the modular ratio in reinforced concrete design (manuscript). a.k

8/12/2019 The Modular Ratio in Reinforced Concrete Design (Manuscript). a.K

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Lehigh University

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Fritz Laboratory Reports Civil and Environmental Engineering

1-1-1937

Te modular ratio in reinforced concrete design(manuscript). A.K.A: the modular ratio - a new

method of design omiing n. Concrete andconstructional engineering, (England), July 1937,Reprint No. 41 ( 37-4)Inge Lyse

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Recommended CitationLyse, Inge, "e modular ratio in reinforced concrete design (manuscript). A.K. A: the modular ratio - a new method of design omiingn. Concrete and constructional engineering, (England), July 1937, Reprint No. 41 ( 37-4)" (1937). Fritz Laboratory Reports. Paper1202.hp://preserve.lehigh.edu/engr-civil-environmental-fritz-lab-reports/1202
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R TZ ENGfNEERtNG l B O R T O ~ VLEHIGH UNIVERSITY

BETHLEHEM P E i ~ I S Y L V i : ~ L ~

_ _ /A_A A fI f t ....r ~ _ R ~ . ( x ~ of ~ t ~ n... I V ~ , JTHE VODULAR RATIO IN REINFORCED C O r ~ C E T E DESIGN

by-Inge-Lyse*I INTID DUCT ION

I he paper on THE 4ODULAR RATIO by Dr. Hajnal-Konyi.in the January , February e nd March issues or ffCOncrete and

Constructional Engineering 1s very opportune contributionon one the most important problems before the engineeringprofession. The progress ot research in concrete and reinforced concrete h s brought forth enlightened understandingor the actual behavior o f s tru ctu re s buil t of this compositematerial, but at t ~ e same time i t has also re-emphaslzed thenecessity vastly more experimental stUdT in this f ield.Recent experimental evidences suoh as those presented y Dr.Hajnal-Konyi have shown that the prevailing methods of analyzing relnforoed _ concrete members on the basis of definite work-ing stresses do not give results which correspond to the fa.ctsand that some more rat ional method of design must be found.Dr. F,ritz Emperger should be given special credit fo r contrib uting very e ff ec tive ly in bringing th is matter before the profession a t large and in promoting international discussion ofth is problem. Tbe time seems ripe for a thorough reconsideration of the design of reinforced conor ete structures and aninternational exchange views should be highly beneficialto r the development of more rational methods.

Research Associate Professor of Engineering MaterialsLehigh University, Bethlehem, Pennsylvania

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Concrete Is not 8 S elas t ic l1l aterial in the same senseas steel The apparent modulus of elast ic i ty 1s a.rrectedb.y 8large num ber of tao tors such as the speed o f testin g moistureoondition or conorete at tes t age of oonorete. composition ofconorete and type t aggregates. and cements uSfi d In a s t ruc-ture the members will continually be sUbjected to the deadload and general ly for a considerable l eng tho t time the l iveload Is also present Because or the large change in moduluswith time which 1s general ly termed plast ic flow. there i s acontinuous ohange 1n the modular rat io during the t i r s t fewmonths the structure 1s under load. Consequently the modularrat io 1s of l i t t l e i f any value In ascertaining the actuals tress condition in reinforoed concrete members The timehonored conception t designing t working s t resses thus becomes inadequate . Modern viewpoint in design tend.s towardabolishing the working stress conception and introducing theuse of defini te factorsot sa fe t against fai lure or any partof the structure. With this conoeption i t becomes importantto establish the ultimate strength of the various memberswhich oonstitute the reinforced concrete structure. th isdiscussion both the oompressive members su Ch as columns andthe flexural members such as beams and slabs will be oonsid-ered.


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COLUMNS x p e ~ m e n t a l studies have shown quite conclu ively

that the modular ratIo has no p ~ a o e in the strength of re inforced concrete oolumns. The strength or reinforced oonorete oolumns with no spiral reinforcement may be obta,inedfrom thetormula:

F .. 0.85 f t An fy l l s c 1)and for spIrally reinforced concrete columns:

85 t ~ fyoAs koffoA; 2 )where:

= strength of columnf t r strength of 6x12-ino concrete control cylindersQ c c: cross-sect ional area conorete in columnf y m yield-point stress longitudinal reinforcementAs r cross-sectional area of longitudinal reinforcementk 0= effect iveness ractor of spiral reinforcementmay be taken equal to 2.0)

f y =; yield-poInt s t ress of spiral reinforcement ~ equivalent cross-seotional area orspiral reinforcement

t should be kept in mind that the ooncrete protective shel loutside the spIral or the column cannot act simultaneouslywith the spiral reinforcement. In other words, the protective shel l must fa i lbe tore the spira l can develop i t s effeotivenesse Thus i t becomes neoessary ei ther to neglect the pro-.te etiv e sh ell in computation of the strength of the oolumn or


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.. 4to reduce the effectiveness fa.ctor in such a m.anner that onlythe strength of spiral in exoess of the strength of shel l beused. Beoause of the f ire protective funotion of the .shell,i t seems logical that i t be considered of no load-carryingvalue and that the net area conorete ( that is, the .area enclosed by the spiral) be used in the design calculations.

The faotor of se:tety to employ in each case . 111 naturally depend upon the type and function of the .s tructure .Various factors may be desired for va.rious percentages of re :-Intorcement and fo r d if fe ren t grades of concrete t 1s thefunction o f t Building Code Authorities to establish theproper factors of safety.

FLEXURAL MEifBERSThe conventional method of designing reinforced con

crete beams is based on l inear distr ibution of oompressive .stress in the concrete, no tensi le strength or conorete, and. steel stress in accordance with a given modular rat io . Thismethod s s u t i u ~ s a straight line stress-strain relation t rconcrete. AS early as 1905 Professor A N Talbot* proposedthat the stress distr ibution i n the concrete should follow aparabolic trend. liowever, the stra ight l ine basis t designwas genera.lly recognized asgiving reasonable values withinthe range stresses permitted under working conditions. Thein i t ia l modulus t elast ioi ty of t he concrete was assumed as

- - - - - - - - - - - - - Bulletin No.4, University t l l inois


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5suitable t the modular ratio an d as information becameavailable re ga rd in g th e relationship between i n i t i a l m o d u - Ius and strength o f a concrete. a variable modtilar ratiowas accepted in many building codes. The .American ConoreteI n s t i t u t e in i t s building Regulations fo r e l n r o r c ~ d Concr et e. assumed the in i t ia l modulus o f elas t ic i ty concreteto increase in d i r ect p ro po rt io n t o th e increase in thestrength or concrete. Thus a varlal.:>le modula.r ratio givenby the tormula: m e 30,000f tc

was Introduc e dln the1928 regulations. This formula f o r themodular r a t i o i s reta.ined in the t en t at i v e 1936 r ~ g u l t i o n sExperimental r e s u l t s have shown tha t the in i t ia l modulus o fe l a s t i o i t y t o o n o r e t e i s n o t p ro po rti on al t o th e st re ng th o fconcrete. In a recent s eries a t tes ts a t Lehigh Universitythe s t r e n g t h o f the con crete was varied from 1000 to 6000 lb .p e r sq in . The modulus of elast ici ty o f t h i s concrete variedonly trom a bo ut 2 ,2 00 ,0 00 to a bo ut 4 ,5 00 .0 00 lb p er sq lnWhen 5 u c h t a c t o r s as p l a s t i c tlow and moisture condition o fth e concrete are considered. th e f a l l a c y or t heebove formulat ormodular r a t i o i s I lpparent. Since th e e f re d t o f the valueo f the modular ratio is relatively small and since the straight

- ~ ~ - - . - - See F i g . 12 t th e paper: A STUDY OF ~ U Q UXLITY THE DESIGN ND rz HE ECONOMY OF CONCRETE by Inge Lyse published in theJo u rn al o f Th e F r a n k l i n I n s t i t u t e . April May lUna }tuly 1936


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6l ine method of design is at best very approximate, i t seemsadvisable that a constant average modu.lus rat io be used inbuilding code regulations unt i l a more rat ional method design has been developed.

In oonsidering rat ional methods o design i t i , 'e11:to recognize the fact that ooncrete beams \t:tll generally givestrength well above that computed means of the conventionals tr aight lin e stress distribution method. ParticUlarly. beamswith so large percentage of reinforcement that fai lure takesplace in the concrete show strength far above the computedvalue. Also beams with very emaIl percentage or reinforcement show strength far above the computed values. In orderto study over-lleintorced concrete beams. an extensive inves t igation was carried out at Lehigh University in 1930* Thevariables stUdied were the effect of ~ h e strength of concreteand the effect of depth beams. For five groups of beamsthe average .strengths of concrete control 'cylinders were 1390,2790, 4070 4800 and 5740 Ib 'per sq in . The effect of this~ r l t i o n in strength s i l lus t rated in Fig. 1 where the mo-ment at fai lure Is plotted aga.inst the strength,of the o n e r e t e ~ t is noted th t except to r the very weak concrete, the momentincreases in direct proportion to the increase in strength ofconorete to r these beams which l l failed due to crushing otth e concre te. In the paper r ef er re d to , t l s shown that the

COMPRESSIVE STRENGTH OF CONCRETE IN FLEXURE S DETERMINEDFROM TESTS OF REINFORCED CONCRETE BE MS W Slater and Inge Lyse, Proceedings,American Concrete Insti tute, Vol. 26. 1930, p.831


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observed mom.ents at fa ilu re were far above those computed by. the o rd inary straight l ine method. n the assumption o raparabolic stress distribution in the concrete, the computedresul ts agreed more closely with the tes t data. For para-bolic stress distribution the ratio o f the distance betweenthe centers of pressure to the effective depth of the beamIs given by:

4= r+l k2 r+2 where : 1s the power t the parabola and i s the ratio of .the distance from the compression surface to the neutralaxis to the ful l effective depth t the beam. The tes t re-sul ts indicated that the neutral axis remained approx111late1yat the same depth 1 or a l l the beams. Assuming the neutralaxis to be located a t the center 1 the beam, that i 8k l / e ;the.degree o t the parabOla Which ..i l l give .oomputed momentsof approximately the same magnitUde as the observed momentsm y readily be s o e ~ t i n e d A f i f th degree parabola was.found to give very satis .factory resul ts In Fig. 1 the dot-ted s tra ight lin e represents the moments computed on. thebasis of a fifth degree parabolio stress distribution in theooncrete. I t 1s uoted that except for the very weak ooncrete,the agreem.ent between oomputed.and observed moment 1s verygood. The design formulas for this oondition become:

. 5+1 1J llIll . . . 2 5 -2 2 3 11 14 - 14


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5o r a.pproximately:

where lit i s the maximum mom ent a t f a i l u r e . The maximtJ;Bls t r e s s in the s t e e l i s computed in the ordinary manner:

7

A comparison between the s tres s . in the s t e e l oomputed in th ismanner and the st r esses observed in the beams i s made inTable I in which the observed values are. fo r loads close tothe ultimate loads carried by the beams. The observed stresses

TABLE I STRESS IN .REINFORCD.E.NT

GroupNo.

1345

Measurements a t Last ObservationConcrete Maxim um oad s t r a i n Observed Computedstrength Load in s tre s s s tr e s sIb/sq in Ib . ..;.lb Steel Ib/s q in Ib/s q in1390 32 520 3 O ~ O 0 . 0 0 1 1 6 33 700 3 8 4 0 02790 44 710 40 000 .00136 39 400 3 8 4 0 04070 6 3 3 0 0 55 000 .00135 39 200 39 9004800 74 830 70 000 .00145 42 000 4 0 0 0 05740 87 410 80 000 .00133 38 600 38 400

were obtained by multiplying the observed s t r ~ s with a moduluso f e l a s t i c i t y or s t e e l equal to 29 000 000 Ib per sq in . t i snoted tha t the agreement between oblJerved and computed s t r e s s n


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the s t e e l i s very satisf actor y pa rt i c ul a rl y so fo r beams inwhich ~ h e strength or the concrete control cylinders exceeded2000 lb per s q l n . The simple method o f design here present-ed in which the modular r a t i o yas omitted thus served verywell fo r th e group o f o v e r ~ r e i n t o r e d beams studied th isinvestigation.

~ b e m ~ designed y the ordinary s t r a i g h t l in e methodthe fa i l ure is always due to th e yielding o f the reinforcementand the sUbsequent r aising o f the ne ut r a l a x i s u n t i l the com-pression a.rea becomes so small t h a t the concrete i s e : t us he d.Professor Sa i l ge r presents a method design for t h i s type o fbeams w bieh g iv es v alu es agreeing b e t t e r with t s t r e s u l t s thandoes th e o on design pr actice. However many variables haveto be considered such a.s the t ns l contribution o r the con-c r e t e and the e x t e n s i b i l l t y o r ~ o n o r e t e fa c to rs whIch vary wIth .the type an d moisture conditions o f the conorete an d thereforevery elusive o f evaluation. t therefore seems to the w rite rt h a t with ~ h e lack o f g e n e ra l evidence s t i l l prevailIng theS a l i s e r method should considered s n i n te r es ti n g s o lu ti on worthy o f fu rth er study. l n y analysis which tends to indicateaccuracies beyond the 11 mlts o f a vai: latlonln the m a t e r i a l sthemselves I s questionable from a pra.ctical standpoint.

A simple basic conception which gives r e s u l t s within areesonable range o f dependability would be p re fe rr ed u nt il thetime a rriv e s when concrete is a m a te ria l w ~ t h more d e f i n i t e


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10properties than at present and when more i s known t theactual beha.vlor t rein forced concrete bealllsln flexure.One simple method t analysis of beams of low percentage treinforcement where the yield point of the steel is reachedbefore. the concrete f i ls in compression may be based onrectangular stress condition In the concrete at fa . i lure.ThisaSSU ed stress condition and the method of analysis are i l lus-trated in Fig. 2. The moment at failure Is given by:

L t As d+d 8)and

A comparison between tbe maximum moments Computed by th is simplemethod and the observed moments at failure i s shown in l ~ 3 t Is noted that l l the observed moments are somewhat higher

than the computed moments The difference is nearly constantthus making the percentage of difference muoh greater for lowthan t high percentage of reinforcement. This is logical be-oause the deformation of the reinforcement at the cracks willbe greater rorsmall percentage 1 steel and th ere fo re th e actualstress in the reinforcement at time of faIlure i s considerablyabove the yield point stress. Considering l l the uncertaintieswhich enter. into any reinforced concrete beams the simple methodhere presented seems to ot ter a satisfactory solution for pre-sent day condi tions s 8 matter 1 fact I t gives results Which

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agree better with the experimental results. than does theordinary design method which employs the variable modularra t io This simple method y also be applied to T beams.

The writer s therefore hesitant a bout advising acomplicated design method of the Saliger type unt anabundance of supporting experimental results have shownthat such s refinement in the analysis of reinforced con-crete beams 1s just if iable.


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the modular ratio in reinforced concrete design (manuscript). a.k

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