lIt)

:ftlqSCIVILENGINEERINGSTUDIES c. 3STRUCTURALRESEARCHSERIESNO.193 PRIVATECOMMUNICATION NOTFORPUBLICATION BEHAVIORANDDESIGNOFDEEPSTRUCTURALMEMBERS PART2 TESTSOFREINFORCEDCONCRETEDEEPBEAMS WITHWEBANDCOMPRESSIONREINFORCEMENT lti.tzReferenceRoOOlment_ CivilEngineeringDe BI06C.E.Building UniversityofIllino Illinois618 By J.R.Winemiller and W.J.Austin Approvedby C.P.Siess Reportto RESEARCHDIRECTORATE AIRFORCESPECIALWEAPONSCENTER AirResearchandDevelopmentCommand KirtlandAirForceBase,NewMexico ContractAF29(601 }-468 Project1 0 8 0 .-UNIVERSITYOFILLINOIS URBANA,ILLINOIS AUGUST1960 AFSWC -TR-59-72 Part 2 BEHAVIOR ANDDESIGNOF,DEEPSTRUCTURALMEMBERS Part 2 TESTSOFREINFORCEDCONCRETEDEEPBEAMSWITH WEBANDCOMPRESSIONREINFORCEMENT Project, No.1080 by J.R.WinemillerandW.J.Austin Approved byC.P.Sies 8 UniversityofIllinois DepartmentofCivilEngineering August1960 ResearchDirectorate AIRFORCESPECIALWEAPONSCENTER AirResearch andDevelopmentCommand Kirtland AirForce Base NewMexico Approved: ERICH.W AiNG Chief StructuresDivision ~ ; : ; ~ ~ColonelUSAF Director,ResearchDirectorate Contract No.AF29(601)-468 TR-59-72 ABSTRACT Theresultsoftestsofsevenreinforcedconcretedeepbeamswithtensile a.ndwebreinforcement and twobeamswithtensile andcompressivereinforce-ment aredescribedinthisreport.Severalpatternsofwebreinforcement were used.Thebeamswithwebreinforcement had aspan-depthratioof about3.0 and thebeamswithcompressivereinforcement had aspan-depthratioof2.32. All beamsweretestedunderuniform,slowly-applied loading.Thegeneral behaviorof thetestspecimensisdescribed andexplanationsoftheobserved phenomena aregiven. PUBLICATIONREVIEW This report hasbeenreviewed and is . L/ -CAY ColonelUSAF DeputyCommande r I., IIo IIIo TESTSOFREINFORCEDCONcRETEDEEPBEAMS WITHWEBANDCOMPRESSIONREINFORCEMENT. TABLEOFCONTENTS INTRODUCTION 0o0 .,.,.,., o000 .,., o0 00 .,f1 000 101ObjectandScope00.,0.,.,.,.,~ 0.,00., 102Acknowledgmentoo.,.,.,.,.,00o'00o. 1.3Notation00000., DESCRIPTIONOFTESTSPECfIMENS .,.,.,0.,.,00.,.,0.,.,.,.,0.,0 00000 201Descriptionof Beams0.,00 202MaterialsandFabrication.,0 TESTEQUIPMENTANDPROCEDURE 0.,b.,000 Instrumentationo.,o0000 LoadingApparatus..,0> 000 TestingProcedureo0.,00.,0., o00 000000000 o.,0.,.,b .,0.,o.00.,o.,.,0., o.,00a0.,00,000 o0- 0a00000 00000".,. 00.,00 .," 0 00 o.,0.,00 BEHAVIOROFBEAMSWITHWEBREINFORCEMENT 000...,0000.,000 401TestResultsand*odesofFailureo0 .,00.,000.,0 Deflections.,.,0o.,.,000 SteelStrainso-.,0 ConcreteStrains..0 o"000 .,0000 .,.,.,00000000 o.,.,0000o. 0.,., o0o.,00000 iii Page 1 1 1 2 5 5 7 10 10 ~ 13 14 14 15 18 22 405TotalElongationofTensileReinforcement.,.,.,.,00.,024 BEHAVIOROFBEAMSWITHCOMPRESSIONREINFORCEMENTo0o.,.,00o., TestResultsandModesofFailureooeo.o..., o.,.,00Deflections 00 SteelStrains.,.,0.,,0 0o0 ConcreteStrains.,00"000 .,0o..,0o0.,00"., .,., 0000f1 00.,0 .,.,.,0.,000.,., 27 27 28. 28 29 .... ..;iv TABLEOFCONTENTS(Continued) VI I> STUDIESOFTEEFLEXURALSTRENGTHANDBEHAVIOROFDEEPBEAMS \olITHWEBREINFORCEMENTANDWITHCOMPRESSION0031 601Effectof WebReinforcementUponExternalBehavior0031 602EffectofUponExternal Behavior000000000I> 00oq0000 PredictionofExternalBehavioro0OOOOQOOO VII.SUMMARYANDCONCLUSIONS.obo0o000o000000 .' Summary 0I> 0 0o00o0I> 00oI>702Conclusions 000000I> 0 VIIIoBIBLIOGRAPHY" 00000o0000o0o0O'0 TABLES FIGURES 35 10 20 LISTOFTABLES PropertiesofA-SeriesSpecimenso PropertiesofC-SeriesSpecimenso PropertiesoftheReinforcingSteel CO" 000 o0' "'- '.o0000l'o0o0 o00 40PropertiesoftheConcreteMixeso000 50TestResultsofC-SeriesSpecimens 0 OOOO()O00 o000000coo0 60TestResultsofA-SeriesSpecimensoe0()0 70ComparativeTestResultso0 0000000000000000 80Comparisonof Measured, andComputedMoments0000 PredictionofSteelStrainsatFailureo00o00 v Page 46 41 48 )+9 50 51 52 53 54 Fig.,No., 1 2(a) 3 4 5 6 7 8 9 10 II 12 l3 l4 15 16 l7 l8 19 20 2l \ LISTOFFIGURES A-SeriesTestSpecimensoOOOOoocrOO()oO NominalofC-SeriesSpecimensandLocation ofConcreteStrainGagesandDeflectionDialso0 PlacementofReinforcementandLocationofSteel StrainGages:BeamC=lo.,000.,0.,00 PlacementofReinforcementandLocationofSteel StrainGages:BeamsC-2andC-300000()00000 PlacementofReinforcementandLocationofSteel StrainGages:Beamsc-4andC-500000000 PlacementofReinforcementandLocationofSteel StrainGages:Beamsc-6andC-700000 TypicalStress-StrainCurvefortheReinforcingSteel.,., TypicalTestSet-Upo0000., .,0e00.,.,.,.,e00 BeamswithoutWebReinforcementAfterFailure..,o., "., BeamswithVerticalSti'rrupsAfterFailure BeamswithInclined BarsAfterFailure0a000 CrackDeveldpment CrackDevelopment: CrackDevelopment: Beam.c-4 Beam.C-50 Beamc-60 0,.00'0 Load-DeflectionCurvesforBeamswith1015LongitudinalSteel0 " ,0 ., 00. ....00 ., 0 Load-DeflectionCurvesforBeamswithPercent LongitudinalSteel., 00000b. 00 ., Load-DeflectionCurveforBeamwith2.09Percent o000 0000 00000 "" 000 Longi tudinalSteel000" 000.,o0., DeflectedShapeofBeamsC-landC-2., DeflectedShapeofBeam.C-3o.,.,.,00 DeflectedShape.ofBeamsc-4andC.;..50 o0,0 DeflectedShapeofBeamsc-6andC-7o.,0o00 Load-DeflectionCurveforSupports00.00.,00 0000 vi 55 51 68 69 10 11 12 73 15 Figo 22 23 24 25 26 27 28 29 30 31 32 33 34 35 37 38 Noo LISTOFFIGURES(Continued) Load-SteelStrainCurvesforBeamC-l .. Load-SteelStrainCurvesforBeamC-2o Load-SteelStrainCurvesforBesunC -Load-SteelStrainCurvesforc- 4000 000 .. " .. 0..0 vii 16 11 78 19 Load-SteelStrainCurvesforBerun000.o080 Load-SteelStrainCurvesforBeamc-6" 0

Load-SteelStrainCurvesforBeamC-7o " Loadvs 0TotalTensileForceinLongitudinalSteelat 81 ,82 Section12in ..'fromBeamsC-l,C-2,andC-3"0.." 83 Loadvs 0TotalT'ensileForc'einLongitudinalSteelat Section12inofrom Beamsc-4,C-5,c-6 andC-70..00'0 000000" 000000 Free-BodyDiagramsofCrackedSpecimens o o0"DistributionofTotalTensileForceintheLongitudinal Reinforcement:BeamsC-l,C-2,andC-3o"000 00"DistributionofTotalTensileForceintheLongitudinal Beamsc-4,C-5,and00" 0" 0 Load-SteelStrainCurvesfortheWebReinforcement0 DistributionofConcreteStrainAlongDepth: ofBeam atMidspan,.Beams C-l,C-2andC- 3.;8dd6aI 8 DistributionofConcreteStrain' AlongDepthof Beam at Beams,c-4,C-5,c-6andC ... 7 20 o . IV 1/: II ; I iI! I ii I ; I I I / ! I ! I / V o o ! ! i : : \ I I i ! I I i i .1 I I i ! , ! Ji , I ! ! , I , ; I i 0.4 8 -----: -i I I I I i 0.8 16 I I I I I " UnitStrain,percent ""'" '\ 1.2 24 FIG.6TYPICALSTRESS-STRAINCURVEFORTHEREINFORCINGSTEEL I . ' -I I -1.6 32 -3' 1/4" MovingHeadofTesting MaChine TestSpecimen BedofTesting~ h n emOWF'9 Roller 4"x.31/8"x2" Loading Block Hydraulic Pump FIG.7TYPICALTESTSET-UP 1"Chrome SteelBall J?l BeamC-lk W=76.2 u BeamC-4k W=102.0 u BeamC-7k '\01=95.9 u FIG.8BEAMSWITHOUTWEBREINFORCEMENTAFTERFAILURE 62 BeamC-2k W= 89.5 u BeamC-5k W=106.0 u FIG.9BEAMSWITHVERTICALSTIRRUPSAFTERFAILURE FIG.10BEAMSWITHINCLINEDBARSAFTERFAILURE BeamC-3 W=94. f u Beamc-6k W=102.6-" u 64 FIG.11CRACKDEVELOPMENT:BEAMc-4 k W =92.2 (Yieldingof tensionsteel) W=l02.0k u FIG.12CRACKDEVELOPMENT:BEAMC-5 k W = 30.0 W = 85.0 k (Yieldingof - tensionsteel) W= lo6.ok u FIG.13CRACKDEVELOPMENT:BEAMc-6 k W..:~ O67 W :::88.f (Yieldingof tensionsteel) k W= 102.6 u 100 80 fa .!f60 ~i .s 40 20 o o " Jd r I ~;,~~~ C 3V V ~"""" t'- C-2 ~~ ~,,-V iO'"i/. ~-..:- ~ 1\ ~ ~~ -~ ~ C l-0.40.81.21.6 MidspanDe!1ection,_in. FIG.14LOAD-DEFLECTIONCURVESroRBEAMSWrnr1.15PERQENTLONGITUDINALSTEEL 100 80 art 60 ~ ~ i .3 40 20 o o0.20.40.60.8 MidspanDefiection,in. $ FIGo15LOAD-IlEFI.BCTIONCURVESFORBEAMSWITIl1.99PERCENTLONGITUDINALS'mEL 0) p. .,;

al S c5 __ __ __ II 80I-- T---+-i---+-1---+-1---t-----t----'i ,1,II I----+I---I-----t----+---t--_r---L 'I---i iII!II:I;I 60I-- -H--+-. L---__'--i------1---t------i------1 I I!:!;!I:.!I I.IIIIi' III1I i----1--... -t- I--+- --+I-; I- ------.;-------tIII ..IIII- -II' III:iI;.:I. lJ- .. --1--+-' -L - --l.. --- -l---J - -- ----+---11- -+--!II' II,I-:I :III!IIIi!:iI iI:IiIIi' i !II ,--T----l--"--i -:-----t------t-----J------t---i- ! i;III.IIII - Ii! !i- i,I!.: 20H------T---i--,----t------,---- --y -----,- --:-- ------t-- -- tit -f"-----,-----III!::iii ii, !III f--:----- -- ----- r- -i- - r.. ---I ---t -I 1--1-1---1 o!IIIIIIIIIU 40 . -'----o0.20.40.60.8 MidspanDeflection,in. FIG.16LOAD-DEFLECTIONCURVEFORBEAM'-lITH2.09PERCENTLONGITUDINALSTEEL ---,--- ....... ! ..i I- l n 4a.t9":z36" f'"-I d0.2' "I"'f ...

o ..,.. ..., BeamC-l --,c..-+--+---I Wm76. u CJ V . o. 4 0.60.2 .

.. s:l 0 .,.; 0.4.., CJ "

0.6 0.8a....-___--'--______ ..... FIG.17DEFI.BCTEDSHAPEOFBEAMSC-lANDC-2 BeamC-2k w:::89.5 U ----.-- --_._--!IIIIIIBIIIIiI 72 4at9"=3611I ~ ~ ~ Io ~ ~ ~ ~0.2 Q OM ~Q BeamC- 3k 0 0.4OM W=94.5 +' u () (!) M ~8 0.6 0.8"--------1-----FIG.18DEFLECTEDSHAPEOFBEAMC-3 . d .,-4 . d ....-4 co.d 0 .,-4 ..., (J "(j 4at9"s.. 36" Beamc-4 ---,,,.c--7t'-------t WU::102. ok 0.4L-----__ ______ ______ ______ 0 0.2 Beamc-5 Wc106.ok u 0.-4 rIG.19DEFLECTEDSHAPEOFB!AMSC-4ANDc- 5 ... J:l o 4at9"=3611+JO. 21'---___ 3 ~ _ ~C) Q) r-{ 'H ~... Q o ''-; Beamc-6k W=102.6 u +:l C) Q)O. 21------o --...,,-L--f-------i BeamC -7k W=95.9 r3 u FIG.20DEFLECTEDSHAPEOFBEAMSc-6ANDC-7 120 / -/ / 100 80 1:1) P1 lJ ... s... G) ~ 60 ~g / / V I ~.s 40 / V / ,/ / 20 ~v o o. 0.0080.016 Deflection,in. FIG.21LOAD-IBFLECTlOKCURVElORSUPPOR;rS .....___________.........,.J:Jr1'\dIIOCI'._J!liAJWU7I roO'"'oj 80 I ----I -...f-1-'... - 1; I i82 85 S40t----#*-+-+---,--.. ;-.-.- ... ._-'-- -.. -.. +-- -._- .. "1. t ..... -. --- .. ".... -.. - .- j !S3I EOI It IEst.ult.sI to

i. i 1 1 1_atmidspan I=0.0230in.jin. I o400800120016002000 Strain,in.jin.x10-5 80,..------------------,.--81

rd

20 s3

H"-I'---;-- -._..-.- ---- - ._... _.. ...- ". o4080120 strain,in.jin.x10-5 168 FIG.22LOAD-STEELSTRAINCURVESFORBEAMC-l .......-------__".. ____ __ ..... ..............1I."5:, 200 __ ,__ .J 1.20 IT ! I I 1V V I / I -----. -------. 85 ----t-""'" ~.,-. I ~( 82 ~I I 80 ~ 83 "1 I E:o II I. 1 iA IC'.I Est.ult. 's .'1 Iataiclepan -, I I- 0.0420in/in. I I IIII o o400800l ~ l ~ 2000 Strain,in. lin.x10-5 80120160200 strain,in./ln.x10-5 FIG.2'LOAD-STEELSTRAINCURVESFORBEAMC-2 78 85 84 80 1----1--+----- .. ---.- ----.-.- -----r-i - -- 40 . - . IE -. I! I IEst.ult. iS ..-t-.i- atmidspan--I II=0.0600in. lin. --+--_.- --_ .. _..-- ....... - .. _- .--.-. ________________________ __ ____ ____ __ _ o4008001200lWO2000 Strain}in./in.x10-5 40 __ __ ____ __ ____ __ __ ____ ____ __ o4080120160200 Strain,in./in.x10-5 FIG.24LOAD-STEELSTRAINCURVESFORBEAMC- 3 80 80 60 o o 19.. I ~1 81 .-AJ.L LoA I ...----~I s, I I I I . I I ,-1I. I I Bst.ult. I 8 I I atmidlpan - 0.0138in./in. ---IFI I IIIII ..80012001600 strain,in. lin.x10-5 ~l7 ~~-~ S3 ~ 0" I J ~ ~V I I ~, I 85... I ~ ~~I I ~ ~ ~ S 3 I I ~ 'S2andS4 Ie ) I Y /I I I V I . I 4080120160200 Strain,in. lin.x10-5 FIG.25WAD-STEELSTRAINCURVESFORBEAMc-4 80 __ __ ____o4008001200 Strain,in./in.x10-5 E.:3t.tilt. .:3atmidspan ==0.0170in./in. 2000 20 o I ---- t __ ... ---I 4080120160 in./in.x10-5 rI y' .. - --_. I f-+-------t--I 200 FIG.26LOAD-3TEELSTRAINCURVESFORBEA'1C- 5 -: 80 I

-

I' I I o : rd m :34.0 I ! o o lEy I I I 400 81. s5 1 . -"'/ I s3 S2 I I I I I EO --I Est.bt.E I s atmidspan I -= 0.0270in./in. ..II __ I 80012002000 strain,in./in.x10-5 83 '-S5 80t-----+---+---+---+-- 60 r----+---+-en Pl

i40r----+-S o4080120160 Strain,in./in.x10-5 FIG.27LOAD-STEELSTRAINCURVESFORBEAMc-6 200 ,..,..-------______.......____________...__.' ...... r .........___..".."..... 82 I____ .oCt-- /'I __ __hI I'llo,I io1,IEstult. HIj,! yI, I1s 11----;=O.Ol}:Jin.jin. --.ti atmidspan ttl A .,-i ..!:4 ...

S a "---10... 1 ______'.'_.....I.-.-i-J-...-I ___ o400800120016002000 Strain,in. lin.x10-5 =-2.r. -w-_-+ 80 ------t

!: I!: IIIIi II lII -J -__._ -. ---'._ ---___ ---+III.II !!II II.: ----- ----t---+---r--j--1 --- -- .-.. -'- -_ .. _----+-----! o_____'- II_.j40801201&J 60 I 40 i I I 20 o200 Strain,in. lin.x10-5 FIG.28LOAD-STEELSTRAINCURVESFORBEAMC-7 i __f ; t._/ , "J.l I

! I -4100 UJPI rl

i 80 60 840 20 o / 1,// I-----1----- r--- .- ,L- f--Vrv iI ,//V I / ./ i / /"C-2 J.-'.-/' Theoretical .I I ... Ioi"

I beambehavior y'/ ,/ ."/',,. ,,'" /'I! V C-l ....... I I-7 I .". I I +y .-' ,//vV' ../II II Yj II K ..,.... ...-"" Theoretical I_l----

.// ,,// archbehavior

, v ,.// I // I .-

a/./ V....

[7./"", ""'" o8162432 TotalTensileForce,kips FIG.29LOADvs.TOTALTENSILEFORCEINLONGITUDINALSTEELATSECTION12in.FROMMIDSPAN: BEAMSC-l,C-2,ANDC-3 ()) \.)l ,rz...'100 80 Ol 60

.,. td cdo H 40 20 o , / // It /' /'" Theoreticalj ,// beam__ -C-';;""5 L ------/ ,1--------tlehavior1/ ; n c-6-----I/ / c-y // ./ I / /

/Theoretical V

---arch behavior(C-7) ///---1 --r---V /-r7'archbehavior 1 L/ (c-4,C-5,C(6)_

'/

/y

1------- -

I ---- I / , ------ f--------/

YI/ " ---1------ ----- --- -- - --- ---------------o16324864 TotalTensileForce,kips FIG.30LOADvs.IDTALTENSILEFORCEINLONGITUDINALSTEELATSECTION12in.FROMMIDSPAN: BEAMSC-4,C-5,c-6,ANDC-1 ". r-i;". _!:. . i, ex>

[ 15" 131/211131/2" T ~ Af vv BeamC-1 Ml T=-jd M1=externalmoment BeamC-2 M- aAf T=2vv jd M2= externalmoment M2< M1 BeamC- 3 M2- bAf T=vv jd b>a FIG.31FREE-BODYDIAGRAMSOF CRACKEDSPECIMENS ~24I~ =--II Theoretical archbehavior 1:_I~ I -~ I ~ I.........{J} ~-r-I ~'"Q) CJ~ .16 ~~ /1'-Theoreti c al ~beambehavior r-i oM{J} I=lQ) 8 r;d8 +' 0 8 6" ~..~ 1 ~ .4at6"=24" LIE I I I ~FIG.32DISTRIBUTIONOFTOTALTENSILEFORCEINTHELONGITUDINALREINFORCEMENT: BEAMSC-l,C-2,ANDC-3 .. . i 1l '1 ... ,' 6;.. .: ; .. .;"';.;.. It..................'.:r'.......ii..:.tJ 4D ""'I'\./I/r/ """"-Theoretical archbehavior P'"I

I'''1 CIlPi .r-f

-- Q) u H 0

Q).. 20.r-f til Q Q)E-f

+' 0 E-f 10 I-< ):1 -r-I ............... ):1 .r-! Q -r-l ttl H +' U) Q) +' Cl>H CJ ):1 0 0 680 400 200 800 600 400 200 600 400 200 BeamC-lk W=76.2 u BeamC-2k W=89.5 u 91 _- _Estimated BeamC-3k W=94.5 u FIG.37DISTRIBUTIONOFCONCRETESTRAINALONGTOPEDGEOFBEA\f 92 000400 611Beamc-4k W=l02.0 u . FIG.;8DISTRIBUTIONOFCONCRETESTRAINALONGIDPEDGEOFBEAIv1 93 101. -f 400 Beamc-6k =102.6W u 200 If''\ I 0 r-I X . 0 .r; .............. Q on "" Q ..-l oj H -I-' m d) -I-' Cl.>400 c.>s:1 0 92.0k u BeamC-7k VI=95.9 u 200 6"4at3"=12"I6".,6" ............ FIG.39DI3TRIBUTIO:'JOFCONCRETESTRAINALONGTOPEDGEOFBEAA 120 C-3...-.... ............. ---~~----.-"""" --~V" ~ ~~C-2 80 .............: 40 o o 80 40 20 I( ~/; !/ 1/ ~o o -0.20.40.60.8 Elongation,in. -- -------.- ._- . -_. ,,- ._.- ._-c-v ~~ ~ .___..C-2 7 ~V /. / ~W V .- ------ ------// V ----I ---.-... - ---0.020.040.060.08 Elongation,in. ~1.0 ---,...._--.-. 0.10 FIG:40ELONGATIONOFTENSILEREIiUi'ORCEr..ffiNT:BEAHSCal,C-2,.rumc.. 3 .. "'"120 95 C-5 c-6 -

... C-4 : c-7

80 #1 :

V 40 v o o0.10.20.30.4 Elongation,in. ... S 20I---ff---+ 0.02.0.040.060.080.10 Elongation,in. ~0 ~ 50.04 s:10.03 rl ... 5:l0 .r! +> cO~ 0 .--t 0.02 r:i1 0.01 o o0.020.040.060.08 TotalLongitudinalSteelStrain,in. FIG.42TOTALEWNGATIONOFrrENSILEREIHroRC:ElvIENTVB.SUMOFWNGI'I'UDINALSTEELSTRAINSBELOVIYIELD: BE.AMSC-l,C-2,ANDc-3 "Iis:1-r-!d 0 .r-!+l cdbO C 0 r-l f:i10.')5I. I- Elongation=}sdTJ I o. 04 -+- .-t----t--.--t-----t-.---+ I- -t- ..-.-..- -+----.- . \--- -_ .. --_ ...... --- -....._........------0.03 1----+--.---- -- C-4i ------r-T--,_- - _+-------+--+----+---+---+------I 0.02 r- -- --r

0.01 1..---- - .. --t----t-------t---- -"- .. t- ."'- t_ -t.......f1-..- o0.020.040.060.08 TotalLongitudinalSteelStrain,in. FIG.1-1-3'.eOTALElDIJGATIONOFTEl>TSlLEREIll'FORCThIElTTvs.SUHOFLONGlTUDNIALSTEELSTRAIl'ISBEL01-;YIELD: BE.ru1Sc-4,C-5,c ... 6,ANDC-7 \Q ,-J tI) ~t) ~.,-t '" " 0 .,-t ..., 0 v ~~~PI ~~tf.) .8 (J = '" ... s::: 0 "r"I .p 0 ~~5 t=lt ~'" ::E! 0.10 0.08 0.06 0.04 0.02 0 Elongation,inches 0.80 0.70 / 0.00 0.50 O.lto 0.30 0.20 0.10 0 / ~V / / C-2V c-y V / V / V / V / 7 / V / V / i/V V 0.10 Elongation,inches .'FIG.44MIDSPANDEFLECTIONVS.ELONGATIONOFTENSILE REINFORCEMENT:BEN'1SC-1,C- 2,ANDC- 3 / / [? [7 to I!J ..!:! t) ~-,-4 po, t:: 0 ol""i+' v cv ,..; r ; ~8 P-I , .,..; ~m ~CJ P OM .. 0 '.-i ~0 V H t'j..f tU ~a, r4 ~~99 0.12 / , / / / 0.10 // V / / ~0.08 0.06 0.04 0.02 0 /' ~ V / 1/ ./' v / ,/ C"'5I if (I c-Gj//f C-4/, V/ 1 / /' / / '/ f I 0.02 Elongation,inches 0.80 0.70 0.60 0.50 0 V / / V / /' c-6 / 0.40 0.30 0.20 0.10 0 // / /v / C-5 / / ~/ / / c-4 ./ V/ / / / /7 /FI if / 0.10 / 1I / Elongation,inches FIG.45HIDSPANDEFLECTIONVS.ELONG.NrrONOFTENSILE REINFORCEMENT:BEAMSc-4,C-5,ANDc-6 / BeamA-3-4 Wz:186.;k u M= 745in ... k u BeamA-3-5k Wu- 179.,2 = 896in.-k 100 'I. 1000 800 U) A .,-j

I Q 600 .,-j ....+l Q Q) ::g 400 A U) rcj -rl

200 / l-r_ iyl

II !/ iI JI ILI 1,1iii--1-----+-__-----, __-----'---!I /1I 1/!I.i I III".:; Iii'II! IIIUnloadedtoI!! ----if -r:lease;i --; r:iI --+--t----+------ir- j---t---t----t--III1I!; -l- 3-2 a a0.20.8 MidspanDeflection,in. b J-l FIG.41 CURVESFURA-SERIESBEAMS 102 m Pc J I !r( I I L...----' ...--U 120 j i 11 /1 IY I (, i I 40 I I I o ,0400 ---SlS2 -120 6at : I s3 i ....& s5t=::: t2: S2

... I I I I ! EO I I I I I I Est.ult. I s I atmidspan I= 0.0308in./in.___ I I I 8001 roo 2000 strain,in./in.x10-5 - --83s4S5 ..... -I'i'/.: r/// -6"=36" , ]80 II IY Theoreticalstrain --+---f-----f----+-....L.-+-----I at mi I oK-__ __ ____ __ ____ __ __ ____ __ __ ____ 04080120200 strain,in./in.x10-5 FIG.48LOAD-STEELSTRAINCURVESFORBEAMA- 3- 4 I I

LL !j I

t:;:--v--I L---:j 82 I -l20 I

I ? I 1183I :1

I I 1/ J JV I0 III 11 I I j I I I Y I I , I I Est.ult. I I s I atmidsp'ID JI =0.0377in./in.-I 1 III JI 40 o o400800120016002000 Strain,in./in.x10-5 l20 40 S2 /"I Theoreticalstrain --f---f----+--t----t---H __ ____ ____ __ __ __ __ ____ __ ___ o4080120160200 Strain}in./in.x10-5 FIG. LOAD-STEELSTRAINCURVE8FORBEAMA-3-5 104 OJ 0.0022in.in. .... IH---..... --.-... -......_.- .-----------------strainsat loadsof 6o.ok 120.0k 140.Sk BeamA- 3-4 k W=186.3 u Est.E=0.009in./in. c ______ IrI ....---1-_ C\J ri Strain3at loadsof 5o.ok IOO.Ok 120.0k -1BeamA-3-5k W= 179.2 u Est.= 0.007in./in. e FIG.50DISTRIBUTIONOFCONCRETESTRAINALONGDEPTHOFBEAMATMIDSP fu"'T, BEAMSA- 3- 4kllDA.. 3- 5 8001 U"\ H . 600 Q .,... '-..... . d ..n .. s:1 J.. .p m 4J .p G) J.. 0 d 0 u.200 174.ak , II '''-12" BeamW== 186., u I. 800 U"\

Q .,... ......... d ...... ... Q -.1400 J.. .p tr.l

t v d 8200 I 150.0k BeamVI u 'ne.51DISTRIBUTIONOFCONCRETESTRAINALONGIDPEIXlEOFBE.AleAt-3- 4.ANDA-3-5 ......o V1 106 NStrain,in. lin . ............r-i o0.0040.008 BeamC-4 O.Ol20.008 OJI............ Strain,in.in. r-I Beamc-6 o.Ol60.012o FIG. DISTRIBUTIONOFSTRAINALONGENTIREDEPTHOFBEAMATMIDSPAl"if: BEAMSc ... 4 ANDc-6 b A s ------+--'. CrosssectionStrains 107 c 0.5 fbkd c T::::Af sy Stresses T (a)BeamsReinforcedin TensionOnly -,..-- ,- AI S -rQ A " s CrosssectionStrains f n C::::Af(fl-EE:') 2$SCS T=Af sy -rd Stresses (b)BeamsReinforcedinTensionandCompression FIG.53STRAINANDSTRESSRELATIONSHIPSATl!"1.EXURA.LYIELDlllG ~ ~.. ro ~b 1 CrosssectionStrainsStresses (a)BeamsReinforcedinTensionOnly b l Al S As CrosssectionStxainsStresses (b)BeamsReinforcedin TensionandCompression T:::Af ss T:::Af ss FIG.;4~ S T R A n ~ ANDSTRESS .RELATIONSHIPS.ATULTIHATEF'l..EALJRALCAPACITY TR-59-72 DISTRIBUTION No ..Cys. HEAD QUAR TERSUSAF 1,Hq USAF(AFCOA),Wash25,DC 1HqUSAF(AFOCE),Wash251 DC 1HqUSAF(AFDRD),Wash25 JDC 1HqUSAF(AFCIN),Wash25,DC 1USAFDepIGforInap(AFCDI-B -3),Nortan:-AFB,Calif MAJOR AIRCOMMANDS 1ARDC(RDR) ,AndrewsAFB,Wash25,DC AFBMD,AFUnitPost Office,LosAngeles45,Calif 1ATTN:Dr.GeorgeYoung 1ATTN:SpaceTechnologyLab 1SAC(DINC),Offutt MB',Nebr 1TAC(TDA),Langley AFB,Va. J1AMC(MCW7),Wright-Patterson AFB JOhio 1ADC(OpsAnlys),Ent AFB,Colorado Springs,Colo 'IAUL,Maxwell AFB,Ala IUSAFA,United States AirFo.rce Academy,Colo ARnCCE!'-lTERS WADD,Wright-Patterson AFB,Ohio 1(Directorof SysMgt,Lt ColJ.Stone) 1(WCOSl} 1(RDSIW) KIRTLAND AFB AFSWC,Kirtland AFB,NMex 1(SWNH) 3(SWRS) 5(SWOI) OTHER AIRF ~ R E AGENCIES 1USAF,Project RAND,,Via AFLiaison Office,(Nuclear Energy Division),TheRANDCorporation,1 700Main Street,SantaMonica,Calif 1/USAF IT ,Wright-Patterson AFB,Ohio 'TR-59-72 DISTRmUTION(Cont'-d) No. {.;ya. ARMYACTIVITIES 1,'Chief of Research and Development,Departmentof the Army,ATTN: Special Wea.ponsand AirDefense'Division,Wash 25,DC 1Director,Ballistic Research Laboratories,ATTN:Library, Aberdeen Proving Ground,Md 1CommandingOfficer,USArmy Engineers,Research and Development Laboratories JFt.Belvoir.Va 1Director,Waterway. Experiment Station,ATTN:,W.J.Turnbull, Box 631,ViCKsburg,Miss 1Chief of 'Eng'ineers,Department of the Army,ATTN:Protective Construction Branch,Wash 25,DC NA VY ACTIVITIES 1Commanding Officer,Naval Research Laboratory,Wash25,pC 1Chief,.Bureau of Yardsand Docks,: ATTN:D-440,Wash 25,DC 1'CanuDapOjngOfficer and Director,Naval ,CivilLaboratory,Port 'Huenem,e"Calif OTHER DOB ACTIVITIES 1Director, SystemsEvalUation Group,Officeof Assistant ,\ Secretary of Defen.se,Room2E1006,The Pentagon,Wash25,DC 3Chief,Defense Atomic Agency,ATTN:"'lS1.a.atand Shock Division,Wash' 25,DC 1Commander,Field Command.Defense AtomicSupport'Agency, ATTN:WET,Sandia Ba.Be,NMex 1ASTlA(TIPDIl),Arlington Hall Sta,Arllneton12,va AEC ACTIVITIES 1US' Atomic Energy Comma/.ion,ATTN:TechnicallleportaLibrary {Mrs.,J.for ,DMA},'Wash25,DC 1'Prea.ident,SandiaCorporation,ATTN:T.B.Cook,Div S111, /SandiaBailie,NMelt 1A iatant Secretary of-Defe1lft,ATTN:H.Facei,W'.ahZS,DC TR-59-72 DISTRIBUTION(Cont'd) No. Cys. OTHER 1AmericanMachine andFoundryCompany,ATTN:T.G.Morrison, 1104 SouthWabash Ave.,Chicago5,III 1MassachusettsInstituteofTechnology,Dept ofCivil and Sanitary Engineering,ATTN:Prof.R.J.Hansen,77MassachusettsAve., Cambridge99,Mass 1 1 1 Universityof Massachusetts,DeptofCivilEngineering JATTN: Prof.Merit P.White,Amherst,Mass Holmesand Narver,Inc.,ATTN:Sherwood B.Smith,824 S.Figueroa St.,LosAngeles14,Calif E.H.PlessetAssociates,Inc.,ATTN:'~ r Peter,Jr.,6399 WilshireBlvd.,LosAngeles48,Calif '--') I ........1 '--