540 43 2^ 60 482 634 .32 2^ 112 493 679 .37 3 28 282 417 .47 3 56 328 512 .56 I 2 *>* 28 187 304 1.63 1 2 5 30 no 183 1.66 *Beams 3x3x30 inches; E. S. Wheeler records in the Report of the Chief of Engineers, U. S. Army, for 1896^ p. 2870, an interesting series of tests, show- ing the relation between ultimate resistances of cement mixtures in tension, in bending and in compression ; the compression tests will not be considered, however, since crude apparatus was em- ployed. The results from the tension and bending experiments are per- haps comparable, although the actual tension values obtained may be erroneous, on account of the use of the ordinary tensile briquette^ This statement applies similarly to the preceding table. The transverse specimens were 2x2x8 inches, broken on a 5 i -3-inch span. The specimens for the two kinds of tests were always prepared from the same batch of mortar ; each result in Table VIII. is an average of 4 to 10 breakings. It will be seen that the ratio of the extreme fibre resistance to the tensile Art. 27.] SHEARING RESISTANCE AND CONCLUSION. 157 resistance averages about ij, having extreme values of I 1-4 to i 9-10. Experiments made with natural cements furnished sim- ilar results. Experiments by Durand-Claye (page 149) and by Bauschinger (page 27) have already been noted, and their results check the TABLE VIII. Mixture Tensile Strength in Lbs. per Sq. In. Transverse Strength in Lbs. per Sq. In. Sand to Cement At Age of At Age of 1 Day 7 Days 28 Ds. 3 Mos. 1 Year 1 Day 7 Days 28 Ds. 3 Mos. 1 Year Neat 1:1 1:2 1:3 1:5 268 588 698 484 i 630 294 , 182 ; 277 733 705 491 338 187 721 379 252 458 III5 607 407 247 1237 915 397 1340 II2I 764 541 286 1 185 582 369 ratios obtained in Tables VII. and VIII.; in conclusion it may therefore be said that the value of the modulus is about ij times the ultimate tensile resistance of the same material when tested in the standard briquette form. It seems doubtful if anything more exact can at the present time be determined. Art. 27. Transverse Shearing Resistance and Conclusion. The resistance of cement mixtures to shearing stresses has not been treated separately on account of the lack of experi- mental data. On page 27 are given the results of some tests by Bauschinger, and on page 95 some results obtained at Columbia University. It is only possible to state that the value of the ulti- mate shearing resistance varies between the extreme limits of 125 to 375 pounds per square inch. The question of shear is of the greatest importance, and accurate and detailed experiments of the trasverse shearing resistance of concrete would be of great value. The elastic properties of reinforced concrete beams have not been discussed in this work, except in connection with results having direct bearing on ordinary cement mixtures; principally because, in the opinion of the author, the elastic behavior of the combination may be deduced by analysis, with the aid of the 158 FLEXURAL PROPERTIES. [Ch. VII. experimental values found separately for the two elements. It is his opinion that the combination of the two materials acts in practice as rational theory might require, although some pub- lished experiments ascribe to concrete, when reinforced, different elastic properties than when not reinforced. APPENDIX I. REPORT ON UNIFORM TESTS OF CEMENT BY THE SPECIAL COMMITTEE OF THE AMERICAN SOCIETY OF CIVIL ENGINEERS T resented at the Annual Meeting, January 21, 1903, and Amended at the Annual Meeting, January 20, 1904. SAMPLING. I. Selection of Sample. The selection of the sample for testing is a detail that must be left to the discretion of the engineer ; the number and the quan- tity to be taken from each package will depend largely on the importance of the work, the number of tests to be made and the facilities for making them. 2. The sample shall be a fair average of the contents of the package; it is recommended that, where conditions permit, one barrel in every ten be sampled. 3. All samples should be passed through a sieve having twenty meshes per linear inch, in order to break up lumps and remove foreign material; this is also a very effective method for mixing them together in order to obtain an average. For determining the characteristics of a shipment of cement, the individual samples may be mixed and the average tested ; where time will permit, however, it is recommended that they be tested separately. 4. Method of Sampling. Cement in barrels should be sampled through a hole made in the centre of one of the staves, midway between the heads, or in the head, by means of an auger or a sampling iron similar to that used by sugar inspectors. If in bags, it should be taken from surface to centre. CHEMICAL ANALYSIS. 5. Significance. Chemical analysis may render valuable service in the detection of adulteration of cement with considerable amounts of inert mate- rial, such as slag or ground limestone. It is of use, also, in determining whether certain constituents, believed to be harmful when in excess of a cer- tain percentage, as magnesia and sulphuric anhydride, are present in inadmissi- ble proportions. While not recommending a definite limit for these impurities, 160 METHODS OF TESTING CEMENT BY the Committee would suggest that the most recent and reliable evidence ap- pears to indicate that magnesia to the amount of *)%, and sulphuric anhydride to the amount of I.75$>, may safely be considered harmless. 6. The determination of the principal constituents of cement silica, alumina, iron oxide and lime is not conclusive as an indication of quality. Faulty character of cement results more frequently from imperfect preparation of the raw material or defective burning than from incorrect proportions of the constituents. Cement made from very finely ground material, and thoroughly burned, may contain much more lime than the amount usually present and still be perfectly sound. On the other hand, cements low in lime may, on account of careless preparation of the raw material, be of dangerous character. Further, the ash of the fuel used in burning may so greatly modify the com- position of the product as largely to destroy the significance of the results of analysis. 7. Method. As a method to be followed for the analysis of cement, that proposed by the Committee on Uniformity in the Analysis of Materials for the Portland Cement Industry, of the New York Section of the Society for Chem- ical Industry, and published in the Journal of the Society for January I5th, 1902, is recommended. SPECIFIC GRAVITY. 8. Significance. The specific gravity of cement is lowered by underburn- ing, adulteration and hydration, but the adulteration must be in considerable quantity to affect the results appreci- ably. 9. Inasmuch as the differences in specific gravity are usually very small, great care must be exercised in making the determination. 10. When properly made, this test affords a quick check for under- burning or adulteration. II. Apparatus and Method. The determination of specific gravity is most conveniently made with Le Chatelier's apparatus. This consists of a flask (D), Fig. I, of 120 cu. cm. (7.32 cu. ins.) capacity, the neck of which is about 20 cm. (7.87 ins.) long; in the middle of this neck is a bulb (C), above and below which are two marks (F) and (); the volume between these marks is 20 cu. cm. (1.22 cu. ins.). The neck has a diameter of about 9 mm. (0.35 in.), and is graduated into tenths of cubic centimeters above the bulb. 12. Benzine (62 Baume naphtha), or kerosene free from water, should be used in making the determination. 13. The specific gravity can be determined in two ways. Le Chatelier's Specific Gravity Apparatus. FIG. 1. 77ZE AMERICAN SOCIETY OF CIVIL ENGINEERS. 1 6 1 (I) The flask is filled with either of these liquids to the lower mark (E , and 64 gr. (2.25 oz.) of powder, previously dried at 100 Cent. (212 Fahr. ) and cooled to the temperature of this liquid, is gradually introduced through the funnel (B) [the stem of which extends into the flask to the top of the bulb (C)], until the upper mark (F) is reached. The difference in weight between the cement remaining and the original quantity (64 gr. ) is the weight which has displaced 20 c\i. cm. 14- (2) The whole quantity of the powder is introduced and the level of the liquid rises to some division of the graduated neck. This reading plus 20 cu. cm. is the volume displaced by 64 gr. of the powder. 15. The specific gravity is then obtained from the formula: ,-. ... Weight of Cement Specific Gravity Displaced Volume. 16. The flask, during the operation, is kept immersed in water in a jar (A}, in order to avoid variations in the temperature of the liquid. The results should agree within 0.01. 17. A convenient method for cleaning the apparatus is as follows: The flask is inverted over a large vessel, preferably a glass jar, and shaken ver- tically until the liquid starts to flow freely ; it is then held still in a vertical position until empty ; the remaining traces of cement can be removed in a similar manner by pouring into the flask a small quantity of clean liquid and repeating the operation. 18. More accurate determinations may be made with the picnometer. FINENESS. 19. Significance. It is generally accepted that the coarser particles in cement are practically inert, and it is only the extremely fine powder that possesses adhesive or cementing qualities. The more finely cement is pul- verized, all other conditions being the same, the more sand it will carry and produce a mortar of a given strength. 20. The degree of final pulverization which the cement receives at the place of manufacture is ascertained by measuring the residue retained on certain sieves. Those known as the No. 100 and No. 200 sieves are recom- mended for this purpose. 21. Apparatus. The sieves should be circular, about 20 cm. (7.87 ins. ) in diameter, 6 cm. (2.36 ins.) high, and provided with a pan, 5 cm. (1.97 ins. ) deep, and a cover. 22. The wire cloth should be woven (not twilled) from brass wire having the following diameters : No. 100, 0.0045 in.; No. 200, 0.0024 in. 23. This cloth should be mounted on the frames without distortion; the mesh should be regular in spacing and be within the following limits: No. 100, 96 to 100 meshes to the linear inch. No. 200, 188 to 200 " 162 METHODS OF TESTING CEMENT BY 24. Fifty grams (l.76oz.) or 100 gr. (3-52 oz.) should be used for the test, and dried at a temperature of 100 Cent. (212 Fahr. ) prior to sieving. 25. Method. The Committee, after careful investigation, has reached the conclusion that mechanical sieving is not as practicable or efficient as hand work, and, therefore, recommends the following method: 26. The thoroughly dried and coarsely screened sample is weighed and placed on the No. 200 sieve, which, with pan and cover attached, is held in one hand in a slightly inclined position, and moved forward and backward, at the same time striking the side gently with the palm of the other hand, at the rat3 of about 200 strokes per minute. The operation is continued until not more than one-tenth of \% passes through after one minute of continuous sieving. The residue is weighed, then placed on the No. 100 sieve and the operation repeated. The work may be expedited by placing in the sieve a small quantity of large shot. The results should be reported to the nearest tenth of I per cent NORMAL CONSISTENCY. 27. Significance. The use of a proper percentage of water in making the pastes* from which pats, tests of setting and briquettes are made, is exceed- ingly important, and affects vitally the results obtained. 28. The determination consists in measuring the amount of water required to reduce the cement to a given state of plasticity, or to what is usually desig- nated the normal consistency. 29. Various methods have been proposed for making this determination, none of which has been found entirely satisfactory. The Committee recom- mends the following : 30. Method. Vicat Needle Apparatus. This consists of a frame (/Q, Fig. 2, bearing a movable rod (/.), with the cap (A] at one end, and at the other end the cylinder (B), I cm. (0.39 in.) in diameter, the cap, rod and cylinder weigh- ing 300 gr. (10.58 oz.). The rod, which can be held in any desired position by a screw (F), carries an indicator, which moves over a scale (graduated to centi- meters) attached to the frame (K). The paste is held by a conical, hard-rubber ring (/), 7 cm. (2.76 ins.) in diameter at the base, 4 cm. (1.57 ins.) high, resting on a glass plate (/), about 10 cm. (3.94 ins.i square. 31. In making the determination, the same quantity of cement as will be subsequently used for each batch in making the briquettes (but not less than and *The term "paste" is used in this report to designate a mixture of cement and water, the word "mortar" a mixture of cement, sand and water. THE AMERICAN SOCIETY OF CIVIL ENGINEERS. 1 63 500 grammes) is kneaded into a paste, as described in Paragraph 58, and quickly formed into a ball with the hands, completing the operation by tossing it six times from one hand to the other, maintained 6 ins. apart; the ball is then pressed into the rubber ring, through the larger opening, smoothed off and placed on a glass plate (on its large end) and the smaller end smoothed off with a trowel; the paste, confined in the ring, resting on the plate, is placed under the rod bearing the cylinder, which is brought in contact with the surface and quickly released. 32. The paste is of normal consistency when the cylinder penetrates to a point in the mass 10 mm. (0.39 in.) below the top of the ring. Great care must be taken to fill the ring exactly to the top. 33. The trial plates are made with varying percentages of water until the correct consistency is obtained. 34- The Committee has recommended, as normal, a paste the consistency of which is rather wet, because it believes that variations in the amount of compression to which the briquette is subjected in moulding are likely to be less with such a paste. 35- Having determined in this manner the proper percentage of water re- quired to produce a neat paste of normal consistency, the proper percentage required for the sand mortars is obtained from an empirical formula. 36. The Committee hopes to devise such a formula. The subject proves to be a very difficult one, and, although the Committee has given it much study, it is not yet prepared to make a definite recommendation. TIME OF SETTING. 37. Significance. The object of this test is to determine the time which elapses from the moment water is added until the paste ceases to be fluid and plastic (called the "initial set"), and also the time required for it to acquire a certain degree of hardness (called the "final" or "hard set"). The former of these is the more important, since, with the commencement of setting, the process of crystallization or hardening is said to begin. As a disturbance of this process may produce a loss of strength, it is desirable to complete the operation of mixing and moulding or incorporating the mortar into the work before the cement begins to set. 38. It is usual to measure arbitrarily the beginning and end of the setting by the penetration of weighted wires of given diameters. 39. Method. For this purpose the Vicat Needle, which has already been described in Paragraph 30, should be used. 40. In making the test, a paste of normal consistency is moulded and placed under the rod (L), Fig. 2, as described in Paragraph 31; this rod, bear- ing the cap (D) at one end and the needle (//), I mm. (0.039 in.) in diameter, at the other, weighing 300 gr. (10.58 oz.). The needle is then carefully brought in contact with the surface of the paste and quickly released. 41. The setting is said to have commenced when the needle ceases to pass a point 5 mm. (0.20 in.) above the upper surface of the glass plate, and is 164 METHODS OF TESTING CEMENT BY . ^, ] Details I for Briquette. 'IG. 3. said to have terminated the moment the needle does not sink visibly into the mass. 42. The test pieces should be stored in moist air during the test; this is accomplished by placing them on a rack over water contained in a pan anl covered with a damp cloth, the cloth to be kept away from them by means of a wire screen; or they may be stored in a moist box or closet. 43. Care should be taken to keep the needle clean, as the collection of cement on the sides of the needle retards the penetra- tion, while cement on the point reduces the area and tends to increase the penetration. 44- The determination of the time of set- ting is only approximate, being materially affected by the temperature of the mixing water, the temperature and humidity of the air during the test, the percentage of water used, and the amount of moulding the paste re- ceives. STANDARD SAND. 45 The Committee recognizes the grave objections to the standard quartz now generally used, especially on account of its high percentage of voids, the difficulty of compacting in the moulds, and its lack of uniformity; it has spent much time in investigating the various natural sands which appeared to be available and suitable for use. 46. For the present, the Committee recommends the natural sand from Ottawa, 111., screened to pass a sieve having 20 meshes per linear inch and retained on a sieve having 30 meshes per linear inch ; the wires to have diam- eters of 0.0165 and O.OII2 in., respectively, i. e., half the width of the opening in each case. Sand having passed the No. 20 sieve shall be considered stand- ard when not more than one per cent, passes a No. 30 sieve, after one minute continuous sifting of a 500-gram sample. 47. The Sandusky Portland Cement Company, of Sandusky, Ohio, has agreed to undertake the preparation of this sand, and to furnish it at a price only sufficient to cover the actual cost of preparation. . FORM OF BRIQUETTE. 48. While the form of the briquette recommended by a former Com- mittee of the Society is not wholly satisfactory, this Committee is not pre- pared to suggest any change, other than rounding off the corners by curves of X-in. radius. Fig. 3. MOULDS. 49- The moulds should be made of brass, bronze or some equally non- THE AMERICAN SOCIETY OF CIVIL ENGINEERS. 1 65 corrodible material having sufficient metal in the sides to prevent spreading during moulding. 50. Gang moulds, which permit moulding a number of briquettes at one time, are preferred by many to single moulds; since the greater Details for^Gang Mould, quantity of mortar that can be mixed tends to produce greater uniformity in the results. The type shown in Fig. 4 is recommended. 51, The moulds should be wiped with an oily cloth beiore using. MIXING. 52. All proportions should be stated by weight; the quantity of water to be used should be stated as a percentage of the dry material. 53. The metric system is recommended because of the convenient relation of the gram and the cubic centimeter. 54. The temperature of the room and the mixing water should be as near 21 Cent. (70 Fahr.) as t is practicable to maintain it. 55- The sand and cement should be thoroughly mixed dry. The mixing should be done on some non-absorbing surface, preferably plate glass. If the mixing must be done on an absorbing surface it should be thoroughly dampened prior to use. 56. The quantity of material to be mixed at one time depends on the number of test pieces to be made; about 1,000 gr. (35-28 oz.) makes a conven- ient quantity to mix, especially by hand methods. 57. The Committee, after investigation of the various mechanical mixing machines, has decided not to recommend any machine that has thus far been devised, for the following reasons: (I) The tendency of most cement is to "ball up" in the machine, thereby preventing the working of it into a homogeneous paste; (2) there are no means of ascertaining when the mixing is complete without stopping the machine, and (3) the difficulty of keeping the machine clean. 53. Method. The material is weighed and placed on the mixing table, and a crater formed in the centre, into which the proper percentage of clean water is poured; the material on the outer edge is turned into the crater by the aid of a trowel. As soon as the water has been absorbed, which should not require more than one minute, the operation is completed by vigorously kneading with the hands for an additional IJ^ minutes, the process being similar to that used in kneading dough. A sand-glass affords a convenient guide for the time of kneading. During the operation of mixing the hands should be protected by gloves, preferably of rubber. MOULDING. 59. Having worked the paste or mortar to the proper consistency, it is at once placed in the moulds by hand. 60. The Committee has been unable to secure satisfactory results with the 166 METHODS OF TESTING CEMENT BY present moulding machines; the operation of machine moulding is very slow, and the present types permit of moulding but one briquette at a time, and are not practicable with the pastes or mortars herein recommended. 61. Method. The moulds should be filled at once, the material pressed in firmly with the fingers and smoothed off with a trowel without ramming; the material should be heaped up on the upper surface of the mould, and, in smoothing off, the trowel should be drawn over the mould in such a manner as to exert a moderate pressure on the excess material. The mould should be turned over and the operation repeated. 62. A check upon the uniformity of the mixing and moulding is afforded by weighing the briquettes just prior to immersion, or upon removal from the moist closet. Briquettes which vary in weight more than 3 per cent, from the average should not be tested. STORAGE OF THE TEST PIECES. 63. During the first 24 hours after moulding the test pieces should be kept in moist air to prevent them from drying out. 64. A moist closet or chamber is so easily devised that the use of the damp cloth should be abandoned if possible. Covering the test pieces with a damp cloth is objectionable, as commonly used, because the cloth may dry out unequally, and, in consequence, all the test pieces are not maintained under the same condition. Where a moist closet is not avail- able, a cloth may be used and kept uniformly wet by immersing the ends in water. It should be kept from direct contact with ths test pieces by means of a wire screen or some similar arrangement. 65. A moist closet consists of a soapstone or slate box, or a metal-lined wooden box the metal lining being covered with felt and this felt kept wet. The bottom of the box is so constructed as to hold water, and the sides are provided with cleats for holding glass shelves on which to place the briquettes. Care should be taken to keep the air in the closet uniformly moist. 66. After 24 hours in moist air the test pieces for longer periods of time should be immersed in water main- tained as near 21 Cent. (70 Fahr. ) as practicable; they may be stored in. tanks or pans, which should be of non-corrodible material. TENSILE STRENGTH. 67. The tests may be made on any standard machine. A solid metal clip, as shown in Fig. 5> is recommended. This clip is to be used without cushioning at the points of contact with the test specimen. The bearing at each point of contact should be }i in. wide, and the distance between the cen- tre of contact on the same clip should be \% ins. Form of Clip. FIG. 5. THE AMERICAN SOCIETY OF CIVIL ENGINEERS. 167 68. Test pieces should be broken as soon as they are removed from the water. Care should be observed in centring the briquettes in the testing ma- chine, as cross-strains, produced by improper centring, tend to lower the break- ing strength. The load should not be applied too suddenly, as it may produce vibration, the shock from which often breaks the briquette before the ultimate strength is reached. Care must be taken that the clips and the sides of the briquette be clean and free from grains of sand or dirt, which would prevent a good bearing. The load should be applied at the rate of 600 Ibs. per minute. The average of the briquettes of each sample tested should be taken as the test, excluding any results which are manifestly faulty. CONSTANCY OF VOLUME. 69. Significance. The object is to develop those qualities which tend to destroy the strength and durability of a cement. As it is highly essential to de- termine such qualities at once, tests of this character are for the most part made in a very short time, and are known, therefore, as accelerated tests. Failure is revealed by cracking, checking, swelling or disintegration, or all of these phenomena. A cement which remains perfectly sound is said to be of constant volume. 70. Methods. Tests for constancy of volume are divided into two classes: (I) normal tests, or those made in either air or water maintained at about 21 Cent. (70 Fahr.), and (2) accelerated tests, or those made in air, steam or water at a temperature of 45 Cent. (115 Fahr.) and upward. The test pieces should be allowed to remain 24 hours in moist air before immersion in water or steam or preservation in air. 71. For these tests, pats, about 7^ cm. (2.95 ins.) in diameter, 1% cm. (0.49 in.) thick at the centre, and tapering to a thin edge, should be made, upon a clean glass plate [about 10 cm. (3.94 ins.) square], from cement paste of normal consistency. 72. Normal Test. A pat is immersed in water maintained as near 21 Cent. (70 Fahr.) as possible for 28 days, and observed at intervals; the pat should remain firm and hard and show no signs of cracking, distortion or disintegration. A similar pat is maintained in air at ordinary temperature, and observed at intervals. 73- Accelerated Test. A pat is exposed in any convenient way in an atmosphere of steam, above boiling water, in a loosely closed vessel, for three hours. 74. To pass these tests satisfactorily the pats should remain firm and hard, and show no signs of cracking, distortion or disintegration. 75. Should the pat leave the plate, distortion may be detected best with a straight-edge applied to the surface which was in contact with the plate. 76. In the present state of our knowledge it cannot be said that cement should necessarily be condemned simply for failure to pass the accelerated 168 METHODS OF TESTING CEMENT. tests; nor can a cement be considered entirely satisfactory simply because it has passed these tests. Submitted on behalf of the Committee. GEORGE S. WEBSTER, Chairman. RICHARD L. HUMPHREY, Secretary. Committee. GEORGE S. WEBSTER, RICHARD L. HUMPHREY, GEORGE F. SWAIN, ALFRED NOBLE, LOUIS C. SABIN, S. B. NEWBERRY, CLIFFORD RICHARDSON, W. B. W, HOWE, F. H. LEWIS. APPENDIX II. CONSTITUTION OF PORTLAND CEMENT. Clifford Richardson, in a paper read before the Association of Portland Cement Manufacturers, at Atlantic City, June 15, 1904, has advanced consid- erably the knowledge concerning the constitution of Portland cements. Le Chatelier and, independently of him, Tb'rnebohm have found, as a result of studies by microscopic methods, that clinker consists of four constituents alit, belit, celit and felit, whose sections have distinct optical properties, and of a fifth amorphous isotropic mass which has no action upon polarized light. Alit and celit are the principal constituents of clinker. Richardson, from his own work, concludes that clinker is a solid solu- tion of silicates and aluminates; alit being a solution of tricalcic aluminate (Al. 2 O 3 3.CaO), in tricalcic silicate (SiO 2 3CaO), and celit a solution of dicalcic aluminate (Al 2 O 3 .2CaO) in dicalcic silicate (SiO 2 .2CaO). The presence of iron, magnesia, etc., exerts no essential influence, although probably adding to the complexity of the solid solutions present. The formation of clinker from pure chemicals at a temperature below fusion is probably due to diffusion and subsequent interaction; this has been shown for other solid substances, as, for example, in the production of barium sulphate and sodium carbonate from a finely pulverized mixture of sodium sulphate and barium carbonate maintained in continued close contact. Concerning, therefore, the manufacture of cements Richardson states, from the viewpoint of the diffusion of solid substances, as shown by the above example, that finer grinding of the raw mixture would make possible the use of lower temperatures in burning, and that therefore the relative costs of fuel and fineness of grinding at any given locality will determine, from an econ- omic standpoint, the fineness to which the raw materials should be ground. Richardson's work, while not settling the constitution of cement mixtures, is of the greatest importance, not only for what it has already accomplished, but also for the possibilities and methods of investigation it suggests; and it may reasonably be expected that in a relatively short time the question of the constitution of cements will be made as clear as is that of the different. forms of iron. His work corroborates the conclusion, previously stated in Chapter I., that a simple chemical analysis of the constituents present in a cement can, as yet, furnish little evidence of its quality or as to its fitness for use. INDEX. PAGE Accelerated tests 39, 167 Adhesion of iron in concrete 61-66 Aggregate ; character of, effect on strength 30-39 Analyses of natural cement 6-8 Analyses of Portland cement 3-6 Beams, concrete .' 142-158 Bending (see flexure). Blowing of cements 3, 39 Briquette, form of, for tensile testing 164 Chemical analyses 3-8, 159 Cinder concretes in compression 83, III, 113 Cinder concretes in tension 78 Clay, effect of, on strength 34-39 Coefficient of elasticity, explained 70-75 Coefficient of elasticity, in compression 99-121 Coefficient of elasticity, in flexure 144- 149 Coefficient of elasticity, in tension 75-98 Coefficient of linear thermal expansion 43-45 Cold, effect of, on cement mixtures 55-61 Commercial physical tests, discussed 9-39 Commercial physical tests, of American Soc. of Civ. Eng 159-168 Compression, author's conclusions on 1 32- 141 Compression, coefficient of elasticity 91, 95, 96, 99-121 Compression, coefficient of elasticity compared to tensile coefficient, 83, 88, 141 Compression, ultimate resistance to 83, 99-141 Compression, ultimate resistance to, hardening in sea water 47 Compression, ultimate resistance to, effect of size of specimen 106 Compression, ultimate resistance to, use of cushions 108 Compression; ultimate resistance compared to tensile resistance 26-29 Consistency, normal 162 Constancy of volume, test of 39, 167 Constitution of Portland cement 1-8, 169 Contraction of cements on hardening. 40-43 Crushing (see compression). 172 INDEX. PAGE Curves, stress-strain, explained 70-75 Curves, stress-strain, for compression. . 88-95, 103, 107-109, 112, II6-II8, 120 Curves, stress-strain, for tension 81, 88-95 Definition of a cement j Disintegration of cement mixtures, in sea waters 45-47, 52 Dry concrete against wet (see wet . Effect of freezing 55-61 Elastic limit, explained 71 Expansion, due to temperature changes . 43-45 Expansion of cements during setting 40-43 Fatigue of cement mixtures 66-69 Fibre stress, extreme, in concrete beams 146-158 Final setting of cements \T >> 153 Fineness test 1 1-13, il Fineness of sands, effect of, in tensile strength 30-39 Flexural coefficient of elasticity 144 Flexural properties of cement mixtures 142-158 Freezing, effect of 55-61 High temperatures 132 Hot water test 39 Impervious concrete 51-55 Initial setting 13^ 153 Loam in sands 34-39 Magnesia, limit of, in cement 3 Manufacture of cement 9 Mica, effect of 1 29 Mixing cement for testing 165 Modulus of elasticity (see coefficient of elasticity). Modulus of rupture in flexure 146-158 Modulus of rupture, ratio to tensile stress 157 Moulds, for tensile tests , 164 Natural cement, definition I Permeability of cement mixtures 51-55 Plaster of paris, action in delaying set 14 Plaster of paris, effect on strength when setting is retarded 18 Plaster of paris, effect on variation of volume during setting 41 Plaster of paris, limit of, in cements 3 Plasticity of concretes (see wet). Porosity 51-55, 140 Portland cement, definition I Pozzalana, addition of, to cements 45-51 INDEX. 173 PAGE Rate of application of stress to concrete 67 Ratio of modulus of rupture to tensile resistance 157 Reinforced concrete, tests in tension 76 Reinforced concrete, author's opinion on 157 Repeated applications of stress 66, 100 Repeated applications of stress, effect on coefficient of elasticity 73 Resistance to stress (see tension, compression, flexure, shear). Retarding setting of cements 57 Rods, adhesion of iron, in concrete 61-66 Salt, effect of, in gauging 50, 56 Sampling cement for purposes of test 159 Sands, variation of, in tensile tests 30-39 Sands, washed vs. unwashed 35-39 Screenings (rock) in place of sand 30-39, 155 Sea water, action of 45-5 1 Sea water, strength in 47-5 1 Setting, effect of plaster of paris on 14 Setting, tests for time of 13-19, 163 Setting, theories of I, 169 Setting under water 130 Shear, adhesive (see adhesion). Shear, transverse, ultimate resistance to 27, 95, 148, 157 Shrinkage during setting 40-43 Sieves, size of 12, 161 Solution, solid, cement as a 169 Specific gravity tests 10, 160 Standard sand for tensile tests 164 Storage of test pieces 1 66 Straight line formula for coefficient of elasticity 132-1^8 Straight line formula for ultimate resistance 1 38- 141 Strength, gauged with salt water , 50 Strength in sea water 47 Strength (see tension), compression, flexure, shear. Stress-strain curves (see curves). Temperature changes during setting 18 Temperature, effect of, on setting 16 Temperature, effect of high, on ultimate resistance 132 Tensile properties, coefficient of elasticity and ultimate resistance 75-98 Tensile properties, conclusions as to 97 Tensile strength, effect on of variations of sands 30-39 Tensile strength, tests of, on standard briquettes 19-26, 166 Tensile strength, tests of, hardening in sea water 47 Tensile strength, ratio of, to compressive strength 26-29 Tensile strength, variations in methods of determining 29 174 INDEX. PAGE Tests, commercial 9 Theory of flexure, applied to concrete 142 Thermal expansion, coefficient of 43-45 Time of setting (see setting). Twisted rods vs. plain rods, adhesion 61 U Itimate resistance in compression 99-141 Ultimate resistance in tension 75-98 Ultimate resistance in flexure 146-158 Ultimate resistance in transverse shear 27, 157 Variation in volume, during setting 40-43 Variation in volume, due to temperature 43-45 Variation of stone in concrete, effect on ultimate resistance 129 Vicat needle 162 Water, hardening under 130 Wet vs. dry concretes 82, 121, 130 AUTHORS' INDEX. ( Italics Indicate Journals. ) Adie 44 American Society of Civil Engineers, Transactions of.... 6, 9, 12, 13, 21, 23, 35, 40, 42, 50, 53, 66, 118, 123, 144, 152, 155, 159 American Society for Testing Materi- als, Proceedings of. . 32, 51, 59, 63, 83, 119 Annales des Fonts et Chausees. ... 20, 31, 33, 43, 45, 52, 65, 66, 75, 148 Arsenal Reports; see Watertown. Assoc. Eng. Societies, Journ. of 24 78 Austrian Society of Civil Engineers. . . 92, 96, 136 Bach,C 71,99-105,133, 138 Baker, B 103 Baker, I. 123 Bauschinger, J 26, 27, 41, 44, 157 Bergerand Guillerme 20,44 Beton u. Eisen 61 Black, A 33 Boston Transit Commission. . . 5, 43, 48, 153 Bouniceau 43 Brown, W. L 147 Busing and Schumann 27, 44, 48 Canadian Society Civil Engrs. , 7V<7 ns. of 60 Candlot 45 Carleton, R. A. W 147 Chief Engr. U. S. Army; see United States Army. Christophe 44 Civil Ingenieur, Der 103 Clark, T. F : 34, 129, 155 Clarke, E. C 13, 21, 23, 26, 35, 50, 155 Coelos, J.A 147 Considere 42, 65 Gostigan, J.S 60 Cummings.U 6 De Joly 65, 66, 75 Derleth.W.T 84, 134 Deutscher Ingenieure; see Zeitsch. des Ver. Dougherty, R. E 44 PAGE Doyle, T. L 131 Durand-Claye 44, 148, 157 Dyckerhoff 47 Engineering News.. 33, 34, 35, 36, 129, 131, 155 Engineering Record 37 Falk, M. S 84, 144 Feret, R 31, 33, 46, 49, 52, 54, 138 Fuller, W. 8 138 Gary, M 42 German Portland Cement Manufac- turers' 1 society 47 Gillmore, Q. A 16, 105 Gowen, C. S 50, 59 Grant, J 13, 25, 26, 41, 126 Griesenauer, S. J 35 Guillerme 20, 44 Hallock, W 45 Hartig 103 Hatt, W. K 63, 83, 136 Hawkesworth, J 84, 134 Heath 50 Henby.W. H 78, 111 Holman, M. L 21 Hunt, R.W.,&Co 24 Institution of Civil Eng., Gt. Brit.. Pro- ceedings 13, 25, 26, 41, 49, 53, 126, 147 Journal of Assoc. Eng. Societies ; see Assoc. Johnson, J. B , 24, 26 Justice, E. R 131 Lanza, G 147 Lamed, E. S 32 Lathbury & Spackman, Inc 5, 13, 25 LeChatelier 1, 8, 45 Lesley, R. W. 24, 53 176 AUTHORS' INDEX. PAGE Marburg, E 119 McCaustland, E J 118, 138, 146 McCurdy, H. S. R 43 Meier 44 Michaelis 45 Mills, C M 37 Mineral Industry ^ 12 Morsch,E * 61 Newberry, S. B. and W. B 1, 8 New York, Report of State Engr. 24, 121, 124 Noble,A. 50 PAGE Technograph, Univ. of Illinois 131 Testing Materials; see American So- ciety for; Proceedings. Tetmajer 26 Tornei 42 Transactions; see American Society of Civil Eng.; see Canadian Society of Civil Eng. United States Army; Report Cliief of Engrs 15, 17, 30, 56, 63, 149, 156 Unwin, W. C 26 Pence, W. D Fonts et Chaussees ; see Annales. 43 Rae, J.G Rafter, Geo. W. Ries& Eckels.. 24, 116, 121, 137, 138 5 Sherman, C. E 36 Schumann, C 27, 42, 44, 48 Spofford, C 61 Sussex, J. W 130 Swain, G.F 40 Van Ornum, J. L 66 Von Schon, H. 152 Watertown Arsenal Reports 3, 4, 10, 14, 17, 18, 28, 56, 58, 64, 74, 105, 113. 121, 125, 127, 130, 132, 135, 137, 139 Western Society of Engrs., Proceed, of, 43, 84 Wheeler, E. S 15, 17, 30, 56, 63, 149, 156 Whittemore, D. T 6 Zeitschrifl nieure .. Ver. DeutscTier Inge- 71,99 14 DAY USE RETURN TO DESK FROM WHICH BORROWED LOAN DEPT. This book is due on the last date stamped below, or on the date to which renewed. Renewed books are subject to immediate recall. NAY 13 '65 -8 PI LD 21A-60m-3,'65 (F2336slO)476B General Library University of California Berkeley "f>tu 14 1942 *V- 3/6SX LD 21-100*J7,'33 YC TI|g:O^VERSITY OF CALIFORNIA LIBRARY