THE UNIVERSITY OF ILLINOIS LIBRARY 192\ N 51 THE RELATION OF FINE AGGREGATE TO THE PROPERTIES OF CONCRETE BY MARVIN CURTIS NICHOLS B. S. in C. E. University of Texas, 1918 THESIS Submitted in Partial Fulfillment of the Requirements for the Degree of MASTER OF SCIENCE IN THEORETICAL AND APPLIED MECHANICS IN THE GRADUATE SCHOOL OF THE UNIVERSITY OF ILLINOIS 1921 Digitized by the Internet Archive in 2015 J o https://archive.org/details/relationoffineagOOnich UNIVERSITY OF ILLINOIS THE GRADUATE SCHOOL JUNJj] 4 1Q9 1 I HEREBY RECOMMEND THAT THE THESIS PREPARED UNDER MY SUPERVISION BY JAARVIM CURTIS NTHTTOLR ENTITLED THE RELATION OF RIRS AGGREGATE TO TT TE PPOP OF CONC RETE BE ACCEPTED AS FULFILLING THIS PART OF THE REQUIREMENTS FOR THE DEGREE OF IvIASTER OF 3CIEECE IR THEORETICAL ilEI) APPL IED ^In Charge of Thesis Head of Department Recommendation concurred in* Committee on Final Examination* *Required for doctor’s degree but not for master’s ' 9 ■ ... » aiOWIJJl ’^O YTISHHVtSI u 4 JOOH03 ^JTAUCAa^ 3HT !*!•' JT . YM sjcjxj u.Wi-JHs m:mi Am xw-rr a'/:Atmajym i ^ . | *. t '^' mmt: .t4 ^jmsxik nrx^AH.^,-^ rn ” . '■' " '1 hr ‘ - ‘ ■ ■ ‘^4,^ . •'* £1 M ^ V Ho-f Am *40 tam mh omitvi ,n'r ha aa:i*tAOOA ah r.os'y ^>A ■'■' ■ '■--•{fe'Ste.’ tigti five'^Tf •'» >f1JM®"J **^ TiiBLE OF COETEETS I Introduction page 1. Preliminary 1 E. Scope and Outline of Tests 3 3. iicknowledgment 4 4. Definition of Terms, Dotation, and Formulas 5 5. Relations effecting the Strength of Concrete 11 II Materials, Test Specimens, and Technique of Tests 6. Materials and their Physical Properties 15 7. Sieve iina lysis E3 8. Specific Gravity and hhsorption 32 9. Ifeight of iggregate per Cubic Foot 35 10. Technique of Mortar Voids Tests 35 11. Compression Test Specimens 41 12. Storage and Handling of Test Specimens 44 13. Method of Making Compression Tests 45 III Experimental Data and Discussion 14. Explanation of Tables 47 15. Explanation of Curves and Diagrams 48 16. Explanation of Photographs 51 17. Relations Concerning the Strength of Concrete 51 18. Discussion of Cement-Space Ratio 60 19. Discussion of Increased Y/ater Content 69 20. Design of a Concrete Mix 72 21. Range of Usefulness of Pine Sands 79 22. Range of Usefulness of Coarse Sands 83 . Effect of Amount of Coarse Material 85 23 E4. General Discussion of the Mortar Voids page Method of iina lysis 88 26. Conclusions 91 IV Tables, Curves, Diagrams, and Photographs 26. Tables 92 27. Curves and Diagrams HE 28. Photographs 224 V Appendix 1 29. Original Data Mortar Voids Tests 246 DIST OF TiBLES Table 1. Table 2. Table 3. Table 4. Table 5. Table 6. Table 7. Tests of Cement 15 Physical Properties of Materials 15 Sieve Analyses of sands 27 Percentage of Voids in Mortar Pilled with Water 92 Voids in Mortar Expresses as Percentage of Voids at Basic Water Content 93 Data of idiiesion Tests, Mortar Test Specimensf 94 Data of Concrete Test Specjnens 95 : BIST OP PHOTOGRi^PHS Ro-Tap Machine and Sample Splitter 224 Specific Gravity and Absorption Jipparatus 225 Mortar Voids Test Apparatus 226 Apparatus for Making Concrete Test Specimens 227 plow Table, Showing plow of Concrete Test Specimens 228 Testing 6 x 12 in. Test Specimens 230 I. . '>■ ■ '■• ' : , '; w?' ■ ' , '• ,1 •' •V' i ■■ 'I ■; • •; ‘:: , r-' . ■' ■': ■' : " ■ I '<'■/ ■ ' ( L . *' ' vi 'U. / «T, '^r;; ■•- os't , , n, . . - ‘-J 1 .r •'.:';u: y’, \ ' f^:■■ '-V ■I. iv:.'/'. 14 > ' ;., . ■ V ■r-i ft, '.7 I . y - , ■* i ij , , -J . , '( • ,, '.I 'j.r !,. v‘-'' •iV'L' . ';, u:-.-- . } i\ 'ft*, s ;v ,i, 1,^ ,. /r < >n. I*' ■- n.t\ ■••'■' TO" '■' . ‘ ' •t-i/ .i:i '-: , *A/:.h^.l£a' . , ' .1 '~ '.: ■ )‘ • y. TRr^v-•>- i n- vyy*y,^, > ■ • P-ge Testing 2x4 in* Test Specimens 231 Representative Samples of Sands 232 I»I3T OP CURVES Am UUGRillS Curve 1. Sieve Analysis Curves 28 Curve 2. Mortar Voids Curve, Accompanying Descrip- tion of Mortar Voids Test g9 Curve 3. Strength Curve, Accompanying Discussion of Cement-Space Ratio 56 Curve 4. Composite Characteristic Mortar Curves, Accompanying Discussion of Cement-Space Ratio 51 Curve 5. Characteristic Mortar Curves of Sand Ro.23, Accompanying Discussion of Increased ?mter Content 7 q Curve 6. Curve Used in Demonstration of the Design of a Concrete Mix 75 Curve 7. Characteristic Mortar Curves of Sand Do. 23 and Do. 3, Accompanying Discussion of Range of Usefulness of Pine and Coarse Sands 80 Curve 8. Characteristic Mortar Curves 112 Curve 9. Curves Showing the Relation Between Com- pressive Strength of Concrete and Cement- Space Ratio 154 Curve 10. Curves Showing the Relation Between Com- pressive Strength of Concrete and Voids- Cement Ratio 190 page Curve 11. Curve showing the Results of iidhesion Tests Curve 12. Diagrams Showing the Percentage of Voids in Mortar Pilled with Water 216 217 wlp'’-,. ;':"-:v,'V',":'S''' v’iii"‘''".V , ' • ■ ’ITjW::. vS '<{ ■■ ■ 1 1. Preliminary * - Within recent years designers of concrete structures and experimenters in the mechanics and properties of concrete have become interested in the so-called "Design of Concrete Mixtures". Considerable information has been accumulated concerning the mechanics of concrete, but not until quite recently * has the study of the scientific proportioning of concrete received particular attention. The recent investigations have led to the proposal of several theories pertaining to the design of concrete mixtures. Most notable of these have been: "Water-cement ratio and fineness modulus" developed by Professor Abrams of the Struc- tural Materials Research Laboratory, Lewis Institute;* "Surface area" proposed by Captain L. R. Edwards, and presented before the American Society for Testing Materials in 1918.** Mr. Roderick B. Young, Assistant Laboratory Engineer of the Hydro- Electric Power Commission of Ontario, has reported some experi- mental and analytical data showing the relation between fineness modulus and surface area.*** Mr. Young in conjunction with * D. A. Abrams, "Design of Concrete Mixtures", Bulletin No. 1, Structural Materials Research Laboratory, Lewis Institute. ** L. N. Edwards, "Proportioning the Materials of Mortars and Concretes by Surface Area of Aggregates", Proceedings of the American Society for Testing Materials, 7ol, 18,1918. Part II. page 255. *** R. B. Young, "Some Theoretical Studies on Proportioning Concrete by the Method of Surface Area of Aggregates" , Proceedings of the American Society for Testing Materials, Yol. 19, 1919. Part II, page 444. 2 Mr. ViT. D. »7alcott, also of the Hydro-Electric Power Commission of Ontario, recently contributed an excellent paper on the measurement of surface area by means of bulking of the sand,* imong the earlier investigators in this country on the properties of concrete should be mentioned Mr, '/Villiam B. Puller and Mr. Sanford E. Thompson, who in a paper before the American Society of Civil Engineers proposed the use of "Puller’s curve of maximum density" as a basis for the proportioning of concrete for maximum density and strength.** The most notable European v;ork on this subject is that of M. Rene'peret, published in Bulletin de la Societe d’Encourage- ment pour 1’ Industrie Rationale, 1897, Vol. .11, page 1604, and also in Annales des Ponts et Chaussees, 1896, page 182. A resume of this 'work may be found in Taylor and Thompson, "Concrete Plain and Reinforced", Third Edition, page 145. Further reference to this work of M, peret is made under "Relations Af- fecting the Strength of Concrete", page 12. It has been felt by a number of investigators in the field of concrete that the theories which have been proposed were in- adeq^uate and did not take into consideration some fundamental * R. B. Young and William D. Walcott, "The Yoliime -Moisture Relation in Sand and a Method of Determining Surface Area Based Thereon", Proceedings of the American Society for Testing Materials Vol. 20, 1920, Part II, page 137, **William B. Puller and Sanford B. Thompson, "Lav/s of Proportioning Concrete", Transactions , American Society of Civil Engineers, 1907, Vol. 59, page 67. < h / / I 1 I » » t I :i I !1 3 features entering into the design of concrete. A series of tests was therefore planned hy Professor A, 1], Talbot as a part of the work of the Engineering Experiment Station with the hope that a method of analysis might be found whereby the properties of concrete and its constituent elements could be more easily under- stood. 2. Scope and Outline of Tests . ~ The investigations on the properties of concrete conducted in the Laboratory of Applied Mechanics in the spring of 1921 under the supervision of Professor A, 1^. Talbot are reported in part in this thesis. Another por- tion is reported in the thesis of Mr. R. L. Brown, "The Relation of Water Content and Consistency of Mix to the Properties of Concrete”, Graduate School, University of Illinois, 1921. This thesis is based on a study of the characteristics of twenty-nine different sands. Twenty-four of these sands were natural gradations, three were artificially graded, one was cement alone as fine aggregate, and one was Standard Ottawa sand. Of these sands, complete data are given in this thesis on the sands listed in Table 3 page 27 . The remainder of the sands are reported in full in the thesis of Mr. Brov/n. 530 6 X 12 in. concrete test specimens were made in the Series of 1921. Of this number 286 are reported in full in this thesis. These test specimens are all that were made with the natural gradations of sand and also those made v;ith only cement and coarse aggregate. Mr. Brown reports in full all specimens made from artificially graded sands Bo. 31, 32, and 36. 4 The test specimens made from the natural sands were made as nearly as possible with basic water content. Basic water con- tent is defined under Definition of Terms, on page 5 , in designing the cylinders the absolute volume of cement, and the absolute volume of coarse aggregate per unit volume of freshly placed concrete were arbitrarily chosen. In most cases the absolute volume of cement per volume of concrete was taken as 06, .10 or .16 and the absolute volume of coarse aggregate per volume of concrete as .35, .45, .46, or .50. ill cylinders were originally designed for basic water content. This thesis also reports the results of tests of 150 2x4 in. mortar test specimens. These specimens may be divid- ed into two divisions; (1) 75 specimens made with natural sands, and (2) 75 specimens made with artificially graded sands. The artificially graded sands were made up from ittica sand to conform to the sieve analyses of the natural sands. In all mortar specimens a constant ratio bet^veen absolute volume of sand and absolute volume of cement of 2.5 was used. Basic water content figured on the basis of the natural sands was used in all the specimens. This thesis deals primarily with the relation of fine aggre- gate to the properties of concrete. The thesis of Mr. Brown already mentioned, deals primarily with the effect of water con- tent. 3. Aoknowledg;;^rnent. - The tests reported herein were made in the University of Illinois Engineering Experiment Station 5 under the direction of Professor A, M . Talbot, Professor of Municipal and Sanitary Engineering, in charge of Theoretical and Applied Mechanics. The writer is indebted to Professor Talbot for many suggestions both in making the tests and in interpreting the results. The writer also desires to express his appreciation to Mr. P. B. Richart, Associate, Engineering Experiment Station, who was in charge of the Laboratory work, for his valuable criticism of the work as it progressed and his careful review of this thesis. Mr. H. J. Gilkey, First Assistant, Engineering Experiment Station, and Mr. R. L. Brown, Graduate Student, were of invaluable assistance in making the tests for this thesis. 4. Definition of Terms , Rotation , and Formulas . - In this thesis certain terms defined as follows are used: (1) Water Content wherever referred to is used as meaning the volume of water per unit vol- ume of freshly placed mortar or per unit volume of freshly placed concrete. This is exclusive of water that may be necessary due to absorption and surface wetting of the fine and coarse aggregate, (2) Basic Water Content is that volume of water per unit volume of freshly placed mortar at which the volume of mortar is a minimum. (5) Relative Water Content of a mortar is the ratio of the water content of that mortar to the i, t, f .3 ■ G l&im \ ^ ' j -VOI €ifiJ .T I » :j “ " " u 1 i ^ i 6 basic water content. (4) A concrete is of Basic Water Content v;hen the mortar therein is made with Basic 7/ater Content. (5) Relative Water Content of a concrete is ex- pressed as the relative water content of the mortar therein. (6) Point of Minimum Volume is that point or state at which the volume of freshly placed mortar is a minimum, iit that point Basic V/ater Content is used, and the voids in the resulting mortar are a minimum. (7) Specific G-ravity, determined as described on page 3E , is the specific gravity after 15 minutes immersion in water. (8) iibsorption, determined as described on page 5E , is expressed in percentage by weight ab- sorbed during 15 minutes immersion. (9) Sand in general is used in its commonly accepted sense: namely, a fine aggregate derived from a natural source all of which will pass, when dry, a Bo. 4 Tyler standard sieve. The fine aggregates used in the tests reported herein are referred to as sands, regardless of occasional non-conf ormat ion to the above definition 7 i'lO) Coarse iiggregate is used to descrilDe that rock, gravel, slag, etc. used in concrete which is too coarse to pass the l^o. 4 standard sieve. In the tests described herein gravel between the s/s and 1 in, sieves was used, (11) The Surface irea of an aggregate is used in this thesis as the summation of the surface areas of its individual particles - these particles being considered spheres, equal in volume to that of the actual particles. (12) Fineness Modulus is a function of the relative diameters of the particles of an aggregate as' calculated from the sieve analysis. Surface Modulus is proportional to the surface area and is a function of the relative surface areas of the particles of an aggregate as calculated from the sieve analysis . * * For a further discussion of surface modulus, fineness modulus, and surface area, see Discussion by Professor A* E, Talbot, Proceedings, American Society for Testing Materials, Volume 19, 1919, Part ll, page 481, 8 Professor Talbot has proposed the use of the following coefficients in the determination of these moduli. Sieve Size Coefficient for Surface Modulus Coefficient for Fineness Modulus 0 - 100 1 0 100 - 48 i/z .01 48 - 28 1/4: .02 28 - 14 1/8 .03 14 - 8 1/I6 .04 8 - 4 1/32 .05 4 - 3/8 l/64 .06 3/8 - 3/4 1/128 .07 3/4- 1 1/2 l/256 • 0 CO 1 1/2- 3 1/512 .09 The percentage by weight of the aggregate of the specified size is multiplied by the proper coefficient. The sum of these products is the fineness modulus or surface modulus as the case may be. (13) Cement-space Ratio is the ratio- of absolute volume of cement to the space occupied by the cement and voids V 9 (14) Cement-voids Ratio is the ratio of absolute volume of cement to the space occupied by the voids (both air and v/ater). The notation used is as follows: k = weight of water per unit volume = 1 in metric system = 62.4 in English system a’= absolute volume of sand in a given mix b’= absolute volume of coarse aggregate in a given mix c’= absolute volume of cement in a given mix w'= volume of water in a given mix = volume of resulting mix if mortar of resulting mix if concrete v'm =volu]'fie of voids in resulting mix if mix is mortar v^o =volume of voids in resulting mix if mix is concrete Q , _ wt, of sand specific gravity x k bi _ lyt. of eoarse aggrega te specific gravity x k , Y/t. of cement ® ~ specific gravity x k 7/t. of V7ater a = absolute volume of sand per unit volume of freshly placed mortar or concrete b = absolute volume of coarse aggregate per unit volume of freshly placed concrete. 10 c a absolute volume of cement per unit volume of freshly placed mortar or concrete WjQ a volume of water per unit volume of freshly placed mortar Wq a Volume of water per unit volume of freshly placed concrete w a volume of water per unit volume of freshly placed mortar allowed for absorption of fine aggregate Wqq = volume of water per unit volume of freshly placed concrete allowed for absorption of fine aggregate w , a volume of water per unit volume of freshly placed concrete allowed for absorption of coarse aggre- gate Wq^ a volume of water per unit volume of freshly placed concrete including allowance for the ab- sorption of both fine and coarse aggregate ^mo *^^sic water content in freshly placed mortar Wqq a basic water content in freshly placed concrete a absolute volume of solids per unit volume of freshly placed mortar a a + c d a absolute volume of solids per unit volume of ° freshly placed concrete a a+ b + c Vjj^ a volume of voids per unit volume of freshly placed mortar Yq a volume of voids per unit volume of freshly placed concrete P.M.V= point of minimum volume S a ultimate load on test specimen in lb. per sq. in. The following assumptions have been made: :tv V .'; rt.-T^ O.'ILJ =.'•'. f 5 i 7 - . .. •- .. ic tij*!.;* -. 7 ' 'l N/. ♦ i 0 "J'. J. V 1 > r 1 Cd‘!.V.. ': . • (? nil . ■ , - .■ i.o J ioT^J. IV' 7 ' oj r*r 3 ^ a B '3 • ^ ( . ^i..- Tvi; ' f.-. o ! ’". iSft- • : ■>& iV '_ 5 ^^ w T'V' * • ! I . Jjiov ^:■ ' .^ '^-U- *vo.-ii --'ji jicarnX/ ' 3 . B- 'i S';-,-; / r , . „ -.ru, Tto:;j' ■’ ,r ’ X • I if - 6 vft*To .. o..:j.i: T XO- ft:?- - . i ■ '.*•'■■;••■ c_ I ".r*,(.>z r. ii Ti 1- ■>• A - ' X' . : : . .. '.y.--. .' ii.. 1. ii ■ . V t: ..:::"^.:y c, •r f-sbitP: ',%‘r.v-iT't - ... . [<^v •.: - £ V. Sf J V e>s/‘ Ovi»X 9 UO 0 ■> »■ tf r •> - ■ “T * ': {. . o. , x“. I c c -1 . t C-^.i 7 -rt'ii'f. 'I O'' i' t-'i V u: ; ' 5-- * ’ '* ' 3 BOOi^ :i LmKi 11 (1) The voids in the coarse aggregate (in the con- crete) are filled with the mortar. (2) The total voids in the concrete a.'e equal to the total voids in the mortar therein. On the basis of the above assumptions the following formulas have been developed: (1) (H) ^0 = (3) ^C = (1-b) Tm (4) a + c . + b = 1 (5) a ’ + c* d,y. * ^ m (6) a* + P * * V I ^ t ^m b» a q'g (7) "c = (1 - b) Wjji (8) w = GX w + w + W - c ca cb 6. Relations i^ff ecting the Strength of Concrete .- In- vestigations conducted by Professor A. H. Talbot in 1920, and substantiated by a study of the Series 83, 122, and 124 of the Structural Materials Research Laboratory, Lewis Institute, have brought out the fact that the strength of concrete is probably directly proportional to the cement content, and inversely proportional to the volume of the cement plus voids. There also appears to be a relation between cement content and voids, that is, between cement content and the space outside the aggregate and cement. These relations may be expressed in mathematical notation*. n < ' 1 1 12 Strength » function of c ( v+c) = function of cement-space ratio Strength = function = function of cement-voids ratio Professor Talbot has prepared a paper on this subject to be presented before the Annual Convention of the American society for Testing Materials in June, 1921, in which may be found curves showing the relations expressed in equations (1) and ( 2 ) • M* Peret, the noted French investigator, realized the signi- ficance of these relations, and in his paper published in Bulle- tin de la Societe d* Encouragement pour 1* Industrie Mationale, 1897, Volume II, page 1604, may be found data lending support to the above theory. The results of peret *s tests are discussed at some length by Taylor and Thompson, "Concrete Plain and Rein- forced”, page 153. Peret' s work, however, was primarily upon the strength of mortars. > - II- mTERIiLS, TEST 3PEGIMEES TECHNIQUE OF TESTS i i / 13 6. Materials and the ir Physical Properties ." Cement . - Universal Portland cement was used in the tests. This cement had been on hand in the laboratory for several years. A portion of the cement had been stored for the past year in large galvanized iron containers in the basement of the laboratory The remainder had been stored in a dry storage room. Before us- ing, all the cement was screened over a Bo. 28 screen to remove any possible lumps. TABiE 1 TESTS OP CBlvEET Sample Uo. Tensile Strength 1:3 Mortar Pounds per Square In. Per Cent ’i/yater at normal Per Cent water Used in 7 days 28 days Consistency Mortar 1 170 270 24.0 10.5 2 155 285 24.0 10.5 3 160 260 24.5 10.6 4 216 315 24.5 10.6 iv. 176 285 The average time of initial set as determined by Gillmore Beedles was 1 hr, 26 min., final set, 10 hr. 00 min. The average specific gravity was found to be 3.10. The cement passed satis- factorily the steam test for soundness. ' T- ■ ■ - - — ^ ‘ () : l' t' ■ Qr2..-zv D'-. i I (■ 14 ^11 tests on the cement were made in accordance with the standard specifications of the iimerican Society for Testing Materials. * Fine Aggregate . » Twenty-nine different fine aggregates were used in the tests. Sand Uo. 0 was Standard Ottawa Sand. Sands Mo. 1-22 inclusive were furnished the laboratory by Professor D, A. Abrams, Structural Materials Research Labora- tory, Lewis Institute, Chicago. These sands were shipped to the laboratory in canvas bags. Approximately 200 pounds of each sand were received. The Lot lumbers given for the sands in Table 2 , page 15, are the identification numbers used by Professor Abrams, Sand Mo. 23 was a fine sand and was furnished by the Illinois Highway Department. Sand Mo. 24 was a natural sand from near the Wabash River, Attica, Indiana. Sand No. 26 was the cement used as a fine aggregate without any actual sand. Cement of the same quality was used in all the tests. Sands No. 31, 32, and 36 were artificially graded sands, made up from certain sizes of Attica sand. A photograph of representative samples of the sands is shown on page 232. *"Standard Specifications and Tests for Portland Cement," adopted January 1, 1917, A. S. T. M. Standards, 1918, page 503. rrtai O ■4 U >> Ij - ..A s i D > ‘3 J d 1 .■ \ ■ ?r _ Cv ”,.*' : ■ . ‘X , _ • ■ ' 1* " : ' . -C . ^VT F/ J ^ t :I:-.^ J %1 i' It J M L’ m L-I- ::.: ■ 1 ,. 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This Ho. 100 material was very friable, resembling finely divided coal particles. The particles in general were round in shape. Some lumps of light colored dirt were present. Sand Ho. This sand, limestone screenings from Milwaukee, Wisconsin, contained a very large percentage of dust. Approximately 40 per cent passed the Ho. 48 sieve. The larger particles were irregular in shape, elongated and flat, and appeared to have a crystalline structure. The general color was dull white, the larger particles being coated with the dust. Sand Ho . _7. - This material, chats from Joplin, Missouri, as originally received contained about 30 per cent coarser particles than the Ho. 4 sieve. In order to use the material as fine aggregate, the particles coarser than the Ho. 4 sieve were screened out. The particles had sharp edges, were irregular in shape, and were flat, elongated and smooth. The general color was dark gray for the larger particles, and white for the finer particles. The aggregate was clean, no visible trash or silt being present. The specific gravity of the chats was 2.60, lower than any other found in these tests with the exception of that for Sand Ho. 16. It is probable that this material consisted of tailings from lead or zinc smelters. Sand HO . _8. - Very little information concerning this sand, which was labeled banding sand, has been obtained. It Id? A ‘1 \ I 20 was pure white in color. All of the sand passed the No. 48 sieve, with approximately 4E per cent passing the No. 100 sieve. The grains were spherical in shape, and had the same general appearance as grains of Standard Ottawa Sand. It is probable that this sand came from Ottawa, Illinois. No absorption could be obtained for this sand by the methods used. In fact, if such is possible, a negative absorption was found. This might be due to the cementing action water had on the very fine particles which was not present when the sand was saturated with kerosene. Sand No . 11. - This was a slag with approximately 10 percent coarser than the No. 4 sieve. From the No. 4 sieve the gradation was almost a strai^t line to the £ opening as shoim by the curve on page 29 . The slag con- tained some trash and dust, making the determination of absorption difficult. The coarse particles were porous in texture, irregular in shape, and in general were flat. The general appearance was dusty gray. Sand No . 16. - This material, a granulated slag, had a glassy brown color. The grains were more or less rounding in shape, with the appearance of being composed of fused substances. The coarser particles were porous in texture. The slag contained some material that resembled coal clinker. The absorption and specific gravity of this aggregate was difficult to determine, due to the lightness and porosity of the particles. This material had the lowest specific » -J t . LK ; C. I - c- -^nrrmBJkse^ V El gravity of any of the fine aggregates used. Sand No . 18. - This was a conglomerate aggregate from the site of the proposed Barrett Dam. The sand contained some pebbles as large as s/s inch, but fine material pre- dominated. The grains were shell-like in appearance, ir- regular in shape, but not flat or elongated. The finer sizes contained an assortment of red, black, and green grains. The principal constituents appeared to be quartz, basalt, and mica. Sand No . 19.- This sand contained a small percentage of pebbles larger than 1/4 inch, but 70 per cent passed the No. 14 sieve. The pebbles larger than the No. 0 sieve ap- peared in general to be of basalt origin, black and very heavy. The coarser particles were smooth, irregular in shape, but generally were not flat. The finer particles were of more uniform size with the grains more nearly spheri- cal. The principal constituents appeared to be quartz, basalt, and a trace of mica. Sand No . 21.- This sand which was from Medicine Hat, Canada, was very clean, being free from dust, silt, or trash. The curve showing the sieve analysis indicates a predominance of fine material. The larger particles were irregular in shape and rather rough on the surface. The finer grains were somewhat angular. Silica appeared to be the principal element. The finer material contained seme mica. Black pebbles and grains were noticeable. The 1 . ve- il 'jn •j .: 2 £ color in general was light yellow. Sand Ho. 25 .- This was a quartz sand from Greenup, Illinois. The sand contained seme trash and lumps of dirt. Practically all passed the Ho. 28 sieve, with approximately 60 per cent between the Ho. 28 and Ho. 48 sieves. The grains were slightly angular. The sand was light yellow in color. Sand Ho . 24. ~ This was a bank sand from Attica, Indiana. The grains were smooth and irregular in shape. The sand was well graded with about 4 per cent finer than the Ho. 100 sieve. The principal elements appeared to be quartz, limestone, and pebbles of basaltic origin. The sand was comparatively free from loam or vegetable matter. coarse Aggregate .- The coarse aggregate used in all concrete specimens was bank gravel from Indiana. Voids in the coarse aggregate were found to be 59.4 per cent. The gradation of the coarse aggregate was not varied in any way. The grading was 60 per cent of material between s/s and s/4 inch screens, and 40 per cent between s/4 and 1 inch screens. The specific gravity was 2.71. An allowance for absorption of one per cent of the weight of the coarse aggregate was used throughout the tests. The methods used in determining the specific gravity and absorption are described on page 34 , The aggregate was composed principally of pebbles of a calcareous origin, and in general they appeared to be rather soft. The pebbles were irregu- lar in shape, and contained a considerable proportion of flat or • /* *l ‘ J.. ..I l; .. ■• -Xc . ; -. 3 'x-j / ] elongated pieces as Water.- Water for all tests and for all test specimens was taken from the tap in the laboratory. The measurement of the water for mortars is described under Technique of Mortar Voids Tests . page 37 • Measurement of water for concretes is described in the thesis of R. L. Brown, 1921, page 21. 7. Sieve Analysis . - The granulometric, or as it is more commonly called, sieve analysis, has been an important considera- tion during the development of concrete. Among the first to use the sieve analysis as an index to the concrete making qualities of sand was M. Feret. Feret devised a unique system of triangles to represent this analysis of a sand. In his work, however, he considered only three sizes of particles, Coarse-G, Medium-M, and Fine-F. These sizes are nearly equivalent to sand screened through sieves of wire cloth as follows: Coarse-G, Passing screen with 5 meshes per linear inch Retained on screen with 15 meshes per linear inch Medi\im-M, Passing screen with 15 meshes per linear inch Retained on screen with 46 meshes per linear inch Fine-F, Passing screen with 46 meshes per linear inch In this country the most extensive study of sieve ana X^s of ^d was made by lir. William B. Fuller in conjunction with Mr. Sanford E. Thompson. From the results of these tests Er. Fuller proposed a method of designing concretes of maximum strength from a Study V ■ i Kl< - '( 24 of the mechanical (sieve) analysis of the sand. This method is fully described in Taylor and Thompson, "Concrete plain and Reinforced”, Third Edition, page 190. Recently Professor Abrams of the Structural Materials Research Laboratory, Lewis Institute, proposed the use of the fineness modulus as an index to the concrete making qualities of an aggregate. The fineness modulus of a sand is a function of its sieve analysis. Professor Abrams has used the Tyler Standard Screen Scale Sieves in his work. These sieves are very generally used in laboratory work. The above discussion indicates the possible importance of the analysis, and for this reason it was felt expedient to describe the method used in making this analysis. So far as it is known to the writer no standard screen scale, or method of mak- ing sieve analysis of fine aggregate for concrete has been adopted by any of the American Engineering Societies. The Tyler-Ro-Tap Sieve Shaker shown in the photograph, page 224, was used throughout the tests.* Prom one to thirteen sieves can be placed in the shaker at one time depending upon the height of the sieve used. The shaker is operated by a l/s h.p. electric motor. The sieves are given a circular motion, combined with vertical tapping by means of an arm actuated by a cam. This arm can be seen at ^ in the photograph mentioned. The Ro-Tap is built to handle 8" diameter testing sieves. It is also operated with a Stop-Rite Switch which eliminates error in timing. ’•'Manufactured by W. S. Tyler Company, Cleveland, Ohio rr>xsB 25 Realizing that the length of time the sand was shaken would have an important bearing on the results obtained, some pre- liminary data were taken to find the effect of time. For most sands it was found that shaking longer than fifteen minutes had very little effect upon the resulting analysis. This length cf time of sifting will in general insure that in one minute of additional shaking not more than one per cent of the weight of the original sample will pass any sieve.* All sands reported in this thesis were agitated in the Ro-Tap for fifteen minutes. It is thought that except for extremely fine sands, this length of time may be expected to give consistent results. Tyler Sieves 8” in diameter were used in the Ro-Tap machine. These testing sieves are described by the manufacturers as con- forming to the Tyler standard Screen Scale. This scale has a starting point or base at the 200 mesh sieve having .0029 inch square openings. Each successive opening is exactly 1.414 or fZ times the opening in the previous sieve. In these tests the following sieve sizes were used, which are in general two sizes larger than the previous sieve. Sieve 200 150 100 48 28 ' ' " Size of opening in inches .0029 .0041 .0058 .0116 .0232 Sieve £ 4 5/8 Size of opening .046 .093 .185 .371 in inches * See Appendix 1, Report of Committee C-9, Proceedings American Society for Testing Materials, 1920, Vol. 20, Part I, page 296 for method used by the committee. TYPICiL MTA SHEET E6 SIEVE AIULYSIS 3-AUB m. 2 LOT 1^0. 3472 Weight Over Computed Bata Sieve 1st Ho. Run 2nd Run Av. Wt. Over Correc Wt. Over t Per Cent Over Per Cent Pass- ing Per F.M. S.M. Cent Remarks Biff. 4 45.1 46.1 45.6 45.7 9.1 90.9 time 9.1 .546 .142 lo^min. 8 240.9 236.0 238.5 238.9 47.8 52.2 38.71.935 L200operator 14 imb • 1 332.9 334.0 334.5 66.9 33.1 19 . 1 . 7 64 1. 184 Braman 28 387.4 385.5 386.5 387.1 77.5 22.5 10.6 .3181.325 48 419.6 417.6 418.6 419.3 83.9 16.1 6.4 .1281.600 100 443.9 442.5 443.2 443.9 88.8 11.2 4.9 .049 2.450 Pan 499.8 498.6 499.2 500.0 100.0 0 11.2 0 11.200 Totals 100.0 3.740 19.131 Bate and time placed in oven March 16, 1921 - 5 p.m. Bate and time gas cut off March 17, 1921 - 6 p.m. Bate and time sieve analysis March 19, 1921 -10 a.m. Het Wt. before drying 1093. 1 grams Set 1 Wt. time S.A* 1091. 7 grams Percentage by Wt. contained moi sture 0.13 SIEVE ANALYSES OE SAUDS o o » -O -P CJ ® o ® Pi o •H p o 3 p o 1-^ o 3 ftl Pi ® CO rH t~ • • oooooooooooct>oooo OOOOOOOOOOOCTkO^OO I — IrHrHrHrHr— IrHrHrHrHrH rH i — I o> 0> rH rH lO CM OOOOOC^OOCOO'M^OrHOC^ ooooooa»a»aoo>oo> rH rH rH H H rH rH CM'^ tOlO vOiO-MtO O • • •• ••••• • oocMx^oto-ioHa»Oao OOiOODOOOiOO-^CJ^OOOt-Ot- rH rH rH rH i — I rH O C> I>- LO « • • • ■«4< O C> CM 0> to • •••••• OOtOt-O'tOrHOUJuSC-tOrHorH OOtrt^C 7 »^tOOCMt>'M‘'^Cr>lO iH rH rH U5 !>• O e- rH to O lO lO 00 CJ> 00 • •••••• HO>CMir30^rHO>OlO^'^^CMOOlO cr>CM'=^iOrHOHt<)CMiOtQo^CM rH OlOrHU 30 CM'ii‘tOCMI>-rHtO'=d< I — I I — I t-O Oi rH rH O^CMOOI>-OOCMlOsHOCMst< C0CM«;}< • •••••••••• ••• >M*rHrH to rH CM ^ O CM lO I — I o lO rH & ® xa tio t»u •rH Pi ® ® u w ® rH ® ft P •a o 'd CO »d p •H P Pi CO Pi d p Pi O ® *d ® p O ® Pi ® CO ® CO <*5 03 Pi Pi ® PI P ® Pi as O CO o t)0 ® ftrH A ® CO CO p Pi rH d as p 03 03 •rH d d Pi Pi 2 ft nH •H ® P nd bO Pi ni »d fd ® d CSS Pi ® Pi •rH S ® ri ® ® S4 d pi ® p p •H Pi ro Pi •rH w rH Pi ® ® ® Pi ® CO ft EH CO p O PP CO C!J CO CO CO o d5 ■»d«CMOOMDa>COOf-* tOCOtOtOtOtOtO-M<'^';ii »; r-'xjrf odJ" oL* .1 £ * ff«Ol 9 ’£1/ 3 Cti 1 1 i- __ _ ^ « 05.?-— oil+oe^T? ‘ ~ ’-t; .'' T- i ' ?'c"t> cfoc'i a (-T" “ "*T> ' . u .1 t‘,: ‘c7v: .-- : ii 3 • m. ' C T s 0 “i ?3 ■ li: a: (f';cco=: IJi.'v; ba’sn. o:!l tfxU 3o;.\j33ni cx;i!C J-- Jj'/.o;? ol"> -ra , 0. \'C‘C'ia:i .acf-oeo. -1 ao n.: Ij fCoo^'T 0 a ‘ 3 .:;--: 7 .b 3 ' : - tJ- ^Xjoaxe 'rcXfxw.^o • . , ■ t - r-j • -.^ A *^'1 r. 'se 4 ? bt j ■*■ I 2 ^ 0 ; Tb 0 . 1 1 iO»q£ X*taii>J':rw S’’ * .7 . . ^ . leX , ■■ . .'. i39oq<^£B - ■<* . 34 frequent intervals. At the expiration of fifteen minutes from the time the aggregate was placed in the flask, a reading of the meniscus was taken# 54 spec if io sravity "volume of mUv Displaced^ The two methods of determining ^ecific gravity gave almost identical results# Coarse Aggregate # - A different method was necessary for the determination of the specific gravity and the absorption of the coarse aggregate. The volume occupied by a given weight of gravel was found by determining its loss in weight when immersed in water# A wire basket was suspended in a pail of water from one of the arms of the balance (weighing to the nearest gram). The weight of the basket suspended in the water was recorded. About 1000 grams of dry gravel were weighed out on the balances# This was then placed in the basket and allowed to remain immersed in the water for fifteen minutes# The v;e ight of the gravel and basket suspended in the water was recorded. Knowing the weight of the basket and of the basket and gravel when suspended in water, the weight of the gravel was computed. The specific gravity of the coarse aggregate (using all weights in grams) was calculated from the equation Specific Gravity = wt. of dry gravel wt.of dry gravel-wt.of gravel suspended in water*" After the aggregate had been immersed in water for fifteen niinutes, it was surface dried and weighed again. The increase in weight gave sufficient data from which to calculate the absorption# f Ite’i- 35 Percentage Absorption by wt The naterial was surface dried by rolling in a burlap sack. The surfaces were moist and damp, but no free water was noticed. 9. Weight of Aggregate per Cubic Poot.- A oylindilcaLmetal measure approximately 8 3/I6 by 6 5 /b in. and having a volume of .208 cu. ft. was used in these determinations. The material was placed in the mold in about 2 inch layers. Each layer was tamped firmly with the tamper shown in the sketch , page 40 . Usually this required 20 - 30 tamps. The last layer was filled to overflowing. Finally the material was struck off with a 1/4 inch round steel rod. The mold was neither rapped nor jarred during the operation. The per cent voids in the aggregate was calculated from these data and the specific gravity of the material. 10. Technique of Mortar Voids Tests .- The accurate de- termination o£ the voids at any water content of a mortar is important. Upon the results are based the computations for propor- tioning the materials of a concrete, and also the predetermined strength of any concrete is dependent upon this test (following the analysis used in this thesis). Great care should be taken to obtain representative samples of the sand. A saiqple splitter is convenient for this purpose. Comparative tests have indicated that the use of a 2 x 4 inch mold gives results as accurate as the use of a 3 X 6 inch mold. The metric system is^ very useful in these tests, and the following discussion refers in the main to its use. The English system may be used but it would necessitate the use of the factor 62.4. t O ' . . V ' • # ^ ' t .J it — . { I 36 Prom a study of the tests reported herein, it appeared that it was desirable to make these determinations (mortar YOids) at varying richness of mix and with different water contents. In general the useful range of sand can be covered by using a ratio of absolute volume of sand to absolute volume of cement of 0, 1, E, 3 i/e, and 6. In order to determine the effect of water content upon the voids of each of these mixes, successive additions of water were made to each batch. It is convenient to use a constant value of a + c equal to some even number. Por the calculations of these tests a+c » EOO was found to be convenient. The absolute volume of a and c re- quired can then be determined for each value of — . The weight c of any sand to be used at any desired mix is then the specific gravity of that sand multiplied by the desired absolute volume. It has also been found desirable to grind the mold down to some even weight, in the majority of these tests the mold used weighed 300 grams. The apparatus used in making the mortar voids determinations is shown in the photograph, page 2S6 . This apparatus consisted of a balance (weighing to the nearest gram), a burette graduated in cubic centimeters (reading to the nearest cc.), a E x 4 inch mold open only at one end, a small wooden tamp about 3/4 inches square, a small trowel, and a pan about IE x 12 x 2 i/e inches. The operation , recording, and plotting as ddscribed below was the method used for the majority of the mortar voids determina- tions. Predetermined amounts of cement and sand were weighed out. These amounts were fixed by the two following considerations: 37 g (1) — chosen as desired. (£) a + c =» 200 cc. This gave a slight excess of mortar and simplified the calculations. After thoroughly mixing the sand and cement dry, a small amount of water was added. The water was measured by means of the graduated burette reading in cubic centimeters, but which for measurable accuracy were considered as gram v/eights. The initial water added was not sufficient to cause a tendency for the mortar to ball up. It is desirable that the first few increments of water be less than basic water content, in general water equal to about Vperosnb by weight of cement and sand may be put in at the beginning. After thoroughly mixing, the mold was filled with the mortar. The mortar was placed in the mold in layers of about one or two inches. Each layer was tamped firmly but not excessively, with the wooden tamp, in general this required 16-26 blows. The operator soon became able to obtain about the same conpactness of the mortar when the mold was refilled. The mold was filled at least twice at each water content. The results in general did not vary more than about four grams near the point of minimum volume. Water was added in increments of about 10 cc. until near tloe point of minimum volume when about 6 cc. was added at one time. Water was added until the mix became rather sloppy and could be poured into the mold. A typical data sheet for taking the original data is shown on page 38 . The following equations were used: 1 . '■ . J'. .•: '■■.' - ('ty .? ovi ‘- r'l.'i^* . ' . a. b f- . •••.. .(.,.»0 V '.t iioi^ ; ■ '' aC‘. jr?i --irfl \ ■ ■... ii-* ' III o.r>.. ’i • 'j :< .'.' *£w ^ r- 'pv.- irf i/ii' 1 3“:; C’i' !f:j .:: I u i j X-Xiii - r-'-trcn a J TO'* '.; &coX ZQ%V'-1 'y;o' t ;- v7 % t 7' w£' OJ X .“.7 ■ » ii& 'rf»v> . ..!;v‘v 7 0rf or'-' 4» p.' '• j o ,, " : , ' *'?r: ‘-C /iJ* ’jit .'i: j r:I n ' *x .•• a '. p .“T' ,*io':. or!vf- iIjJt' Cttr ; 10':;5- / . . ^nca cv.t -^m:o i . .;. d- , ..."i • loSCTXL orf^ J-nod’iD Jo t. •. Cjc t:-- • _••:.! G-r:ic«>iii OP" . ^ r- . ' r' U J ,!•*.* .. - « u j i ^ . t‘v :c£lll: pr\. JoL;.::: ir=^ .0. V .1 £ 0 - .' n ■; J iiOj;i-!f 'rrj'io.^ 1- . 2a ju- OSS e '•.'■> * *'* '.iO j ' ' C**3. '*■< •• •3 j- •< ■<■ 'i'-. ',. ..•' 'J OtCiJ 7 ■■^.. , 7 * . V '■ ■ -I fli .-voBk- 6 7 - - J. '., VI or -. •' 7.,;- J '-. • 7 ' ..■"’.i '' 0 . .*>7f 03 C— ¥ ;7,-i«ir£ir. V- .. .-•.I xii : -S '; .. .»., t- • .; Tv .--V, . • . ■ 0f.;(5 r jJCLi tiv7 77 . *i .*v.i.': • ,'n . '. 'I r rt/k ■ 7 oi:o OOHHCMCVI tOtOtQ -HrH r— trHrHiHrHrHrH H(— I rHHt-HiHr— IHH <-0 o CO • • CO o >H o M £H EH M !> a o CO « ft ci) o EH 1— 1 ft ft ft M O o ft ft ft ft CO ft 0> CQ i nd Jh -P P •H d) »H rH O ft O > !=) >. voOlq^O^O'^CVI LQ CVJOOl — — I tOtOtOtOtQtOCQst^ o CVJ CO o o 03 • • . • • • • • • • nO • o o- 00 CO cO o 1 — 1 •H O 1 — I cr^ 00 CO o iH o O o o 1 — 1 rH rH rH > t=> •d o CO CO CO o o • • • • • • • • # • t>Q • o £> 00 CO CO a> o H «H •fH H o 1 — 1 Gi 00 00 a> o H o o 5h •H o CO CVJ C\2 CVJ CvJ CO CO CO O ?H o O O o lO o o o (0 03 +3 P • TO H-> O ?H C\J CV2L000t000Cv2O H LQ lO LQ 'vi^ CO 5h CO ra fd -P E • H j::} cC p o CO o ^ OOOOiOOOO • ••••••• OJ CVILOCOtOGOCVIO H ■=4 JS(XII>-£>(M(Mjv- CVJ CO^s;HcQJ>-a^H to to to to to cr> H 00 CO o <0 CO o EH O i-q Jh cq 0 ) a • -p ca OO lOOOtOioo -p d ^ c 02 >- l>-C3o>Ocv2lO ^ ^ M rH rH I— 1 m - o CO o o • +3 (D rH s CO O C3 CVJ (D • a • • a • o> o P CO 00 si CO o 1 — I rS fH CO -H Sh o CUD rH £»D o 's}^ O • CVJ ft M • • « o o ft - CJ ft CVj o CVj o CO O ft o CO u rH O nG «d CO CVJ H rH fd rH O iH O fd II II m O O Co (Q • - «H tp CO • a O P CO CVJ . rH o &: U + OO O • 0 tUD •H N • 1 — ! p - ?H *H p O CO CO EH CO > p ft caj O • CO inSSKK ipHBp^y.5^ iSSii iiaiil lo y V . C ! ).;o'’ M .. O' ;,; J .•\'-'ioi 9' X- . J - • ^ 'J 'iO.i' -X- V. 0 . ox : c ■ . ' ■' r; . f>L’r: ' ,\j .Liv. c.L^ 0 i'’xo •■i C'XM® .•; •-■■-' n-_ o"i ; X jii^ a I ' ,\j i„ i. i- . J '' i'f’ ‘■’^ ;; . . . 0 - tA- ;:v..: ■r-i-qgic?-. - '.. 0 o', , O • O - 43 Test cylinders were capped with a good stiff neat cement mortar. The cap was smoothed out by means of a piece of plate glass. The glass was prevented from sticking by the use of oiled paper between the glass and the cap. The cylinders in most cases had been made one to four hours when capped. Unless damaged in handling, the lower end was not capped. Mortar Test Specimens . - The mortar test specimens were made in 2 x 4 inch molds cf drawn seamless metal tubing. All specimens were made by one operator; he had had no previous experience in laboratory work. The specimens were made under the same conditions and by the same method as the mortar voids tests were made. The average of three mortar specimens is reported in this thesis, no numbering system has been used other than that the specimens made of natural Sands are referred to as Al, A2, A3, etc. The artificially graded sand mortars are referred to as Dl, D2, D3, etc. A plate glass base plate was used. The method of capping was similiar to that used for the concrete cylinders. In both concrete and mortar test specimens, the actual re- sulting proportions in each cylinder were determined by the use of the known volume of the mold. The molds were not measured just before being filled, but were measured at the beginning of the tests and these values were checked at the conclusion of the tests. 44 12. Storage and Handling of Test Specimens .- The test speci- mens, both mortar and concrete, remained in the laboratory where they were made approximately 24 hours before the molds were re- moved. The average temperature was about 72 ®F. At the end of 24 hours the molds and glass plates were removed, and the speci- mens stored in moist air. The humidity of the moist room was practically constant at unity. The temperature was also approxi- mately constant at 70*^. The air was kept moist by means of two atomizing humidifiers furnished by the American Moistening Company These atomizers , being operated under an air pressure of about 50 lbs. per sq. in., sprayed a fine mist. One atomizer was placed on the north side of the moist room and the other on the south side. These were placed so as to spray in opposite directions. This gave a tendency for the moist air to circulate. At times when the air did not seem sufficiently moist, the old sprays, which operate under water pressure only, were run until the air became saturated. These old sprays are not very satisfactory as they do not set up a foggy atmosphere. The specimens remained in the moist room for 26 days and then were removed for testing. They remained in dry air 24 hours before testing. The 6 X 12 inch test specimens were moved on trucks or buggies. Approximately twenty cylinders could be moved at one time. This method of handling eliminated unnecessary breakage. Extreme care was taken both in loading and unloading the specimens to avoid in- jury to the caps. The 2x4 inch mortar specimens were placed in a large pail or bucket, which one man could easily carry. Approximately 36 45 of these cylinders could be placed in the pail (half bushel bucket) at one time. Care was taken to avoid any damage to the specimen proper or to its cap. It was necessary to carry the 2x4 inch specimens to the Laboratory of jipplied Mechanics Building for testing. 13. Method of Making Compression Tests .- All specimens were removed from the moist room twenty-four hours before they were to be tested. The temperature of the room in which they were stored during this twenty-four hour period immediately preceding testing was practically constant at 72®F. Before testing, all concrete cylinders were weighed, and the diameter and height were measured. These data were usually taken on all of the day*s specimens, in the morning before testing began. All specimens were examined for faulty caps and defects due to workmanship or other causes* Test specimens which were found to have faulty caps were tested with plaster of paris caps. ^ 2. l^-ch Concrete Test Specimens . - All concrete test specimens were tested on the 300 000 pound Olsen, Pourscrew Uni- versal Testing Machine. The machine was operated at its slowest speed - the crosshead travels about 0.05 inches per minute under no load. Load was applied through a carefully adjusted spherical block bearing against machined cast iron bearing plates. On all concrete specimens tested curves were taken by means of a Rapid Semi -Autographic Device, which indicates the form of the stress-deformation curve. As no study is made in this thesis of the 46 elasticity of the specimens, no description of this apparatus is given* The ultimate load was determined by means of the drop of the beam. The beam was kept carefully balanced as the load was applied, ^t the ultimate load (ultimate stress on the specimen) the beam would drop, and further downward movement of the crosshead would not ra ise the beam. In general, specimens were not tested to destruction. — — — Mo rtar Test Specimens .- Ill mortar specimens were tested on the 50 000 pound Riehle, Two-screw Universal Testing Machine. The slowest speed was used - the crosshead travels about 0.05 inches per minute under no load. lo data on elasticity were taken. The method of applying load and of determining ultimate load was the same as for the concrete specimens* = X m 0-, ‘ ^ *V/ rt -;i:^inio 9 cr 8 ••-’i- i :*i oiifr :!' ¥ :* /r 'T f;dJ t ' oc.: ,i iei-i '.Ti x>£;oI L ^ t/ t>. e^- tt>onr.:nci r.llvls-xBo t?»w it-- : ‘ c?.-.* .- • :j- / L-J.l o C o )— #. ?,X. 7 . M or^sFv'i.e ...•j :.. j --' oji.. ■XSriJlc;^ L.u , rj*^ Mubtr . -oecf orJ ettifli o-on ■>. '' . ‘j. ^'. u v:'j3“ cu^aloQCQ jj.w:ion8g r:l -„:fv: urror. o r' XJ.' - ■ «il£l • -'•'Jii -i .r.'i-iS ■ •■' ■ --CT. , 'r.-ir,;;-. t.-BCu 000 PS oiL* no ioi i_’i^r ^4- .t-O^C* V,' Qb3.'- if i-’I 3 i* - ■ . -‘9^' . omlo' .‘■}«j. on ' Ov 'J.iiu. 137 aoilo^l oC.^ 9 v.*”-: oiirl jn. T.X ' u ' O fiorfXoi:: c/‘‘T . ||| eiccoo siii" i-->i 8B oraa o/^J" hj w ‘v ' *''!*'• V" -i Kl -III- EIPERB'IEIJT^L Dili Am DISCUSS lOE 47 14. Explanation of Tables .- Table 1.- Table 1, giving the results of tests of the cement was made up from data furnished the laboratory by Mr. E. E. Bauer of the Civil Engineering Department, who made the tests. lable 2.- Table 2 gives the data of the physical properties of the fine and coarse aggregates used. Professor Jibrams of Lewis Institute furnished the descriptive data of Sands 1 to 22 inclusive. The values given in the table were found by the methods described under the various technique of tests. The fineness moduli and surface moduli were obtained by the use of the coefficients proposed by Professor Talbot. 3.- The sieve analyses of Sands Eo, 0, 1,2,3, 5,6,7, 8,11,16,18,19,21,23, and 24 are given in Table 3. Table 4 gives the percentage of the voids in mortars filled with water at w^^^, 1.2w^^^,and These data are given for tne sands enumerated above. Thase values were obtained from interpolation on the curves plotted between the volume of water per volume of mortar, and voids. Table 5.- Table 5 gives the percentage of increase in voids corresponding to a given increase in water, jill percentages are referred to basic water content. The quantities in this table were computed from the relation : the percentage increase in voids at a given relative water content is equal to percent age of voids filled with water at b asic water content percentage of voids filled with water at the spec if ie'd "water conia^ .'.> « •■.” -HU • ;.. -J,l\ •^1 r j:* . -a .1 V ,. -v-v.' ’-ij:. V. ,-n J: - oivio ,cl' ' :-;::ii '-u fij; ;J, 7 ./I. ' '■’t '■ •" / ' 48 multiplied by the relative water content (as 1.2, 1.4) and by 100 per cent. The data for the computations were taken from Table 4. Table - Table 6 gives the average of the results of three mortar test specimens. Specimens were made at a constant Q — = 2.5. The artificially graded sand mortars were made from Attica sand to conform to the sieve analysis of the natural sands. The natural sand mortar test specimens were designed for basic water content and the same total quantity of water was used in the test specimens made from the artificially graded sands. The numbers following the letters indicate the sand number, as Al, Sand No. 1. Table 7 _,- Table 7 gives the results of the concrete test specimens made with the natural sands. The notation used in the column headings is described under Definition of Terms. The cylinders made with a given sand are referred to as 1 N , 10 N , etc. The first set of digits preceding the letter N indicates the sand number. All tabulated quantities were computed from the original data, assuming that proportional parts of all the materials were placed in the mold. All calculations of quantities were based on wet concrete. 15. Explanation of Curves and Diagrams . - The curves and diagrams will be explained in the order in which they are given under LIST OP CURVES AND DIAGRAMS, using the curve number given there to designate the curves or tsrpe of curves 'being discussed. i <-) 49 Curves 1 and - Curves 1 and 2 will not be explained here as they are explained in the text which they accompany. Curve 3.- Curve 3 is plotted on logarithmic paper from the equation S = 27000 ( . ^ ^ ^ , V + c Curve 4.- Curve 4 consists of the Composite Characteristic Mortar Voids Curves, Characteristic Basic Water Content Curves, and Characteristic Cement-Space Ratio Curves. These curves were taken from the curves plotted from the original mortar voids test data. These original curves are explained under Curve 8, Curve 5.- Curve 5 gives the Characteristic Mortar Curves of Sand Ro. 23 at basic water content and at 1,4 basic water content. Curve £•- Curve 6 gives the Characteristic Mortar Curves of Sand Ro. 23 at basic water content. It also shows the curve of bulk of mortar for a given absolute volume of cement and a fixed a — . Further explanation of this bulk of mortar curve is given under Design of a Concrete Mix. Curve 7,- Curve 7 shows the Characteristic Mortar Curves of ♦ Sand Ro. 3 and 23 at basic water content. Curve _8, - Curve 8 consists of the Characteristic Mortar Curves at 1,0, 1.1, 1.2, and 1,4 basic water content for Sands Ro.O, 1, 2, 3, 5, 6, 7^, 8, 11, 16, 18, 19, 21, 23, and 24. Characteristic Mortar Curves are given for the remaining sands at basic water content only. These last curves were taken from the thesis of Mr. Brovvn, The original data of the mortar voids tests is plotted with volume of water per volume of mortar (corrected for absorption) as abscissa, and voids in the mortar as ordinates. Usually a 50 well defined point of minimum volume was found. Occasionally it was necessary to produce the two sides of the curve to an intersection. This lowest point was taken as the point of minimum volume. it the point of minimum volume "basic water content and the corresponding voids were read from the curves. The voids at 1.0, 1.1, l.E, 1.4 basic water content were then read from the curve and plotted. The c (cement per unit volume of mortar) was plotted from the j. • _ ^ 1 c equation c * • q — . The curve was plotted by combining o’ the various values of ^ the corresponding values of c and Vj^. Curve £. - The strength of the concrete test specimens are plotted against the cement-space ratio on Curve 9. ill of the specimens (that is the averages of each set) are plotted on the master curve. Prom these data the equation S = 27000 ( - ) ' 2.4 V + c was determined. The test specimens made from each sand including mortar specimens are compared to this curve of strength. Curve 10 . - The strength of the concrete test specimens are plotted against the voids-cement ratio on Curve 10. The equation 2.4 3 = 27000 f- — 2-^) was transformed to the form S = _^.*^000 V + c (1 was found to fit the data very closely* The strength of the test specimens made from each sand including mortar specimens are compared to this curve of strength. ii* ■■ Curve 11 gives the comparative strength of the 2 X 4 in. mortar test specimens. They are compared to the equation S = 27000 ( ^ 9 . _ ) * , being plotted with 5 as abscissa. The V + 0 A* ■! i •j ■ 3 > iu ■ >, 1 '. results of the tests of both the specimens inade v/ith natural sand and with the same gradation of ittica sand are plotted. 51 Curve 12 . ~ Curve 12 consists of diagrams showing the per- centage of the voids in mortar filled with v/ater at three water contents. These values were found by interpolation from the Characteristic Mortar Curves. 16. Explanation of Photographs .- It is not thought necessary to explain the photographs in detail. The photographs of the sands show the natural sand as used in the concrete test specimens and also the corresponding artificial gradation of ittica sand which was used in the adhesion tests. 17. Relations Concerning the Strength of Concrete .- it is generally conceded that the strength of concrete, and in general most of its other properties, depend upon the cement content and the density. Before taking up the discussion of strength further, it is desirable to quote some authorities on the elements entering into a proper design. fl) "With given concrete materials and conditions of test the quantity of mixing water used determines the strength of the concrete, so long as the mix is of a work- able plasticity".* (2) "The sieve analysis furnishes the only correct basis for proportioning aggregates in concrete mixtures".* -^'brams,"Besign of Concrete Mix tures", Bull e tin t\io~T structural Materials Research laboratory, lewis institute, p^geS. I *1 r f »• • *• 1* , /(#! 5E (3) ”We have found that the maximum strength of concrete does not depend on either an aggregate of maximum density or a concrete of maximum density”.* (4) "Water content is the most important element of a concrete mix, in that small variations in the water cause a much wider change in the strength than similar variations in the cement content or the size Or trading of the aggregate. This shows the absurdity of our present practice in specifying definite gradings for aggregates and carefully proportioning the cement, then guessing at the water. It would he more correct to carefully measure the water and guess at the cement in the hatch".** (5) "The tests did, however, bring out emphatically the essential dependence of strength on the water ratio, which is quite contrary to the statements found in most of the textbooks to the effect that the strength of concrete is proportional to the amount of cement used".*** *I>. ^ibrarns, "Design of Concrete Mixtures", Bulletin Do. 1, Structural Research Laboratory, Lewis Institute, pagel ** D.A.Jibrams, "Design of Concrete Mixtures", Bulletin Do. 1, Structural Materials Research Laboratory, Lewis Institute page EO. ***D.i. Abrams, Engineering Dews -Record, Vol. 8S, June IE, 1919 page 1147. tr - . t C.' 'Lil .'-v\3'; 3.23 J/. ! • t- Y V *; . r ^ i ' "^1 ? ? f < r 0 I ' vr >* \^i 55 (6) "On the otherhand, many different series of tests niade in this laboratory have shovm that the quantity of cement is not a criterion of the strength of concrete unless at the same time we take into account the quantity of water used". * (7) "In ordinary proportioning with a given sand and stone and a given percentage of cement, the densest and strongest mixture is attained when the ■volume of the mixture of sand, cement and water is so small as just to fill the voids in the stone”. ** (8) "These tests indicated that the strength of concrete varies with the percentage of cement con- tained in a unit volume of the set concrete, also with the density of the specimen. With the same per- centage of cement, the densest mixture, irrespective of the relative proportions of the sand and stone, was in general the strongest”. *** (9) "The strength of concrete depends primarily upon: (a) the amount of cement used, (h) the density of tlie concrete, (c) the proportion of water used, and (d) the age of the specimen. Within the usual proportions the strength will he about proportional to the amount of cement * D. A. Abrams, Engineering Eews-Record, Vol. 82, June 19. 1919, page 1204 ** Taylor and Thompson, "Concrete Plain and Reinforced" Third Edition, page ^95. * ^^ylor and Thompson, "Concrete Plain and in 19m^hv 1-0* Tests referred to were made in 1901 by Hr. p„Her. E 19B. Gardiner, «nd ,,v.« -r -«**-• * 0 ,?. r-,; •• j* • ; •'.• ’* ’1^ i ^.'Xl. y ^ 'i o --I-."’ f«M;X n: -J >-. ao ■> f'JS .,. . ..ik i X. ■ - J C> . Mf, ( •r: .. . ■ »>*' V ^ '. V • . 1 , .iJ: ••:••• •* ( 7 ) ■'Ar f '“ . M' . . ' H . trr : * . i. .. T. .-.j^ 'i>. ‘.05 n I) ".;:- *•. n.:r'-o r-.'.‘\> {Jl^/A ‘ < * ^ I i k . I J ^ ‘ Ev J ^ i.' "1 J . . . » ■ J wi , i.. , ' >! ^ .'•4;' ' 2 ^' -fff) . / 0.^=1 >/;Cj ‘ 4 'i "i i. !>.:./« c^;?' :.■;' . ✓ ' •< a . •;i‘ u .J-LOuV-T '-V {V ' «.’ t!/' ' 4 y 'vu ■- • ~ \ , ' • yr**. •. •■'; ■I'. -4^ ^ j . . * .?'. s ■ it :')J: * .■ I J..- . t. J J ',■ i *■ .. ,^' " j ’i ii t- J I 'j ! 'X‘ > . . , kj- ' .. r M « 4 .-k' V j X ■'• :•;; c voc^c-i-?'. x ^ - k/' - o-..-..' , t " *n V »'...., -w* • jfc- 54 employed and for like proportions of cement the strength increases markedly with the density’’.* (10) "Factors contributing to the strength of con- crete are then, the amount of cement, the amount of mixing water, the amount of voids in the combination of fine and coarse aggregate and the area of surface of the aggregate" .** (11) "Density is a good measure of the relative compressive strength of several different mixtures of the same aggregates with the same proportion of cement to total aggregate".*** ( 1£ ) "For the same per cent of cement and the same aggregate, the strongest concrete is made with that combination of the sand and the coarse material which gives a concrete of the greatest density".**** (13) "For concrete made of good materials under normal temperature conditions three very important * Turneaure and llaurer, "Principles of Reinf orcedcon- crete". Third Edition, page 12. ** Professor A, R . Talbot, Proceedings American Railway Engineering dissociation, Vol, 20, 1919, page 905. *** Technologic Paper Ro. 68, Bureau of Standards, page 92. *^** Baker, "Masonry Construction", Tenth Edition, page 138. 55 factors in determining its compressive strength are: (1) age, (E) richness of the concrete in cement and, (3) amount of mixing water used”.* (14) "Generally speaking, for maximum strength, maximum resistance to passage of water, maximum re- sistance to wear and maximum resistance to disintegration hy such agencies as acids, alkalis, or electrolytic action concrete should be of maximum density " . ** (15) "With the same proportion of cement, with like consistency and like materials the strength and imperme- ability increase with the density of the mixture".*** (16) "Inasmuch as the density of a mixture is so often a criterion of other physical properties (strength, impermeability, fireproofing, and abrasion previously discussed - writer’s note), the more scientific methods of proportioning are essentially schemes for securing maximum density".**** (17) "With the density remaining constant and with making and curing conditions similar, the strength of concrete increases in nearly direct ratio to the propor- tion of cement for the mixes commonly used".***** * Moore, "Materials of Engineering" , Second Edition, Chapter on Concrete, by H. F. Gonnerman, page 245. ** Moore, "Materials of Engineering" , Second Edition, Chapter on Concrete, by H. F. Gonnerman, page 209. .*** "Johnson’s Materials of Construction", Fifth Edition Re- written by M. 0. Withey and James Ashton, page 426. * **** "Jotinson’s Materials of Construction", Fifth Edition Re- Withey and James j\shton, page 427. ’’Jotinson’s Materials of Construction", Fifth Edition Rewritten by M. 0. Withey and James ishton, page 459. I 56 The above references were to concrete, the following authorities are quoted on mortars. fl) "The strength of a mortar depends primarily upon (a) percentage of cement in a unit of volume, and (b) density’.’’* (Z) "yyith the same aggregate, the strongest and most impermeable mortar is that containing the largest percentage of cement in a given volume of the mortar".** (3) "With the same percentage of cement in a given volume of mortar, the strongest, and usually the most impermeable, mortar is that which has the greatest density, that is, which in a unit volume has the largest percentage of solid materials".** (4) "por any series of plastic mortars made with the same binding material and inert sands, the resistance to compression after the same length of set under identi- cal conditions, is solely a function of the ratio -2., what- ever be the nature and size of the sand and the proportions of the elements,- cement, inert sand and water,- of v/hich each is composed".*** (5) "Prom very numerous exper inents. . .M. Peret evolves the approximate formula S is proportional to C c ) **** c + V *Taylor and Thompson, "Concrete Plain and Reinforced"' Third Edition, page 143. **Taylor and Thompson, "Concrete Plain and Reinforced", Third Edition, page 144. and Thompson, "Cnnerete Plain and Reinforced" , Third Edition, page 153. This law is the conclusion of M. peret. Rotation changed to the nomenclature used in this thesis. + . Thoqipson/'Concrete P^sin and Re info reed" , Third naition,page 155. Rotation has been changed to conform to the nomen- clature used in this thesis. Jk J i) , .■' ■ ) '> -w fj « -i. • ^.• • ? a - t ( ,-;Y .y < j j irijl ,-Jl‘. Vi i •■ f • *V*' *< !* *• >{'\ ^ . t f ■J • * . - 1 57 The majority of the authorities quoted above on concrete are in accord with the theory that the strength of concrete is proportional to the cement content and to the density. The data of the tests reported herein have substantiated the theory that the strength of concrete is proportional to the cement content and to the density. In order to study the relation be- tween cement content and density curves were plotted between cement-space ratio and the compressive strength of the concrete test specimens. The curves shown on page 164 and page 190 are plotted from the results of the average in general of three test specimens (natural sand concrete test specimens only). The data from which these curves were plotted are given in Table 7. Prom the data plotted between the cement-space ratio ( - - ) and compressive strength (pounds per square inch) an average curve was drawn through the plotted points. This average curve was plotted on logarithmic paper and its equation was found to be S = 27000 - in drawing in this curve some ?/eight was given the data of other tests at the University of Illinois (Series 20). T;:e curve shown on page ISO is represented by the equation S = _ ^7Q00 This is simply a transformation of the equation "iTl + ]^2^.4 S = 27000 c ) 2.4. - On this curve tie strength of the concrete V + c test specimens are plotted. The curves on page 165 to page IS Sine lusive and page ]Slto page 215 represent the variation from the average curves of concrete test specimens made from a specified natural sand. The results of the adhesion tests of mortars (made from both the natural sands and the artificially graded sands) are also plotted on these curves. .«'v^, ’’ , 0 ^ •■V ’ ■■ ■ .' , ' .fur-fi ’ c->n» 'iu. <' ■*':i:.j^ ■>. X ii- n'C ' 1 ' ’ ' ,' ‘'’J. ■■ , iiM" -A'zw: .' ' ^ t -ii ' H ■ ■••'■' ' ' x .. ' .. ( !■: ■ X ' ' '"'V^ '► . ■ 4. ■ ftfci'. »<, •> 7 ,'.? ■" . 'i . ' - ■ * rv'--’ ■ 1 , -t ;1‘ ' •'. 1 . t'o. > ' .' ' '.,ii . :U'x.' • ' •^. .. ■ i: ^^-^3 ■' - lai.. \c , X •.( • f :i i)V' f ‘V i. ■/'. ’'j* . . /, I- ^ -■ > .. ••■ ?. V^’5^' " ' Vh| 4' ■'? i‘ •> v.iMvi* ^‘ ' ' ' ' ' 4 . '. V. ^ tio'l ■ : "S I't 1 ,'j'iv ' 4 ,/ v!.. , v.::;-^ \ ,..xr. ilj. ---.ro.' /^6 .a; • . , (; , , ' ' ' 0 / , ' 'y , (' 4 ■'t)^v^, ', ‘ I r ■+ . ‘ i' TI '.'. C 1 >'‘ I?*' . V .,'., ..; •-. '^ . . ' ■*«. ■' ■ ■ ■ ' ' ■ . .. ' .... ,■ ■x.J' -V^ . ' •-.. ■' ? V ■' -.'•v > ''■^’ V '■ ■« ' ' ,v '" . ■« 'U- .' ■'•. '< fe •I iM '^1.^ • I 4,1 ' j. ‘.'i *' .' J , -J-W V ^ u ^"*.1 •Jo''’ ■■.r/r,'J'.. C\ r/ir? t-raVr;V:-, ^:, V V%r ' 7 :.:J I ' v'vx ■■: 1 ; ;. J c.i'v .. / n,... . '"-JW J; •:''■> :X! .0 ^ ’ , _ j, - .,/ i, ■ . .. -, ta. ^ ; , L ,■; 4 ^ . ' w f ■ .■' ■■■;•; ' ■ ^ - ;v' '"/ X >' ,. '^V ■■ . :•■ ,;. '■ ■ ' >•/■. ...■■, .aaai ' ' * . -■ / I , - ^ 58 The maximum deviations from the average curve are the test specimens made from Sand Uo. 6. This sand was limestone screen- ings with considerable fine material. It is ^ dry mixes at which these specimens were made (Wj^q to the fine material had a cementing action which increased the strength above that which would be exoected from the density and the cement content. Mo. 7M59, the value which is high as seen from the curve Showing the comparative strength of Sand Mo. 7 is the result of only one test specimen, the companion specimens were not made. MO. 8m75,_c = .32E, S = 2197 is high due to results of the C v+c specimen which had a much higher compressive strength than did A and B specimens. All concrete test specimens made with Sand Mo. 11 are above the average curve. The adhesion test indicated that the adhesion of Sand Mo. 11 was higher than the average. Both the concrete and mortar test specimens made with Sand Mo. 12 are above the average curve of strength. Tests specimens made with Sands Mo. 13 and 15 do not fall on the curves for the higher values of ■ ^ ■■■■» ^The test specimens V + 12 at the higher values of . 9 were in general more erratic in v + c their behavior than ¥/ere test specimens with lower values of — . v + c It is noteworthy that the test specimens made with Sands Mo. 20 and 22, both Elgin Sands, show similar characteristics as regards strengths. Test specimens made with natural Attica sand gave higher values of strength than did the average of all the specimens. 59 Adhesion Tests . - Addi.tional information is needed in order to study the adhesion of various sands* The curve on page 216 indicates that the mortar test specimens gave results in nearly every case lower than that indicated hy the average curve of strength* It appears that at "basic water content, the mortars follow about the same general law as the concretes, being repre- sented by a curve somewhat below the curve representing the strength of concrete* 60 18. Discussion of Cement - Space Ratio . - Rrom the results of the concrete test specimens reported in this thesis, it appears that for cylinders made at basic water content, or at least near basic water content, the strength in compression may be expressed as a function of the cement-space ratio. By definition cement-space ratio is the concentration of the cement per unit volume; that is, cement-space ratio = c V + c (see page 8 ). If the assumption is made that the voids in the coarse aggregate (after being placed in the concrete) are filled with mortar then in general the total voids in the concrete will be equal to the total voids in the mortar therein. This as- sumption does not take into consideration whatever additional voids in the concrete may be produced by the presence of many surfaces (surface areas of the coarse aggregate) to be coated with the mortar. On the above hypothesis the total voids in the concrete and also the total volume of cement in the concrete will be contained in the mortar. This leads to the conclusion that the cement-space ratio (— — ^ — ) is dependent upon the V + c mortar in the concrete. A study therefore of the c V + c curves for various sands to be used as fine aggregates is valuable as a basis of comparison of the probable strengths that might be expected from concrete test specimens made witn a particular mortar. Before considering the curves for the different snnds V + c ’ it is desirable to call attention at this point to the relation ■'', it V ■ ,t . r '. I ', : , • '-'I w - M X J I,.' yhft.si. ■■' - ■••’•» ■■■' ....;.■ ■• ":■{ . ■'. ■- 3 '> f<’ •■■' ■:? ■.' ■- •■”B ••■» . .^) ?!• >^ B d i?--i ■ ■t’.''. V ' Th ", •') -.lb- ■’ ■t) \- I T' I 1 ' ■ '”,• i ' ■ i ^ U'i '. '■■‘\ ^ - ^ * 'V''. t. >< 1^'. f) V ' « £< .> >i",t '' *., ■ ' {JC J •* t, ^ ft 8-^ 'i h^" I Vj .''.■ ' i .fc J ^, “At'i • ■ ■ • lV » k xiL\i ^^iJ'i.Oi'.' h- ’ V ''.M .. .,; :ui fcftvri.-i, i '4j:':jf:::' 't'>ii. ] c •' rf! &*•/.< • •■ .,:.r \:a,:-vi^' .-'>t t j' •.'. V I C' - '' ■* ' -'• • ■■ ^ '' 'C'' * t) .'• {' t’*'"' ' ' * >i -4i)i vi'fctS , • v. ■■•;,•;"- ■■ L> ■ •■, ■ .. . , ■.•'.ft-s',;. 1 1. ';,?^..;';,;y OYvU'»: ' '^a , »■' Vf ;- . .:\£Jw' . <'/lJ4.,t >:■ A ■ 4/ y^ Oj r . ■ ' j-f A..O.' .'■.«*■ WHj-“ '-•^' 1 lui , 0 ^ 5 ’ Si* .. '■■ ■ x'y ^ ,y' . y’:' . ;■ 'f' . ^ ■: . .. . , ,,., , >V. • . . , ■ : ','■ ■•/... *' ■• •^" - '• ■' tY- " ' ' ' ■ ' ^ '■ ‘■xaLib ;-o'. '>i!H 'iM as • 'v" 'r ' •*’■ £■*'• W- I ' ' ' '.' ' » 4 . 1 -- i' . ' ■" -:- 0 . iS; --, Vj »v 1 Vi i * v-'v/ •TS, '; i , i 67 between ^ as determined from the mortar tests and as V + c determined from the results of concrete test specimens, ill the test specimens reported herein were designed for c of 0.06, .10, and .15, and b of 0.35, .45, .46, and .50. Examina- tion of Table 7 page 95 indicates that the actual values of c and b obtained were very close to those for which the test specimens were designed. Professor i. U. Talbot in a paper to be presented before the imerican society for Testing Materials at the Annual Convention in June, 1921, makes this sjjatement based on the data of these tests, "The observed voids in the concrete test specimens checked rather closely with the predetermined values obtained by calculation from the mortar curves. The average variation from the expected value of 60 sets of test specimens examined was less than 1 per cent of void^ Prom the above cons iderations it seems reasonable to discuss the probable mortar-making qualities of a sand (quality as a mortar in compression test specimens) from a consideration of the — - — curve. V + G Comparison of Various Sands at Basic Water Content . - The curves shown on page 64 and page 65 indicate the c j V + c I curves at basic water content for twenty-eight different sands, 1 twenty-four of these sands were natural gradations of sand, one was Standard Ottawa, and three were artificial gradations made up in the laboratory. The following discussion is made without reference to the relative mobility of the sands or their respect- ive adhesions at basic water content, por practical purposes it would be necessary and advisable to compare a fine sand at a < r * f -» >'■ '■ :' t.‘- - i. . ^ '■ . * Pi'.Tv ^ * -- r?#'’ ■' ■ • tfxVJ ■j J ^ . S ■" ''^u ^ . , .'A .ttJH ' J *.' J J \ ■ • ifO^ " ■■ . t I I I ' -.'f /. ' ’ .* I I \ lA-’V t ;;0 ui ' >’ •! ’ A '’- 1 -- ’ '- po; .'• i ; A r •* I 'i ^ ^ *4 f ' ^ I 'i*' / 4- f fr-. V t 68 higher relative water content than a coarse sand in order to discuss them on an equal basis as regards mobility* Mobility will not be considered here* The curve plotted on logarithmic paper page 66 is the curve found to fit the data of these tests reasonably v/ell* In comparing probable strengths of various sands reference will be made to this curve. For a given ratio (if fine aggregate to cement (~), and with a certain water content, the resulting^ mortar will have a definite c * From the c of a given mix of mortar V + c V + c made at basic water content, it is possible to predict the strength of the concrete in compression made with that mortar. It will be seen from the cuiwes page 64 and page 66 that at 77 = the range of — of the sands considered is from *483 to .544, being the values of Sand Ko* 1 and Ko. 36 respect- ively. This from the strength curve referred to above would indicate a strength of 4800 lb* per sq* in* to 6350 lb* per sq. in* or a percentage increase of 32 per cent, ^t S. = 1 the G the minimum 9 . = .423 (Sand So* 1) and the maximum is .533 V + c (Sand so* 0 and 36.) This indicates a difference in strength of 3500 lb* per sq. in. to 6000 lb* per sq. in*, being about 71 per cent based on the lowest value. At £ = Sand So. 1 lias a ° Q of *304, Sand So* 0 and 36 haie a ^ = *484. The corresponding probable strengths would be 1500 lb* per sq. in. and 4800 lb. per sq. in. respectively, being about 220 per cent increase. At a = 3*6, of So. 1 is found to be .220, c V + c f * J y . > i V “ » , f U i- 1 1 t /: t 5 ; t: 1 69 strength = 710 Ih. per sq. in, Ho* 13, — - — = .411, strength = V + c 3E00 lb. per sq. in., being about 350 per cent increase. At £ = 6.0, c of No. It is equal to .178, strength = 430 lb. ° V + c per sq. in. c of Uo. 13 is equal to .33E, strength = 1950 V + c lb. per sq. in., being an increase of about 355 per cent. Prom the above it is seen that the probable strengths of concretes made from the various sands considered would show less variation at the richer mixes. At the leaner mixes the varia- tion in strength for the same ratio of fine aggregate to cement seems to be greater than at the richer mixes, the percentage variation being about the same at — =3.5 and 6. c In general for the range of^=Sto £=6, the -- - curve c c ’ V +c (see curves pages 64 and 65 ) approximates a straight line for these sands, the intercept and slope of the curves varying with different sands. 19. Discussion of Increased Water Content .- The exact effect of an increased water content of a mortar or a concrete upon its strength is still a mooted question. The mere presence of additional water may perhaps affect the adhesion or grip of the cement paste upon the inert aggregate. It seems reasonably certain that the loss in strength will be at least equal to the loss indicated by the increase in voids. In other words with an increased water content, the mortar will in general decrease in density, por rather dry mixes the increase in voids will not usually be as great as the increase in relative water content. The following discussion considers only the loss in strength that would be predicted by the increase in voids corresponding to an 5 ° •'D* • f 71 increase in water content. The strength of concrete at 1.4 w mo will be assumed to follow tne same law as that found for con- cretes made at basic water content s = 27000 ( — - — )2.4. V + c Referring to the Characteristic Mortar Curves of Sand Ro*23 given on page 70 , at basic water content V + c is equal to .292 at — = 3,5, On the curves just below, 1,4 wwin.— - c mu»y Q is equal to ,259 at an ^ of 3.5, From the curve of strength (page 66 ) S s= 1400 lb. per sq. in.,. S = 1050 lb. per sq. in., V + c . 292 .= .259 V + c The strength of concrete made from these respective mortars might be expected to show at least this much difference in strengt! Data available at this time from the thesis of Mr. Brown, "The Relation of Water Content and Consistency of Mix to the Properties of Concrete" seem to indicate that with an increased water con- tent the loss in strength will in general be somewhat greater than that indicated above. Consider a richer mix, say E = 1 l/g c w mo 1.4 w mo V + c .260 .432 S 3650 V + c .243 .387 S 2750 At this mix the strength of the concrete at 1.4 w^^ might be expected to be not over 75 per cent of the strength at w^^q. 1., i*-- K : V •;'■'*•,> *;:V t " ;.L .. J >: * ^ V V ■' c .I ■' 5 . L>’’- J V .. u> J .f ittSuij 72 The values above are only illustrative and are not offered as a basis of comparison. It is quite a common practice among contractors to retain the same ratio of cement to fine aggregate even after additional water has been added to secure an increased mobility. In order to offset this loss in strength, a richer mix should be used than was being used at the drier mixes. Even though it should later be foimd that there is an equa- tion that is a more exact statement of the governing elements of the strength of concrete, it should be possible to predict the effect of additional water by methods similar to the one given above. Design of a Concrete Mix . - Up to the present time the design of a concrete mix has been a more or less arbitrary matter. Roughly the methods of attack commonly used may be divided as follows; (1) Arbitrary selection such as 1:2;4, 1;3;6, 1;2 1^5, 1:3:7, etc,* (2) Determination of voids in the stone and in the sand, and proportioning of materials so that the volume of sand is equivalent to the volume of voids in the stone, and the volume of cement slightly in excess of the voids in the sand,* (3) Pilling the voids in the coarse aggregate with mortar. Mortar to be used determined by test or judgment,* fay lor and Thompson, "Concrete Plain and Reiniorced’’ “ThlFd™" Edition, page 176, (4) Mixing the sand and stone and providing such a proportion of cement that the paste will slightly more than fill the voids** (6) Making trial mixtures of dry materials in different proportions to determine the mixture giving the smallest percentage of voids, and then adding an arbitrary percentage of cement, or else one based on the voids in the mixed aggregate** (6) Mixing the aggregate and cement according to some predetermined mechanical analysis curve* This method is usually known as ”Puller*s Method".* (7) Making volumetric tests or trial mixtures of concrete with a given percentage of cement and different aggregates, and selecting the mixture producing the smallest volume of concrete; then varying the proportions thus found, by inspection of the concrete in the field.* (8) Fineness modulus and water-cement ratio*** (9) Surf ace area.*** Within recent years attention has been given to the scientific proportioning of the materials in order to produce an economical concrete* Once the laws of strength have been determined, the next *Taylor and Thompson, "Concrete Plain and Reinforced". Third Edition, page 176* * , Dosign of Concrete Mixtures", Bulletin Mo* 1, Structural Research Laboratory, Lewis Institute. Proceedings American Society for Testing Materials. 1918 Part II, page E35, 1919, part II, page 444. * •■i V ^4 f' .V.'-ii y*-^. i -. -^-1 -i. . ■■ - . . :u]- •. ^: 0 .: • ■ .. « •:■ 'S t ^ • • .. . ■ ■ «>S i'-ie^ S ' > 1 ■; ?!. ^ V •\' • i/ w''.T.c ' j:> ,.•' • ‘i'j\ (.1 > 7 < ‘ > • •• i I . ' ■ , I ! < ' V :•■ j a , I - .11 :/r' /• ■> -A : ' , : ' •V "■■■:l' '•■ /• I, .'■i* ■^ , ' i-' 1 i ’ ■ v;^:: 9 f 74 ’ ■: 4 . ; .■■j -JT. t' ■ . ^oj-^n. 1 - • ' ■ ■LJ.A f 5 ^' V : , ^ ^ ■ ' !.'V' fl’.'- -■■ A * /i!> b) •> * l *■ i- '■'M ■ 7 < B, 4 74 logical step is to devise methods to proportion a concrete to have a certain strength. On the other hand for laboratory study it is often advisable to eliminate several variables in order to study the effect of remaining variables. It is thought that the Mortar Voids Analysis furnishes a method to proportion the materials of a concrete in order to obtain a certain strength. The analysis was also found very useful in designing the test specimens of this Series, in which a certain amount of cement and coarse aggregate was desired. This last method is particu- larly adaptable and useful for comparative tests in laboratory work. The general theory and notation given heretofore will be used in the following discussions. The curves on page 75 will be referred to in the following demonstrations, ill designs will be made at basic water content, a rather dry but workable mix. The physical properties of the materials will be taken from Table E. Method i Design for a Specified Strength .- Talbot*s Mortar Voids Method of inalysis has indicated a new method of attacking the problem of design of a concrete for a certain desired strength. The demonstration here given is based upon the theory that the strength of a concrete at basic water content is a function of the cement-space ratio. This function will be taken as S = 27000 ( — ^ Any reasonable value of _s and b may be chosen. For this demonstration S = 2000 lb. per sq. in and b = 0.35 have been srbitrarily chosen J- '., ,■-*‘ 1 .’ ^ • A, 'ip'^. (v'uf o,f ' •■ ' '’■»: A^,.‘.»V . - , ,.‘ ■ - V ‘ . '.*•_ \JU U 7 ..'‘, ..:^t. .PJ ,. V., •■ ■ ■ ' > ••/; ‘ric^Ar;.. , 'V , ,r „ . ■ A ... , . j « ,•.%//•] .*,j \r '•I I :v .-'''< •‘•■‘•A. ;;^ .{J *?,(?4 o;> , ... ■ . .. ' T- 'V ) : V.. c.. . ^.^■: r.vv^-oo't-^'vr' ^i.- ;t5>'J>':' '« ’ ■ s . r ' ' ' — - ' >>•! .-j r-v 0 . 3 “, ‘ ','? o;,;- O. €■■ .-e ;\ ";f.!^;.( 3 i^lv■>-'’•^' V'-r-r'’" ■•;,;■ • I :^. j j *. .,(j w’ ' t I- . /■ ■■ •'”=*■• . •*,.: J<-. , ) i«jr»;-5>V •?,7£ / ‘:-A .' :; .-/vj, «.• dfi'. ;.''.>o- .'•:> • ' - ‘ ‘Jw-, ' tivr- . ^y;,'^ % ’)C o^' ‘tti; f.ii'' * y '; ■) ' f' ' '• V ^ ■ •■ ^... f >!*-■ ' .^: '■ ■■ ■ A. •7, ‘.' ■' 3V3Ji.r; V ^ 1.*' - I • ;:■ i ; ; -i ;->-;o:tC‘J'e-f- •j:'„,'.':;c ” ’. 5*. .osfiA'^^ , . ■ ■ ' y .'. Jfe ■'* . ' t: St. ' ''X X a Vi a i r.‘- I A; t X >>?.i • u ■ ■' ., )ilv 1 ■ '■> '‘./ 'l.MrA- A. '.'. 1 A>ij I ' . '•'■xy; / , . 'Ar ’ ,■■• ., . / ^ .. ■ "‘■J. (' 'v 4 r!'“' .'. »4i)^ 3ill5vpirl^7 ... -ri'jv.j’ . ,"V.SSr ■■ . 'A'l' V .V .'. T-. 7 .;rf .» 7 ^ ' .;- Jwjiins i’ V. &trt- 'rttio^ ^(*3? .a- iJ; B 90 j . - .-.f l;■^.^■^r|.•.•' .'--^:>»^ "'’' f- J ' ■ . >’’.V . ■ t- U ' • . 7/ ' ;A . , r .:•> ^ . jf-' ' P ^ V ■ ■4W ■■ ( .1'-'' ■ 7 :Vi-A -/ ,v; , ..X i '..^.^ - 'A It .- A J \ v > ■ ' ''■..i J . !.» . J i*3i; , ■ C /i i-X 't A> X *>’ 76 The Characteristic Mortar Curves for Saud Ho. 23 at basic water content will be used. The v and w,^ curves are found m in directly from the original data. The cement curve (c) is plotted from the equation c = ^ giving at any value ^ + 1 of £ the amount of cement per-unit volume of mortar. The c — curve is plotted by combination of the y_ and c curves at a particular a. c Prom the curve page 66 it is found that for a 2000 lb. concrete, - ^ = .339. Referring to the c curve for Sand Ro. 23 the following values are taken from the curve. I =. 2:70 c = .178 Wq2=! . 236 If a value of b » 0.36 is used, the quantities per unit volume of concrete are c = f.l78) (.66) = .116 a = (2.70) (.116)= .313 b = .360 .779 Wg= (.236) (.66) » .163 Wqq=( .313 )(2.63) (.0066) = .006 Wq^=(.360) (2.71) (.01) = .010 168 77 Designation Unit V 0 lume Specific Gravity Wt. Lb. per cu. ft. Concrete a .313 2.63 51.4 b .350 2.71 59.2 c .116 3.10 22.4 .779 133.0 .221 ^CX .168 1.00 10.5 Total Weights 143.5 Method B. Design f or Laboratory Use « The following method was used in the design of all concrete test specimens reported in this thesis. Various combinations of a, b, c,w^, and d^ could be made. For this demonstration let c = 0.10, b = 0.S5, and = Iff , all calculations to be based on one cubic foot of freshly placed concrete. Referring to the curves on page 76 the curve marked Bulk Volume of Mortar per Unit Volume of Concrete is plotted from the a equation q*^ =( I =/ 1 + c ,) c. Using c = .10 this becomes a o' ) (0.10). q'^ is then the volume of the mortar at any •■m containing an absolute volume of cement of 0.10. If a value of b of 0.35 is to be used, go out along the dotted line marked b = 0.35 (obviously b = (1 - to its intersection with the Bulk Volume of Mortar Curve, jit this intersection OftD 78 f = 3.23 C := 0.100 a = .323 b = 0.350 mo = .228 w CO - .228 (i-b) = .228 (.65) = .148 ca =(.323) (2.63) (.0065) = .006 cb =(.350) (2.71) (.01) = .010 w cx . 164 Designation Unit Volume Specific Gravity I7t. lb. per cu. ft. Concrete a .323 2.63 53.0 b .350 2.71 59.2 c .100 3.10 19.3 .773 131.5 .227 ^cx .164 1.00 10.2 Total Weights 141.7 Check on Voids ■^m = .350 = (l-b)v ' m = (.65) (.35) = .227 Probable Strength c 10 .10 V + c ,227 .10 .327 S ^ = 1550 lb. sq. in., from curve page 66 . i 79 SI, Range of Usefulness of Fine sands , - in a great many localities fine sands are available but their use as a fine aggregate has been restricted by existing building ordinances, specifications, and codes. The Mortar Voids Analysis furnishes a means of investigating their usefulness. The following discussion will be made for Sand Ho, 23 at basic .vater content. Reference will also be made to the cement-space ratio at • Sand Mo, 23 was a very fine sand from Greenup, Illinois, and in general a sand finer than this would not be available for concrete purposes. For actual use in concrete construction a mix somewhat wetter than basic water content v;ould be required. For the same strength, richer mixes than indicated below would then be necessary. In order to compare the amounts of cement required per volume of concrete for this sand and for Sand Mo, 3 discussed in the following topic, a constant value of b of 0.45 is arbi- trarily chosen. The relative amounts of cement per volume of concrete will then be in the same ratio as the volumes of cement in a unit volume of the respective mortars. Concrete having a strength of 2000 lb. per sq. in is very often specified. From the strength curve (page 66 ) —5 =.339, V + c when S = 2000. Referring to the Characteristic Mortar Curves of Sand Mo. 23 on page 80 £ = 2.70, when - . Q * ,339 c V + c c = .178, when V + c 339 1 aa sasa aMiaaga IPEBSSIISS k^m 1 1 5 i -I I I 'i* A' .% i' _ } 9 81 BxiSIC ’JATm COIJTEBT s c a c in c in V + c c Mortar Concrete 1000 .253 4.45 .120 .066 2000 .339 2.70 .178 .098 3000 .400 1.93 .225 .124 4000 .450 1.28 .280 .154 5000 .493 0.60 .383 .211 The table above indicates the ratio ^ for c the various strengths . ilssuming the cement to weigh 94 lb. per cu. ft. , and the fine aggregate to weigh 100 lb. per cu. ft. loose the f ollo?;ing ratios of bulk volumes are obtained: Bi^SIC COKITEI'IT S 0 Mix of by Bulk Volume 1000 l;3i55 2000 1;2.15 3000 1:1.55 4000 1:1.02 5000 1:0.48 Prom the use of the Characteristic Mortar Curves of Sand Uo. 23 at 1.4 (see curve page 70 ) the values given below v/ere computed. It should be borne in mind that at wetter mixes c may not be an accurate index of strength. V + c 82 1.4 BASIC WATER o o s c V + c a c c in Mortar c in Concrete Mix of Mortar by Bulk Volume 1000 .253 3.63 .131 .072 1:2.90 2000 .339 2,25 .192 .106 1:1.80 3000 .400 1.25 .265 .146 1:1.00 4000 .450 0.30 .400 .220 1:0.24 5000 .493 It is felt that a concrete made with Sand Eo, 23 would be workable at a relative water content considerably less than 1*4 A mix leaner than £ equal tO about 2.6 (1:2 by bulk) c would hardly be expected to give a concrete of greater strength than about 2000 lb. per sq. in. A mix with an — of about 3.5 c might be expected to give a strength of something slightly over 1000 lb. per sq. in. It is seen that with increased water content for the same strength, c would have to be increased. This amount of increase in cement would probably have to be somewhat greater than indi- cated from a consideration of cement-space ratio above. Qualitatively, at least, it can be said that it would be possible to make a concrete from the Greenup sand to give a strength of 2000 lb. per sq. in., if an not greater than about 2.5 be used. Sands giving voids as high at basic water content as did Sand Uo. 1, v/ould require for 2000 lb. concrete at basic water content an|- not greater than about 1,70 ( see Characteristic 85 Mortar Ciirves for Sand Uo. 1). It is felt that this method will he of yalue in determining the possibility of using fine sands in concrete of a required strength. A comparison of the quantities of cement per unit volume of concrete for Sands ho. E5 and ho. 5 will be made under the following discussion. 2E. Range of Usefulness of Coarse Sands . - That a sand to be used as fine aggregate for concrete shall be a coarse sand is a very common specification. If the measurement of the aggre - gates is to be by bulk volume this specification will in general insure a better concrete than would be obtained by the use of a fine sand, neglecting adhesion and other effects and consider- ing as the base concrete made at basic water content, the follow- ing discussion indicates the possible range of the usefulness of a coarse sand. Reference will be made to the Characteristic Mortar Curves of Sand ho. 5 given on page 80 . In order to com- pare mixtures of the mortar made by bulk volume the weight per cu. ft. of loose Sand ho. 5 will be taken as 115 lb. per cu. ft SIC W^TER COhTEhT S c a c c Mix of Mortar by Bulk Volume V + c c in Mortar in Concrete 1000 .255 2000 .539 4.05 .141 .078 1:2.92 3000 .400 2.80 .187 .105 1:2.02 4000 .450 1.90 .245 .135 1:1.37 84 Referring to the Characteristic Mortar Curves of Sand Ro, 3 at 1,4 on page 123 : 1.4 B3SIC 7/^ TEH CORTERT s c a c c Mix of Mortar V + c c in Mortar in Concrete by Bulk Volume 1000 .253 5.00 .111 .061 1:3.60 2000 .339 2.80 .174 .096 1:2.02 3000 .400 1.40 .254 .140 1:1.01 4000 .450 0.60 .352 .193 1:0.43 5000 .493 A concrete made v/ith a sand similar to Ro. 3 might be expected to be workable at a water content slightly above A 2000 lb, concrete then could probably be made with this sand with an betT?een about 2.80 to 4.05, say 3.50. Comparison of Fine and Coarse Sand . - Assuming the same workability, neglecting adhesion and other effects, and using an e(iual amount of b per unit volume (b = .45) the following comparison is made: B^SIC CORTSRT RO. 23 RO. 3 °23 S _a c c in Concrete a c c in Concrete "3 looo 4.45 .066 2000 2.70 .098 4.05 .078 1.26 3000 1.93 .124 2.80 .103 1.20 4000 1.28 .154 1.90 .135 1.14 5000 0.60 .211 1.18 .172 1.23 85 1.4 BiSIC l7iTER o o s HO. 23 HO. 3 ^23 a c c in Concrete a c c in Concrete ^3 1000 3.63 .072 5.00 .061 1.18 2000 2.25 .106 2.80 .096 1.11 3000 1.23 .146 1.40 .140 1.04 4000 0.30 .220 0.60 .193 1.14 5000 Prom the a bove it would appear that a 2000 lb. concrete could "be made with Sand iio. E3 with about 15 to 20 per cent more cement than would be required with Sand Ho. 3. This would not be considered excessive under certain conditions as; (1) fine sand available at reduced cost, (2) proximity to cement mill, (3) coarse sand obtainable only at high cost, (4) necessity for speed requiring the use of local materials. 23. Effect of amount of Coarse Material .- Using the same mortar as additional coarse material is added to the mix, in general the cost of the concrete will be reduced. The principal advantage of a well graded coarse aggregate when viewed from the standpoint of the Mortar Voids analysis is that for the same workability, more coarse material can be used than would be possible with a poorer gradation of coarse material. The fact that additional water will in general be needed to produce the same workability should be borne in mind when determining the amount of coarse material to be used. The tests recently conducted under the direction of Professor 1 Talbot have indicated the dependence of mobility upon the amount of coarse material used. It seems reasonably safe to draw the conclusion that additional coarse material does not necessarily indicate an increase in strength. If additional water is re(iuired to produce a workable mix at the higher values of b, then the strength may even be reduced , due to (1) decreas- ed density of the mortar, (E) possible reduction in the adhe- sibility of the paste. If the same v;orkability is assumed, these tests indicate that for concretes made with or near basic water content, the amount of c ( in the concrete) required for the same strength decreases as b increases. This can be readily seen from an examination of the equation c (in concrete) = (1-b) (c in mortar )i In the discussion of the Design of a Concrete Mix, for a EOOO lb concrete made with Sand Ho. E3 at basic water content it was found that the mortar must have c = .178. For various values of b the cement per unit volume of concrete would be: b c concrete 0 .178 26 .134 35 .116 45 .098 50 .089 87 I? i\ssuming the mix to be workable at b = .50, the saving in cement would be 50 per cent. Maximum Amount of Coarse Materials .- There is a distinct need for further investigation to show the relation between mobility with an increasing b and the mortar content therein. It is usually considered advisable to have no voids in the coarse aggregate that are not filled v/ith the mortar, even thoug] such a concrete may have qaite a high strength. In general other requirements and conditions would prohibit the use of such a concrete. Certainly the Mortar Voids Method of inalysis would not be applicable to such concretes, even though the cemenl space ratio might be indicative of the strength. The results of these tests do not furnish sufficient data to discuss quantitatively the maximum amount of coarse material which may be placed in concrete. In these tests it was found that for practically all the sands b of .45 at w could be mo used. It should be borne in mind, ho’wever, that the coarse aggregate used was of poor gradation, and that some of the sands required consiierable tamping and rodding when filling the mold. With an increased water content doubtless additional b could be used, but a decrease in the strength would be predict- ed. If the voids in the coarse aggregate are just filled with mortar, then the bulk volume of coarse aggregate will be equal to the volume of concrete. Due to the wedging action of the mortar between the coarse aggregate particles the maximum bulk volume of coarse aggregate which can be used will be somewhat 88 less than the volume of concrete. In the paper of Professor Talbot mentioned heretofore he estimates the bulk volume of coarse aggregate that could be used to be about 90 per cent of the volume of concrete. Jidditional data are needed before definite conclusions on this point can be drav/n. 24. Greneral Discussion of the Mortar Voids Method of jlnalysis . - is pointed out heretofore concretes may be designed from a consideration of the mortar voids tests, it least it is possible and practicable to design a concrete for any reason- able value oi a, b, c, d, and and combinations thereof. If the above quantities can be predetermined, then there are various methods of estimating the strength. It is probable that near basic water content the strength may be expressed by an equation of the form S = constant ( — - — )^. it hi^er relative water contents it may be found necessary to introduce a new relation. The mortar voids test can be quickly made and after makir^a few concrete test specimens the desired water content could be determined. It would then be possible to design for certain fixed ratios of materials in finished concrete. Quantities of Materials .- In the Report of the Committee on Research at the 1921 Convention of the imerican Concrete Institute, Item 2 of "Some Things to be Learned about Concrete" may be found the statement that collection and correlation o£ data to show quantity of set concrete which can be made from given amounts of different aggregates is needed. It is thought that the mortar voids method of analysis will provide for this 89 need. Prom this analysis it is possible to determine the hulk of a given mortar at a given water content. The hulk of the concrete when freshly placed if there are no voids not filled with mortar will then he approximately the sum of the hulk volume of the mortar and the absolute volume of the coarse aggregate. It would be necessary to provide additional material to compensate for the reduction in volume due to setting, evaporation, and shrinkage. issume that the concrete is to have an ^ of 3, c = .10, w and that at the relative water content to he used d^^ = .70 0 = .10 , |- = 0 a = 3c = ,30 a -t- c .10 + ,30 .40 a + c ^ T j" - ■ + h 5S 1 h = 1 -.57 = .43 Therefore in one cubic foot of freshly placed concrete at the desired water content, a,c, and h would he known. These quantities for practical use can he easily converted to weights of the particular materials. If desired the weights could he transformed to hulk volumes. Consideration should he given to the fact that the conditicn of the mortar voids tests and of the mixing of the concrete will he different. This fact could he taken account of by using a value slightly different from unity in the equation^— + -fa ~ q If it is found that the voids in the concrete are generally high- er than the voids found by the equation v = ( Q + Q ) v the 0 di^ m equation above could he written as a + c + h=.98-.99 etc. •> J . s 1 '■..Jv' y 90 as was necessary. Similarly if the conditions of test were such as to produce in general a denser concrete than would be expected from the mortar data, the equation could be wtitten as — + b = 1.01, l.OE, etc. as the conditions of the test might demand. Fine Material in the Coarse Aggregate . ~ In the application of Professor Talbot*s M.ortar Voids Method of Analysis the limitation must be imposed that whatever fine material is pre- sent in the coarse aggregate must be included in the fine aggre- gate as such. An examination of the specifications for concrete of a number of state Highway Departments has sho\m that there is a marked tendency to permit the use of a coarse aggregate having 5 to 15 per cent passing the l/4 inch screen. In applying Talbot’s Analysis to a concrete made from such a coarse aggregate it would be necessary to include the fine material in the coarse aggregate with the sand or other fine aggregate used in making the mortar voids tests. Basic Water Content and Point of Minimum Volume .- All of the sands studied had a reasonably well defined point of minimum volume. For the sands in general this point appeared to be more pronounced at the richer mixes. At the lean mixes the curves plotted with volume of water per unit volume of mortar as abscissa and voids as ordinates are in general flat in the region of low voids. This makes the determination of water content more difficult. Th© voids at the point of minimum volume are in ^rmsl better defined than the corresponding water content. It appears that further experiments are needed to devise 91 methods that will give a more accurate determination of basic water content. A study of the phenomena of these tests indicates that the water in the mortar at the higher water contents is more than the calculated voids. This apparent discrepancy may he due to absorption, evaporation, lack of knowledge of the specific gravity to use, or need of more accurate methods. E6. Conclusions. ~ From the study of the tests reported herein the following conclusions are thought to be justified: (1) Basic water content furnishes a convenient iiase for the comparison of the water contents of mortars. (2) The relative water content of a concrete can be con- veniently expressed by the relative water content of the mortar therein. (3) At or near basic water content the strength of concrete at 28 days, cured under the same conditions as this series, can be expressed by an equation S = constant ( — 5 V + c (4) Talbot *s Mortar Voids Method of Analysis can advantage- ly be used to proportion a concrete for certain desired combina- tions of a, b, c, d, and w . (5) The Mortar Voids Method of Analysis furnishes a satisfactory basis for determining the range of usefulness of sands to be used as fine aggregates in cnncrete. (6) Concretes of a specified strength can be designed by the use of the Mortar Voids Method of Analysis. (7) This analysis can be used to determine the quantities of materials required for a given volume of concrete. (8) The Characteristic Mortar Curves of various sands m^y be expected to be quite different. - lY - TABLES, CURVES, BliiGRiMS ,ilID PHOTOGRIPHS . TiBIiES, CURVES, DLAGR^MS,iI© PHOTO GRiF'dS 92 TiiBLE 4 PERCEHTiGE OP VOIDS IH MORTAR PiLDEL \nm WATER BA 210 \W2BB COHTEHT sand a c sand a c Ko. 1 E 3 4 6 HO. 2 4 0 87.3 88.5 77.8 67.1 61.6 15 91.6 94.5 90.8 83.3 74.5 1 8E.6 80.5 77.8 76.7 77.0 16 87.3 89.5 81.7 78.5 77.4 E 91.7 94.8 97.1 99.2 100.0 17 79.5 74.4 69.0 65.1 60.8 2 96.7 98.0 94.7 87.1 78.7 18 88.7 91.6 86.0 80.4 74.6 4 90.6 90.6 91.3 9E.8 95.0 19 84.0 82.2 81.3 81.1 82.0 5 86.6 78.5 70.8 64.1 61.7 EO 86,5 86.3 86.8 85.7 83.7 6 86.7 87.6 84.0 81. E 78.5 21 89.8 86.4 80.3 74.2 66.9 7 96.7 98.0 89.4 79.6 67.8 22 88.8 88.8 86.3 84.8 84.0 8 79.1 73.0 67. S 61.7 58.5 23 87.0 76.1 66.7 65.2 71.5 9 97.1 lOO.O 85.0 70.0 59.8 24 96.3 88 . 6 78.9 81.3 92.5 10 80.4 74.0 70.5 68.1 67.0 26 11 89. E 93.0 94. S 9E.6 90.2 31 91.8 89.0 82.2 77.5 74.0 IE 98.6 97.4 96.4 94.0 92. 6 32 82.6 75.6 69.3 66.0 63.7 15 79.8 87.1 86.6 81.8 74.3 36 87.0 85.0 77.8 72.7 68.7 14 77.6 86.0 81.8 74.3 66.2 Ay* 88.0 88.5 84.3 79.4 75.2 Ay. 87.7 85.2 79.8 76.6 74.9 1. E B/iSIC WiiTER COHTEHT 1.4 BASIC V/ATER COHTEHT Sand a c sand a c HO 1 E 3 '4 5 Ho. 1 2 3 4 — 5 0 95.8 88.1 79. S 74.5 71.2 0 103.6 98.6 90.0 81.8 77,0 1 95. S 95.1 9E.8 90.8 88.7 1 102.3 104.5 103.5 101.3 98.3 E lOS.l 103. S 104.7 103.2 100.0 2 106.8 108.9 105.5 104.3 102.8 5 105. E 104. S 100.0 95.5 90.0 3 109.0 111.5 108.8 102.3 94.5 5 98.8 89.6 81.8 76.0 71.3 6 106.0 98.8 91.1 84.6 80.0 6 96.5 95.5 94.4 93.4 92. E 6 104.8 102.0 100.0 97.8 96.0 7 104. E 100.0 g 3.4 85.3 75.0 7 108.2 104.2 94.3 88,4 85.6 i 8 90.0 81.4 76. E 72.0 68.9 8 99.0 90.0 84.8 80.8 76.7 11 100.0 100.5 100.0 97.8 95.3 11 106.0 106.2 102. 8101.4 102.8 i 16 98.6 93.8 89.8 89.7 90.2 16 104.5 101.2 96. 8 94.8 96.8 : 18 98.5 96.6 90.1 86.8 82.9 18 107.0 102.8 96. 0 91.0 88.4 ; 19 95.5 9E.6 90.3 90.5 92.2 19 104.6 100.0 100. ODO.O 100.0 El 101.0 93.7 88.3 83.8 79.0 21 109.3 102.8 97. 5 90.9 86.8 E3 97.4 87.7 76.2 74.9 79.9 23 105.5 96.6 84. 5 81.6 89.0 E4 104.8 97.8 88.6 85.3 lOE.O 24 108.8 104.3 97. 0 93.4 109.8 Ay. 98.8 94.6 89.7 86.6 85. E Ay. 105.6 102.1 96. 8 93.0 92.3 .L'* * 93 TiBLE 5 VOIDS in MORTi^H EXPRESSED A3 PERCENTAGE OF VOIDS AT BASIC WATER CONTENT 1.2 BASIC WATER CONTENT 1.4 BASIC ¥fATER o o Sand a c Sand a c no. 1 2 3 4 '5 NO. 1 2 3 5“ 0 109.5 120.5 117.8 108.0 103.8 0 118.0 125 . 8 121.0 115.0 H2 0 1 106.2 lOi.3 100.5 101.3 104.1 1 113.0 107.8 105.2 106.0 1D9. 6 2 107.8 110.1 111.3 115.3 120.0 2 120.4 101.8 128.8 133.2 326.1 3 110.2 112.8 113.6 109.4 104.9 3 124.1 123.0 122.0 119.2 31^5 5 105.1 105.2 103.7 101.1 103.8 5 114.3 111.2 108.7 106.2 307.9 6 107.7 109.8 106.7 104.3 102.1 6 115.8 120.0 117.5 116.1IL4.5 7 110.2 117.5 114.8 111.8 108.4 7 123.8 132.6 132 . 6 126.0 HEO 8 105.3 107.5 105.8 102.8 101.8 8 111.8 113.4 110.9 106.8 306.8 n 106.9 111.0 112.9 113.5 113.5 11 118.8 122.5 128.2 127.8 122.9 , 16 106.2 114.4 109.2 105.0 102.8 16 116.8 123.9 119.4 115.8 311.8 18 108 . 0 113.8 114.5 111.1 107.8 18 116.0 124.8 125.4 123 . 7 118. 1 19 105.4 106.4 107.9 107.5 106.7 19 112.4 115.0 113.7 113.5 314.8 21 106 . 6 110.5 109.1 106.2 101.5 21 115.0 117.7 115.2 114.3 307.8 23 107.1 104.0 105.0 104.4 107.3 23 115.4 110.4 110.5 111.8 312,4 24 110.0 108.6 106.8 114.4 108.8 24 123.8 118.9 113.8 121.7 318.0 Av. 107.5 110.2 109.3 107.7 106.5 Ay .117.3 119.2 118.2 117.11147 V „ , *v. .['A } • ' ' y ' ' .'*U; ^ • I ( ' . < , ■ ■ '•> 94 TiiBLE 6 DA’HA OF iiDHESIOM TESTS MORTiR TEST SPECIl^RS Natural Sands Artificially Graded Sands Cyl. c V w V Eo. c 0 S Cyl. c V V c S V + c Ro. c v'+c AO .209 .268 .225 .168 .413 .362 AZ .205 .281 .270 AZ .202 .292 .270 A4 .211 .260 .230 A5 .190 .337 .271 A6 .196 .314 .277 A7 .202 .292 .273 A8 .183 .359 .253 A9 .211 .262 .249 AlO .180 .370 .297 ^11 .203 .291 .285 A12 .205 .280 .260 A13 .214 .249 .228 A14 .186 .347 .274 A15 .202 .293 .292 A16 .181 .368 .316 A17 .186 .349 .258 A18 .203 .289 .265 A19 .208 .272 .246 A20 .203 .289 .256 A21 .210 .262 .241 A22 .207 .276 .262 A23 .188 .341 .237 A24 .207 .275 .265 1.282 2.455 1.370 1.445 1.232 1.772 1.602 1.445 1.961 1.241 2.054 1.433 1.365 1.163 1.865 1.450 2.032 1.875 1.423 1.307 1.423 1.247 1.333 1.812 1.328 .438 2320 DO • 289 1210 Dl .422 3555 D2 .409 3210 D3 .448 2885 D4 .361 1570 D5 .384 3675 D6 .409 2795 D7 .338 1450 D8 .446 4100 D9 .327 1147 DIO .411 3110 Dll .423 3610 D12 .462 3295 D13 .349 1315 D14 .408 2525 D15 .330 1265 D16 .348 1420 D17 .413 3575 D18 .433 2625 D19 .413 2750 D20 .445 2700 D21 .428 3140 D22 .3 56 1400 D23 .429 2995 D24 .209 .268 .225 .173 .394 .373 .206 .277 .273 .200 .299 .267 .202 .290 .220 .183 .357 .262 .199 .304 .280 .207 .274 .279 .177 .380 .289 .214 .258 .253 .179 .375 .289 .205 .283 .287 .207 .274 .263 .208 .272 .234 .189 .338 .277 .201 .296 .290 .188 .341 .338 .176 .385 .244 .206 .279 .268 .203 .289 .240 .203 .289 .256 .209 .266 .239 .207 .276 .258 .193 .325 .247 .207 .274 .266 1.282 2.275 1.344 1.495 1.435 1.950 1.527 1.323 2.146 1.205 2.093 1.380 1.323 1.307 1.788 1.472 1.814 2.187 1.354 1.423 1.423 1.272 1.333 1.683 1.323 .4382355 .3051650 .4263876 .400 .410 .339 2840 2390 1550 .3963338 .4302892 .3181655 .4533133 .3231575 .4202648 .4303370 .4333480 .359 1780 .405 2390 .355 .314 .425 .413 1870 1086 ^035 2735 .4133163 .4403328 .4282858 .3721502 .4303523 . f 95 £> o o p o to O- £> C- t- O 00 1 — 1 I 1 02 1 — 1 CO CD CD CO lo o m Lo l> I> O 0> O (T> 02 02 02 02 P rH rH iH ol o & 1 to to to to P P P P 02 02 to 02 02 02 CV2 02 fH rH rH p ■P E5 o 0 > ^ - to tjH 02 in 02 to Jh ?4 o 0 (D H O P P P O P o o P o o o p H 02 H o o O o pop p p p p p p p p p p p p rH P P P rH iH P p O to H 0> rH o- 02 O- o o o o p P O O O ^ 00 j>- H to in C7» in tn 02 o to 00 00 CO H lO H 00 00 o 00 O- 02 02 £> 02 02 P 02 £> CO t> LO P P 02 p to to £>- to p p p p to to to to Rr tQ COi 00 P 02 p n}< CO 02 to cr> P P02. 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tH tH Tit £> CO tH tH O tH tH tH rH tH CO CO 00 to CO tH O rH tH tH tH tH CO O lO CO CT^ H O O H ^ O W O to cr> O co cr> t- cr> CO cr^ cr> CO rH rH rH O O CO o> to t- o to tj< to to CO CO to to rH CO «;it rH CO err to err to to CO CO CO CO E- CO tH {>• CO CO CO CO E- to E- CO 00 H err to E- O ' (J^ CO CO to to CO J>- rH rH CO CO CO CO CO CO C- to CO cr> J> CO E> ^ to to to 1 — 1 1 — 1 to to O CO E- 0 LO 00 CO O E- err or j>- to to tO iH CO O rH or CD E- 00 to tO tO tO ora M ra /A lO H o> O cr» cr> o CO 00 cr> CO CO CO O CO rH rH to CD CO 00 CO LO ^ LO LO rH rH iH i 1 tH rH CTr O iH iH O tH O H O CD o o o o O O o o o o o o rH iH tH tH tH tH rH tH o o lO to to lO (W (XJ (X2 CV2 CT> tO CO CO to CO CO CO CO CO os to to CO CO to CO to CO CO CO CO to err to o tH rH tH iH CO CO CO CO O E- O or to to tO lO CO CO CO CO to to CO 'tH lO to LO to CO CO CO CO w mo CD O O to to to to to - CO H to to to iH iH rH rH to CO CO 'sH to to to to rH rH rH iH rH 'sH to to to to to tO tH rH rH tH lo to CO o CO to CO to iH iH tH tH to tH to to LO to to to tH tH tH iH E- to LO to E- E- E- E- rH rH iH tH W c iH CT> CD to «s}^ to to rH iH rH iH CO CO to to to to to iH iH rH rH O CO CO CO to to to to rH iH iH rH O Cjr CO to H H H H rH tH rH rH tH O rH tH rH 'tH 'tfl tH tH tH iH to LO rH to to to to to tH iH tH tH 0+A 0 CO CO CO !>- O to to lO -tiH ^ to cr> CT5 tO ^ to CO CO to to to CT» CO t>- eo tji to CO 'sH iH err 'sji CO err o err err to CO to tH 1 — 1 err E^ CO CO CO CO CO CO CO CO rH Cjr E* Or O err err (Jr CO tH tH tH »>lCJ to r;J< to to 00 00 viH CO (J> rH rH CO o o E> £> CO £> CO CO 00 ^ to H I>- to CO CO CO CO CO CO CO to to o CO to ^ tH to to to CO err err o CO CO to fH CO to CO 'tH to CO LO to CO CO 00 CO or O O O rH I— I 1 — 1 rH rH rH rH tH t — 1 rH 1 — 1 tH tH tH iH CO CO CO CO to 'H 'tH 'tH olt> CO to to CO CT» rH 's}^ CO J> O CO CO •r-l • • CO O 0> CO to J>- to rH rH rH rH s!^ to to CO £> to CO to to to to CD ^:ii tr- tO H £> O I> CO 0-2 CO ejr 1 — 1 err to to to to to o ^ E~ rH O CD err or to CO CO CO H 00 to 00 to 'tH 'tH CO CO C^i CO J> to £> to 00 GO CO iH iH rH rH err H tH err CO (jr err rH rH rH iH ^ to H to ^ to to tH rH rH iH O 00 CO CO o o o o CO CO CO CO (jr (X2 to CO CO 'tji -rii CO CO CO CO o CO O CO ^ to sd^ rH rH rH rH H O O O O O O O (H rH iH iH 2 >- o err err lO rH tH rH iH or H O O or O O O O iH tH H O err o O to to O to o o o o O O O O to tO tO tO o o o o ,Q CO to to o CO to ^ to to 1 — 1 rH CO to to to to CO to to to to o c- t> ^ to '^ii ^ CO to CO to •si< £> to CO err to to to ^ CO TtH E- to lO to to to rH TsH •tH '=H rH CO O CO to LO to to to to CO CO o3 CO to to cr> to CO rH CO CO CO CO CO CO to to to to to to to CO err to to tfl O tH tH t— CO CO to CO CO to to 1 — to err or CD CO CO CO CO CO or rH t— ' 00 O CO CD CO CO CO ce E- to to to rH tH 'tr' "tH CO to CO to oJlo to o o to to to • • • rH rH rH CO CO CO to to to • • • CO CO to 2.10 2.10 2.10 E~ CO CO to CJr CJr ... CO CO CO tH rH tH E- £> E- ... 'vH -sH CO CO CO E- E- E- ... to to LO • • 1—1 o o to pq o . is; !> 'st* <=i to pq o • ^ > til pq o CO pq o « ^ > •tH «a 00 pq o to > to err pq o » CO {> \ is; to TABLE 7 Cont’d Y \ M ■I i I w c c CO CD CT> 00 (7^ C7> (0» to to to to |H CO CO CM lO LO LO iH CM CO fcf J CM t- O !>■ C- to CO £> O £>■ C- to Ht CO 'tf HI ^ iH rH iH iH H H H H rH iH rH iH H H H H CM CM CM CM CM CM CM CM Per Cent Flow O CO O rH rH rH tH rH rH rH CM CM O LO iH rH CM iH rH rH iH rH H O lO O O O O iH iH iH rH O CM CM O O O O rH |H rH iH O LO (74 LO O O O O rH rH rH iH C- £> LO O O O O rH iH rH rH xn CO m vO to CM CJ> CM 1 — 1 CM ( — 1 to lO 00 £> C7> CO O O CM LO CO rH rH rH rH O 00 O 00 CO to 00 CM to to CO CO CO CM CO O O o o CO O CM iH O O- LO CM CM CM 1309 1343 1200 1284 rH 07 H* rH O LO O t>- LO LO to rH iH rH rH CO H CM D- yo r> O l> £> C- 00 O CD LO O 00 O O o C- to £> CO LO 00 00 C~ O £> C- O CO O rH (7^ 00 CO 00 O 00 00 H CM LO CO O C>- CO 00 CO CM 00 rH to CO to rH 00 00 £> 00 w m w mo £> O to C- o o o o HC 00 to to o o o o 00 CO CO H O O O CO CM lO CO O O O O (74 to CO CM O rH rH rH LO Cf4 to rH H O H rH rH r— 1 rH rH rH rH rH O iH iH rH rH rH rH iH 1 — 1 1 — I 1 — 1 rH rH rH iH iH w m <7> O O C7> CO 00 00 CM CM CM CM to H* rH O lO to to to CM CM CM CM to CO CO rH to I>- C- C- CM CM CM CM O 00 CM to LO to to CM CM CM CM CO CM rH C74 LO LO Ct2 CM CM CM E- CO rH to to LO to CM CM CM CM OUI o o o o C- J>- t- t- CM CM CM CM lO LO LO LO Hc CM CM CM CM H LO lO £> £> to O to CM CM CM CM CO CO to CO LO LO lO LO CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM to CO CO CO CM CM CM CM M o rH CM O iH to tO to to iH iH rH rH £> rH O C7> 00 00 I> rH rH rH rH tO to to tO LO to rH rH rH rH .185 .184 .188 .186 LO (74 O CO £> £> CO O rH rH iH rH CO 1 — 1 00 rH to to LO to rH iH rH rH w c tO tO to 'vH iH iH rH rH C> O CT> cyi to I>- to to rH rH iH rH O CM 0> O LO LO CO rH rH rH iH O Cr> to rH l>- to o- H H H H O CO CM to to tO to rH rH rH rH LO H CO rH rH rH rH lo O + lO CO CM t0> to CO CO to O I>- C»^ rH O O CM CO CO to £> CO lO CM LO CM to to CO CO CM CO lO CM H CO CM CO to CO CO CM LO l>- H to CO CM CM CM CM CM O 'tH to (74 to LO CO CM CM CM CM }>Io CJ^ (7^ cr> CM CT' O lO CM CO cr> <7^ LO cr> o 00 00 LO to to CO rH CM CM to LO CT> CO O CT> CO 00 o CO (j> iH CO O rH O CO to 00 rH rH <7> O O O C7> LO CV2 CV2 ^ C7> (M LO LO CO (74 CM 00 (74 CM O rH rH iH rH CM CM CM CM rH CM rH rH CM CM rH CM CO CO CO CO CM CM to CO Ol> to O O CM CM H CM lO lO lO to CT» CO CM rH H lO C7> lO CM rH lO LO lO to 00 O rH £> lO rH 00 LO o 00 to lO £> o o (74 CM CO to CM H H to CM LO o to CO CO CO to > 00 cr> CM O 00 CO <7> o> H H H H to 00 to I> CO rH CM CM CM CM CM CM H lO 00 £> O CO CO rH CM rH rH 00 LO to O H <7^ O CM CM rH CM LO LO to CM H Cf4 (74 O CM rH rH CM CO CO H l^- tO C> <74 O iH rH rH rH o CT> 0> CO Oi CT> (T> CT> o o o o cr» rH O O O O O O O H H H 00 to CD 0 <7^ <7» cr» O O O O (7> 00 O CJ> <7> (74 O C7> O O H O 00 O O (74 lO tO tO LO O O O O (74 <74 (O (74 LO LO LO LO o o o o rQ CO CM CO cr> (ji cr> o> O to CM CM LO LO to CO CO CO CO O LO CO LO C7> CO LO H* H* O CM 00 'sfi LO CO to to CO CM O (74 £> LO to CO CO CO tO H* iH LO LO LO 05 c7> a» 00 c7> rH iH rH rH CM CM CM CM 00 lO CM CM rH CM CM CM CO CO CO CO LO 00 to C7^ CO LO J>- LO CM CM CM CM to «sH CM I>- H* LO CO CO CO to LO LO LO CM CO (74 (74 (74 CO CO CO CO C- ?>• H H O H CO CO CO CO o3|o CM CM CM CM CM CM • • • CM CM CM O O O CM CM CM • • 1 • CO CO C<^ O 00 00 £>■ O • • • CM CM CM O O O lO LO LO • . . CO CO CO CO 00 CO to LO LO ... tO to to 5.30 5.30 5.30 • • H O O 5IT40 B c AV. H pq O • > 1^ LO 61154 B 0 AV. LO pq o . LO |> S |2i < to o pq o LO >• to •A’ I .f I. ( i I I ( i ) 4 TABLE 7 Cont*d 99 * CD U3 IS rH O O I^~ to to o o o o IS IS CO IS in CO CO o 03 03 H 03 C\3 rH O O tC3 tcj t5^ ^ ol o • • • • • • • • • • • • • • • • • • • • ^ 1 rH iH tH f— 1 H H rH rH rH rH iH H rH rH rH rH rH rH rH rH •p ^ O O O 03 o> (ji in «o to c> cr> in o O O tD in j:J o to i<3 tn tn iH iH O rH rH rH o O O rH rH rH o o o (D 0 H • • • • • • ♦ • • • • • • • • • • • • pH o Ph rH iH rH rH iH rH rH rH rH rH r— i H rH rH rH rH rH rH rH lo in o o 03 03 00 O O <33 o O (J> to O i> O in in IS cr^ O to rH 00 00 rH in O lO to to to Is O 00 H rH C7> 03 to in to H rH O vD tO IS IS IS o in ID in rH C7> m rH rH iH rH pH 03 CV3 to to to to to (03 (03 Cv3 <03 (03 rH (03 (03 l>- CT> ^ CO CO IS C- to iH rH to Is ^ H to m <7^ t>l{> in lO 03 ^ >!;H CO CT> in m 00 «D IS Is O (03 <7^ ^ I £> 00 CO 00 in in 0> 00 CO 00 00 CO ID Is IS Is to IS IS ‘Xj • • • • • • • • • • • • • • • • • • • • o C- £> in IS (03 IS ID IS in tD IS tD al a o o o> cr> O O O O o o o o • • • • • • • # • • • • H H o o rH H H H H rH rH rH to <7» (J> 03 03 o in in ID O CD (j> 00 (03 tD <03 B to O C- ID rH rH in IS IS ID CO 00 CD O CJ^ C7^ IS CD 00 CO 03 03 CV3 03 03 CV3 03 C3 03 03 03 03 (03 to <03 (03 <03 (03 (03 03 • • • • • • ♦ • • • • • • • • • • • • • o rH rH H to to • o o o o tD to tD tD s to ID w 00 00 rH CD 00 CD 00 to tO tD tD 03 03 •H 03 03 0} (03 (03 (03 (03 (03 (03 (03 Cv3 • • • • *H • • • • • • • • O ri M to 03 03 03 00 -P CO iD IS CT> rH 0 rH 00 m in tD 00 C7> 00 o ID CT> CO 03 d 03 IS 00 CD 00 ID P ID O O O in m in m rH rH rH rH H S - rH rH rH rH rH rH rH <03 (03 (03 rH rH rH rH to 03 03 03 m -p in tD is CJi • cr> ^ 1 — 1 rH 1 — 1 1 — 1 rH 0 rH rH rH rH rH rH 0 rH iH iH iH iH rH H rH H • • • • • *H • • • • • • *H • • • • • • • • • o o rH CO O O 03 *H 03 00 to in 03 to *H to IS ID rH ■<;j( to to C7» <03 lo 03 rH 03 03 O O m rH 03 to in in IS IS Is rH <03 03 (03 o + to to to to to 'H t<: 'si^ «hl to to to to to to to tco l{> • • • • • P # # • • • • P • • • • • • • • • W w to H H in C!> d CJ> H H CD o> CO d CD <03 CT> IS CD 00 rH rH O rH 03 03 O *H C o 00 03 in rH o *H = o CD m (T> Is C7> lo rH rH rH rH to to H 'sH to to C3 (03 OO VD ID ID rH O O H • • • • • • • • • • • • • • • • • • • • 03 03 03 03 Cv3 •« 03 rH rH rH rH rH •* H rH rH rH rH <03 <03 (03 03 0 © to O- 03 rH to fd to ID to CO 03 Is nd IS H <03 (X) m in CD O A 0 C- tO £> C- to aj to ^ o to 03 d CV3 to o CD cr> in IS <7^ 10- ^ ^ ^ a s CD is IS IS CO a E 00 m ID m in • • • • • • • • • • # • • • • • # • • • m 03 O O -P o ID CT> 03 ^ ^ P to C7> to H to m o tD {> O rH rH O rH O rH IS O O (7^ IS o IS IS m in rH o o o 03 03 03 03 03 d e 03 rH 03 03 rH H d C rH (03 <03 (03 <03 (03 <03 <03 (03 • • • • • • • • • • • # • • • • • • • • t> CTk CO iH •* H C7> IS C7> CO ■vjl *> -sf< in o <7> o IS 00 00 CO O (T^ C% O'* nd CT> ^ ^ nd ^ m ^ in (7> 0> C7> C7> O O O O O 0 O H H H H rH 0 rH rH rH rH rH O o o o # • # • • d • • • • • • d • • • • • • • • • © 0 03 «D IS in to 0 tD IS IS VD O 0 o <7^ O CD in O to CT^ ,o ^ m Pt in ^ CO d CO to in ^ 00 O <7» CD to to to to o to to to to o to t^i to to ^ • • • • • we • • • • • • w c • • • • # • • ♦ • o to CO to to 00 O 03 O 03 (03 to H O H in IS <7^ IS cd m ^ ^ rH 03 O O rH O H o m m in o O O O to to to to 03 05 ca tcj to to to 03 C3 C^3 (03 (03 (03 (03 <03 <03 <03 (03 • • • • • *H • • • • • • • • • • • • • • • d d in £s IS £S 0 Is o to to O 0 00 00 CO (03 03 <03 UD to p to 03 O O ID O vD rH rH rH oJ|o • • • • o5 • • • • • CO # • • • • • to to to 03 gC 03 03 03 03 rH rH rH (03 (03 03 • • CO pq o • CS^ PQ O • O PQ O • H PQ O ♦ ^ PQ O • in B G • H O in > m > O |> ID }> ^ > IS > S c 3 •H o •p •p •H O * 100 j II i i i' o t- c- c- cO lO to to O to CO CD vO vO vO vO LO LO* LO CO E- CO CO o o o o I>- E^ C- l>- lO VO VO lO E- E- E- E~ 02 CO CO CO CD CO CO o| O tH rH rH iH & 1 rH rH rH iH rH tH tH iH rH tH tH tH tH tH tH tH H H rH w to lo to CO 0> 00 vo CO E- O o o c> vo to to o CO iH VO t< j fH JZj O O O O O O O O O to CO to t^J Ht to to H O tH tH tH rH tH (D O iH Ph O Ph rH rH iH rH rH tH tH tH tH iH rH tH tH tH tH rH iH rH tH iH iH tH VO C- 00 00 CO O O O E~ LO LO O to 00 vO CO iH E~ CO LO CO 00 lO ^ vO vO CJJ O E- lO O O vO vo to CO vo (7> VD 00 H lO VO to to CO to CD to to to to to VO CO E- iH rH rH iH to to to to rH rH tH rH rH rH tH tH tH rH tH tH CO CO CO rH tH iH rH '<;H to to VO E- vo E- vo E- CD VO H' tH to to vO to VO CO O 00 to CO rH CO C7> E^ CD E- HI E- vO LO E- vO CD VD vD ^ 1 C- t> 00 o E- vo E- vO VO vO vO I>- E- E> E- I> E- E- E- E- E^ E- to «0 vO lO CO CO O rH LO iH o cr> CO O tH tH tH CO CO E- vO LO vO , O o o o o H HH H (T> o o cr» O O O O O O o O O O o Ls rH iH rH iH tH tH rH tH O H H O tH tH tH rH tH rH H rH iH rH tH O £>- rH O vO CO to O E- vO CO to H CO O CT» LO CO CO CO iH iH rH iH E^ E^ vO vO <5^ lO vO lO vO «0 vo vO CO a-> 00 cr> cj^ CO cjs to t E- E- E- tfi to to t<: CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO M CX2 to to to to to lO LO rH LO to H CO to to vO LO to LO • o t- l> £> C» 00 00 00 00 lO vO vO vO CO 00 CD CO o o o o o o o m H H H rH tH tH rH tH H H H H iH iH tH rH CO CO CO CO CO CO CO -p S 00 o> O 0^ vO to to CO CO rH CD H CO H to E- CO CO o cr> CO cr^ o o lO to vO lO D- E^ E- E- to to E- E- E- E- GO CO CO CJ^ CD CO CD o rH rH rH rH rH rH tH rH rH rH rH iH iH iH tH tH iH iH H rH tH rH rH VO tH 00 C\2 HI CO O to CO CO vO CJ> to to E- CO o HI O to W lo rH CO (M W 00 H cr» cr> O O O O O E> CO CO cr> (3> 00 CD s o + ^ CO CO CO CO to CO CO to to CO to to to to to CO CO CO CO EH 00 CO lO CO o O CJ> vo C7^ rH CO CT> CO H to VD LO LO LO o o >\o o i> to C- O CO CO J-O 0^ rH vO H C7> LO tH to O H to vO to to to to ^ iH to to to CO W CO CO vD VO vo lO H^ rH rH rH rH CO CO CO CO CO CO CO CO CO CO CO CO H H • rH CQ (D CO CO CO CO CV2 o|> O CTi 03 C7^ E~ to VD cr» C7> LO E- H^ CO VD o vO lO CO vD CJi LO E^ H CO CO rH tH 0> O to CO H to H CO H to O H •H iH rH O CT> O £> J>- !>• l>- HI to H H H H VD vO +3 vO HV H^ to HI !>. to to O CO O E> CJ> to vo H O lO vo CO H ■P S vO to E- to CO t> O O CJ^ O to O tH CvJ rH CO to CO CO H o3 HI H* to HI CO CO rH CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO fi CO CO CO CO CO 00 cr> 00 0 0 0^0 to to to CTi CO cr> CT> O H iH rH rH O rH o o o o cy> (T> CTi (Ti ot CTi LO LO tH LO O O o o rH rH rH rH rH tH O rH o o o o o o o o tH H C5 rH iH tH tH tH H to to to H H E- O E- rH CT» CO vo H to LO O CO •rl tOrH LO to o to rQ o cr> CT> to to to CO CO rH CO H H H H LO lO •H LO LO LO lO LO to to to to to to to to to to u to to to to to o5 m vo £>• vo a> E- rH E- LO CO rH CO rH O CO to to rH CJ^ cr> lo m to lo o o o o E- vO vO vO to CO to to LO lO HU2I O cr> cr» cr> rH iH rH tH to to to tf J CO CO CO CO to to to to CO CO •rl CO to CO CO CO lO lO lO E- E- E- lO LO LO LO lO to CO CO O E- E- E- csJlo O O O o o o CD CO CO tco to to VD vo Oi CT> CT> • • • • • • • • • • • • • • {4 • • • H H H to to to CO CO CO to to to rH tH fHf ’ CO CO CO vD E- # • vo pq O • E- pq O • vo pq o • E- pq O • ■H pq o • HI pq o • E- |> (T> CT> {> > ^ < O O o 00 CD 1 cr» rH iH * Omitted in average ! 1 I TABLE 7 Cont’d. o o +3 ^ Sm O (D O H pH O CO Ol > o SL S o a o o o o a c3lo H O O >\o Ol{> 101 O W CO CO cr> £> * CO to CO CO CO to to to H to CD o o o O) H 00 O CD 00 00 CO lO O • rH 1 — 1 iH iH H H H H CO to CO H H H H H H H H CO CO CO H 03 O o to C- CO to CO to 00 CO CO LO CD tD o> to to H iH O 1— 1 O O O CD to to to O H H H O CO H H O CO H • rH rH H iH H H H H iH iH jH H H H H H H H H iH H iH CO H cn o> lO to (3^ C3> to LO O I> 00 LO CO to H CO rH 03 H H H H O o H to 0> sf H to 00 LO ^ il3 <3» O to CO o H t> to CO J>- t- CO C3> C3^ O to CT» 00 o O C3> (3> CO W rH CO to to to CO H H CO CO H H CO rH 03 H CT> 0.1 H to O CO CO H 00 cr> to LO o CO £0 o o LO O rH CO Or> £>- •■sfi to to CO to 0^ iH ^-O 0^ to to C3> C3> o to E> I>- 5>- C- o c- c> o to c- to 00 00 C3> 00 C7> CO 00 CD CD l> £>■ l<3 «vH 0- CO CO O H LO to LO o lO H CO C3> H H LO to O CTV (J> CJ o o o o CO cr> 00 H o H O O C3» O O O* C3> a* • HO O O H H H H o o o H H H H H O H H O O o O CO t<3 CO to to CO O o to o <7^ I> to to H to O E> CO 00 to 0> OD OD t- O <3^ 0^ lO CO LO 00 o cr> 00 O !> t>- t- t> CO CO CO CO to CO CO CO CO CO CO CO CO to CO CO CO CO CO CO CO CQ • H CO 00 o 00 H H to to to to to to to to LO to lO to LO to lO CO l>- £> £> (3^ CT> 0» <3> 0^ C3^ o t~ o c- I> t>- ?>• CO CO CO CO CO CO CO (M CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO Cv3 • lo o H CO o> O CO to o o o to C3> LO CO 00 tD to LO CO C3> CD OD to vD to CO I> o 00 o CO CO 00 CD (T^ (T> CT* to £>• to H H H H H H H H H CO H H H H H H H H H rH H rH • 03 to bO CO to CO o> LO LO LO 00 -sf* (3> E> to O H 1 — 1 00 t> to ^ 'vj' ^ lO to tO IQ to 00 to tO tO to to 00 00 GO CO -iHt to lo H H H H H H H H H H rH H H H H rH H H H H rH rH • tO H £> lO C» to to C3> O C3» o CO 1 — 1 tO O CD !>■ 00 00 CO o to to to to H O H cr> C3> cn CO lO to H CO CO 's}^ H CO to to CO bO H H iH to to to to to to to to CO CO (XZ o o o o cr» to o CO o o o LO to o O CO O C3> CO LO CO CO C- CO O CO C3> to CO . to CO H O to to LO lO to to £> LQ cr» o o CO to CO o O CO 0^ 1 — 1 CO O'i C3» H O O iH • • • • • • • • • • • H • ♦ • • • • • • • • • CD • H CO H H H H H H 03 'sti H CO H H H CO CO CO to to nd IQ c3 ITD lO CD to to O to H LO C3> ^ to 00 to to to o CO C3> to a CO 0(3^0 0 I> H £> CO to ^ to H E> to H H to CO OD H to G* LO ^ lo m {>• to t>- CO CO +3 CO m to LO to to CO CO H • O 03 <3^ O CO H cr> J>- Z> £>- j> H £> CO to H to to LO LO o CT> CD cr> O C3> H 1 — 1 O 'tf to CO O £> CO C3> H O O CD H o HCO H CO H CO CO CO CO CO •CO H CO H H H CO CO CO H CO CO vi rH 0^ * — 1 1 — 1 o cr> O CO C3> 00 C3> •H 00 t> to CO E> O CD cr> <3^ 0 ^ c3 CO C7> O O O •«;}< to lO lO Jh lo 0» CTi CT> C3» O (3> C3^ C3> LO LO •H uD O H rH H H H H H o o O O o o O O H O O O O O 5h O • • • • • # • • • • -P • • • • • • • • • • • - o> cr> LO O LO a o £> 0 ^ to to 00 CO to LO lO CO cs5 to (T> lO lO to 0^ ^ ^ tO to CM ^ to lO to a ';}< to to to ^ ^ to to to to • CT> H to H o O GO <3> to (3> to CO C3> to o CO CO H O o to O ^ to tO C3» CD I> LO LO •H LO O C- 00 £> to ^ to LO O Gi •H (3> CO CO CO CO H H H H to to CD to CO CO CO CO to to to to to CO O CO •H • tH o o> o» £> t> 00 00 pS O I>- t>- !>£>£> CO CO P5 H to to o CO CO o o CQ 00 00 00 lO LO LO o o CQ • • • • • • # • • • • • • • • • SP CO CO CO H H H to to M CO CO CO to to to LO LO H CO pq o Crt PD O CO pq O to CP o ^ CP o LO pq O ^ • <3^ « <3> • C3> < Gi • ^ > ^ !> s > * S o ■r} Sh c3 ,c: •H (D M o J-4 PP ll TABLE 7 ContM. O o o o to to to to o> O CTi cr> to to to to iQ a> (j> H H O O O lo uo to lo to to to to lO to tO tO tO O o to tQ tQ tQ o| o ^ 1 W W CV2 cvj H H H H C3 C3 02 02 H H H H 1 — 1 O O 1 — 1 H i~l H H •p ^ ca 00 CO o» J> to 0> O 02 CO CJ> to o O to 00 (3^ «;}( o lO rH O H to o o o O O H H O O O O O H O O H O H 0 0) H Ph O Ph r*4 rH rH rH • H H H r-l H H H H H H H H H H H H H H H CO iH *st< tO to H to cr> -tjH to H O to H O O O E- tQ O D O C7» •«;J< to 03 to to O to ct 2 02 lO H CO CO to to O tQ E~ ^ H O i— 1 H rH t to , 't}^ H to to to 00 H CD £> t- (02 (02 (02 tQ H C7> IQ (J^ crv OlJ> ^ lO to lO to H H to CT> O cr» 00 CO O CD O 00 00 to tQ IQ IQ ^ 1 CO 00 CO 00 CO a> CO CO CD CTj CO CO 00 00 C7i CO E- 00 E- E- 0> E- E~ E- o CO a* Gi (T> O CO to to to CO 00 C7^ 00 •sf< O CJ> H to CT> C?^ Cj^ 00 CO CO CO C3^ o o> a> o o o o o o o o O O (7^ O <02 CT» CT> >• 1 r» o o o o O H O O 1 — 1 H H H H H H H H H O H H o O <5 B to c- o O to to cr> H CO ct4 E" E> CO to cQ CD -=4( E~ E- £> to to to to to >sH ^ to to to J> t- £> E- tQ (02 <02 <02 lO G» G> G> (M CQ 03 CO C'3 03 02 02 02 02 02 02 (02 (02 (03 (02 (02 <02 <02 (02 <02 H H H om £> J>- C- C- o o o o •^}^ to to to to IQ IQ tQ tQ <03 O O O «X) to o o to lO to to to to lO to IQ to to lO (02 (02 <03 (02 o o o o 03 02 02 02 03 02 02 02 02 02 (C2 (02 (03 (02 (02 <02 (02 Cv2 <03 C\2 (02 (02 (02 M lO lO to 02 lO H to H H H H O O O O E- to CT» iQ CT> C7> cr» o to to to to l> C- to to to to 10- I>- E- E- to tQ tQ IQ E- tQ tQ tQ H H H H H H H H H H H H H H H H H H H H H H H H 02 to to to H to O H O CD J> £> to tO E" to >tt( E- to <3^ cr> cTi cr» o lO lO to to to to to to 'ttl kJI "til IQ to IO to to ^ 's}( to (02 (02 (02 H H H H H H H H H H H H H H H H H H H H H H H H lo 02 to to ^ to to to H lO to to to to to to E- cr> 03 CJ> IQ D D D o + io to to to to to to ^ to to to tO IQ IQ IQ to (03 t;l( tQ o to to to \> 02 Cv2 02 02 t^i to tPJ to CQ 02 CN2 02 tPo tPj to IQ ■5c}( bJ tQ tQ tQ cr> O O H ^ IQ E- O CD ^ E~ to D D D to 02 02 b3) o o to ^ 00 to CT> CO bQ tQ H (03 sfl <03 to E- tO H H H J>lo o> o» cr> (j^ CO o cy> C- C- E- 00 00 CO CO tQ CO Cv2 (02 to E- E- E- 03 02 02 H H 02 H 02 02 02 03 H H H H H H H H H H H H !>• to to H H to 02 to O 02 O' O to to <02 CD to ^ H O (02 (03 <03 c V to *v}H O to CT> H tO to to to t}( ri( to ^ H C7> CO Q CO CO CD to to to to to to lO to to to to IQ IQ to IQ E- 00 E- E- to tQ tQ IQ H 00 CO to £> O ^ to to 00 t>- l> t> I> to to to tO E- E- E- E- CT^ CO CO 00 E^ E- E- E- H H H H H H H H H H H r-l H H H H H H H H H H H H H H H H I>- CT> £> CO 0 ^ CT> cr> o> to to to to E- CT> CO CD (02 cr> (3^ cr> o to to to to CTi Gi (Ti to to to to G> G^ G^ "sH ^ O c^ C3^ cr^ o o o o O O O O o o o o O O O O H H H H H O O O to to to ■t:H 02 00 o to to to 02 to to to t> to tQ CD to iQ LQ lQ IQ IQ lo m to to rjl «vl! lO to to to tQ tQ tQ tQ ^ IQ 'tj( ■ti< to to to to to to to to ■t}( «sjH ^ «v}( bj tQ tQ tQ tQ tQ tQ tQ to to to to GO to cr> ^ to to (02 (02 IQ C03 tQ O (J^ J> t G^ Gi 1 — 1 (02 H H E- D 00 D ^ r;Jt to to tcj tcj to to to to (02 <02 (02 (02 tQ tQ tQ tQ tQ tQ tCJ tQ to to to J> t> E> o o o H H H tQ IQ tQ O <03 (02 to tO to t> t>- I> to to to O O O H H H to CT> C7^ g5|0 • • • • • • • • • • • • # • • • • • to to to to to to to lO to tQ tQ tQ (02 (02 (02 tQ tQ IQ 03 pq o to pq O pq o IQ pq O to pq o E~ iCq o • • CO • CD CD . 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