ABRAMS (1924) - Design of Concrete Mixtures

8/14/2019 ABRAMS (1924) - Design of Concrete Mixtures

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DESGN.OF CONCEE XUESBY DU A. ABRAMS

Pi SSORN CHARGO LABORATORY

The de sign o~ concrete mixtures is. a subect of vital interest to akl inee rsh.d constructors who have to do with concrete work. The problem involved maybe one of the following:

1,

2.

3.

4.

o;k~ is necessary to produce concrete of proper strength for a given

.ith given materials what proportions will givi the best concrete at min.irnwn cost?

ith di fferent lots of materials of di fferent characteristics which is bestsuited for tbe purpose?

hat ~s the effect O . strength of concrete fmm changes in mix, c.ons i~tenqo sux and grading of aggregate ?

PmpO~tiO?ing concrete frequently ,involves ecti of materials aS ~c]l their combmahon. In general, the question of reIatlve costs is also present.

The term Desigrl ii used in the. title of this article as distinguished fromproportioning since it is the intention to imply that each element of the problemis app roached with deliberate purpose in view wh~cb is guided hy a rational methodof accompli sbmm t, ___

The design of concrete mixtures, with a view to prodllcillg a given result in tl, emost economic manner, involves many complications wbicb have heretofore de fiedanal ysis.

Many different methods of proportioning hpve been suggested; the most im .portant ones may be characterized as follows:

1.

2.

3.

4.

5.

Arhitmry sele ction, wch as 1 :2;4 mix, without reference to the size mgrading of the tine and coarse aggregate;

Density of aggregates in which the endeavor is made to secure an aggregateof maximum density;

Density of concrete in wY ,ch tbe attemp t is made to secure concrete ofmaximum density;

Sieve analysis, in which the grading of the aggregates is made to app rox-imate some pred etermined sieve analysis curve which is consid ered to givethe best results ;

surface area of aggregates.It is a matter of common experience that the methdd of arhitmry selection in ,

which fixed quantities of fine ad coarse aggregates are mixed without regard tothe size and grading of the individual materials, far from satisfactory., Our expe ri-ments have shown that the other methods menhoned above am also subect to sermuslimitations. e haw found that the maximum strength of ccmcrete does not dependm ei ther m aggregate of, maximum density or a concrete of ,nuyz inmm density,and that the methods wh,ch have been suggested for proportlomng concrete bysieve malysis of aggregates are based on m erroneous theory. All of the methodsof proporticx g ccm.rete which have b:. propos~d in tbe pmI h,ave failed to giveproper ,attentlon. to tbe water content o the mm. Our expermxm ta.1 work basem phasized the nnpcm tance of the water q concrete mmtures, and ,shpwn ,tbat thewater is, in fact, the m?st important nqredg.t, since very small varmtmns m .y. t.rcontent prodcwe more tmp ortant v M m tmm m the strength and other prope rties ofconcrete than similar changes in the other ingredients.

R. i.t.d fom M inutes of the A..ual eeting of the Po tland Cement Association, heldin New ? k, Decembe, 1918.


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2 STRUCTURALMATRIALS RSARCH LABORArORY

New Sf.dies of Co..ret. MLrtur..During the pas~ three years a large number of investigations hae been under

way at the Structtiral Materials Research Laboratory, Lew is Institute, Chicago,which throw considerable new light on the subJect of propo~tlo.ing co.cret Theseimestigations are being carred out through the cooperatmn of the Instdnte andthe Portland Cement Association. These studies have covered an investigationof the inter-relation of the follow ing factors:

1. The consistency quantity of m ixing water).2, The size and grading of aggregates. ,3. Tbe m ix proportion of cement).

Any comprebe.siye study of proportioning concrete must take into account all ofthese factors.

During ths perod about 50,0Xl tests have been carried out which have abearing on this subect. These tests have bee: largely confined to comp ressiontests of concrete and mortar. These mvest,gatlo?s have gwm m a new insightinto the facto,rs which underbe the correct proportioning of concrete m ixtures andshow the lim ,tatiom of older methods. Certain phases of these investigations arestall under way,

The following may be mentioned as among the most imp ortant principles which have been establi shed w ith refere?ce to the design of. concrete m ixtures.1 a brief report of thm kind it is imp racticable to present more than an outline ofthe methods of app lying ~be principle? to p .ractlcal Problems. In onh a few instances... - are experimental data gven on which these conclusmns are based .

1. ith glv en concrete materials and conditions of test the quantity of m ixi?gwater used determm es the strength of the concrete, so long as the mmn of a workable plasticity.

2. The sieve analysis furnishes the only correct basis for proportioning a~gregates m concrete m ixtures.

3. A simp le method of measuring the e cctiv,e size and g~ading of an ag-gregate has be en developed . This gw es r,se to a function known as the ~fineness modulus of tbe amzrexate..

4. Tbe fineness modulus of tbe aggrgate furnishes a rational method forcombining materials of different size for concrete m ixtures.

5. Tbe sieve analy~is curv~ of the aggregate may be w idely different in formwithout exertnu? any udhcnce on the concrete streniith.

6. Aggregate of equ~val~q t concrete-making ciual~ties ma; b. produced by anm fimte numbe r of d ,ff. rent gradings of a gw en mater] al.7. Aggregates of equivalent concre~ e-making qualities may be produced from

materials of w ,dely different s,ze and grading.8. In general, fin and. coarse aggregates of widely diff?r:nt size or gradingcan be combmed m such a manner as to produce smnbm results in m-

.ete.9. The ?gg ,-cgate gpd i,,g wbi,ch produces tfie strongest concrete is d that

gv?ng the q=x lmum dn~ty lOw est vO ,ds ).. A grading coarser than thatw ,mg max,muln dens,ty ,, necessary fOr highest concrete trength.

10. The richer the m ix, The coarser the grading shodd be for an aggregate ofi~ en maxmum s,=; henc, the greater the discrepancy be tween max-imum density and best grading

11 . A mm p~e te anal~s,is of the wate~ -req~i rcmcnts of concrete shows that thequant,ty of m ,xmg water reqmred ,s governed by tbe follow ;ng factors:

a) The condition of plasticity m we,-kability of concrete whichmust be used-the relative consistency;

b) The, normal consistency of the cement;c) The size and grading of the aggregate;


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d) The relative, volumes of cem ent and aggregatethe mix;c) The absorption of the aggregate;f) The mutame d water in aggregate.

12. There is an intimate rela~ion between the grading of the aggregate and thequantity of mater requwed to produce a workable concrete,

13. The water content of a concrete mix is best considered i terms of tbcvolume of tbe cem entthe water-ratio.

14. The ibape of the particle and the quality of the aggregate have less in-fluence on the concrete strength than bas been reported by other ex.oerlmemers,

E ff i-et of . Qua?ttity of Mixing Water on the Stmtgtk of Concretei. 1 shows tbe relation between the compressive strength and tbe water con-

tent for 2day tests of 6 by 12-in. crmcrete cylinde rs. Mixes from 1:15 to neatcem ent were used ; each mix was made up of aggregates ranging i size from 14 -rnesh sand up to 1~,-in. gravel ; x wide range i consistmcies was used for allmixes and gradings.

Tbe water content of tbe concrete is expressed *S a ratio to the volume ofcem ent, considering that the cem ent vmigbs 94 lb. pe rcu. ft. Distinguisbin marksre used for each mix, but no dktinction k made between aggregates of rfferentsize m differm t consistencies,h

k.,jL Z42f,m .b

ote - lio Y 7e of ement ~- XFG. L ELA ON BE EEN S ENGH OF CONC,EE AND AE CONEN

wenty-eight-day wmnpessim t.ses of 6 by 12-imh .ylimdes. Sake 83.)

hen tbe comp ressive strength is platted against the water ratio in this way,a smooth curve is obtained , due to tbe overlapp ing of the points for di fferent mixes.Values from dry concretes have been omi tted , If these were med we should obtaina series of curves dropp inra downward and to the left fmm the c.r.e ,shown. I isseen at mm . that the u.. and gradrng of the aggregatend tbe quam of cem ent. no longer of ay ~m portauc. excep t m so far thes~ fators in flmme theq.a,mi ty of water w. ,red ~. produce a w?rkable m ,x.. This gves us an entirelynew concep tmn of the fmxtmn of the- constituent matenak entering into a concretemix and is the most basic principle wbicli bas been brbught out in o.. studie s ofconcrete.


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4 STTJCTURALMAT .IAIS RmARC LA AT Y

The equation of. the curve is of the form ,

s=; .................................1)where S is the comp ressive strength of concrete and x is the ratio of the volumeof water to the vol~me of cement in the batch. A and B are constant whose values .decmnd on the cwahty of the cement used , the age of the concrete, c.rmg conditions,et:This equation expresses the law of strenh of concrete so far as the pro-portions of materials are concerned . It is seen ,that for given concrete materialsthe strength depends on only one factorthe o of mater t? cement. quationswhich have been proposed m the past for this purpose c?ntam terms which takeinto account ,such factors as quant of cement, p~opo rtlons of fine and coarseaggregate, votds. m aggregate, etc:, but they have muf orm ly mm tted the only tamwhich is of any importance; that 1s, tke water.

or the conditions of these tests, equation 1) becomes,14 ,m13s. ,,,...,.,.., . . . . . . . . . . . . . . . . ..2)7X

The refation given above holds so long as the concrete is not too dry for max-imum strength and the aggregate not too coarse ,for. a given quantity of cement;in other words, so long as we have a workable x.

Other tests made .in this Iahoratory b?ve shown that the character of the ag-gregate nmk~s little difference so long as it is lean amd of. stmctm .lly deficient.The ahsorptlon of the aggregate must be taken mto account ,f comparison is be ingmade of dzfferent aggregates.

Tbe strength of the concrete responds to changes in water, regardless of thereason. for these changes. The water-ratio may be changed due to any of thefollowing causes:

1. Change in m ix c ement content). 2. Change in size or grading of aggregate.3. Change in relative consistency.4. Any combination of 1) to 3).

In certain instances a 1:9 m ix is as strong as a :2m i, depending only onwater conte, ,t. It should not be concluded that these tests ind,.ate thzt lean m ixes .can be substituted for richer ones without lunit. e are always lim ited by thenecessity of using sufficient water to secure a workable m ix. So in the case ofthe grading of aggregates. The workability of the m ix w ill in all cases dictate them inimum quantity of water that can he used. The imp ortance of the workabilityfactor in concrete is therefore brought out m its true relation

The problem of designing concrete m ixes resolves itsel f into this:To prod.. a workable concrete which bas z given water-ratio using a.m inimum

auantitv of cement; or the converse, to produce a workable concrete with a m inimumwater-ratio using a iven quantity of cement. The methods for secnrimg the bestgrading of aggregate and the use of the driest concrete which is workable are thusseen to be only devices which enable us to accomp lish the above-mentioned results.itwness Modulus of Aggregate

The experimental work carried out i. the laboratory has given rise to what weterm tbe fineness modulhs of the aggregate, This fm .tion furnishes a method ofmeasw ing the size and grading of the aggregate. It may be defied as follows:The sum of the percentages in tbe sieve analysis of the aggregate divided by 1K .

Tbe sieve analysis is determ ined by m ig the follotvig sieves from the Tylerstandard series: 10, 4 23, 14,8, 4, - i., - i. and I .-in. These sieves aremade of square-mesh vmre cloth. ach sieve has a clear opening ust double the ,


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DSIGN O CONCRTSMrxmmm s 5.Table 1

MTHOD O . CALCULATING INNSS MODULUS O AGGRGATsThe sieves used are commonly known as the Tyler standard sieves. ach sieve

has a claw opewiitg m .t double that of the precech.~ one,The sime a.alysis may he expressed i terms of volume or weight.The finenes< ntods of an aggregate is the sum of the percentages given by

the sieve analyms, div,ded by K il.

size ofslew b OwingSk in. mm F

A) B) C3 D) E) F )82

1

46 fl g 1124 44 1 11 25 1 o 95 1

66 86 9255 lF im.css odulus, . ~ 31 646 -i ix 57

im tka Octobe r, 1922.) he No. 48. 28, .d 14-m.sh sieves giveNo, SO, 30, ad 16 mow u in the ,.tat,v. Q@od af .,, f.,.s. fo Conce.t of.. the Amen... Society fo e8t,ng ateials he

OL I I I 1 1 I I , I , u 1 I 1 I

FG. 2.s-eves.>. 2@scz??) -

EliOD OF PLO NG S\EVE ANALYSS OF AGGEG.4ESSieve .F s ..>.. fo aggegates B, E ad G in able 1.


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6 STRUCIYJRALMAT,>I,LS RSARCH LABORATORY

wid th of the preced ing one, The exact Clmensions of the sieves and the methodof de termining the fineness modulus .wiR be found in Table 1. It will be notedthat the sieve analysis is expressed m terms of the pe rcentages of material byvolume or weight coarser than each sieve.

A well -grade d torpe do sand up to No, 4 sieve will give a fineness rnodlus ofabout 3,C0; a coarse aggregate grade d 4-1 in. will give fi?eness modulm of about7.IXi; a mixture of the above matertals in prope r proportmm for a 1:4 mix willhave a fineness modulus of about 5.80. A fme sand such as drift-sand may have afineness modulus as low as 1.50.Siwe Aatysi of 4ggwg0te

There is an intimate relation between the siev,e analysis curve for the aggregateand the fineness modulus; in fact; the fineness modulus .m.bles us for the first timeto prope rly interpret ,the sieve analysis f an aggregate, If the sieve analysis of anaggregate M platted m the marine< md lcated m ig. 2; that is, using the pe r centcoarser than a green s,eve as ordinate, and the s,eve size platted to logarithmicscale) as abscissa, the fineness modulus of. the aggregate is measured by the areabelow the sieve analys,s curve. The dotted rectangles for aggregate G showhow this result is secured . ach elemental rectangle is the fineness modulus of thematerial of that particular size, The fineness modulus of the grade d aggregate i:then the summ ation of these elemental areas. Any other sieve ana.lYsIs curve whichwill give the same total area corresponds to the same fineness modulus and willrequire the same quantit of water to produce s mix of the same plasticity andgives concrete of the same strength, so long as it is not too coarse for the quantityof cem ent used .

The fineness modulus may be considered as an abstract lmmber; his iri fact asummation of volumes of material. There are several db?erent methods of com -puting it, all of ,which will give th~ same result. The method given in Table 1is probably the szmplest and most drect.

Some of the mathem atical relations involved are of interest. The followingexpression shows the relation between the fineness modulus and the size of theparticle :

m=7.94 3.3210 gal, . . . ........ . . . . . . ...3)where m= fineness modulus

d = diameter of particle in inchesThis relation is pe rfectly general so long as we use the standard set of sieves

mentioned zbovc. The constants are fixed by the regular sizes of sieves usedand the units of me asure. .Logarithms are to the base 10.

This relation app lies to a single-size material or to a given particle. Tbefineness mod.lm is then a logarithmic fnctim of the diameter of the particle.This formda ne~d not be used vnth a graded materkil, since the value can besecured more easdy and dkectly by the method used m Table 1. It is app licableto gaded mateials pavided the .elati-e quantities of each size ae ommidered ,and the dkmneter of each group M used . BY app lylng the formnla tO a grade dmaterial we wodd be cakulatig the values qf the separate elemental rectanglesshown in ig. 2. wtes. Modulus Shwgth Relatio?t for Co cwte

Many di fferent series of tests have shown that for a given plastic ~ndi tion ofconcrete and the same mix there is an intimate relatio? be tween the fineness modulusof the aggregate and the strength and other prope rtms of the concrekz e haveseen that the reason for tbm result w fotmd in the fact thzt the fineness modulussimply retlects the changes i water-ratio neqessary to produce a given plasticcondh ion.

igs. 3 md 4 give the results of certain comp ression tests wliich bring out therelation be tween, the strength of tbe ccmcrete and tbe fin.mess modhxs of the*ggICg ?tC. It III be noted fr?m ,g. 3 that a sepuate m rve may be drawn foreach mx. In each case there IS a steady im rease i the compressive strm~ tl. of


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a STRUCTURALMA,,,IAM R~sM.ttcII LABO.OEY

Tl=r --L/ -J4-70 zoo 6702,6,.2,6902,4402,8903.04


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10 S UCUAL AE ALS ESEACH LABOAOYthe concrete a? the fineness modulus of he aggregate increases, until a certain valueis reached which corresponds to a max,mum point, It wdl be noted also that thismaximum point m r~e sponds. to higher and higher values of fineness nmdulm as thequantity of cem ent ,n the mx k w .r= ,ed. In other words, the maximum strengthcome. at a fineness modulus of about 5.8Q for the 1:9 mix and about 6,4Q for the1:4 mix. In these tests the different v.lqes of tbe fineness modus were securedby usi.g ? prepond.er=ce ,Of the coarser s1.=, but in all case, maintaining the samelimiting sine, that M, 1 m.

In ig. 4, is found a similar relation be tween the strength and the finenessmodlm , excep t that no maximum point is found, This condi tion arises from thefact that tbe rnaxirzmm ,size of the aggregate is increasing without changing thetype , of the sieve ?n.lyss curve, co.s~quently the fineness modulus Strength CUWcontmmes to nse mdefim tely. Tbe height to which the curve rm.es s bm,ted onlyby the maximum size of aggregate which may be used. It is Important to notethat there is no conflict be tween the indication of igs. 3 and 4.

or all practical purposes and for ordinary ranges in concrete mixes the fine-ness modulus strength ,relation m,ay be assumed as a linear OR The comparisonof the true and app roximate relat]on n brought out in the discussion of the aterormula be low .

A .en value for the fineness modus of an aggregate can be secured withany combination ? f p,ercent?ges in tbe s: eve analyws which giyes th,e same total,ccmseqwntly, a m fim te varie ty of gradings may be fonnd wbtch gw e aggregateof the same concrete strength. Table 2 gives the results of groups of tests whichbring m t the wid e varia~ion which may be made in tbe grading of aggregate with-cm t prod~ cing any essent,al vartatlon in the concrete strength. Tw~nty -seven di ffer-ent gradings of the same aggregate were made up. These gradings covered thewidest possible range, but they had one property m common; that is, a finenessmodulus of 6.04, All specim ens were m ixed w ith tbe same quantity of cement andwater, Se parate sets of specimens were made of two different consistencies. Themean variation from the average strength is about 3 .

Table 2 also furnishes some interesting data o the sm face-area method of ,,proportioning aggregates. It is s.. that there is the widest variation in the surfacearea of the. aggregate wv thout any app reciable difference i the concrete strength.Ow studies have clearly shown that surface area is not a satisfactory basis for pro-~ortiomng aggregates,Deigti of mowt M ixes

In accordance with our previous statem ents tbe problem of de signing concretem ixes using given materials resolves itself into that of finding the ,c?mbi.?tionwhich with a given water-ratio will giye a concrete of suitabie .wO rkabd lty using aminimum of cement.

Tfie follow ing outline will make clear the steps to be followed in the designof concrete mixes on the basis of our studies of concrete:

SEPS N n. DESGN OF CONCEE XUES1. Kmnuing the compressive strength required of the concrete, determine by

reference to ig. 1 tbe maximum water-ratio wbicb may be med. Sub-seq et steps in the design of .omxete mixes are only. ,devices for.securig a workable concrete using this water-ratio and a mm,m.m qu*n-tity of cem ent. It is obvious that a give wate-atio can be secnred witha rninmrn of cem ent if the agq.gate is grade d as coarse .s De:missibleco rmde rmg its szze and the mm used ) and If we use the dr,est mixwhich .. be pr.y plac~d. Smmi:g a ccmrs,e, well-gra~e d aggreg?te,using rcb rmxes, employ?ng the drmst practlcabk cons, stem y, mpgnmchamcd methods of pla,cmg mmrete, etc.are all methods .of prod,ucmga work?ble mix with ,., mmimum water-rat,?. xpe rience or trml n theonly gw de m determmmg the relative consistency of concrete necessaryin tbe work. Obviously the driest workable consistency should be used.


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f,

DESGN OF CONCEE XU 11

The size of, aggregate ayailable, or wb~ ch must be used, and the otherfactors will furnish a gu]de as to the m ix. The mix is expressed as onevolume of cem ent to a given nmnbe r of volumes of aggregate; that is,the combmed fine and coarse aggregate. In general, sotie allowancemust be made for tbe high strengths m Iabgratory tests, In other words,a water-rat,o somewhat lower than th gwe~ for the required strengthin ig. 1 should be used . or co.nvem ence m the subsequent steps wcshall deal w ,th concrete strength instead of water-ratio as in ig. 6),although it should be unde rstmd that it is the water-ratio which fixes thestrength so long as we have a plastic mix.

2. Make sieve analysis of fine and coarse aggregates, using Tyler standardsieves of the follow ing sizes: 103, 40, 28, 14, 8, 4, ,, and Iz in.xpress sieve amd ysis in terms of pe rcetag.es of matem al by weight o rseparate volumes ) coarser thm each of tbe standard sieves.

3. Compute fineness modulus of each aggregate by add ing the pe rcentagesfound in 2), and divid ing by 103.4. Determine the maximum size of aggregate by app lying the following

rules: If more than 15?7. of aggregate is coarser than any sieve themaximum size shall be taken as the nex~ la~ger sieve in the standardset; if less than 15 is ,coarser than c~rtam sieves, the smallest of thesesieve sizes shall be comwde red tbe max,mum size.

5. rom Table 3 determin~ the, maximum value of iineness modulus whichmay ,be .s~d for the m,x, k,n.d and size of aggregat~, and the work unde rcons, de rat, on. The values m Table 3 are platted m ig. 5.).

6. Compute the pe rcentages of fine and coarse aggregates required to producethe fineness modulus de sued for the final aggregate mixture by app lyingthe fornmla:

ABp.lm . ...,.,...,,......,...,;.....,...3)A,C

whe p = pe rcentage of fine aggregate in total mixttire.A = fineness modulus of coarse aggregate.B = fineness modulus of final aggregate m ixture.C = fineness modulus of fine aggregate.

ig. 7 may be used for solving quation 3, and for making comparisons oftbe effect of certain changes in proportion of fine and coarse aggregates. Thedistinction between fine and coarse aggregate is solely for convenience in secur-ing a uniform grading; the division may be made at any de sired point.7. ith t~e estimated mix, fineness modulus ancl consistency enter ig. 6 and

de termine the strength of concrete produced by the combination. If thestrength shown by the diagram is not that required , the necessary read-ustment may be made hy changing the mix, consistency or swe andgrading ?f the aggregates.

The quantity of water required can be determined from ormula 4 below ,or app roximately from Table 5.

IMPORTANT NOT: It must be unde rstood that the values in ig. 6were de termined from compression tests of 6 by 12 -in. cylinde rs stored for days in a damp place. The values obtained on the work will depend on suchfactors as the consistency of the concrete, quality of the cem ent, methods ofmixing, handr,ns, placing the concrete, etc., and on age and curing condi tions.

Strength values higher than given for relative consistency of 1.10 shouldseldqm be consid ered in de signing, since it is only i excep tional cases tl aconsm tency diner than this can be satisfactorily placed . Fo wetter concretenmcb lower strengths must be considered.


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12 STRUCTURALMATRIALS ESEACH LAEKXAO

Table 3

MAXIMUM PRM ISS IBL VALUS O INNSS MODULUSO AGGRGATS

or mixes other than those given in the table, use tbe values for the nextleaner mix.

or mazimuwt sizes of aggregate other than those given in the table, we thevalues for tbe next smaller size.

ine aggregate includes all material finer than No, 4 sieve; coarse aggrt-einclude s al material coarser tban the No. 4 sieve. Mortar is a mixture of cem ent,water and fine aggregate.

This table is based on tbe requirem ents for sa d-atd-pebble o I aggregatecomposed of app roximately spherical particles, in ordinary uses of concrete in rein-forced concrete structures. or other materials and in other classes of work thenw .xi,?um pe rmissible VlCS of fineness modulm for an aggregate of a give sizeis subect to the followm. corrections:

i) If crushed ston; or Lzg is used as coarse aggregate; ?+?dtw. Yal.es intable by 0,23, m crushed material consisting of unmually flat m elcmgatedparticles, educe values by 0,40.

2) or pebbles mmsisti.g of flat particles, reduce values by 0.25.3) If stone scrt?.?cifig are used as fine aggregate, reduce values by 0.23.4) or the top course in awcvete roads, radttc. the. values by 0.25. If tinisb-

ing is done by w ,c)wtiicd wmm, this reduction nee d not be made,(5) In work of wtassiue firo~ortions, such that the smallest dim ensim is larger

than 10 times the maximum size of the coarse aggregate, additicws may be nwdtto the values in the table as follows: for - in. aggregate 0.10; for 1- in. 0.20; for3-in. 0.30; for 6-ire 0.40.

Sand with fineness modulus lower than 1.50 is unde sirable as a fine aggregatein ordinary concrete mixes. Natural sands of such fineness are seld om fmmd.

Scutd w scwenitig. med for fine aggregate in concrete mum not have a higherfineness modulus than that permitted for mortars of the same mix. Mortar mixesare covered hy the table and by 3) above.

Cvush.d siow mixed with bo~h finer sand and coarser pebbles equies oreduction in fineness modulus provid ed the quanti. of crushed stone is less than30 of the total volume of the aggregate, ix Size of Agtwgate

0. 0.1 i,l.. o.lz 0.2.10.4,..4,60 5.00 5.35 5,75 6.20

4.25 4.6S S.00 5,40 5.80 6.254.35 4,75 S.15 5,55 5.9S 6.434.45 4,85 5,25 5.6S 6,05. 6.504.60 S.00 5.40 5.80 6.20 660

5.20 5.60 6.00.. 6.40 6.855,50 5.90 6.30 6.70 7.155.90 6.30 6.70 7.10 7.S5

Cem..Am1-12. ,. .,.1-9. . . . . . .1-7. . . . . . .1-6. . . . . . .1-5. . . . . . .1-4. . . . . . .1.3. . . . . . .1.2.., . . . .

-28 14 8 4 312 18 24 29S 33513 185 24S 3 S 34514 195 255 32 35515 2 5 265 33 36516 215 275 345 3817 23 29 36 4185 25 31 39 32 27 34 42 46

4-m38539s4 5424447SS

4851545

0.4 . 0.61..6.60 7,006.65 7,0568 72o69 737 74572S 765735 85 *

1-1. . . . . . . 2.2S 3,00 3.80 4.7S 5,25 5.60 6,0S 6,S0 6.90 7.3S 7,75 8.20 8,65 9.,0.Consideed .S h.lf.size,, sieves not used i. c.mp.ti.g tienem modulus .

*


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DSIGN O GiNCXT MIXTURS 13

Calculation of Water Required fov ConcreteBecause of the impotant influence of the quantity of wate in the concete it

is de sirable to haye a sound basis for proportioning the water. The quantity ofwater necessary for given proportions and condi tions may be determined by thefollow ing formula:

3[(

.Ox ~D 1. ,, . . . . . . . ...4)l,26rn

where x wate, quied-aio to volume of cement ti batcb water.rat,o )

R = Relative consistency of ccmcm te, cm workability factor,,.Normal consistency relative consistency = l,CO ) requiresthe w .. of such a cpsant,ty of mixing water .s will cause aslump of ~ to 1 in. i a freshly mold ed 6 by 12 -in. cylinderof about 1:4 mix upon withdrawing the form by a steady,upward pull. A elative cmsimency of 1,10 requires the useof 10 more water and nndcr the above condi tions will givea slump of shout 5 to 6 in.

p = Normal consistency of cem ent ratio by weight),m = ineness moduus of aggregate, an exponent).n = VOlunte~ of tmxed aggregat to me of cement the mix),a = Ab,orptmn of aggregate, ,at,o of ~ater absorbed to oIunle .f

aggregate. Determined after immersion in water for 3hours. Averaze values for cmshed limestone and nebbles. . . . .. .may he a.ssurn~d as 0,02; porous sandstones may reach 0.08:very light and porous aggregate may reach 0.25.)

c = Moisture om tained i aggregate, ratio of water contained to .volume of.. aggregate. A ssume as zero for mom -dry ag.gregate. )

This formula takes account of all the factors wbicb affect tbe quantity of waterrequired in a concrete mixture. These factors nu.y be classified as follows:

1. orkability factor, or the relatw . consistency of the concrete, This isdictated by the kmd of work be ing done; concrete must be more plasticwhich generally rneam a wetter comntemy) in reinforced concretebuilding constmction than is necessary in mass work. The term R) inthe eqwz ti. takes care of ~is factor. R) may yary from, say, 0.92 fora dry concrete to 2sN or hlgbe r for very wet nuxes,

2. Cement factor, which is made up of two parts: the WAY of cement so faras normal consistency is concerned p) ; the qua,ttity of cement in themix n).

3. The aggregate factor. This include s the, three terms within the parenthesisin q.ahon 4. The first term, mvolvmg m ), takes account of the size ,and grading; the second a) the absorption, imd the third c) the watercontained m the aggregate.

In case adm ixtures of any kind are used , another term mast he ins.ert~d in theequation, This relation has been fully worked rm t, bt i d included in thisreport.Simplified Water ormulo

hile quation 4) rep resents the true water relation, it is somewhat com -pl icated by the fact that the fineness modulus m ) app ears as an exponent. lequation can be expressed in a sim pler form as follows:[ mx=R ;P 0,2= . C). 1 . . . . . . ..5)This equation gives values for ordim.ry ranges of mix and grading of aggregatewhich are sensibly the same as given by quation 4).

*


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14 STRUCTIJRALMAT,RIALS RSARCH LABORATORY

.

OF f 1 1 1 [ 1023, 4S 678 90

~ - L6 77es c7fAgy7ey7@ {0one of Cemen/FG, 5. AX U pE SSBLE VALUES OF FNENESS ODULUS OF AGGEGAE

Gwhical .wod.cti.n of able 3. hese cuves ae bssed m the qnienmm of sand..d pebble .g eg.te. Fo c.sl]ed stone .wg wate the .alnes must be ed.ced as noted inthe table.Mdwun erm issible Values of ineness Modulus of Aggregates

Since a maximum practicable value of fineness modulus is found for each sizeof aggregate and mix, i is, necessary to place certain ~mi ts O the v?lue whichmay be used for proportlo.nmg materr.ls for concrete m,xes. Table 3 gw ,es Iim i swhich will be found, practcablc. Subsequent expcrtence may d,ctate certain modi -fications m the de tads.

Ihe purpose of Table 3 is t? avoid , the attem pt to secure an aggregate gradingwhich is too coarse for its maximum size and for the amount of cement used. Itis also useful i,, wohibi ting attanpts to u.? sands which ae too . . ..ss fo bestesu lts in concete mcitues. Fo 1.stance, t would be found fom this table thatthe US. of a sand. of the natue of standad Ottawa sand is not pemitted excepti nuxes 12 . . tcbe.

he cuves in Fgue 5 ae platted diectly fom the values give. fo the stand-ad sieves in able 3.

Chart fov Design of Concrete Mixesig, 6 is a nom.graph~c chart for the de sign of concrete mixm. This chart

takes account of the follow ing four factors: ,,1. The mix c em ent content).2. The relative consistency.3. The grading of aggregate f ineness modulus).4. The compressive strength of concrete.


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DESGN OF CONCEE XUES 15

G iven any three of these factors the chart enable s us to solve for the fourth.This chwt is, of course, based on the results of certain tests. or practical supplic-ation these values musf generally be reduced by certain factors, which will dependon tbe udgment of the de signer. I orde r to furnish some basis for comparison,commission tests of 1:3 standard sand mortars from the ement used in these testsare - e.

Supp ose we consider the case of concrete for road construction. This is gen-erally spe cified as a 1 :1: 3 or a 1:2:3 mix, with aggregate grade d up to 1in. These mixes are about the same as wbst have been termed a 1:4 mix, the exactequivalent depending on the particular size and grading of the fine and coarse ag-gregate. Assume that gravel aggregate will be used, graded to 1 in. Table 3shows that we may use a fineness modulus as ~gh as 6.CQ .25 = 5,75. Know ingthe sieve analysis an,d fineness mod~ lus of both sizes of aggregate, app ly the formulaor ig. 7 to determme the proportmns of each aggregate wbicb must be m ixed tosecure this value. Assume that the concrete will be mixed to a relative consistencyof 1.10, which is of such plasticity as will give a slump of 5 to 6 in. in tbe test de -

scribed shove. Place a straighted ge in ig. 6 on mix 1:4 and fineness modulus5.75, and mark the point where it crosses the reference line for consistency; fromthis point proect the fine horizontally as indicated in other examples) to relativeconsistency 1.10. It will be seen that this gives, a compressive strength of 3,I lb.pe r sq. in. at iS days.

Table 4

Ex.4hfPu3 OF INFLuENCE OF QUANTITY OF MIXING WATERON THE STRENGTH OF CONCRETE

Values calculated from equation14 ,KQs=;=8.2X

here S = Compressive strength of coricrete Ih. per sq. in.).s = ate-atio an exponent).

A and B are constants whose values depend on quantity of cem ent andother condi tions of tbe test. The values given for A and B are based on2day tests of 1:4 mix, p ebble aggregate grade d tll in., fineness modulus5.75.

The water-ratio is equivalent to the cubic fee t of water to 1 sack 1 cu. ft.)of cem ent,

The strength values are SOMY for comparative purposes in showing the influ-ence of changing the water content.

Cdmes,ie Stewth of Concete ,,28 Dayswate in a 1.Bag Batch eative CmsistencF, Lb. Pa ?,q. n.

Gallonselative Stength

atec-atia x) Pe Cent s) Per cent5.75 .77 100 2,770 1006.0 .80 104 2,600 946.25 .84 109 2,400 87.. .s, ,,3 fg S17,0 .94 122 707.5 1.01 . 131 1670 608.0 1.07 139 1,470 539,0 1.21 157 1,100 4010.0 1,34 174 830 3012.0 1.60 208 480 171s.0 2.00 260 200 7


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16 STRUCTURALMATRIALS ESEACH LABOAOY

Table 5QUANTITY O MIXING ATR RQUIRD OR CONCRT

3[(

.30Calculated by formula: x = R ;P 1 ac n:L26m

here x = ater required -ratio m .mlume of cem ent in hatch water-mtio).

R = Relative consistency, or orkabilit. . ..

ty factor. here R = 1.111the concrete is mid to be of


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.

DESGN OF CON~EE XUES

/-23L

/e./o/fii@75/5 cyFG . 6. DAGA FO HE DESGN OF C0NCE2 lxuE5

his chat is beed m .mumession tests of 6 by inch cylindes am 28 days stoed indamp sand.he cement .eed .za.e cyn ..ss. tmnmhs in 1.3 standad sand mota as follows. hC.

ested in the f.m of 2 by 4-1.. cylm.de.sA.. Lb. DC ,S.. n.

1,9003,2004,2004,300


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18 S UCUAL AEXALS ESEACE LABOAOY

The effect of sing other mixes, gradings or mmistencies on the strength canbe seen at CUR from the diagram. or instance, if the water were increased to arelative mmistmcy of 1.25 not nearly so wet as is frequently seen in mad work)the strength will be reduced to 2,70Q lb, per sq, in.a reduction of over 20 . cent.If the m ix were changed to 1 ;4 and othm factors the sametbe streb would be 3,230 lb, per sq. in. e shcwld haveas lean as 1 :57X i order to secure the mm. redwtion in :above for a cbamge fmm 1.10 to 1.25 consist enq= .

as in tbe first ample,:, to change the mix tostrength as was found

By ming the wetter of the two, consistencies we secure concrete of the samestrengfh as if we had ys,ed one-thmd less cement and tbe drier mix, In otherwords, increasing tbe mmmg water 137. tames the same reductmn m strength asif we sholcf omit 33 of the cem ent. This example shows the reason for em pha-sizing the itnrtance of prope r control of mixing water in concrete,

This chart enable s us to answer such qwstions as the following:hich is the stronger, a 1:3 mortar cm a 1:5 concrete mixture?Assuming that concrete of the same plasticity is used , the relative strmgtbs will

depend, of mmrse, on the grading of tbe aggregates and the mix. In me case wehave assumed 1:3 mix with fimness modulus equal to 3.03, This will give a strengthfor normal consistency of 3,0Ctl lb. per sq. in Tbe 1:5 mix f ineness modulus 5.70)gim a str.nsfb for normal COn,isten.y of about 3,300 lb. pe r sq. in. The stre.gtbsfor other comistmcks can be found by rea.d ing horizontally across the chart as in-dicated by the dotted lines

Unfortunately, we now have O proper basis for absolute valms for strengthof concrete. his, of couse, makes h necessay to efe to paticula tests as i ig.6. This condi tion em phasizes the importamx of working out a test of cem ent whichwill give m at once the mncret strength for given materials, m ixes, etc. ith thepresent method of testing cem ent it is impossible t. do more than make a roughguess .s to the strength of concrete from the results of briquet tests.Quantity of Water R quived fw Cotwet.

The fomm las given above 4 and 5) show the e lem ents which makeup the wmer-requirem ets of a concete mix. Table 5 gives the qwm tity of water required forcertain mixes and values of fineness modulus, Quantities are ~iven in terms ofgallons pe r sack of cem ent. In this table ~he net absorption that is, the qwm tityof water taken p by the aggregate in add ,t,on to that already contained ) is ,wsmn.d.s 0.02 274 by volume). This tabl,e is of interest when we consider that it hasbeen found that a gi.p ,water-rat?o corr~sponds to constant concrete strengthregardless of the mmbmat,on of mix, ccms, tency m grading of aggregate whichmay be used , so long as we have a work.bk concrete.utthw Diwum ion of Co..... ,ifizm

The importance of the water-ratio on the strength of concrete will be shown ithe fcdlow inn consid erations:

One pin; more water than necessary to Produce a plastic concrete reduces thestrength to the sane extent as if we sbmdd omit 2 to 3 lb, of cement from a l-bagbatcb.

Onr studies give .s an m tirely new ccmcepti.m of the f.nctio performed bythe various co?stitent materials The use of a coarse, wel l-graded aggregateremits in m gam i strength nnless we take advardzge of the fast that the ammm tof water necessary to produce a plastic mix cm thus be reduced. In a similar waywe may say that tbe use of more cem ent in a batcb does not produce any beneficialeffect excep t from the fact that a plastic, workable mix can be produced with,a lowe wate-at,..

Tbe reason a rich mixture gives a higher strength tbm a km one is not thatmore cement is used, but be came the mmrete cm be mixed md usually is mixed)with a water-ratio which is relatively lower for the richer mixtures than for thelean ones. If adva,tage is not taken of the fact that in a rich mix relatively less.w?ter can ~e wed , o benefit will b? gained as compared with a leaner mix. In d]th,s discms?on the quantity of water is. compared with the quantity of cem ent in tbebatch c b,. fee t of water to 1 sack of cemm t) and not to tbe weight of drymaterials or of the concrete as is generally done.


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D?,I cm CONCRT XUES 19

1

7D0

z?? ForSo/v/hg 6-80.+yhbn,= /fOAe< 45-0, .,

FG. 7. DAGA FO DEE NNG QUAN Y OF SAND EQU EDN CONCEE XES


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1. Design of Concr.fe M ixtures, by Duff A, Abrams 1918).

w the effect, of quantity of mixing water, and size and wadkw of a pex.testhe : c.m pr.sslve stmwiil of concrete. futlinis. z new methcd of eswn dmete mixtur.s: based . . the water:canem ratio and the fimness modulus ofasz,exates.

BCLLE N 2, Effect of CuinS Condition on the l?~ca anif Stength tif Concete,bx DtIff A. Abrams. ,

R


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ABRAMS (1924) - Design of Concrete Mixtures