Digitized by the Internet Archive in 2019 with funding from University of Illinois Urbana-Champaign Alternates https://archive.org/details/strengthofconcreOOhump DEPARTMENT OF THE INTERIOR UNITED STATES GEOLOGICAL SURVEY GEORGE OTIS SMITH, Director Bulletin 344 THE RESULTS OF TESTS OF 108 BEAMS ^FIRST SERIES) MADE AT THE STRUCTURAL-MATERIALS TESTING LABORATORIES By RICHARD L. HUMPHREY WASHINGTON GOVERNMENT PRINTING OFFICE 1908 ✓ (oZOA H ■ • I CONTENTS. -* > < • Page. Introduction. . 5 Scope of investigations. . 5 Methods of testing. .. 6 • Results of tests. . 6 Acknowledgments. . . 8 Tests of constituent materials. . 9 Cement... . 9 Preparation of typical cement. . 9 Results of tests.. . 9 Sand... . 16 Aggregate. .18 Preparation of test pieces. ... 18 Methods of proportioning. 18 Method of mixing and consistency.._ - -.-— - vr:V.r.:. - 19 i Mixing. . 19 Consistency . . 20 Method of molding. . 21 Beams . . 21 ft Cylinders and tubes. - . = ^r-.. . 21 Moving and storage . . 22 Methods of testing. . ....;. ... 22 Beams. ... 22 v Long beams. . . 22 Apparatus. . . 22 Method of zero deformation.... . 23 • Method of testing. .. 27 — Short beams. 27 Cylinders and cubes. .. 28 c* Results of tests. .. 28 Beams of constant span. ... 28 ■9 Beams of variable span. ... ! ... 55 ci Cylinders and cubes. ... 55 A Illustrative diagrams. .... 57 A f . | Survey publications on tests of structural materials.... 59 0 49559 4 ILLUSTRATIONS. Page. Plate I. Concrete beam in machine ready for testing. 22 Fig. 1. Diagrams illustrating method for computation of concrete beams. 25 2. Effect of age and consistency on the strength of cinder concrete. 28 3. Effect of age and consistency on the strength of granite concrete. 29 4. Effect of age and consistency on the strength of gravel concrete.. 29 5. Effect of age and consistency on the strength of limestone concrete_ 30 6. Compression-stress deformation diagrams of cinder concrete. 30 7. Compression-stress deformation diagrams of granite concrete. 31 8. Compression-stress deformation diagrams of gravel concrete. 32 9. Compression-stress deformation diagrams of limestone concrete. 33 10. Deformation curves of cinder concrete in flexure. 35 11. Deformation curves of granite concrete in flexure. 54 12. Deformation curves of gravel concrete in flexure. 56 13. Deformation curves of limestone concrete in flexure..... 58 % TABLES. Page. Table 1. Chemical analyses of the individual brands used in the preparation of typical Portland cement... 10 2. Physical tests of individual brands of cement. 10 3. Strength tests of individual brands of cement. 11 4. Physical properties of cements used in concrete beams. 14 5. Mortar tests of Meramec River sand used in concrete beams. 17 6. Physical properties of sand and other materials forming aggregates.. 17 7. Strength tests of cement (Ct. 140) used in testing Meramec River sand. 18 8. Tests of 13-foot concrete beams of constant (12-foot) span; ages 4, 13, and 26 weeks. 36 9. Tests of concrete beams of variable span; ages 4, 13, and 26 weeks.. 42 10. Compression tests of concrete cylinders and cubes accompanying beams; ages 4, 13, and 26 weeks. 48 4 W t- THE STRENGTH OF CONCRETE BEAMS. By Richard L. Humphrey. INTRODUCTION. SCOPE OF INVESTIGATIONS. The tests of concrete beams described in this bulletin form a part of a comprehensive series of investigations undertaken by the United States Geological Survey for the purpose of determining the strength of concrete and reinforced concrete. The work involved in these investigations consists of a study (1) of the constituent materials of concrete, (2) of its strength when molded into various structural shapes, and (3) of the methods by which its maximum strength may be developed through various forms of metallic reinforcement. Although it is true that concrete possesses but little strength in tension and must be reinforced with metal to resist tensile stresses, it is believed that no study of concrete would be complete without a series of tests establishing its strength without reinforcement. The tests herein reported indicate that concrete is unsuitable for use under conditions where it must resist tensile stresses, because of the small loads it will sustain and particularly because of the suddenness with which it fails, in striking contrast to the behavior of reinforced concrete, which usually shows a gradual development of cracks preceding failure. This first series of beam tests covers 144 beams without rein¬ forcement 8 by 11 inches in section and 13 feet long, together with the corresponding compression test pieces, consisting of cylinders 8 inches in diameter by 16 inches in length and of 6-inch cubes. Of these tests those on 108 beams of 12-foot span, with their cylinders and cubes, and those on 108 beams of variable spans, 6 to 9 feet, which were made of the larger part of the 13-foot beams after rupture, are herein reported and comprise all of this series except the 52-week tests. An attempt has been made to bring out, if possible, the compara¬ tive value of gravel, granite, limestone, and cinders for use in con¬ crete; the effect of age and consistency on the strength, as shown by the modulus of rupture of the long and short beams and by the ulti¬ mate strength of the cylinders and cubes; and the influence of age and consistency on the stiffness, which is indicated by the unit 5 6 STRENGTH OF CONCRETE BEAMS. elongation of the long and short beams and by the initial modulus of elasticity, as determined by tests of the cylinders. Three consistencies — wet, medium, and damp — were . somewhat arbitrarily chosen, and are described on pages 20-21 in greater detail. Tests were made at the ages of 4, 13, 26, and 52 weeks. There are, then, as indicated in the following table, but two variables—aggre¬ gate and consistency—for each age. Outline of tests of concrete beams. Consistency. Aggregate. 4 weeks. - .v 3 13 weeks. 26 weeks. 52 weeks. Granite. Wet. Med. Damp. Wet. Med. Damp. Wet. Med. » » W A * Damp. Wet. Med. Damp. Gravel.... . .do . . .do . . .do ... ..do . . .do . . .do ... ..do . . .do . . .do ... . .do . ..do . . .do ... Limestone. . .do . . .do . . .do ... . .do . . .do . . .do ... . .do . . .do . . .do ... . .do . . .do . . .do ... Cinders. .. - ; . .do . . .do . ..do ... ..do . . . do . . .do ... . .do ; . .do . ..do ... . .do . . .do . . .do ... Note.—T hree beams, three cylinders, and three cubes were made for each variation shown in the table. METHODS OF TESTING. The methods of testing beams of 12-foot and variable spans, together with cylinders and cubes, have been described in consider¬ able detail in Bulletin No. 329. It is thought best, however, to repeat and in some cases amplify matter which appears there, as the intelli¬ gent interpretation of much of the test data is greatly aided by ready access to an account of the methods of testing that were used. RESULTS OF TESTS. No attempt has been made in this bulletin to generalize the results of the tests herein presented, or to draw any conclusions, however warranted they may appear from an examination of the test data. It is hoped that the matter herein contained will provoke discussion, and in order to promote this end extended expressions of opinion or attempted applications of theory to results have been avoided. A running commentary on the results of the tests, however, emphasizing matters of particular interest and indicating a few points that might lead to interesting analyses, is included in this report. When the results of the 52-week tests become available it is the intention to publish a thorough analysis of the entire series in another bulletin. The purpose of this series of tests was to determine— (1) The effect of age on the strength of concrete; (2) The effect of variation in the consistency on the strength of concrete; and (3) The effect of different types of aggregates on the strength of concrete. The first question is perhaps the most important, since an early attainment of considerable strength and no subsequent decrease in INTRODUCTION. 7 strength are two essential qualities in concrete, in order that a struc¬ ture may be put to the use for which it is intended as soon as possible and that there shall be no subsequent deterioration in strength. The least age at which any tests were made was four weeks, and at that period in no case except that of the cinder concrete, wet con¬ sistency, did the compressive strength fall below 2,000 pounds per square inch, while the cinder concrete had in every case a compressive strength of at least 1,000 pounds per square inch. In every instance the compressive strength shows a substantial increase from four to thirteen weeks, with the single exception of limestone concrete mixed to a wet consistency, for which a decreased strength is indicated by the tests, a decrease which continues to the age of twenty-six weeks. This decrease in the strength of the lime¬ stone concrete is unexplainable, and the results of the 52-week tests on this material will be of value as indicating whether or not this decrease continues to the latter period. The other aggregates show either the same or a slightly greater strength at twenty-six weeks than at thirteen weeks. The transverse tests on both the long and the short beams bear out very closely the fact indicated by the compression tests on the cylin¬ ders and cubes, and lead to the belief that the tensile and compressive strength are affected alike by both age and consistency. The effect on the strength of the variation in the consistency is clearly shown. In almost every case the concrete of the damp consistency is the strongest and that of the wet consistency the weakest. This is true for the three ages at which the concrete was tested, and is confirmed by the tests of the beams as well as of the cylinders and the cubes. Attention is called to the fact that the damp consistency used is much wetter than the damp consistency used in making mortar building blocks, for which the same conclusions may not apply. The difference in strength of the stone and gravel concretes of the three consistencies is more pronounced than in the case of the cinder concrete. The effect of the consistency on the strength seems to depend to a great extent on the behavior of the concrete while being tamped and to the method used in tamping. Great care was taken to tamp all the concretes in the same manner. The thorough mixing of the concrete is absolutely essential and has a marked influence on the consistency. The relatively slight influence exerted by the consistency on the strength of cinder concrete may be partly due to the structural weak¬ ness of the cinders themselves, which in the drier mixtures were to a great extent broken up by the tamper, while in the wet mixtures, the cinders would move from beneath the tamper. While it is true that in almost every instance the drier mixtures give the greater strength, it does not follow that dry (or damp) 8 STRENGTH OF CONCRETE BEAMS. mixtures should be used in construction. Practical considerations warrant the use of a wet mixture. The difficulty in securing efficient tamping and a smooth finish in a damp concrete, the loss of strength due to the unavoidable drying out of the concrete used above water, the difficulty of securing in reinforced concrete an intimate union with the steel, and the far greater ease of placing wet concrete all seem to warrant the sacrifice of what in many cases is but a slight difference in strength for a greater ease of manipulation and a thorough bedding of the steel, which is of the utmost importance in reinforced concrete work. It is dangerous to draw any general conclusions as to the relative value of concrete made of the four aggregates used unless the char¬ acter of the aggregates used in this particular series of tests is care¬ fully kept in mind. The gravel, granite, limestone, and cinders were used as available representative types of aggregates, and while the results indicate that the granite makes the strongest concrete, it should not be assumed, therefore, that a granite concrete is stronger than a gravel, limestone, or cinder concrete. Every material should be accepted or rejected on the results of the tests of its qualities, regardless of the tests of other materials of the same type. Appar¬ ently insignificant differences in two materials which appear to be similar often cause considerable difference in the strength of concrete made from them. For instance, two limestones from the same quarry crushed and screened under similar conditions—except that one was screened while wet, which caused the dust to adhere to the surface of the stone—would make concretes of considerable difference in strength. Because the hard, flinty gravel used in these tests gave excellent results, it does not necessarily follow that a similar well-graded gravel, but composed of soft limestone or shale, would give like results. No series of investigations, however elaborate, will do away with the necessity of careful inspection of the materials to be used. The rela¬ tive value of materials reported in this bulletin should be recognized, therefore, as applicable only to the particular materials from which the reported physical properties were obtained. ACKNOWLEDGMENTS. All the material used in the tests herein reported was donated by the following companies, who deserve credit for their interest and hearty cooperation in advancing the work: ' f"\ V i-s • ■rr>rr r > Cement .—Iola Portland Cement Company, Iola, Kans. Atlas Portland Cement Company, Hannibal, Mo. Whitehall Portland Cement Company, Cementon, Pa. Universal Portland Cement Company, Chicago, Ill. Edison Portland Cement Company, New Village, N. J. Omega Portland Cement Company, Mosherville, Mich. 9 TESTS OF CEMENT. Old Dominion Portland Cement Company, Fordwick, Ya. Lehigh Portland Cement Company, Mitchell, Ind. St. Louis Portland Cement Company, St. Louis, Mo. Sand .—Union Sand and Material Company, St. Louis, Mo. A recent river sand dredged from Meramec River at Drake, Mo. Gravel .—Union Sand and Material Company, St. Louis, Mo. A recent river gravel dredged from Meramec River at Drake, Mo. Granite .—Schneider Granite Company, St. Louis, Mo. A hard, red granite quar¬ ried near Graniteville, Mo. Cinders .—United Railways Company, St. Louis, Mo. These cinders were obtained from the Dehodiamont power house, St. Louis, and gave better results than those selected from other sources. Limestone. —Fruin-Bambrick Construction Company, St. Louis, Mo. Obtained from a quarry in St. Louis. The tests were supervised by Louis H. Losse, and the results were computed and collated by Harry Kaplan. TESTS OF CONSTITUENT MATERIALS. CEMENT. PREPARATION OF TYPICAL CEMENT. The cement used in all the tests in these laboratories is known as typical Portland cement. It is prepared by thoroughly mixing to¬ gether a number of Portland cements. The method of preparing the typical Portland cement that was used in the tests herein reported and in the tests on the second and third series, reinforced beams, including in all 576 beams, cylinders, and cubes, was as follows: One thousand eight hundred sacks of cement, 200 from each of nine companies, were used. Two hundred sacks of one brand were spread over a concrete floor 25 by 40 feet in area and thoroughly mixed by hoeing from side to side. Two samples were then taken, a 50-pound sample for tests to be made by the constituent-materials section, and a smaller one for chemical tests. The cement was then resacked. When all the brands had been separately mixed in this way, two sacks of each brand were spread on the floor in a layer about 3 inches thick. One brand was spread upon another in blanket form, making nine separate layers of cement for the nine brands used. The mass was mixed very carefully with shovels until a uniform mixture was obtained. A 10-pound sample was taken for physical tests and the cement was sealed in air-tight cans, two cans of 800 pounds capacity each being required to hold one mix. RESULTS OF TESTS. Table 1 contains the results of the chemical tests of the individual brands, made on samples taken as indicated above. The average of the columns may be taken as the analysis of the typical Portland cement. 10 STRENGTH OF CONCRETE REAMS. Table 1 . —Chemical analyses of individual brands used in the preparation of typical Portland cement. Cement No. Silica (SiO,). Alumina (AI 2 O 3 ). Ferric oxide (Fe 2 0 3 ). Lime (CaO). Mag¬ nesia (MgO). Sul¬ phuric anhy¬ dride (S0 3 ). Water (H 2 0). Ignition loss. Unde¬ ter¬ mined. 200 . 20. 34 9. 36 3.04 63. 40 1.35 1.47 1.04 201. 22.12 6. 50 3. 22 61.39 2. 58 1.89 0.94 0.55 .97 202. 20.96 8. 08 2.80 62. 68 1. 45 1.54 .18 1.61 .70 203. 20. 52 8. 54 2. 68 62. 47 1.92 1.50 .29 1. 43 .65 204. 20. 04 7. 70 2. 74 63.26 2. 24 1.56 .08 .96 1.60 205. 22. 04 9.50 1.42 61. 46. 1.68 1.58 .55 .84 .93 206.. 22.80 9. 56 1.06 61.04 1.37 1.82 .64 .77 .94 207. 22. 96 9. 34 1.32 61.20 1.47 1.81 .28 .86 .76 208. 23. 48 «. 22 1.80 61.10 1.62 1.68 .44 .81 .85 Average. 21. 70 8. 53 2.23 62.00 1.74 1.67 .43 .98 .94 Table 2 contains the results of the physical tests, except those for strength of the individual brands. All these tests were made accord¬ ing to the methods recommended by the special committee on uni¬ form tests of cement of the American Society of Civil Engineers. Table 2. —Physical tests of individual brands used in typical Portland cement. a Cement No. Residue on sieve (per cent)— Specific gravity. Water (per cent). Time of set (minutes). Normal pat tests. Vicat. Gilmore. Air (70° F.). Water (70° F.). 100. 200. Ini¬ tial. Final. Ini¬ tial. Final. 200. 5 9 20.9 3.136 21.0 184 340 155 325 Normal. Normal. 201. 5. 5 22.1 3.058 20. 5 93 378 110 486 . .do. Do. 202. 7.8 24.6 3.121 20. 5 138 329 152 393 . .do. Do. 203. 4.4 20.6 3.099 21.5 117 315 150 352 Crack 1" long Do. from edge. 204. 2.0 12.0 3.087 24.0 124 416 229 458 Normal Do. 205. 6.0 22.2 3.165 21.0 127 370 178 394 W arped J*" Do. from edge. 206. 5. 3 21. 5 3.127 21.0 113 338 195 441 Normal Do. 207. 6.0 23.2 3.129 20. 5 146 391 182 372 . .do. Do. 208. 3.1 21.6 3.141 22.5 170 332 217 400 .do. Do. Average.... 5.1 21.0 3.108 21.4 135 357 174 402 a In the accelerated pat tests, in water at 212° F. for 3 hours and in steam maintained at normal pressure for 5 hours, the results were normal in each case for each brand of cement. Table 3 contains the results of the strength tests of the indi¬ vidual brands. Tests were made for both neat cement and 1: 3 mortar with Ottawa sand, in tension, compression on 2-inch cubes, and modulus of rupture on a 1 by 1 inch prism tested by a center load on a 12-inch span. All tests were made according to the methods rec¬ ommended by the special committee on uniform tests of cement of the American Society of Civil Engineers. Strength tests of individual brands used in the preparation of typical Portland cement. 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Table 4 contains the results of all the physical tests made of the typical Portland cement that was used in the present series of con¬ crete beams. In the column “ Register No.” is given the register number of the cement used. Each number corresponds to two cans of 800 pounds each of typical Portland cement. The sample for each test was taken as already indicated. As these tests were made with the sole idea of checking the uni¬ formity with which the typical Portland cement was prepared, a full series of neat and sand tests was thought unnecessary and undesir¬ able, for it would entail too much routine work on the part of the constituent-materials laboratory. Accordingly, only tension tests on neat cement were made. SAND. The same sand was used with all the aggregates tested. It is known as Meramec River sand, and is composed of flint grains having comparatively smooth surfaces. The yellowish-brown color of the flint imparts a tint of the same color to the sand as a whole. Tables 5 and 6 (p. 17) give the results of the physical tests on this material. The granulometric analysis in Table 6 shows the sand to be rather finer than desirable. The percentage of voids was com¬ puted from the weight per cubic foot and the specific gravity. Table 7 (p. 18), which contains the results of the tests made on the cement used in the preparation of the test pieces reported in Table 5, will aid in the interpretation of the values given in the latter table. Table 5. — Tests of mortar made with Meramec River sand ( Sd. 43) and typical Portland cement ( Ct . 140) in concrete beams. TESTS OF SAND Fh 0 Ph GO 360 days. O OO cu Co "V O oc tH 0 O to 05 O O to 05 CO O Td rt 0 180 days. lO O O 04 O »0 H 05 00 00 to 05 O to 0 OMO CO CO to 00 0 CO O O to 1OON to to co to r- to .2 *s bD rH rH 00 0 r- 04 rH 05 O Ph . tO t^tjT Tp' CO co co' co CO CO CO* co O CO tO O rH O cc TP 04 to £50 ti.S d G 04 co id co CO O >> tO »o 0 04 04 to CO co CO UO *OOM 04 O rH CO 05 00 0 00 O O to OlON TP TP CO 00 0 TP co • cu Cfl P< © be -H a rH GO §2 £ oj QQ P ® S3 T5 lO irfiO to CO CO CO 1 CO CO CO CO CO e O 00 00 O CO O Tp CO 04 O co *co so <£> Fh Ph 00 00 >> 10*0 0 L- »0 O rH O 0 0 O O to *0*0N TT CO CO 04 05 co OOO to O to t - 1- CO § O2 CJi 53 CO O Tp to Tp rH C D c3 tj Tp'rp'rp' Tp' of of of of of of of of trj © 0 Fh - *0 (M CO 04 CO rH CO to to to c- r- 04 CO CO CO 00 to CO to O to MOM Tp tp Tp rH Tp • g Tp 06 CO Tp* CO ofofof of rH rH rH rH rH rH rH rH to 04 O 00 O Tp 04 rH 05 Co s • • • • • CO CO TP CO F-h © Ph 00 360 days 0 CO co 00 00 TP Tp tp 0 00 Tp rH 00 CO O O’ H Tp TJ1 TP 408 O 04 GO co d- co CO CO CO 367 "5 ’ cS 1 rH SO H GO tP CO 0 NCOO CO O OOO 00 00 05 to 00 to Tp H040 04 04 04 to rH 04 £ e c«s 04 Eh. C3 'O DT . <3 /-N Water. 68.0 68.0 68.0 Co CO • CO ^5 O to 0 05 co 00 to 00 05 to to TP T31 to © O s % rH oi 04 04 04 1. bb «HH O , CD Proportion mortar. CO rH Average... TP rH [ Average... 1:3. Average... H W -4 •G © o3 Cinders. Granite. Gravel. Limestone. Meramec River sand Fineness of sand. Passed J-inch screen. Size, 30-40. a «w 0 p 0 • •H « 37206—Bull. 344—08-2 18 STRENGTH OF CONCRETE BEAMS. AGGREGATE. The results of the physical tests on the granite, gravel, cinders, and limestone used in the plain beams are reported in Table 6. The crushing strength of the 1:2:4 concrete made of these aggregates is given in connection with the results of tests on the plain beams, in Table 10 (pp. 48-53). Table 7. — Tests of cement 140, used in testing Meramec River sand (strength in pounds per square inch). Kind of test. Neat. 1:3 mortar. 1 day. 7 days. 28 days. 90 days. 180 days. 360 days. 7 days. 28 days. 90 days. T80 days. 360 days. Tension. Average. Compression. Average. Transverse. 362 375 372 370 3.425 3,275 3,300 3,333 756 792 774 774 ' 710 700 718 709 9,300 9,325 9,175 9,266 1,440 1,440 1,476 1,452 696 705 709 703 10,512 11,125 10,497 10,711 1,872 -1,908 1,944 1,908 775 792 781 . 783 12,288 12,612 12,862 12,590 1,998 2,016 1,962 1,992 827 811 813 817 13,980 13,725 13,803 13,836 1,944 2,088 2,034 2,022 846 853 831 843 14,274 14,410 14,320 13,335 2,142 2,232 2,124 2,166 342 375 364 360 1,570 1,555 1,735 1,620 527 540 531 533 3,200 3,300 3,0^5 3,175 445 445 413 434 3,698 3,400 3,549 405 388 394 396 5,025 5,025 4,800 4,950 414 408 405 408 5,500 5, 425 5,239 5,388 Average. Remarks.-*- Fineness: Residue on No. 100 sieve, 6.8 per cent; on No. 200 sieve, 22.8 per cent. Specific gravity, 3.12. Time of set: Initial, 142 minutes; final, 428 minutes. Soundness: Pattest in air at 70° F., normal; in water at 70° F., normal; in water at 212° F., 3 hours, normal; in steam at normal pressure, 5 hours, normal. Water used in mixing: Neat, 20.5 per cent; mortar, 8.9 per cent. Temperatures: Of air, 71.0° F.; of water, 68.0° F. PREPARATION OF TEST PIECES. METHODS OF PROPORTIONING. A 1:2:4 volume proportion was adopted for all the concrete used in the following tests. Since, however, the volume of a given weight of dry sand is greatly affected b} 7 ^ the percentage of moisture present, it was thought best to do the actual proportioning by weight. The weight of 1 cubic foot of cement was assumed to be 100 pounds. The weight per cubic foot of the dry, loose sand and the dry, loose aggre¬ gate as determined by tests in the constituent-materials laboratory, was used in reducing the proportions by volume to the proportions by weight. With this as a basis, the necessary weight of dry material for the desired batch was determined. Since the sand and stone,, as stored in the bins, contained an appreciable amount of moisture, the dry weight of the material had to be increased by the weight of the mois¬ ture present before the batch could be weighed out. The percentage of moisture was determined on a 500-gram sample of the sand and stone each day on which beams were molded. PREPARATION OF TEST PIECES. 19 The above method of correcting for moisture was followed in the series of concrete beams and in the greater part of the first reinforced beam series. It was noticed from time to time, however, that the concrete when dumped from the mixer was not always of the same consistency, in spite of the fact that the total weight of water present (weight of water added plus the weight of the moisture in the sand and the stone) was a constant. A moisture determination was then made on a sample representing as nearly an average of the material in the bin as it was possible to obtain, and this was then maintained constant and gave much better results. The effect on the consistency of a given change in the weight of the moisture in the sand or stone does not appear to be the same as that of an identical change in the weight of the water added to the batch, the difference probably being due to the fact that the moisture test is only local and does not represent the true average of the material in the bin. It should be noted here that the proportions by volume of the cin¬ der concrete are nearer 1:2:5 than 1:2:4. This is due to an error in making the moisture determination at the time the weight per cubic foot was determined. The weight per cubic foot of the cinders, in¬ cluding apparently 11.1 percent moisture, was reported as 68.1 pounds. Using these figures gives 61.3 pounds per cubic foot for the weight of the dry, loose cinders. These determinations were accepted as cor¬ rect until a sample, which had been forgotten in the oven, showed 23 per cent moisture present. This error in the weight per cubic foot, due to insufficient drying of the test sample, was not discovered until the series of cinder beams was almost completed. While a new deter¬ mination of the weight per cubic foot was made and the proportions by weight and volume modified accordingly, it was thought best to use these proportions and the correct weight per cubic foot on the re- „ maining cinder beams rather than the 1:2:4 volume proportions, in order to make the cinder beams comparable among themselves even if not strictly comparable with the beams of other aggregates. The weight per cubic foot, as redetermined, was found to be 47.0 pounds. METHOD OF MIXING AND CONSISTENCY. MIXING. All concrete was mixed in a motor-driven cubic-yard cube mixer, which is equipped with a charging hopper. All water used in mixing concrete was weighed and was supplied to the mixer through a hose attached to a water barrel, which is mounted on a platform scale on a support above the mixer. To insure uniform conditions the interior of the mixer was wetted down each morning before the first mix of the day. All concrete was mixed two minutes dry and three minutes 20 STRENGTH OF CONCRETE BEAMS. wet, after which it was dumped on the cement floor, shoveled into wheelbarrows and wheeled to the molding floor. Sufficient material was charged into the mixer to make two beams, two cylinders, and two cubes from the same batch of concrete. CONSISTENCY. Definition .—The three consistencies, wet, medium, and damp, as here used, represent each a certain characteristic behavior and appear¬ ance of the concrete in the mixer, on the floor, and in the mold when subjected to tamping. In order to eliminate the personal equation as far as possible, the amount of water required to bring the batch to a desired consistency for a particular aggregate was carefully deter¬ mined by trial before the test pieces were molded. Thereafter the weight of water to be used with each aggregate for that consistency could be obtained by making a simple correction each day, depending upon the percentage of water contained in the aggregate as it came from the bins. The total amount of water, including moisture, was expressed as a percentage of the total weight of the dry material and was maintained constant. A brief description of the consistencies is given. It should be recog¬ nized that the consistencies as defined are purely arbitrary, but each, it is thought, represents a characteristic appearance and behavior, and, with a little practice, is readily distinguished from the others. Wet consistency .—Concrete of wet consistency has a smooth and somewhat viscous appearance in the mixer, or immediately before dumping. It flows back from the ascending side of the mixer without any tendency toward “breaking' 7 over at the top. The upper sur¬ face of the concrete in the bottom of the mixer rolls underneath the mass smoothly and is carried upward by adhesion to the metal. When dumped, it stands on the floor in a low pile, having a smooth surface, and showing neither voids nor individual stones. It can not be compacted by tamping in the molds, but splashes under the action of the tamper. When finished, water stands from one-fourth to one- half inch deep over the surface of the mold. Medium consistency .—Concrete of medium consistency has a smooth appearance in the mixer, but shows a tendency to lump. As com¬ pared to that of wet consistency it flows less smoothly and is carried higher by the ascending side of the mixer, part flowing back smoothly and part breaking over at the top in lumps. When dumped, it stands in a higher pile with steeper side slopes, exhibiting a somewhat lumpy appearance, and showing individual sfones, but no voids. The stones show an even coating of sand mortar. No water collects on the sur¬ face of the beam in the mold. The surface is easily finished with a trowel. PREPARATION OF TEST PIECES. 21 Damp consistency .—Concrete of damp consistency is decidedly granular in the mixer with little tendency to lump. The material is carried to the top of the mixer and falls in individual stones and frag¬ ments of mortar. When dumped, it stands at the same angle as medium concrete, showing both individual stones and voids. The surface of the pile is irregular. In the mold it offers considerable re¬ sistance to tamping, but compacts fairly well under hand tamping. No water flushes to the surface and it can not be finished smooth by troweling. METHOD OF MOLDING. BEAMS. The beam molds consisted of three long steel channels with flanges turned outward, forming the sides and bottom of the mold. The ends were closed by short pieces of channels. The side and end pieces were removable. The molds were oiled before the concrete was placed, to prevent adhesion to the surface of the steel. In molding the plain beams the concrete was deposited in three layers of about equal thickness. The tamping was done by hand with a 13f-pound tamper having a rectangular head 1J by 3§ inches. The tamping was started at one side of one end of the mold and the tamper moved toward the opposite side, the width of the tamper at each stroke. The tamper was then set forward and the process repeated. In this way each part of the layer was tamped once. The mold was gone over twice in this way, after which the concrete was spaded back from the sides of the mold and the layer tamped a third time. The same operation was followed for each of the three layers. The surface of each beam was finished as smooth as possible by troweling. The side and end pieces of the mold were removed at the end of twenty-four hours, and the beam was covered with burlap and allowed to remain on the bottom channel until moved into the moist room. CYLINDERS AND CUBES. In order to make the compression test representative of the true crushing strength of the concrete in the beam, the cylinders and cubes were molded from the same batch as the beam of the same number. They were molded in cast-iron separable molds, which were oiled previous to placing the concrete. The concrete was deposited in layers approximately 3 inches thick, and each layer was tamped twice, a circular hand tamper 31 inches in diameter and weighing 7 pounds being used for the cylinders and a rectangular tamper 3J by If inches, weighing 13J pounds, for the cubes. In molding the cubes an effort was made to “spade” back the con¬ crete from the sides of the mold, as was done in molding the beams. 22 STRENGTH OF CONCRETE BEAMS. The top surfaces of the cubes and cylinders were finished smooth with a trowel. All molds were removed at the end of twenty-four hours, and the test pieces were marked and transferred to the moist room. MOVING AND STORAGE. The large number of beams to be molded and the small space avail¬ able made it imperative that the beams be moved as soon as possible. In no case could they remain where molded for more than 12 or 16 days. Since a concrete beam without reinforcement, and weighing about 1,200 pounds, has very little tensile resistance at this age, it was very important that they be handled at points that would prevent any chance of injury when being moved to the moist room. The following plan was followed, and was entirely satisfactory: The channel forming the bottom of the mold was placed with the flanges turned down. At the points where the beams were supported in moving them, the webs of the bottom channels were cut away for a width of l t \ inches. Prior to molding this slot was closed by a filler resting on the uncut flanges. When the beam was to be moved, this filler was driven out and a slightly narrower piece, which projected 1J inches beyond each side of the beam, was substituted. A stirrup hanging from the chain blocks suspended from trolleys running on overhead I beams, was hooked under these projecting ends and lifted a 13-foot beam at two points 8 feet apart, which give equal positive and negative bending moment, and consequently minimum stresses in a beam of that length. The beams in the moist room were stored six high, being supported at the same points as when brought to the damp closet. All test pieces were sprinkled from a hose three times each day— at midnight, at 8 a. m., and at 4 p. m.—both before and after being placed in the moist room. The temperature on the molding floor and in the moist room was recorded on a self-recording thermometer, and Was maintained as near 70° as possible. METHODS OF TESTING. BEAMS. LONG BEAMS. APPARATUS. PL I shows a photograph of a beam in place. The supports “P” for the beams have cylindrical top surfaces, and are so designed as to give a slight yielding motion outward, the object being to prevent any restraint of the beam which might follow from the lengthening of the lower fiber. geological survey CONCRETE BEAM IN MACHINE READY FOR TESTING. METHODS OF TESTING. 23 The deformeter yokes (E, E') are fastened to the beam by tighten¬ ing the nuts A, which force the contact points (b) and those directly opposite on the far side of the beam, against the surface of the con¬ crete. The yokes are equidistant from the center of the beam, the contact points being 29.25 inches apart for the outer yokes and 24 inches apart for the inner set. The contact points of the outer set were 10 inches apart vertically and those of the inner yokes 5.75 inches apart. Both yokes were centered on the horizontal axis of the beam, thus bringing the contact points of the outer yokes 0.5 inch below the top and 0.5 inch above the bottom. The inner yokes were used only on some of the earlier beams in order to test the con¬ servation of plane section. Four pins directly in line with the con¬ tact points on E engage cylindrical holes in the ends of the four rods? the other ends of which rest lightly on hard rubber rollers fastened to the arms C, which are rigidly connected to the yoke E. Four micrometer screws reading directly to 0.0001 inch work in bushings fastened to the yoke Eh When any micrometer screw is brought in contact with the end of the corresponding rod, an electric contact is made, which causes a click in the telephone receiver F. Both yokes are divided into two vertical halves by rubber insulation, thus making it possible to read micrometers on both sides of the beam simultaneously. METHOD OP ZERO DEFORMATIONS. The deformation of concrete in compression in a beam is obtained from a reading of the upper micrometers, while the lower ones give the elongation of concrete. The readings of both upper and lower micrometers, making the usual assumption of conservation of plane section, fix the position of the neutral axis. The beams were all tested on a 12-foot span by two equal loads, applied at the third points of the span. The load apparatus consists of a box girder (II) built of two 6-inch channels with a J-inch cover plate on the top and the bottom. The load is transmitted from the testing machine to the box girder through a spherical bearing block (I), and from the box girder to the beam by two 2-inch steel rollers (J) bearing on two steel blocks (not shown) set in plaster of Paris. The upper surface of these blocks is a cylin¬ der of very large radius whose axis is parallel to the length of the beam. With the exception of these bearing blocks the entire load apparatus is suspended from the top head (L) of the testing machine by a bolt passing through the spherical bearing block and engaging a plate on the inner surface of the box girder. The steel rollers (J) are kept in place by the casting which extends a trifle below their axis. 24 STRENGTH OF CONCRETE BEAMS. On commencing a test the bearing blocks are removed and yokes (K) are passed under the test beam and over the box girder directly above the 2-inch rollers. The head (L) is then run up until the reaction at the ends of the test beam has been so reduced that the total positive bending moment area is equal to the total negative bending moment area within the gage length, considering the beam as a continuous girder over four supports, viz, the two end supports and the two intermediate yokes. This method is used for the following reason: In tests of beams as usually made, the upper and lower fibers of the beam are already deformed and are under stress due to the weight of the beam when the first, or zero, reading of the deformeters is taken; the deforma¬ tions computed from these readings are too small by an amount which becomes relatively more and more important as the breaking loads decrease and which in the case of plain beams (many of which fail by a load but little in excess of the weight of the beam) becomes a very large part of the ultimate deformation. When a beam rests freely on supports, the upper and lower fibers are deformed on account of the bending moment due to the weight of the beam. When the supports are at the ends of the beam the upper fibers are shortened and the lower are lengthened. For equal moduli of elasticity in tension and compression, which are constant for con¬ crete under small loads, the deformation at any point of the beam is proportional to the area of the bending-moment diagram over that length. Therefore, when the total positive bending moment area in the gage length of the deformeters equals the total negative bending moment area in the gage length, the net total deformation in that length is zero, and both the upper and lower fibers of the beam have the same length as when unstressed. For a particular reaction at the ends of the beam the positive bending moment area in the gage length is equal to the negative bending moment area. In order to> get this reaction the beams are supported at the third points by the head of the machine as previously described. As the stirrups under the third points of the span take more and more of the weight of the beam the end reactions become smaller and smaller and the character of the bending-moment diagram within the gage length changes until the desired condition is reached. METHODS OF TESTING. 25 The method of finding the required reactions for total zero defor¬ mations within the gage length, in terms of the weight of the beam and other known quantities, may be understood by reference to fig. 1, as follows: ^k <0 1 1 \ _ i z. 9 -H z. L , Z Hr K s * - s z r- s — /=■ Tig. 1.—Diagrams illustrating method for computation of concrete beams. Upper diagram: Nota¬ tion used. Lower diagram: Curve of bending moment within gage length (beam supported at third points). Let L = distance between the supports, gage length of deformeters. overhang of beam at each end. or & Z L 3 — = distance from each support to force exerted by each stirrup. W = total weight of beam. — R = force exerted by each stirrup at a distance of ^ from the supports. R = each reaction at end. SS = any vertical section within the gage length at a distance, x, from one of the gage points. M x = bending moment at section SS. . M 0 = bending moment at deformeters, where x = 0. O’ M c = bending moment at center of beam, where x = |. m = constant bending moment over the gage length due to the weight of all attachments, such as bearing blocks under the load points and the deformeters. This weight is applied outside of the gage length and equally on each side of the center of the beam. The bending moment at section SS, considering forces to the left only, is as follows: -| + x ) + 0-K)(j. -f + *)- 2 (L + jizy ■ Q + Z-| + x) 2 + m. 26 STRENGTH OF CONCRETE BEAMS. Reducing to a simpler form gives: -t(s+ z > 4 w + m. The bending moment at the end of the gage length (x=0) is as follows: M 0 RL Wg 2 +m. The bending moment at the center of the gage length follows: lVi r . = RL W/L ' 3 4^6 +Z + m. is as The moment diagram between the third points, when there is both positive and negative bending moment in the gage length, is shown in fig. 1, in which xx' is the horizontal axis of the moment diagram. The curve bee'b' is a parabola and crosses the axis at two points (viz, e and e') between the ends of the deformeters. Then in the gage length cc' there is negative bending moment from c to e and from e' to c', and positive bending moment from e to e'. The dotted lines cb, c'b', and bb' are drawn for the purpose of demon¬ stration. Then the distance M c represents the bending moment at the center of the gage length, and M 0 represents the bending moment at the end of the gage length. The negative bending- moment areas within the gage length are cbe and c'b'e', each being represented by — B. The positive bending moment area within the gage length is eFe' and is represented by A. The condition that the positive bending moment area is equal to the negative bending moment areas is represented by the equation A = —2B. Adding the quantity —C to both sides of the equa¬ tion gives A+( —C) = — 2B —C. The first part of this equation is the area included between the horizontal line bb' and the para¬ bola bFb'; that is, A + (— C) = ^g [M c + (— M 0 ) ]. o The second part of the equation is equal to the area of the rec¬ tangle bcc'b'; that is, —2B —C = —gM 0 . 2 Therefore “g [M c + ( —M 0 )] = —gM 0 . Whence 2M C = —M 0 . Methods of testing. Substituting the values of M 0 and M c as found above gives: Wg 2 2RL WAL , , 0 RL WAL _\ 1 3 2V_6 +Z J +2m 3 +4 V 6+Z y 16 ^ Whence RL = +Z Wg 2 , 16 (J +Z ) h z 3m —m. , „ 3WAL r7 \ Wg 2 and R =,( w- +Z ) H-^ 4LV - 6 J 16L0+Z) 3 in L ' In almost all the beams tested at the laboratories L, Z, g, and m are constant. It only remains to find W and to compute R. A table computed by the above formula has been compiled for all the usual values of W, from which the corresponding value of R in any case can be directly read. METHOD OF TESTING. When the test is commenced, the top head is run up until the reac¬ tions causing equal positive and negative bending moments over the gage length are developed at the ends of the beam. The sum of these reactions will appear on the weighing beam, the testing machine having been balanced before the weight of the beam and all test apparatus comes on it. A full set of deformeter readings is then taken. After the readings at zero total deformations in the gage length and when the beam rests under its own weight are taken, the load is applied in increments of 200 to 1,000 pounds, depending on the stiff¬ ness of the beam, the top and bottom set of micrometer readings being recorded on the log sheets. Wood blocks are placed underneath the beam during the test, so that the distance it falls at rupture is not more than one-fourth inch. SHORT BEAMS. The longer portion of each beam after first failure is again tested on as great a span as its length permits, thus making a secondary series of short beams. The load is applied by the same apparatus as that used for the long beams, but instead of being applied at the third points it is applied at points 2 feet from the center of the span. The short beams are not suspended for zero deformation readings, since for such small spans the deformation of the beam under its own weight is very small. On all short beams the outer yokes having a gage length of 29.25 inches are alone used. 28 STRENGTH OF CONCRETE BEAMS. CYLINDERS AND CUBES. The cylinders and cubes are tested on a four-scre\v, 200,000-pound Olsen machine. To insure an even distribution of load over the entire cross section the ends of the cylinders are bedded in plaster of Paris to a thickness of about one-half inch on a piece of plate glass (previously oiled to prevent adhesion of the plaster). The bearing surfaces are made normal to the axis of the cylinder by means of a spirit level applied to its sides. The cubes are not capped with plas¬ ter of Paris, but a thin piece of asbestos is placed on a spherical bear¬ ing plate when under test, in order to take up all nonparallelism of the ends. The load is in each case carried to failure, being applied continu¬ ously to rupture in the case of the cubes and in increments of 5,000 pounds, or approximately 100 pounds per square inch for the cylin¬ ders. For each increment gross deformations are read on two oppo¬ site sides of the cylinder over a gage length of 12 inches. RESULTS OF TESTS. 9 BEAMS OF CONSTANT SPAN. The detailed results of the tests of concrete beams 8 by 11 inches in section, 13 feet long, tested on a 12-foot span by two equal loads applied at the third points are given in Table 8 (p. 36), comprising the IIG. 2. Diagrams showing the effect ol age and consistency on the strength of cinder concrete. RESULTS OF TESTS. 29 three ages of 4, 13, and 26 weeks, and some of the results are graph¬ ically shown in figs. 2-5 and 10-13. Fig. 3.—Diagrams showing the effect of age and consistency on the strength of granite concrete. The percentage of water is expressed in the table in terms of the total weight of the dry material. This percentage includes the weight of the moisture in the sand and aggregate, which varies from 30 STRENGTH OF CONCRETE BEAMS. 1.5 to 2.0 per cent of the weight of the stone, from 3 to 4 per cent of the weight of the sand, and may include as much as 21 per cent of the weight of the cinders. A simple computation, using the proportions Fig. 5.—Diagrams showing the effect of age and consistency on the strength of limestone concrete. Deformation per unit of length Fig. 6.—Characteristic compression-stress deformation diagrams, cinder concrete of medium consist¬ ency; ages 4, 13, and 26 weeks. by weight, will show that this 21 per cent moisture forms as much as 43 per cent of the total amount of water, including moisture, that is necessary to bring the concrete to the desired consistency. Deduct- RESULTS OF TESTS. 31 ing this 43 per cent moisture from the total percentage of water leaves about 12 per cent of the total weight of the dry material as the weight of the water added plus the weight of the moisture in the sand. This does not differ so very much from the percentage of water used for the other aggregates. As already indicated, it would seem that the influence of the water present in the stone or cinders and even for usual values of 3 to 4 per cent in the sand does not influence the consistency as greatly as does the same weight of water when added to the batch. Column 6 of the table gives the consistency of the concrete and must be compared with the defini¬ tions of wet, medium, and damp concrete already given (p. 20). Columns 7, 8, and 9 give the dimensions of the beam, the span being kept constant at 12 feet. Column 10 gives the total weight of the beam, which is obtained by weighing the beam on the testing machine. The er¬ ror in weighing is in no case greater than 5 pounds in either direction. Col¬ umn 11 gives the weight per cubic foot of the beam. Column 12 gives the unit elongation of the lower fiber when the beam rests freely on a 12-foot span subjected only to its own weight and the weight of the deformeters. This value is obtained by first taking a reading for zero total deforma¬ tion as already described (p. 23) and a second reading when the beam rests as above. This value is included for the reason that in all tests made up to the present time deformations due to applied load only were read. If it is desired to compare the present tests with others already made the unit elongation as given in column 14, which was measured at a load just previous to rupture, when decreased by the 4000 3800 3600 .3400 ■3200 3000 2800 2600 £ 2400 1 2200 2000 1800 1600 1400 1200 1000 800 600 400 200 ** S kS J y _5< /v P "A A ./ A ' ^ / / ?/ 7 wl V > A J1 / u r if o rjr r ft f y rr r* / i w 7 3 T o o o o o o o Deformation per unit of length Fig. 7.—Characteristic compression-stress deformation dia¬ grams, granite concrete of medium consistency; ages 4, 13, and 26 weeks. 32 STRENGTH OF CONCRETE BEAMS. value in column 12 will give the unit elongation at a point near rup¬ ture for the applied load alone. Column 13 showsp4 3 (pounds per square inch) for the last load previous to failure. The relation of this value to the breaking value in column 19 is readily seen by comparison. In computing all the M values of p^ 2 given in these tables the nominal values 8 inches and 11 inches were used for the breadth (b) and the depth (d) of the beam. Column 14 shows the unit elongation of the lower outer fiber for the load previous to rupture. An unsuccessful attempt was made to obtain an exact value for the unit elongation of the lower fiber at rupture, but it was found impossible to take a reading of the mi¬ crometers at the exact instant of the breaking of the beam. Just previous to the break the concrete in the lower fiber elon¬ gates so rapidly that it is impossible to revolve the micrometer fast enough to maintain contact with the rod. While the lower micrometers on both sides of the beam may be read as the beam breaks the values obtained are so erratic that they have not been included in the tables of this bulletin. The unit elongations reported under “ Final def ormeters ” (columns 13, 14, and 15) in Table 8 are the values obtained at the last full set of readings preceding the breaking of the beam, and it must therefore be recognized that while they approximate the elongations at maxi¬ mum load they are not absolute. Attention is called to the apparent ir> o o o o o Oeformation per unit of length Fig. 8.—Characteristic compression-stress deformation dia¬ grams, gravel concrete of medium consistency; ages 4, 13, and 26 weeks. RESULTS OF TESTS. 83 relation between the values in columns 13 and 14. Separating the aggregates into cinders on one hand and the three stone concretes on M the other, the elongation seems to bear a direct relation to or the load carried. This comparison, however, can not be made for the cinders, owing perhaps to the nonuniformity in the strength of the clinker itself. Column 15 shows the position of the neutral axis for the load pre¬ ceding failure. This is obtained from the usual assumption of propor¬ tionality between defor¬ mation and position of the neutral axis. The maximum load ap¬ plied at the third points of the span (column 16) excludes the weight of the deformeters. The corresponding M; is 1 bd 3 shown in column 17. Column 18 shows the ^ for the weight of the beam, taking into con¬ sideration the effect of the 6-inch overhang on each end and also the constant weight of the deformeters. Column 19 shows the M bd 2 ’ 4000 3800 3600 3400 3200 3000 2800 2600 -C O c £ 2400 C3 =3 Z 2200 co o 1600 c 3 1400 1200 1000 800 600 400 200 a 7 A r M /? / 7 V V ¥ 7 w ¥ \ to o o o o o maximum total DO.' Oeformation per unit of length which is equal to the Fig. 9.—Characteristic compression-stress deformation dia- SUin of the values in col- grams, limestone concrete of medium consistency; ages 4, 13, , and 26 weeks. umns 17 and 18. Column 20 shows the modulus of rupture in pounds per square inch. These values were obtained by multiplying those in column 19 by 6. The method of computing the modulus of rupture should be empha¬ sized. It is based on the assumption that the coefficients of elastic¬ ity in tension and compression are equal and constant and that 37206—Bull. 344—08-3 34 STRENGTH OF CONCRETE BEAMS. consequently the neutral axis remains in the center of the beam. An examination of the table shows, however, that the neutral axis actually varies from 30.4 to 63.0 per cent of the depth of the beam below the top. Column 21 gives the distance of the break from the center of the beam, which in few cases is more than 1 foot. 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CM CO ^ X CM CO H s X 05 05 iO X Q rH LO X r- rr x cO iO >o 00 S R 3eS|P g ft CO CO Tf o rH GO lO CM X 05 lO to o co X X X CD O 00 rH O CO Tf ^ »dcoco od 05 *o r- 05 cd X iD 05 05 iDhX X ^ coco X XXX X X X X X 05 X X 05 O 05 rH 05 1 © gf. ft ft s 1 • 05 10CX) rH O *0 05 LOiON 05 XCNiO X x o CM CM X rH o 1 O © Lt P7-< ^ ft g 2 o 00 05 X CO X iO N lO iO XXX CO HTJ<(M CM rr CO XNiO r- 0| o CO CO CO cd cd cd cd cd CO CO CO cd T-H T —i T—\ rH O t-H 05 o opo cd -oa -*H rH t-H t-H r-H rH rH rH rH rH rH rH rH CM CM CM CM CM (M h 04 lO cd oo cd x cd 04 X ^ od Q »D 00 »D ^ ^ od ^ X ■^r XXX X XXX X io r r ^ ^ TJ1 tT co tfXN X X O 04 X X 05 rH X CO 05 rH 05 o 04 ID 05 o X 05 X X X 04 05 X N04X rH 05 rH rH o CO CO iD ID 04 04 04 Ol 04 X 04 CM rH rH rH ci^-3 rH t-H rH rH rH rH rH o O Q O o o o o o o o o o o o o o o o o o o o O O O 5 «05 g c o o O O' o Q o o o o o QQO -C J cDj o o o o o o o o o o O O o O ill o3 l^H -IP) ^ 'o o 4^> > CM O' I GO CO CO CO CO CO CO cO 04 05 rH X 04 04 05 05 X CO rH O 04 O cc r- *b GXO X O' x X CO O co X rH rH lD 04 OO ID e O H 04 CO cd ID CO 04 00 05 00 od ^ cd o o 05 ID 00 X rr X X X XXX X CO X I^ X X X X 05 05 05 •a p d - ft

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o o o o o o o o o o o o o o o o e o o o o o o o o o 00 o CO CO O GO co lO 0C- tU CO U- LO 05 O ^ Tp LO Tp ;D LO r*j fc'* CD H rH 1- o 00 CM rH CO cO 03 t'- "T 1 oo CO CO CM 041- r- 04 g ft £ CO o o o d rH CM O 05 O 05 05 cd CM 05 GO CM rft cd LO CM 05 05 ^ ft O co rr CO LQ "TJH TJH CO YT CO CO 00 05 00 X 05 05 05 O 05 05 05 4ft> e rH tOiON cO to 05 05 00 rH CM 05 rH rH TP rH 04 05 CO rH rH H ,-» i * tt rf N 1 Tf lO rf Tf TJ’ CM 04 rH CM 04 04 CM Ol rH 04 CM CM .Lft ^ r/i o o o o o o o o o o o o o o o o o o o o O O O O Unit elongi jr p-. r O c3 05 C5 G5 05 05 05 05 05 05 05 05 05 CM CM CM CM 04 CM 04 CM rft rH 04 04 o ft FH rH rH rH rH rH rH rH rH rH rH rH H ft |co |co IrHtHOC Ir- |co Ko |co |r |r» jrH « IC ° |HrH|0OH|X _tCC„|*sD H|N W |rt W H ‘ih^ihhM H |C ° H|« HWIOO rH CO H rH rH rH rH rH rH rH r-H rH rH rH rH rH rH rH o3 03 a o 03 03 ft 33 rH i-H H rH rH rH rH rH rH rH rH rH • 1 rH rH rH rH rH rH <+H •rH • O'® CO 03 P rP o 03 m 03 1 1G i 1 16 1 1 6 |C0 ICO IrH |rH J<0 h|oOh|cC O CO 00 00 00 00 00 00 00 00 CO 00 00 GO XXX XXX o o m £ 5 P W 03 H f;oS MASS'S D* lOlOOftlfJCClCO U?|COH|N«|00 wiaoioicowlH «5|O0«|O0CO|H «|H*h!MW|H IO|X»0|COH|M P 03 P 03 cO p--< o_ , ft d o • • 1 ft 1 1 ft o d -d c o ft • ! d-P r» 0.2 a Tj O O goo goo 03 r^ r^J aS'C'O « 3J 33 05 T3 ft (U'3 r 3 caa) 3J O 03 +* 03 bC (M JS o o -S ft ft a 1 ! ’■o ft ft a ! ! tv\ .ft o o ft o o ft o o S bo bo 333-3 * • Ph • • POO c3 • • p4 • ’ POO • • Ph ' • • < 5 : ; o . . 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JCO h|0C W M W M c? 10 n|H r-H r-H t-H t-H t-H r-H • t-H t— « rH rH rH rH rH rH rH rH rH t-H t-H t-H t-H t-H t-H • rH t-H t-H rH rH t-H rH rH rH rH rH rH § +H o tH| 00 n|X JSO rH|0D H • jco i h|00h|QC H .KO .|C0 H |tH nice ^ico^Ho 2: 00 00 00 00 00 00 • 00 00 00 00 00 oo 00 00 oc 00 oo oc a »0| r ^) r rd >'3fl . > r O "O 2 ts -a © T3 2 TJ 'O ce • • c3 • • • GC • • s ■ ■ g • • B ■ • ^ 1 * *H 1 * 1 Sr ' ' . — 1 ‘ o : : o : : : o : : p5 : : p5 : : : ; . . . . . . a> bo : : : tuD : : : be be be bo • i • a ■ • • c3 ••• 03 . , , 03 • • • c3 • • • c3 • i i ?H • i i Jh aai »-H ■ ■ i • i • u ■ i • • i • 03 • i i o • • • iii > . . i > • • . > • . • > i \ i -< CONOO -<5 1 02 O r-H < Tp LO CO <1 TP LO GO <1 00 05 O <1 tp io CO o o o r-H CM CM CO CO CO Tp Tp io LO LO CO 05 05 05 rH t-H t-H r-H t-H t-H rH t-H rH rH rH CM rH CM CM Table 9. — Tests of concrete beams of variable span. TESTED AT FOUR WEEKS. 42 STRENGTH OF CONCRETE BEAMS. l o GG O >*! _ 1 . r>- . • CM ^ O CM • to X 05 CM to ^ i ireal toit cen¬ ter inch es). Ol • H • • T-4 CM rH • rH CM t 5 § 3 01 * * • • • • • i • • • • ■ f. A '<* IOC5X CO O X to Tt« X O CO X to ^ co to X X CM CO CM CO h o O Ol XC5N X X X CO 05 X 05 O 05 05 05 co X r - nr r- O 1-4 —4 X to to to CM s o L +j w ^ rH rH r-H rH CM r-H r-H i-H i-H i—4 CM T—4 XXX X ^ Ml TJ< tji to i -H r-H *. • O O X CO O CM ^ 05 to 05 r- O O 05 X to co co o i—4 r>. i-H s X •pg te ® ^ w 05 CM t- 05 X x to X ^tox 1—1 X CO 05 r-H CO CO CO CO 05 to c3 o'* Lo o ® o CO 00 o XhN CM 0 T ^H to to o 05 00 to to oo CO a -4 4J 1 X X CM X X X CM X XXX X CO CO co CO I- t- t- XXX X •4-5 1 ^ • « r- io —( X to X HOi’f • **f X o • X CO CO • CO 05 CM • ? M-f o| oS S'? T3 g 05 CON X 05 ^ tb O O 05 ^ ^ CO O CM X ^ co ^ 1 O X CM CO lO >c 1 05 o o cb cb • • • r-H CO i"H cb to cb * • • • • ^ . CO to to 05 05 cm r - co ^ O X CO CM 05 NOO to X 05 • « & . i, 3 G N S "3 ® ft ^ !,c o ® GC CM CM tO ^ X to co CO CM to X • 53 T3 fi.s r-i cc oi rr r- co co to 05 05 05 tO c^i oo ^4 • 05 O CM • CM CM CM X CM CM CM CM CM tO tO to NCON i X X • 'x g TJ o o o • • ooo ooo ooo ooo ooo • • O 1 - I- • CM O CM O’t X to o o ooo ooo • S 03 C3 -rj< 50 Hf< to ^ 05 Hti oo 05 o o ooo ooo o • i-A i-4 ^ CM to ^ X • • ^ CM X NXC5 X 05 X O X ^H r-H r-H r-H m « £ S .2 0.2 2 X! 91 ao iO (M O ^H CM X to X ^ 00 X co r- 05 05 CO CO X 05 to X GO lO CO XHN cO lOCIH to 05 X o o t- to tb ^ 05 u 0 > ft +-> 3+* 3 co -3 -t 1 X XXX X XXX X ^ to TJ 1 "T tT rf rt< 1 lOOH ^ O tO ^ 05 X X 05 to CM ONO o CM 05 to 05 H ■ 3 c3 - *H *H • X to 05 CM X O CM X 05 X CM to 05 r- r ^ X 05 05 o 05 X CM CM CM .TZ be C ® a; c H n >P ^ i® NNH CM CMXh CM CM CM CM CM ooo o O O -H o -H y-H rH rH o o o o OOO o OOO o ooo o ooo o OOO o ■T -1 — O r- _Q P 5 P 2 o tfl — o o o o ooo o ooo o ooo o OOO o ooo o a; O O o o ooo o ooo o ooo o ooo o ooo o X3 © o /■> ^ 05 CO £ X r- r-H x x rH o X X to to -f X o WH 1x3 if ^ U 2 o tO N X HSN CM CM CM CM 05 ^ X CM cb ^ CO CM to CM CM 05 CO 05 co COON X X 05 4-5 CM CM CM X CM H CM CM CM to to ^ CO O co ^ i>- r- ~.2+i CO ^ to X T—4 X 05 o X 0)>0h CM i Hl30 HHoo • wl® • t'jOO |H 3 Ox rH rH rH 1—4 i-H rH • i—H rH i-H • rH rH rH • rH —4 rH • 1—4 i-H H 08 o> o 8 2 o ft i-H rH i—4 r-H rH r—4 • i—4 rH i-H • i—4 r-H rH • 1—4 r-H r-H • i—4 i—4 r—4 6 1 16 h|H • H|H . JCOiOK© • Hr4(H • J® • Ihh|oo o CO .3 o 05 XXX XXX • XXX • 00N00 • XXX • XXX CG W > • • G t * O 1 *s 2 • X NOO • • X CO 05 , co O O . N OCO • O CM 1-4 • CM X CM • • 3 4H HH • 4-5 £ : : § : : : Pi : : : : : S : : •O'* • Mi. • • • c3 hi o 4H to O X CO -r -r ■cf' • OOO • (MOO . X r}4 • 05 05 05 A 3,3 i—4 i-H i—4 ooo • 05 05 05 . 05 05 05 • N00 00 . cb o o QJ CM CM CM rH CM CM • rH 1 —* —4 O XXX X ^ • -^4 r-fH rJ4 • CM CM CM • O CM CM • CM CM CM XXX X to to * Hf rf Hji • XXX • XXX • XXX 4-4 CM CM CM o i CM CM • cm oi o i • XXX • XXX • XXX bo CM CM CM cm r- t- ooo • i—4 i-H rH • rH rH rH • rH r—4 r-4 • rH rH rH 3 o "3 OOO . OOO • OOO • ooo . OOO CM CM CM oi cm oi • CM CM CM • CM CM CM • CM CM CM • CM CM CM H4 i-H rH i-H r—> —4 rH • r—4 rH i—4 • rH —4 i-H • i-H rH rH 1 o P4 o CO CO CO CO O O • 05 05 05 • Tf rJ4 Hf4 . Tf4 -rf4 r^4 • Tfl Tt^ 0) ooo o ^ 'T • rH rH i—4 • CM CM Ol .. • .. • ... . . • • ib tb to • CM CM CM ■ CM CM CM r— 3 1C >o o to to to X . • • • • • • • rH rH r—4 • —' CM CM CM CM CO co • CM CM CM • • • • • • • ■co© « rH • rH rH rH CM CM rH r-H ■ • b 4-5 c3 • • • , * * • • • : : > . . r • . ^ > ■ ■ < • ■ P • ■ < • • < r - x 05 x x x MCCX > < 00 03H rH r—4 'J’XCI CM CM CM x tt o -H Tf lO ‘O O CO RESULTS OF TESTS 43 co co co • GO CD • h dj *d ■ 05 CO LO © rH Tp 05 © rH l • • • rH t-H • t • • t t-H i • • rH rH rH t-H 10»0»0 CM t-H Tp t-H OOCN 00 rH CD 05 oq © © C J3 h|h H • i rt ioo M l2H2 • JCO |n^|-HM|00 t • H H H wicoioKo rl|00 H|Hri|H rH rH t-H t-H t-H t-H i rH rH rH rH rH rH rH rH rH rH O © t-H t-H t-H t-H rH t-H • t-H rH rH rH rH rH rH rH rH rH rH t—H J® Hlav M h|ooh|oo |tH • JfO tH|00 ItH • .ICO M JfO *0 h H H H 1 * 0 |h oo oo oo 00 00 00 • t i 00 00 oo • • • • 00 00 00 00 GO 00 00 00 00 • • • CO 05 Ol • OND • • rH O CD • • CM rH rH • © © © rH rH 05 « • t-H • « • ( 1 rH rH i • • rH rH * • • • NON t • cd co CO • • i © • i © © • • • « • • a : : I • • • • • ft : : H o o Tl O C goo +J o o d O O goo 0) T T S'O'O a> t 3 x) £ : : S : : o : : • • £ : : § : : ft : : »OiON CD CD O CD CD CD 00 00 O © © © Tp TP TP • . 05 © © GO 00 05 t- ooh © © © 00 oo 00 rH t-H t-H rH t-H t-H : o o o o o o o o o rH rH rH rH rH rH rH rH rH • | t-H t-H t-H rH t-H t-H rH rH t-H 05 05 05 © © © © © © ^P TP TP Tp TP Tp Tp Tp TP cd co cd co cd cd co co cd T—H t-H t-H rH rH rH rH rH rH rH rH rH o o o o o o o o o o o o © © © © © © CM CM CM cm~cm~cm cd cd cd cd cd cd oj cd cd CM CM CM t-H t-H t-H rH t-H rH rH rH t-H rH rH rH rH rH rH rH t-H rH • TP tP tP TP Tp TP TP tP tp ^P TP TP Tp TP TP Tp Tp TP : CM CM CM (NCUN (NCUM CN Ol oi * * CO O O ■4H • • WOO . . W ° ° : >73-0 > T T 2 ^ r 3 ®X)'C Si T T cd • • ce • • cd • • g : : g : : 9 : : u • 1 u • • D 1 ' o : : o : : o : : 1 3 : : ft : : ft : : 05 05 05 05 05 : : ; 05 • • i bJ3 • . i ho hfl . . . hfi . . i u . . • W) <33 • • i od • • • cd cO • • i a • • • cd • i • • • • • • • *H ^H • i • *H • • • fcH 05 • • • 05 05 05 i • i 05 • • • 05 > • • • r> it* • • • > • i * > • • • > • • • < O H CM < CM CO LO <1 00 05 © < t-h oj CO < © H CM oo 05 o o o o rH t-H t-H Ol O l CO Tp TP TP LO LO LO oo oo o: rH t-H rH H H H rH rH rH rH rH rH HHH Table 9.— Tests of concrete beams of variable span —Continued. TESTED AT THIRTEEN WEEKS. 44 STRENGTH OF CONCRETE BEAMS. 1 1 © GO © •rH H 1 P § Jx! r~ 1 O 1-H X 05 O 03 ^ rH O t © © © © rji O • r O «h 01 >rea fron cen¬ ter inch es). 03 03 CH t-h i-H • « • H 03 H rH - t 1 1 • rH rH 03 • i • • 03 1 r—* — • 03 rf) 1 fl) • OlOOC o X 05 X X 05 PO X rH © Tfl X to 03 © 03 © © ^ © 03 03 X O as co io rr ^COJ 03 X X rH X © rH sss X © 03 © H o 005^ o rH X X o r-H GO Tf X X 38.0 05 rH X 05 05 CO TT X © rH © d 03 03 © X 03 x d d © © © X ^ c+-> 'w' T—' ^ CO TT XXX X XXX X XX© X © © © rH © -*p> 1 r-* t • s 1 • g 5 © ^ W 4H» Tf CSI Tf X 05 C© © kO Tf © rt< ic COO © X © he o O u & + °'g: ^a Si iO N CO ioiod I - CO O T?i ^ XNH CO d ^ X 03 rH © kO © as os o; - ^ H,0 — o o o o o o o o © © © © © © © © © © © © ©•© © © © p> 5 o oc o o o o o o o o © © © © © © © © © © © © © © © © © o r-H c3 3 P4 72 io ^ I — c© X to ko 1 1 © X 03 © © © X 03 ^ i_j OONO lO h 05 ko • X X © ^ X © © 03 rH p s ,© O rH i-i os eo CONCO X X 05 © rr © © 05 03 X 03 +3 CO 03 CO X 03 X X X 03 I- 1^ I- X XXX P tc •5PC »H © |P P* o « p ^ CO CO GO CO iO X 50 03 X rji rf rf IO TjS X X 05 ^ CO kO to rH N N 05 © X 03 © 03 © © © rH tO X tO © © ^ © CO rH tO pH 3 O r-H r-H r-H r-H t-H r—H rH rH r-H rH rH rH r-i rr Tfi iO H 'CT r}H TJH Q *H r—l rH rH H H rH rH rH r-n rH rH rH rH rH rH rH rH rH rH rH rH rH rH rH i © D i> o 03 ^ O 05 X ^ © X X X © X © X © © © 1 ^ » 03 NiOO r—H r-H X © X 03 03 © © © © © X 10 10*0 IO 1C O to ^ © © © to © © to o H SP. P£S hInhIch CO CO CO H|N r-l|C3 n|a< H|f3 © r- © © © © r- © © — ZO'-' . P _.|C0 W H H|« to HHco «ES w |c0 ^ h M|cOh|mW5|0O UjICClClCO g r-t _ © V r-H r-H r—1 rH r-H rH rH i—n rH rH rH rH rH r-H rH ^ r-H O c3 © o ^ .X © O o © Q — r-i t-H r-H rH rH rH rH rH rH rH rH rH rH rH rH rH rH rH r© d .ICC _P0 ICDUTiCO <4—1 © H h|qC rt|COH|O0 pier H |H |H r-HH o m co~ r O i? St XXX XXX XXX XXX XXX x x a o • • X 05 X X ^ X X rH 05 05 © © © © rH © © x © c • H H-H HH « © he • a PI © t- X t - CO XN© X © © 1^ © p P P I’* ' , >, . . . • • • p : : • • • ! ! ! p : : «D +J o o ^ o o £ o o POO U o o a o o C •- r ce t3 -3 OJ 'O r o o rz rs 0) P "O oi'O'O o © +H ^ : : a : : p : : £ : : S : : p : : • • • fcO • o3 oj WS r-H X O ^ o o © © © I - t- © 03 03 © © © © i E P c 03 03 03 rH rH © 05 X X X © XXX © j © © 03 03 03 03 03 03 rH rH rH ■ C5 O IO H lO lO ^ Tfi rfi 03 03 03 03 03 X 03 03 03 03 03 03 rf T?i ^ TP XXX x x XXX HP ,jd 03 03 03 03 03 03 03 03 03 X X CO XXX XXX hr, 03 03 03 03 r H rH rr rH rH rH rH *© o o o o o o © © © © © © © © © © © © © 03 03 03 03 03 03 03 03 03 03 03 03 03 03 03 03* 03 03 +3 fH o r-H ^H rH rH rH rH r— 1 rH rH rH rH rH rH rH rH rH rH rH P. o O 05 05 X rH rH © © © *-< © X I - h 03 03 rH rH rH © i rr P d d »6 to kO to rji Tt< ^ ^ ^ X •r h r 3 w 03 03 03 03 03 03 03 03 03 03 03 03 03 03 03 03 03 03 o rH r-i r —1 rH rH rH rH rr rH rH rH rr rH r-H rH rH rH rH d 1 i • • • t i • * * . . . ' ‘ * . . . . . . -h 1 • • • • • • i • • • i V . . ® . . 0> . . he 73 , w Poo Poo Poo t- fl T3 r C coo 0 T3 'O to c : : P 1 i a ■ • o3 • • *H ' * c3 • • t-4 • • c3 • ■ >H • • <; 5 : : 6 ; • 5 : : a : : o : : • o : : (h 1 © • • l © • » • 0) © • 1 * • i o ! ! ! d © he . . I he * t . be he • . * he • i i he w 6 cd ’ ' ’ * • • 03 Q3 « • • C3 • • i 55 J-H P- Sh u, • • • Sh • • i tn Sj^ h © © V © • i i > >> > P • i * • « t 03 X 05 • x © r-H 03 © X X © © < © © rH XXX rf -r^ rt- to to to © © I- X X RESULTS OF TESTS 45 ^ NO i—1 U5 - CO X • 03 ^H 03 03 03 T-H rH rH rH i i H05 0 CO 05 CO CO 03 00 05 N OlO o ^^03 O rH rr iO CO T-H 00 00 00 t - r-H o 05 O ^ 00 — rH CO r-H 03 rH O X o CO TT ^ TF rr Tf to to to to ^ »o to to to »o to to Tf to CO t''» to CO 00 CO t-H O CO to N10 05 O O to to 03 CO CO X ^ 03 00 ^ CO ^ to T t' CO co t-H ^ 05 t'- o N0 03 CO O»0N Tfl CO cd CO 00 © 05 to ^ CO ^ 05 O to »d 05 to co to ^ O cd 10 NN CO oo oo 00 00 00 00 00 00 00 X XXX X XXX X HlOCO to 00 to t-H CO tO 03 CO rH 03 r-H 03 CO 05 CO U- 05 oo ONO o o o rH 05 05 r— 1 r-H X O 05 05 lO 00 tO to to tO tO 05 trftON to to to cd co 03 (M h 00 O 00 05 o o to 05 00 X 05 CO x co o H lO ^ CO 05 CO CO CO CO CO 05 00 lO 00 T 05 to X rH I- t ^ Tfi rr ^ Tfotfi 05 CO 03 o cd 05 X co CO to CO CO oo u- x X X t- o o o o o o o o o o o o o o o o o o ONO o o o O O CO O O to o o ^ o o o o to O o o c O O 05 O O 05 O O CO oo o J t to 05 00 O 03 03 CO to CO rH CD CO ^ o O I- X T-H t-H t-H t-H t-H rH rH rH rH t-H O TT 05 00 03 ^ t-H 03 O co Tf o to 03 rH CO X CO o o CO X co o 00 CO 00 03 00 to to 00 00 00 to 05 cd cd —i ZC o O 03 ^ t - tO Tf TJH H H H CO rf H}< Tf TT to ^ to to TT rf Tji TJ1 I '” 00 T-H 05 t-H 03 CO CO 05 ^ 03 03 rH r-H tO CO CO to to 03 03 CO 00 00 03 X rH o to 05 00 t-H O 03 05 O rH Cl O rH TH CO rH co o o o o t-H CO t-H -H O O rH —"H r-H rH t— i r—1 T—1 t-H r-H t-H t-H o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o c o o o o o o o o o o o o o o o o o o o o 03 O 03 00 T-H GO 05 03 03 hhH 1 05 rH X 05 CO X co o 1—1 O 05 co co • 03 05 05 LO X CO 05 to X HO® 00 ^ CO , CO CO 03 o cd ^ QO cd CO to O to NON CO u- CO , 1-^ X CO X X t— oa 031>- CO to CO CO to NOh 05 CO CO to ^ rH CO O T-H CO to HlOCO CO cd co co 03 to ^ CO cd cd cd to Tt^ cd co to Tt' ^ Tji TT H h h Tf< Tji ^ TfH rn ^ Tf Tf rf Tf Tf< t-H t-H t-H t-H t-H t-H t-H t-H rH t-H t-H rH rH t-H t-H rH r-H rH rH rH rH r-H rH rH to 00 00 O Tf to 05 U- 03 CO O ^ to co o 05 t'— 03 03 to CO 05 CO 00 05 05 CO co CO CO 03 CO ^ CO 05 co co CO O to tO»ON CO CO u- to CO CO co CO HjM r-l|M CO 00 CO rllC* nlNHlN He* NOO co CO 00 CO CO I - O CO CO O N N w!® «!COrH|30 H «R JfO HHoo r-lx "H es|« Hrll-* to ICO t-H t-H t-H rH t-H r-H r-H r— t-H r —1 rH rH r-H t-H t-H t-H t-H t-H t-H t-H t-H t-H t-H rH t-H t-H r-H rH t—H rH rH rH I0£0 ICKO 10|CD to I® WlCOiOlCO^ICO HXrr. r-H 00 00 00 00 00 00 00 X X X X l> GO O O i« 00 03 00 O 05 CO rH rH 0 05^t Tf 05 t-H t—H U- 00 t- r- o co co 00 cO X O CO NXN ! i • • • • ft : : 1 . . . 1 1 a : : +JOO -d o o goo +5 0 0 d o o goo © 'O © T3 'C ci'O'O © r-. © r d"+ oS'O'O £ : : a : : Q : : £ : : S : : o : : 05 05 o o o CO t-H o o o TJH O ^ ^ 05 05 05 05 05 05 00 00 t-H t-H t-H o o o X X 00 r-H r— 1 r— rH t-H r-H o o o o o o o o o rH —h t—-• rH rH r—H rH t-H r-H t-H t-H t-H t-H t-H t-H rH rH rH 05 05 05 05 05 05 05 05 05 Tji Tf ^ Tj< HtH H h H CO co co c<^c6 c6 cd cd cd t-H t-H t-H t-H t-H t-H rH rH rH rH r-H t-H r-H T-H t-H o o o © o o o o o o o o o o o o o o oi oi 03 03 03 03 03 03 03 03 03 03 03 03 03 03 03 03 rH t-H t-H t-H t-H t-H rH t-H t-H rH t-H t-H r-H rH rH rH rH rH Tf TJH ^ ^ Tj< ^ H t? 1 H Tf Tt^ Tji HHH Tji Tji C3C3C3 03 03 03 03 03 03 03 03 03 03 03 03 03 03 03 t-H t-H t-H t-H t-H t-H t-H rH t-H rH rH rH rH rH rH rH rH rH • . • • • • • . . 0 ■ • 0 • • 0 ’ ' • i i • • 1 1 1 1 o • • o • • o • ' _< • • ,_, • ,_, * * -M * * +H ’ ’ 4H ' ' © o o © o o © o o WOO jp O O co O O > T3 TJ > TO T3 >’O r O © +3 -O © rH' T? © "O c3 • • <3 • • • ■ £ • • S ■ ' I- 1 • fH • ' *H • ‘ • t-H ' o : : o : : o : : h : : h : : h : : i . . d : : : d I I I d • • • d 1 : : d : : : d • • • bo bo • 1 1 bO . • . Ui . • . Wj • * • 00 i . i od . . . o . 1 . cS . . . * • • i i • C3 Sh 1 • 1 !- Ui • . . © . © . . . © . T f © . . « © • i i © i • . > . . . < 1 • « > t I 1 )> > > • i • < co tj< to CO X < rH 03 CO < ONO 50 rf tO < HC3W o o o rH t-H t-H co CO CO 03 03 O lO lO Ci 05 05 rH rH rH rH rH rH r-H rH t-H rH t-H rH rH rH rH Table 9. — Tests of concrete beams of variable span —Continued. TESTED AT TWENTY-SIX WEEKS. V 46 STRENGTH OF CONCRETE BEAMS. 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OOO OOO OOO OOO ODN CO T 1 CM CM 05 C5 2 OOO OOO OOO 0 0 O' 0 02 0 OOO O 05 C5 G 1 5 I'* 00 GO GO 00 06 06 00 00 GO GO 00 GO 00 GO 06 00 00 06 m Vi . . S : : c3 Q ’o o !77 • o o o o 73 X3 © • • £ : : Cl £7 O O c^-d c3 • • • O O Ut © tn ^ ■*2 a t3 >. w o> £ o O 00 O r-H r-H rH CM CM CM cr- o o o o o O 05 Ci CM O O 05 C5 05 CO Tfi T* 00 00 05 05 05 d d d iO»ON 05 05 05 a o •I—» £ ! ft 00 00 00 • 0077 • Tf Tf ’’7' • CM CM CM • C5 CM CM • CM CM CM • OOO . CO CO co . co io >o • tJ’ tT» tT 1 • 00 00 00 • 00 00 00 • 00 00 00 • r-H rH rH 4-5 d: CM CM CM • CM CM CM • CM CM CM • co c6 c6 • cb cb cb • cb cb cb • TT ' r T bo CM CM CM • C5 1 ,—i r—t r-H • rH r-H rH • rH rH rH • rH rH rH • rH -H rH "© OOO . OOO • OOO • OOO • OOO • OOO • OOO CM C5 CM rH r-H rH ■ C5 CM CM • rH rH rH • CM CM C5 • rH rH rH • C5 C5 CM • rH rH rH • CM CM CM 1 r-H rH rH • CM CM* CM • rH rH rH • CM CM CM • rH i-H rH 4) 3 3 r-« o > co O O O O O O LO ID to cm cm cm co o o o ^ ^ iO »o 10 (M CO CO • • o o 05 05 05 rH r-H r-H d d d cm cm cm ^ Tfl Tt 1 cm cm cm Tf< Tti T* cm cm cm Tfl Tt^ 05 05 05 ^ TT1 CM CM CM © 03 bQ © »h CD CD Ol © 03 a o o o 7303 u* © 2 O e Sb£ © P3 rr^ 73 03 s * o : © CD c3 d © 00 05 i-h H H Ol 4°° r 0 r 3'3 g ; be ft *— © oo o: CM CM CM © o o C33 c3 f-< o t- 00 05 CO co CO . - o c3 Sr a © .tJ c o C ^ 03 c3 o © © © ! © © bJD b£j fcc : bn tJD C3 1 1 t cj Fh Jh *H • ^ • 1 1 Fh © © © . © III © > > • > i -1 1 > < cb tt d < r- 7 IO < CM CO GO 1 • 1 sss-e © o > c3 ?h o iO ‘O CO 5 00 05 RESULTS OF OJIOH on © • O © • CM © HNTf © rH CM CO IO co © © © CO © © CO CO xr 05 oo H u- tt © © © CM 00 r- 00 © © 00 U- • N* tN 10^0 IO xF 00 © 00 © iO © « rH rH CO O 05 N- rH IQ 05 CM LO co N rH TP iO iO IO 00 CM © 00 In IN 00 iO rH xr 00 CO 00 rH CO rH O xr XT rH © tT © © © © © © © co O CM CO rH © CO © © © CO N co CO CO CO CO XT Tfl Xjl xT idOCM e © CM CO CM CM CO TP TP TT' H H (N © 05 05 rH O CO rH © © rH 00 © © 00 CO IO iO CM CO cm CO CMTPN ib CM © ib © CO CO tji* In © 00 oo Tjl XJ1 Tjl rr xT XT rr XT XT XT xr XT XT Trr Tpi T-fi XT rH rH t-H rH rH rH rH rH rH rH rH rH rH rH rH rH rH rH rH rH W^co 05 CM CO xji CO CM xji xT N- LO © rH rH rH o o o rH rH CM rH <© rH © © © cb cb cb cb cb co • « t cb cb cb cb cb cb © © © CM IN CM CM CO N CO 05 00 00 CM CM co © 00 - ; OCJO O O 05 O 05 05 © © © © © © cb »b cb cb cb ib cb ib ib ib cb cb © ib ib XXX XXX XXX XXX XXX CM CM CM CO N CO 05 00 00 CM h co © oo OCJO O O 05 O 05 05 © © © © © © cb iO c£j cb cb ib cb ib ib ib cb cb cb ib ib o o o o o o o o o o o © © © © © © © © © o o o o o o o o o o o co © © © © © © co © © © © O CM CM 05 CO CM rH IN 00 rH 00 00 IO CM 00 rH rH rH rH rH rH rH rH rH rH rH rH rH o o o o O O O o o o o © © © © © © © © © o o o o o o o o o o o © © © © © © © © © o o © o o o o o o o o © o o o © © © © © © © o' ib © o o' o' © ©ib CO © rH 00 © © ib' CM ib © ib IN CM O >0 ^ xT CO 00 © © © CO CM CM CM © CO © 00 00 CO 00 N o ^ 00 Tfl © •r t-~ t-h TJ1 © © CM CO CO CO e CO ^ CO CO xn CO CO CO CO CO CO CO CO TP TpTP xr © © CM rH In CM N N- rH rH Xp< CM © 00 CM © xP 00 CM CO CO 05 N O XT' © 00 00 lO 00 rH © © CO TJ1 O © xf CO CO xj< N iO 00 © 00 xr CO © rH In IN 00 CO CM CO CM CO CM CO e CO CM CM CO co CO CM CM CM CO CM CM CM CNN N- In 05 05 00 CO iO CM Xf LO © © © CM 00 © IN CM CM CM CM rH O CM rH N* ib CO ib ib lo cb © cb © © 00 Xj< Xfl xr Tfl Tf TT XF xji Tji xr xr ^ TJ 1 rji Tp IO TP XT rH rH rH rH rH rH rH rH rH rH rH rH rH rH rH rH rH rH rH rH © 00 00 © 00 CM N ^ rH 00 Tt< CM IN CM ©} rH rH O rH O * o o o rH © © CM © rH cb cb cb cb cb cb i cb cb cb cb cb cb cb cb cb rH rH rH t rH rH rH • rH rH rH rH rH rH rH rH rH cDa® i • 05 rH tN t • © CM IN © tN rH COOOtP ( OCiC5 • OHO • © © © i © © © © © © • 00 N N • • i oo oo oo i t • • oo oo t • t tN IN 00 00 In 00 • • ; o o • ^ o o • • o o • ! o o * H O O • T3 t3 T3 C'O'O • 'd'OxJ G'O'O 7 CM CM rH rH rH ■ • t t i rH rH rH i • t rH rH rH rH rH rH rH rH rH • • * • i * • • • • • * J i i Q) • . d i i • « • • • • £ • • £ • • c ■ • o • • o • • o • • ( _, • • ,_, • • +-> ' ' +-* • • ■H * ' © o o © o o GO O O w O O to O O >-0-0 > T3 T) Qj'CJ'O o3 • ■ oj ' • s • • B ' • B ■ ■ • Jr * ' t-4 ' * • o : : o : : 3 : : 5 : : > • • HH • • 0 ) ! ! © > . « # > > . . . > O rH CM < cm' cb ib 00 05 © < rH 07 CO < rH CM CO < o o o rH rH rH CM CM CO Tf ^ Tjl IO IO LO rH rH rH rH rH rH rH rH rH rH rH rH t-H rH rH 37206—Bull. 344—08-4 o Not included in average. Table 10. —Compression tests of concrete cylinders and cubes accompanying beams —Continued. TESTED AT THIRTEEN WEEKS. 50 STRENGTH OF CONCRETE BEAMS. ® i m O j- ro ” (- +$ or e+3r3 m u o o o> O GG © Hr-CO lO lO CD Cj t - X CD CO O 00 00 ON 6 ' # § g 0^0 O 00 O O h to o ^ CO 1 co oc cr. o o Ncooo t- .JL Cj w NOW CO OO CM 000 oT oT t-T 10 CM 00 ^ co OhN hNh O CD O th 000 co o oc i- 00 0:^0 J- »C' (M I- o to Tf to t- rr 8 n ^ I- o O CO 1-0 irT tcf CM to O Tf< O ^ - - 0 ?i ^ wio ^ m 33 3 o * .SP g ® 2 3 .^ 0^=0 to 00 00 1C Tf O to o oi CO “ to CO ^ 00 Tf Tf to cm o o tT tH CiOCO rH CO CO CO to to 00 ^ rf t*« 3 o 00 o 00 x < 0 . w C • O 03 'm a> C 0) 0 s.s & bo © ai cZ H ^ O rH OOO 0 CD 0 Tt« n- OOO OOO N- to to rH rH CD CD CD to Tf (NINO CD CD CD 1 6.20 ! 6.14 6.11 i (NCOH 1 r—1 *H • OOO ^ ^ CO b- T* 01 tO CD CO to N- CO CDHIO ■ (M CM O OOO 0 0 TH OOO OOO OOO ■ OOO CD CD CD CD CD CD CD cD CD CD CD CD CD CD CD . CD CD CD XXX XXX XXX XXX XXX : xxx tF ^ CM N- O' i-H t- co 0 to i—i CM rH CO . rH00(M OOO O O r-i OOO OOO OOO • OOO CD CD CD CD to CD to CD to CD CD CD CD CD CD • CD tO CD © Jh gg OOO O OOO 0 OOO 0 OOO O OOO O OOO O be © OOO co OOO 0 OOO OOO r- OOO CO OOO I- 0 ® 3 0 3 Ph s 3 r H <3 >> 01 rH ^ CD CO TF ^ CO to tO ' , T I to Tf CO (M CO r-H rH rH • OOO O OOO O OOO O OOO 0 OOO O O O' 0 O OOO O OOO 0 _3 _-4H OOO O OOO O OOO O OOO 0 3<*h '§ OOO nT O O to tef OO to to OOO co" 13 Op 0 ^ co to CM CO N- r- CD O s ^ O CM oc O w lQ N- N- 0 hOcD CM O ^ to 00 CD CO CM (H iH ^ A ^ s 1 co T-H CM CM CO CM t-* CM t-H t-H t-H rH ^ CO rr OOO O O' o OOO cTo o O 00 CO 00 N- CO OOOOO O OOO o OOOOO OOO ^XN co cm i- o rf Tf ^ 10 ^ sf s£ cn m 10 T-H CO 00 tO CD N- CD O CO ^ co ^ 00 O tO O CM CM O CD CD CM 00 N- >0 CM 05 O 0 T—1 8 CD 0 CD 00 0 0 OO N- N» CD t- to T-H CO to GO t-H rH rH rH rH t-H t-H rH rH rH i—H rH co co co co r^ CO • rH , ■£> 0 ^ 3-3 0^ A c 3 CO CM 05 O N* t-H to CD to 06 ^ co CD tO CD ‘O CO CM rH to oi OON CD ^ CD rH CD O 00 to rH CM CO CD NON I '- 00 00 JN- Tf Tji ^ T? ^ Tf 0 X a tH rH t-H rH rH rH rH rH rH ^ tt rr 0 f Tj ^H t-H f-H H rH tH rH rH rH H tH rH rH rH tH rH rH tH rH rH rH rH rH rH £3 0 00 CO to 05 CM • 1 to to co 0100 CO r-H • O H O GO ft O 00 h 1- Oi O • H rH O rH rH O’ rH CM O 1 <0 rH rH 3 • 00 CD 10 <£> to to CD CD CD CD CD CD CD CD CD CD , O CD CD © rH t-H rH rH rH H rH H rH rH rH rH rH rH rH 4 rH rH rH 03 © Crd S .9 1 CM CM rH ODN ONO O CO rH . to CO 00 fa 5 -h OOO OOO OOO OOO OOO • OOO •rH p § ^ • 4 h -*h N 06 00 00 00 06 06 06 06 00 00 06 06 00 06 • 06 06 06 Q " 1 4 H .21; CD • 0 0 • 0 0 H C O • O O • 0 0 : &00 3 3 "O © • • <3 • • © • • . s ^ ^ • c 3 • • ! s • • 0 : : £ : : s I • : o : : u to © ?H /* '• 4 P (1) rH CO O ■H O O OOO t-1- 0 CM CM CD • OOO ciaB CM oi CM r-H ^ O 0 0 00 06 06 O CO 00 oc . ONN CM CM CM CM CM CM rH rH t-h O to to rH tO tO ^ rt< CM CM CM CM CM 00 ■ OI CM CM , CM CM CM ^ Tr ^ Tf 00 00 00 00 00 IN • 00 X 00 4 H & CM CM CM CM CM CM oi oi oi co co co CO CO CO . CO CO co be -r CM (M CM CM rH rH ^H r-H rH rH rH rH rH rH 1 rH r-H »-H © OOO OOO OOO OOO OOO • OOO 3 CM CM CM CM Ol CM cm oi Cl CM CM CM CM Ol CM . oi oi oi 0 r"*’ • • • • • • • • • • • • ■ •••••• rH rH H rH t-H rH rH rH rH rH rH rH rH t-H t-H rH rH rH 4 H Jh O / p CO 05 O CO rH rH OOO 0 . 00 N- N» H CM l> • 1 1 t> • • * > • ' ' £> • • * • -H < 0 : : : : : ; ! ; CM 00 05 co co co to to to 00 o o OON 00 00 RESULTS OF TESTS. 51 r C. 13 pn 03 13 M o d OQ © P a to co 05 CD CD O 00 t-H • • < CO 04 N- Tt< I- N- 05 OO t • • 00 00 00 00 00 on 00 00 • • 1 t-H O 00 05 00 05 CD 00 -x -x 00 05 CO t-H N- 0 04 00 CONN 0 O N CO CO GO to O co to 05 O r-H 0 0 0 00 05 Tt< ^tdtd tT TP T»i CO ^cdcd cd' M © a> p N Sh xn -X +? m 1 • • co to to 00 CO 0 4 U- Tt< t-H O CO go © © r-H co co cd CO CD to N- cd 4^+f pH Ht< ^ HT ^ -Tfrl ^r< ^ TP d d C/3 • 1 1 • • • t-H t-H t-H r-H t-H t-H t-H r-H t-H t-H t-H t-H 3 pi PH • 1 1 CR ® q lO CO --5 05 rH O tO U- to DDCO 04 N- CO T'- O t-H O ^3 t-H t-H t-H t-H t-H 4H -4H Tji cd cd cd cd cd cd CO CO O CD CD cd o3 tO COlOH o o o ZC cD CD XXX CO lO 04 o o o CO CO CO to to CO O O CO CO CO XXX O to o t-H <^) rH co co cd CO to to o o o CO CO CO XXX 04 ^ CO o o o cd cd cd H CO CO T-H O O CO co CO XXX t-H oi CO 000 cd cd ODN t-H N- CO tH H Tt< 0 0 0 ID 04 0 04 to CD NCO O O 05 O 05 O OOIH T—1 td cd co tO 04 to td Ht< n! cp cd tD CD CO 05 00 CO CO ^ ^ Tf ^ ^ Tji ^ r-H t-H t-H rH t-H t-H t-H rH rH t-H t-H rH rH rH rH rH rH t-H t-H rH rH rH rH rH N CD N OCON tO CD 00 CO 04 O CD t-h*N» HC40 CO T-H co t-H t-H t-H rH t-H t-H 04 rH rH H H 04 ^ 04 04 CD CD CD cd CD CD CD cd CD CD CD cd cd CD cd 000 t-H r-H t-H rH rH t-H t-H t-H t-H rH t-H rH rH rH t-H rH t-H H HHCO 05 to CO 04 t-h CO ID005 CO to 04 04 O 04 OOO OOO OOO O O 05 OOO OOO GO 00 00 00 00 00 06 00 00 00 00 N- 00 00 00 OO 00 GO • 0 0 • 0 0 • 0 0 ■ 0 0 &o 0 T3 T3 T3 q -o os -gOTJ £ : : 73x5X5 Hx5x5 03 . . c3 • • 13 . . c 6 ■ • £ : : PH • • 1*3 • . Q : : S : : 0 : : Oi 05 OOO CD O rH OOO ^ T}i O rt< rji 05 05 05 05 05 05 1 - 00 06 rH rH rH OOO 00 00 00 V rH rH rH t—H t-H t-H OOO OOO OOO rH rH rH rH rH rH rH rH rH r-H t-H t-H t—H t—H t-H t—H t-H t-H 05 05 05 05 05 05 05 05 05 HJH Tf *d ''d Tji Tf 1 ^ ^ cd cd CO cd cd cd co co cd t—H t-H r-H rH t—H t-H 1 t—H r— > t-H rH t-H t—H T—< T—1 T— rH rH rH OOO O O O' 1 OOO OOO 000 OOO 04 04 04 04 04 04 04 04 04 04 04 04 04 04 04 04 04 04 i-H t-H t-H r-H t-H rH rH rH r-H rH rH rH rH rH rH rH rH t-H ^ Tji Tt< Tt« ^ ^ Tf Tt< -.r rf< tT 04 04 04 04 04 Ol 04 04 04 04 04 04 04 04 04 04 04 04 t-H rH t-H rH rH rH rH rH rH rH rH rH rH rH rH rH rH rH '■ • • • • • 3 3 : '• '■ '» j i> 1 ! d i i . . . 1 1 . d • • C ' ' C5 • • • 1 1 • 1 • 0 • • 0 ' ' O 1 1 i ' • • , • • 1 * 1 PH ' ' pH ' ' PH * * 0) 0 0 0 0 0 13 O O B O O BOO GO O O >X*T3 >-0 73 ® T3 T? ® X5 X5 2x3x5 o3 ' * 03 * • cl * ' s ■ • q ' ■ S : • Sh • 1 N 1 ' u • ' 0 : : 0 : : 0 : : 3 : : si : : * r si : : . . . 13 ! i . 13 ! ! ! 13 ! ! 13 ! ! I • 13 ! ! ! 13 • 1 • be * * t>n be be be be Cl , , aj a3 • • 1 Cl 03 • • • d • 1 1 Jh • 1 • N ■ 1 1 Sh • • 1 N u ■ 1 1 Sh • < • 13 • • • 13 • 1 • 13 • 1 1 13 13 • 1 1 13 . . . > • • • > • • • > ' • j r- rs» > ! ■ 1 > ! . ; CO ^ to CD N* 00 < rH 04 CO ^ G O'p ,-H _ O M O o3 05^ 3 00 £ c*fco ro P ^io'* ” ® te 03 -2 PH 03 «+H PdP oi O d O £ oS £ XJ pi 73,0 fH X5 S-< Sh ©•— © 0) •d 'd *d .s $5 ,s .2 K*% d K*> 0000 S **» r< *«• 03 03 <0 Sh 03 03 03 03 03 03 13 13 13 S- N P. 4H -M ^ 03 03 03 PH pn Pi d d 03 d d d+> • 05 o> 05 *d ^ N iO Cl g 03 a> d 4§ cd'cd'cd'oo 2 *03 d d ® ,?3 .o3 o3 ^ ,Q «i-i «w «M ^ 0 0 0 3 .3. p| (h C' m issso wddd 3 ?H Sh £h Jh r d 13 13 13 13 *3 dddd^ .3.3.3.3 9^ t>> £>> ?*■> d OOOOO Q rO <-> *> HCJCO 03 03 03 Table 10. — Compression tests of concrete cylinders and cubes accompanying beams — Continued. TESTED AT TWENTY-SIX WEEKS. 52 STRENGTH OF CONCRETE BEAMS. 0 O 2 0 « oox t- x —ico 05 xr^ro t^O500 00 00 00 t" l~ 00 f- 1' t- s ^ M 03 0-^0 lO o , OOO co cc o 04 ^ 04 ! o co co '. OWN • o oo ^ • h 04 N d -*H ooo • ooo OHO . ooo i <0 rH , ooo • (M > o Cl oo rH HCDO CO O lO rH IO • rH rH LO CO N05 0 Ol op CO 05 o ^050 . cococo 00 COOH o HhQ5 (M 05 oo o <05 a -o CJ « "a 'e . C^i . ^t 4 Tt< lO K rs r, r >N •N ^ 1 1 ^ ^ hcJci (M 04 04 rH of H H d rH • 1 • CO CO CO • hs co 0 X SiSS-g a go ^ «fH © (MOO CO CO ^ ^ (M ^ CO O CO CO tj5 (M . .2 >. CQ o d d O 0 o t—< • 03 5h -—- 4H 03 4H «5 CS ft P t* w 0 > O • o o ■gT3T3 • o o Td xJ 0 . . 3 : : rt 1 o o Pt3t5 oj • • o o 'S'P'P ■ o o T3 OJ Td 03 . . S : : S' o o d'd'd I . • o o I'O'd ^ Tf CO o 05 05 05 05 05 05 d o £ o o. o tH Ph rd bO iO iO 00 (M • • > • i • > > > > I I <1 , , < < < < 1 lO CD id .*o ^ iO 05QH r* 4 id - !>. tO © O CO OOC'O 936 H CO H 00 CO CO o t-h 982 t-H t-H t-H © O © T—< CO rH 00 H 1 1C 00 o 00 Hi" CM CM 00 o Hi © CM lO H^ H' 4,884 3,167 3,860 3,354 3, 460 OCOlO O H CO CO Hi © co'co'h*' 3,896 00 tO CM t-H O'! CO (MC0»O Hi'to'to' 5,025 10 05 0 o o o o o o o O O CO Hf O O 00 CO cm o cm H< Hi H< rH r-H H 3 rH h< Tf © Hi H< Hi r-H rH t-H Hi H 1 i-H HP HP HP r-H r-H r-H CO Hi t-H r-H rH r-H 00 Hi rH O00N tO H H r-H t-H t-H GO H< t-H »OON o o o o o o o o u- © ©CO r-H CM O o o o o o o o o o © © © CO cO CO CO CO CO CO CO cO CO CO CO CO © CO O CO CO o o o o o o O O ' © tO © o o o o o o o o o o o o © © © CO CO CO CO cO CO CO CO CO CO CO CO CO © lO XXX XXX XXX XXX XXX O CO CO O O O o o o O O t-H © © O O O o o o o o o o © o © © © to to CO CO CO CO zO cd t5 CO CO C6 to lO CO o o o o o o o o o o o o o o o © © © © o co iR 3 CO o o o CO CO GO o o o I- © © © to T—1 CO UO © —s. 1 • CO t-H U— T-H © © © iO © © © • "C C Cfc . ©HTf CM © • coco CO co' CO CO co co' Hi U- © © © © IO oo CO 00 IO CM 00 CM © Hi CM CM CO CO lONN © H< LO CO to US to © to © 00 Tf 1 Hi © -T Tf Hi H H H Hi Hi Hi Hi Hi Hi Hi Hi Hi t-H t-H t-H rH t-h t-h t-h r-H rH r-H rH r-H rH r-H r-H rH rH rH rH T-H h cm CM CM © © CO © to co © co © © t-H t-H t-H © © © © © © © rH O rH rH rH © © cb © © © r O to to © © © © © © r-H t-H r-H r—H t-H t-H t-H rH r-H rH t-H t-H rH rH rH t-H © t-H © CO © CM © CO © CM © CO © © o o o © © © © © © © © © HOlO 00 00 00 00 00 00 00 00 GO GO 00 GO GO 00 • c o a o o • o o ■ o o c o o T3 © © «©© 'O X} t3 T3 'O R T3 0) . , cd • • a? * • cd • • s ’ • A : : £ : : S : : A : : t-H t-H rH t-H t-H © © © © © © to to to © © © 00 GO 00 rH rH rH © © © 00 00 00 rH t-H t-H rH r-< rH © © © © © © t—H t-H rH T-H r-H r-H r-H H rH t-H t-H t-H T-H t-H t-H © © © © © © © © © H H H -tf 1 -tf 1 © CO CO CO CO co co CO CO CO t-H t-H t-H r-H r—* t-H t-h t-h t-H rH rH rH © © © © © © © © © o o o o o o CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM t-H t-H t-H r-H t-H t-H rH t-H t-H t-H r-H r-H rH t —1 rH -T -tf 1 -'f Tf Tfi Tf *rf H 1 H* Hi Hi Hi Hi Hi Hi CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM rH t-H t-h r-H t-H t-H t—H rH rH rH t-h rH rH rH rH • i ■ • • • ©© t>©© ® 'O'O 4 'O 4 -J cd • • ci ■ ■ s ■ • s • • s • * U • • ?H o : : o : : a : : a : : a : : a cd U Jh • i i • • • *H u 0) O) • • i a; , , a) a) . . . > • • i > • « • > © u- 00 < © © T-H iO to < Hiooo < 00 © © © © © rH CM CM co co co Hi Hi iO to to © rH r-H r-H t-H r-H t-H r-H t-H rH T-H rH CM rH CM CM a Cylinder did not break at 3,950 unit stress. « Cylinder did not break at 3,969 unit stress. h Cylinder stress approximate. b Cylinder did not break at 3,989 unit stress. /Cube did not break at 5,556 unit stress. * Machine vibrated compressometer. c Cylinder did not break at 3,959 unit stress. o Cylinder did not break at 3,978 unit •’tress. /Cylinder did not break at 3,858 unit stress. d Cylinder did not break at 3,979 unit stress 54 STRENGTH OF CONCRETE BEAMS. oot S6 06 58 08 S L 0 L 59 09' SS OS Sfr; 0> SC 0£ SC 02 SI 01 s 0 0 L S9 09 SS OS St- Ofr’ i sc OC sc OC > SI 01 s 0 0 L S9 09' SS os st ov sc. OC sc OC St 01 s p jo |uao jaj pq-t-w JO san l E A Information per unit of length Deformation per unit of length Deformation per unit of length Fig. 11.—Characteristic deformation curves for flexure, granite concrete of medium consistency; ages 4, 13, and 26 weeks. RESULTS OF TESTS. 55 BEAMS OF VARIABLE SPAN. The detailed results of tests of the beams of variable span are given in Table 9 (pp. 42-47), and some of the results are graphically shown in figs. 2-5. The information given in columns 1-14, 17, 18, 21, and 22 of the table is identical in character with that given in the corresponding columns of Table 8. Column 15 contains the unit elongation of the lower outer fiber for the applied load only, since the short beams were not suspended for zero total deformations as were the long beams. The values of the unit elongation, including that due to the weight of the beam and the deformeters, may be approximated by increasing the values in column 15 by an amount obtained from the averages in column 12, Table 8, on the assumption that the elongation is directly propor¬ tional to the values for M IxP which is approximately true for values below those for the weight of the beam plus the weight of the deform- M eters. The values for for own weight and deformeters are given L A 2 o to in column 19 and, as may be seen by comparing with the maximum total values in column 20, are in the majority of cases but a small percentage of the total. Column 16 gives the position of the neutral axis in percentage of the depth below the top of the beam. These values are not strictly comparable, with those in column 15, Table 8, since they are based on deformations due to the applied load alone. CYLINDERS AND CUBES. The detailed results of the compression tests of cylinders 8 inches in diameter by 16 inches in length and of 6-inch cubes are given in Table 10. Some of the results are also graphically shown in figs. 2-9. Columns 1-6 contain the same kind of information as is given for the beams in the corresponding columns of Tables 8 and 9. Columns 7 and 8 and columns 13 and 14 show the dimensions of the cylinders and cubes, respectively, in inches. Columns 9 and 15 show the weight in pounds per cubic foot, as figured from the dimensions and the actual weight of each cylinder and cube when tested. Columns 10 and 16 show the ultimate strength of each cylinder and cube in pounds per square inch. The initial modulus of elasticity (given in column 11) was obtained from a curve showing the relation between the unit gross deformation and the compressive stress in pounds per square inch, by drawing a line tangent to the curve at the origin or where possible coincident with the straight line or initial part of the curve. The range in pounds 56 STRENGTH OF CONCRETE BEAMS o o r c i, 6 < \ > 1 > i— c \ ooi S6 06 58 08 St 0 L 59 09 ss. OS' St Ot sc os S2 02 51 01 s 0 0 t S9 09 SS OS' St ot sc OS 52 02 51 01 S 0 0 L S9 09 SS OS St ot sc oc 52 02 SI 01 S E + 5 d 4 jr Deformation per unit o! length Deformation per unit ol length Deformation per unit o! length Fig. 12.—Characteristic deformation curves for flexure, gravel concrete of medium consistency; ages 4, 13, and 26 weeks. RESULTS OF TESTS. 57 per square inch within which the line drawn coincides with the curve is also shown (column 12). Column 17 gives the ratio of the ultimate strength of the cylinders to that for the cubes. It is to be regretted that the capacity of the machines composing the equipment was exceeded by the strength of many of the cylinders and cubes at the time these tests were made, preventing the accurate determination of the actual growth of strength with age. There is, however, in almost every case a substantial increase in strength with age. The effect of consistency on the strength is much more noticeable, and leads to much more uniform results for the cubes and cylinders than for the beams. This would lead one to believe that the effect of consistency is much more noticeable and much more uniform on the compressive strength of concrete than on the tensile strength. Owing to a breakdown of the engine it became necessary to apply the load by hand for a number of tests. The beams and cylinders, being deemed the most important, were tested in this way, but because of the difficulty of turning the gears of the testing machine by hand the testing of the cubes was omitted. { ILLUSTRATIVE DIAGRAMS. Figs. 2, 3, 4, and 5 show graphically the effect of age and consistency on the ultimate compressive strength of cinder, granite, gravel, and limestone concretes, as obtained from the tests on the cylinders and cubes and in the modulus of rupture as given by the tests in the beams of constant and variable span. Figs. 6, 7, 8, and 9 show graphically several characteristic com¬ pression-stress deformation curves obtained from tests on the cylin¬ ders, while figs. 10, 11, 12, and 13 show the deformation curves for a few of the beams of 12-foot span. 58 STRENGTH OF CONCRETE REAMS T3 -Q 2 I 5 o ifi 3 p )0 JU90 J8J ; pqH-^ jo San|B A Deformation per gnit of length Deformation per unit of length Deformation per unit of length Fig. 13.—Characteristic deformation curves for flexure, limestone concrete of medium consistency; ages 4, 13, and 26 weeks. ) > SURVEY PUBLICATIONS ON TESTS OF STRUCTURAL MATERIALS. The following reports, published by the Geological Survey, relate to structural materials, etc.: Bulletin 238. Economic geology of the Iola quadrangle, Kansas, by G. I. Adams, Erasmus Haworth, and W. R. Crane. 1904. 8°. 83 pp., 11 pis. Bulletin 243.* Cement materials and industry of the United States, by E. C. Eckel. 1905. 8°. 395 pp., 15 pis. 65c. Bulletin 260.* The American cement industry, pp. 496-505. 1905. 40c. Bulletin 324. The San Francisco earthquake and fire of April 18, 1906, and their effects on structures and structural materials, by G. K. Gilbert, R. L. Humphrey, J. S. Sewell, and Frank Soule. 1907. 170 pp. Bulletin 329. Organization, equipment, and operation of the structural-materials testing laboratories at St. Louis, Mo., by R. L. Humphrey. 1908. 85 pp. Bulletin 331. Portland cement mortars and their constituent materials; results of tests made at the structural-materials testing laboratories, St. Louis, Mo., by R. L. Humphrey and William Jordan, jr. 1908. 130 pp. Water-Supply Paper 143. Experiments on steel-concrete pipes on a working scale, by J. H. Quinton. 1905. 8°. 61 pp., 4 pis. Mineral Resources U. S. for 1901,* 1902, 1903,* 1904, and 1905.* Cement. A series of annual articles on the cement industry and the production of cement in the United States, by L. L. Kimball. 50c. for each volume. Mineral Resources U. S. for 1906, pp. 897-905. Advances in cement technology, 1906, by E. C. Eckel. Reports marked with an asterisk (*) are out of stock, but may be had from the Superintendent of Documents, Washington, D. C., at the prices named. The others will be sent free to anyone inter¬ ested on application to The Director, United States Geological Survey, Washington, D. C. 59 o r