ACI-Strut and Tie

7/29/2019 ACI-Strut and Tie

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~{tJ [:]11:l"-'"",~""-I:;~IC8j1 :l~~1 II=~; ~ ~~I ~~-;r=;lTitle no. 99-846Evaluation of Strut-and- Tie Modeling Applied to DappedBeam with Openingby Brian S. Chen, Michael J. Hagenberger, and John E. BreenStrut-and-tie modeling is a valuable tool for designing irregularconcrete members. The ACI 318-02 Building Code contains pro- f ; 381visions pertaining to design using strut-and-tie models. This paperpresents the experimental results oftests conducted on small-scale, 229-simply-supported dapped beams with openings. The design of each '"'" 127 mmtest specimen was developed by independent student teams usingthe ACI provisions for strut-and-tie models. Each of the tour spec- ~imens resisted loads greater than the factored design load and 3 in, x 3 in, Elastommc

h .b ' d l . 1 d ' . 1 d 1 1 TI. ,l:' l BearingPad(TypicaJ) 127mm 26,7tNex I Ite 1ft e Istress at servlce oa eve s. ,ne successJ" test Jseries illustrotes the applicability and conservative nature of strut-modeling for designo 305 mm 305 mm 76 mm

, NOte: Specimen tbickness equaIs 89 mm,Keywords: beam; p1asticity; structural concrete; strut.

Fig. l-Test specimen geometry.INTRODUCTION

In fue past, engineers had little guidance when it carne to .. . . ..designing nonstandard and unusual structural concrete mem- venficatlo~ o~ fue a~phcatlon of strut:and-tle modehng andbers. The development of strut-and-tie modeling has provided show that lt lS posslble to use very different models on fueengineers with a conservative and rational design approach. sarne structure.In theory, plasticity-based strut-and-tie modeling produces gafe,~ower-bou?d d.esigns. .A~ a result, the.method lends itsel~wellto RESEARCH SIGNIFICANCEmcorporatIon mto building and deslgn codeso AppendIX A of Strut-and-tie modeling is a valuable tool for designingthe ACI 318-02 Building Code contains provisions pertaining complex and unusual structural concrete members. Whileto fue use of strut-and-tie models. While there has been a signif - there has been a significant arnount of literature on fue theoryicant arnount of literature on fue theory behind strut-and-tie behind strut-and-tie modeling, there has been relatively littlemodeling (Schlai~h,. Sch"fer, and Jennewein 1987;. Mutt?ni, experimental verification of its application. In addition, fueSchw.artz' and ~ur~ann 1 ~97), th.ere ~as been relatIvely little ACI 318-02 Building Code contains provisions pertaining toexperImental venficatIon of lts applicatIon. strut-and-tie models. This paper presents the experimental

This study presents fue experimental results from a series results of test specimens designed using fue newly adoptedo~four.test pecimenswith he.sameverall.geometry,nd strut-and-tierovisions. he successfulestseries rovidesWlth remforcement deslgned usmg strut-and-tIe models, The important experimental verification of fue application ofspecimens tested in fue experimental program were scale strut-and-tie modeling.models of a dapped bearn with a large opening. The overallpurpose ofthis test se?es was twofold. One object~ve was:o EXPERIMENTAL PROGRAMdemonstrate that vanous gafe and workable deslgns exlst .using different strut-and-tie models to solve fue sarne problem. Test specl~ens .The other objective was to determine whether fue new Appen- The expenme~tal test prograrn c?nsl~ted of four red~ced-dix A provisions could be applied by practitioners with rela- scale beam speclmens. .As shown m Flg. 1, e~ch speclmentively little experience in the use of strut-and-tie modeling. measured 762. mm (~O m.) long, 254 mm (~O ~n.) deep,. ~dThe presence of a re-entrant comer at midspan and an open- ~9 mm (3.5 ~n.) thlCk. The t.wo geometrlc lrregularl~lesing creates large discontinuity regions where fue plane-sec- mcorporated mto fue test speclmens were a 127 mm (5 m.)tions beam theory does not apply. Strut-and-tie models are dap at midspan and a 51 mm (2 in.) square opening locateda conservative and intuitive design methodology for solving between fue load point and fue left support.these types of problems. Three groups of graduate students, The beams were designed to resist a concentrated factoredworking independently and in competition (based on the load of 53 kN (12 kips). The corresponding service load wasratio of capacity to weight of steel reinforcement), designed deterrnined to be 34 kN (7.7 kips) by assuming a load factorSpecimens 1 through 3 and tested them to destruction. In addi- of 1.55 that corresponds to equallive and dead loado A valuetion, the senior authors designed and tested Specimen 4. All ofthe designs used fue provisions for strut-and-tie models pro- ACI Structural Joumal, v, 99, No, 4, July-August 2002,Posed for ado p t ion in the ACI 318-02 Bui ld in g Code that ,MS N?',OI-286 re,ceived September 5" 2001, and review~d under In~titute publica-

tion pollcles, Copynght @ 2002, Amencan Concrete lnstitute, All nghts reserved.were appended to an introductory article by fue Chair of including !he making of copies unless pennission is obtained from !he copyright pro-ACI 318 (C 1 200 1 ) Th t t ' d . t 1 prietors, Pertinent discussion will be published in !he May-June 2003 ACI StlUCtural

ag ey . e es s proVl e expenmen a Journal ifreceived by January 1.2003,ACI 8tructural Journal/July-August 2002 445


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ACI memberBrlan S. Chen is a doctoral candidate at the Unillersity of TexasatAustin,Austin, Tex.He receilled is BS rom Puroue Unillersity,West afayette,nd., in1997,and his MS rom the Unillersity ofTexasat Austin n 1999.ACI memberMichael J. Hagenberger is a doctoral candidate at the Unillersity ofTexas t Austin. He receilledhis BS rom Bucknell Unillersity,wisburg, Pa., n 1992,and his MEfrom Comell Unillersity, thaca, N.J:, in 1993.ACI Honorary Member John E. Breen holds the Nasser . AI-Rashid Chair in CillilEngineeringat the Unillersity ofTexas at Austin. He is a memberof ACI Committees318, Structural ConcreteBuilding Code; and 355, Ancharage o Concrete.

b) Sub-mod.12

b) ModeIZ(ZO%) eCompres,ion -Ten,ion1on;e"hownarekN 26.7 c) Sub-model

~ ".'""c;,;,..~"'~'"t ";J;':~"f'; '-

26.7d)Cnmbinedmodel "'. 4 S nd . d 1 .hfi fi S ' 3lg. - trut-a -tle mo e Wlt arces ar peClmen . Fig. 2-Strut-and-tie models with forr:es or Specimens1 and 4. using the strut-and-tie provisions in Appendix A of ACI Table 1-Relnforclng steel propertles 318-02. Although each group used fue sarne design process, Barsize Area,mm2 in.1 Yieldstrength, Pa ksi) Capacity,N (kips) the. fin~ st:rut-and-tie models and reinforcement layouts 6 mmcII 28.4 0.044) 620 90) 17.6 3.96) vaned sIgmfican,tly. . . 4 125 0019 630 92 As a first step m fue deslgn process, each group mdepen- fmm cII . (. ) ( ) 7.78 (1.75) dently performed a two-dimensional finite-element analysis' 10gage 9.7 0.015) 610 89) 5.94 1.34) (FEA) to establish ue elastic stress ields in fue structure I. . This processs suggestedy Schlaich,Schiifer,andJenneweinIof =1 wasassumedor fue esIstanceactor smce ue actual (1987) and Bergmeisteret al. (1993) as a useful irst step o l

1 . b . d fmaten a properties were o lame . promote visualization of fue force paths in unfamiliar appli- 1 Pea-gravel oncreteand small steel einforcing bars were cations.For this particular problem, ue FEA was probably l used o construct ue test specimens. he concretemixture not essentialand only confmned ue initial ideas about ue was a prebagged ement and aggregatemixture combined force distribution. From fue flow of forces llustrated n fue .th d h. h d . d . th . . Wl water an a Ig -rangewater-re ucmg a Ill1xture at FEA, a strut-and-tiemodel was chosenand oadedWlth ueyielded an averagestrength of 31.7 MPa (4600 psi). The applied forces. Strut-and-tie orces were computed using concretestrength asdeterminedrom 76 x 152mm (3 x 6 in.) simple truss analysis echniques, nd ue nodal zoneswere testcylinders hat werecastand estedat fue sarne ime as ue checked.Reinforcement attemswere hendeveloped sing beamspecimens. he steel einforcingusedconsisted f 4 and fue tie forces provided by fue analysisand ue geometryof 6 mm-diameter eformed arsand 10 gagesmoothwire. The fue strut-and-tiemodels. Graduatestudentsperformed ue properties f fue einforcingsteelaresummarizedn Table . detailedcalculationsusing AppendixA of ACI 318-02with no direct supervision rom a strut-and-tiemodel experto Deslgn process Specimens1, 2, and 3 were designed ndependently by Strut-and-tle models three groups of graduatestudents.Specimen4 was a slight The strut-and-tie models developed for the tour test variation of Specimen 1. Each specimen was designed specimens re shown n Fig. 2 through4. Each design eam 446 ACI Structural Journal/July-August 2002.: i


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4mm 4mm 10p,wi~:

lid I-.ok Iten".)Speelmen1 b)Speebaon2

2.10 ,M'" 4mm cilj2-6..."'kod.. _n2-6mm"'kod.. _n1 6 mm (bnok S shown)1-4mm(omithook)2-4mm8shown bookod.. shown SId. bnokltendlt) SpeelnIeD d) Speeboen

Fig. 5-Reinforcement layouts.employed different approaches for developing its final strut-and-tie modelo These approaches included breaking oneoyerall strut-and-tie model into several submodels, super-imposing wo overlapping strut-and-tie models, and using asinglemodel for fue entire structure. While some strut-and-demodelsmay be more efficient than others, it is importantlO ote hat there is no uniquely correct modelo Each of fueresulting trut-and-tie models represents a unique lower-bound r conservative estimate of fue true capacity of fuebeam. hese estimates, however, assume that failures suchas tability or local crushing are precluded.

Thestrut-and-tie model for Specimens 1 and 4 was developed. o. o, three b od 1 h . F. 2 Th b d 1 Flg. 6-F orm and remforcmg cage or Speclmen .usmg su m e s, ass own m 19.. e su mo e s con-sistedf a simple truss for fue right half of the beam and twooverlappingrusses for the left half. The submodel shown The strut-and-tie model for Specimen 3, shown in Fig. 4,inFigo (a) was developed o resist he shearcreatedby fue consistedof a single russ model for fue entire beam.Largeappliedoad, and consisted of compression struts above and compression struts carried fue flow of forces around fuerelowueopening.Thesestrutswere ied togetherat various opening or fue left half of fue beam,while a more widelysing tension tiesoThe submodel shown n Fig. 2(b) spaced truss was used for fue right half.waseveloped o resist fue moment or couple created by fuecompressiontrut and tension tie from fue right half of the Reinforcement layout and designt should be noted that, during the design process, The reinforcement layouts for each specimen are shown inIhe esign team discovered that one of the compressive ~ig. 5, and were selected using ~e tie for~es in ~e strut-~d-ut through fue edge of fue opening. The design team ~lemodels. In ~eneral, fue 10c~tIonand onentation ~f fue tIeshis mistake, but was unable to correct fue error m fue model dlctated where remforce~ent was re~ulred. ~et~ dueo fue time constraints associated with fue class project. number of .b3!~ needed was determIned .by taking fue tIeTheubmodelor fue right half of fue beam, shown n Fig. 2(c), force and divldmg by fue ~r?duct of fue Yleld str~ss and barf struts and ties oriented in a more familiar truss area. Because the competItIon was based on ultImate loadfue configuration.he three submodels were superimposed to performance, typical service. load detail~, such as barscrealeh ti al trut d ti. od 1ti S . 1 d 4 around fue comers of fue opemng, were offiltted.e m s -an - e m e or peclmens an . o .fue . . . . The reInforcement layouts for Speclmens 1 and 4 wereTh,etrut-and-tIe model ~or Speclmen 2, shown.In Flg. 3, designed to maximize constructability. This was accomplishedwere conslst~df two overlappl~g models of the .entIre beam. by arranging the reinforcement in an orthogonal grid andThedeslgne~ e~ectedo asSlgn80% ~f.the applied oad to ~ne providing standardbar configurations as shown n Fig. 5(a) andof nKxlel,hownm Flg. 3(a), and fue ~m~g 20% afilie applied (d). To accomplish this, fue tension ties oriented diagonal-loadlo second model, shown In Flg. 3(b). The reason for ly in the model were resolved into horizontal and verticalassigninga majority of fue load to one model was to reduce ue components.The reinforcement was sized basedon fueseverti-bove fue opening. This is evidencedby fue large cal and horizontal force componentsand hen evenly distributed11N ompressionstrut extending from fue load point to fue in fue location of fue tension ties in fue modeloThe reinforce-uearelowue opening in Fig. 3(a). Similar to Specimen 1, fue mentlayoutforSpecimen4 was similartothatofSpecimen 1-test liooyerlapping odels were superimposed to establish the fue only significant change was fue addition of confining re-team finallrut-and-tie model for the specimen. inforcement above fue opening and below fue load point.

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1: clc" ll'L--, >;;..., ",.,' ,!i;: : "a'1;~:f':;:i3"{~~;.':: luitialcrw:k0,4

2 s) Specimen2 st servlce osdO 1 2 3 4 ',j.'.'.~.;'.").:'..'i'.'.;~:;',~ ;.

Speclmen Number ,':.,,:..,.,,;,~ ' . ., . Fig. 7-Testspecimenfai1ure 10ads. ".,;f!;;";'i ',,:"::':~;':;,:~:'

':""";':,.: ".;:;:~::;;'~.:;":.:';:.;:~':~,;:;;;~;::: ':, ; ,..~ ,:'..;;;l.;;~'.'..::::...,.~~,;;:.::,:~::,;~.; : : : : : : . -.., ~ :: : : 1, 1 : ""', b)Specimen2stfailure

,.. Fig. 9-Concrete crackingpattemsat service10ad ndfai1ure, for Specimen .

a) Spedmen 1 at servlce oad.. ",., ,'." ,; l .l"."". .'J.. ,., ,-o;: : 'l j " : , ~';'-':

, .,., ,j.,...,. ""';"';' i."'",,-.. ," ' '.'.-:, , .',, , "., , '". - . , . ~. , . . . . . . . . , -:. .. , . . , . .. . ~, . . -: .'

) Specimen at fanureFig. 8-Concrete crackingpatternsat service10ad ndfailurefor Specimen.

The reinforcement ayouts or Specimens and 3, shownin Fig. 5(b) and (c), were designed o coincide with the ori-entationof fue tension ies n fue strut-and-tiemodels.Whilethis resulted n a more accurate epresentation f fue strut- b)SpedmeDst aBoreand-tie models, t complicated ue constructionprocessand. . .would probably add extra costoWhere multiple bars were FI.c' 10-Concr.ete crackIng pattems at servlce 10adand trequired for a single tension tie, fue bars were groupedas faure for Speclmen .close to the tie location as possible. Examples of thisgrouping can be seen n fue four diagonal ies ust to fue eft Test results and discussion !of the opening in Fig. 5(b) and the two groups of three Each of the four test specimens arried more than fue lvertical stirrups on fue right half of fue beam n Fig. 5(c). factored design load of 53 kN (12 kips). The maximum IIn addition to fue tension ties, confining reinforcement load carried s listed n Table 2, and ue ratio of ultimate estwas incorporated in afeas of high compressive stress. load Pu/t' to the factoreddesign oad Pdess summarizednHigher compressive tresses an be handledwhen confining Fig. 7. At serviceoad,eachof fuespecimensadonly a single ireinforcements provided Roberts 990,Breenel. al. 1994,HP visiblecrackoriginating rom ue e-entrant omerat midspan.Commission 1999).This enablesdesigners o accommo- Thesecrackswerequickly arrested y fue reinforcementanddate nodal zoneswhere potentialIyhigh compressivetresses werenot a factor n fue ailure mechanisms f any specimen.maybe encountered. onfining ies wereused n Specimens The failure mode and final cracking pattems, illustratedthrough 4 under ue oad point, above he opening, or both, in Fig. 8 through 11, varied among the four specimens.as shown n Fig. 5. A picture of the reinforcementcage or The oad-deflection esponses,hown n Fig. 12, ndicated a ,Specimen1 is shown n Fig. 6. generally linear responseup to the factored design oadot448 ACI Structural Journal/July-August 2002 ...


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shouldbe noted that fue serviceability imit of span/180 s failuremechanism. ailureof fuespecimen ccurred t 58.3kNshown nIy for reference, s ue specimens erenot designed (13.1 kips) and s pictured n Fig. 13(a).for fue serviceability imit state. Specimen failed as a result of instability. The nstabilitySpecimen1 exhibited a shear ailure mode.At service oad was initiated when the concreteon one edge of fue beamlevels, he onIy visible crack originated from the re-entrant under fue load point spalled ust above he factoreddesigncomer at midspan and extended ust past fue longitudinal loadoSubsequentoadingcausedue bearingplate o rotate oreinforcingbar as shown n Fig. 8(a). Subsequentoadingup the side and the beam to rotate out of plane as shown nto fue factoreddesign oad developed ue inclined cracks n Fig. 13(b). The test was terminated at a load of 66.5 kNfue ight side of fue beamas well as he comer cracksat fue (15.0 kips) before fue load point slippedoff fue specimenopening.At loads greater han fue design oad, a diagonal Extensionof the confinement einforcementunder ue loadcrack ormed from fue oad point andextended cross ue op point might haveprevented ue total spallingof fue concreteof fue opening as shown n Fig. 8(b). This openingcreatedsubstantialeparation n the beam and ultimately was the Table 2- Test results

Concrete Cage Maximum. . . .. . . ,::: : : : : :.: .;:::',,;'- strength,MPaeightWc,estloadPu/": : .~.';'.:."'.':.'::.: : : ; ~ ~ Specimenno. (psi) kg(lb) kN(kips) PuJtlWcPuJtlPde."'. .. ".. -"'.. ..."-..;; . .:. I 31.8 (4610) 2.14 (4.72) 58.3 (13.1) 2.78 1.092 33.8 (4900) 2.63 (5.80) 66.5 (15.0) 2.58 1.253 31.8 (4610) 2.21 (4.88) 68.3 (15.4) 3.15 1.284 30.6 (4440) 2.50 (5.52) 65.804.8) 2.68 1.23

f;; 'oa) Speclmen4 at service oad ",.~,

60,?~ 5i -Specimen*l

~30~-Specimen#3i5 : .~. Specimen 4

Note;DialSagesmoved rior o ~.b) Specimen4 at failure 4 6 8 JO

'. DeOection (mm)Fig. 11-Concrete crackmg patterns at servlce load andfailure for Specimen . Fig. 12-Load-dejlection responses.

a)Speclmen b)Speclmen2

) Speclmen3 d) Speclmen4Fig. 13-Test specimens atfailure.

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and ue subsequenttabilityproblemo espite ueseproblems, shownby fue strongvariation among ue modelsdeveloped ti,the specimenperformed well and exceeded he factored by fue variousdesigngroupso ll strut-and-tieest specimens ;:design oad by 25%0 he crackingpattemat service oad and carried oadsgreater han he factoreddesign oad specified, c'failure are shown n Figo90 proving fue underlying ower-boundnature of strut-and-tieSpecimen3 ultimately failed in shear. At fue factored modelingo he use of orthogonal einforcementpattems odesign load, a crack was present that extended rom the simplify fabrication was both a valid and useful technique.bottom eft comerof fue openingdown to fue bottom aceof Finally, specimensdesignedusing fue ACI 318-02 Codefue beamas shown n Fig. 10(b)0Subsequent racks devel- strut-and-tiemodelprovisionsforthisloadandreactionconfig-opedabove ue opening,but werecontained y fue reinforce- urationweresafeand elativelysimplememberso constructoment presento t 6507 N (14.8 kips), fue concreteunder ueload point spalled Figo13(c.The presence f confining ein- ACKNOWLEDGMENTSforcement llowed or redistribution nd urther oad-can)'ing Theauthors ouldike o thank ll of the ndividual embersf thecapacityo Additional vertical cracks extended from the designeamsor theircontributions.hosendividualsnclude abriela

o d o. Arce. Francisco Brenes, David Figurski, Taichiro Okazaki, Pedro Quiroga,re-entra.nt corner at mi span to the lo~d pomto Fal1ure of Ruben Salas, and Jorge Varela. We would also like to thank Blake Stassney,fue speclmen occurred at 6803 kN (15.4 kips) when fue dowel Mike Bell, Patrick Wagener, and Jennifer Tanner for their assistance duringaction of the longitudinal bars at fue top and bottom of fue fue construction and testing of the specimens.beam was overcomeoSpecimen 4 behaved similarly to Specimen 1 up to the REFERENCESdesign load, but exhibited a flexural mode of failureo Just " Ber.g~eister, K.; Breen, J. E.; ~~a, J. o.; and Kreger, M. E., 1993,above fue design load a crack developed from fue load point Detalllng ~or Structural C~ncre~, Research Rep~rt 112~-3F, Center for, o o . Transportatlon esearch, mversltyof Texas t Austln, Austln, Tex.,300ppoandextendedpastthetopoftheopemngasshownmFlg011(b)0 Breen, JoE.; Burdet, o.; Roberts,c.; Sanders,Do; and Wol1mann,G.,The shear failure mode seen in Specimen 1 did not occur in 1994, "Anchorage Zone Reinforcement for Post-TensionedConcreteSpecimen 4 because of fue additional reinforcement present Girders," NCHRPReport356, Transportation esearch oard,Washington,above the opening. At 6207 kN (1401 kips), the concrete D.C., 1994,pp.33-34. .o o o Cagley, J. R., 2001, "Changmg from ACI 318-99 lo ACI 318-02, What'sunder theoload poomt spalledo As m Speclmen~, ~e p!esence New?" Concrete lnternational, V. 23, No. 6, June, pp. 69-182.of confimng remforcement allowed for redlstrlbution and AP Cornmission 3, 1999, FIP Recommendations 1996, Practical Design o/further loadingo Specimen 4 failed in flexure due to crushing Structural Concrete, AP Congress Amsterdam 1996, Fdration Internationaleof fue concrete below fue load point at 6508 kN (14.8 kips) as de la Prc~ntrainte, Lausanne, Switzerl.:m?o .shown in Fig 13(d) Muttom, A.; Schwartz, J.; and Thurllmann, B., 1997, Deslgn o/Con-

o o creteStructureswith Stress ields,BirkhuserVerlag,Switzerland, 47pp.Roberts, Co L., 1990, "Behavior and Design of Local AnchorageCONCLUSIONS Zone in Post-Tensioned Concrete," MS thesis, University of Texas atU sing strut-and-tie models based on plasticity theory, Austin, .Tex., .280 pp. o . , .different designers can, and probably will, develop differing S~hlalch, J., Schafer, K., and Je,?newem,M., 1987, ~oward a Conslstento " " th d o Th o 1 1 Deslgn of Structural Concrete, PCI Journal, Speclal Report, V. 32,relfuOrCement pattems lar e same eslgno IS was c ear y No. 3, pp. 74-1500

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ACI-Strut and Tie