1.054/1.541 Mechanics and Design of Concrete Structures (3-0-9) Outline 7 Shear Failures, Shear Transfer, and Shear Design

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1 1.054/1.541 echanic an Deign of Concrete Strctre Spring 2004 Prof. Oral Bykoztrk aachett Intitte of Technology Otline /1.541 echanic an Deign of Concrete Strctre (3-0-9) Otline 7 Shear Failre, Shear Tranfer, an Shear Deign Strctral behavior o Strctral member are bjecte to hear force, generally, in combination with flexre, axial force, an ometime with torion. o Shear failre are brittle failre primarily becae hear reitance in R/C relie on tenile a well a the compreive trength of concrete. Althogh cracking introce complication it i till convenient to e claical concept in analyzing concrete beam ner hear failre. Sch concept inicate that hear failre i relate to iagonal tenile behavior in concrete. R/C beam mt be afe againt prematre failre e to iagonal tenion. Failre moe e to hear in beam o Diagonal tenion failre en o Shear-compreion failre graal o Shear-bon failre In general, the eign for hear i bae on conieration of iagonal (incline) tenion failre. Failre of R/C by incline cracking o Incline cracking loa + + c cc ci where hear tranferre throgh the ncracke portion of the cc concrete, 1 / 8

2 1.054/1.541 echanic an Deign of Concrete Strctre Spring 2004 vertical component of the aggregate interlocking force in ci the cracke portion of the concrete, an hear force carrie throgh the owel action of the longitinal teel. o Shear trength of the beam withot tranvere reinforcement i bae on the interactive effect of hear tre v K1 an flexral tre b leaing to epenence on the ratio of v K. f fx K2 b 2 Bai of eign o Total ltimate hear force φ n where φ the trength rection factor for hear, an n nominal hear trength. o ominal hear trength n c + where incline cracking loa of concrete, c hear carrie by tranvere reinforcement. o Shear trength expreion of concrete given by ACI: ' ρw ' c 1.9 fc bw 3.5 fcbw where ' f c compreive trength of the concrete, in pi, A ρ w longitinal tenile teel ratio, b w b w the effective with of the beam, in inche 2 / 8

3 1.054/1.541 echanic an Deign of Concrete Strctre Spring 2004 total bening moment of the beam, 1, in lb-in, the effective epth of the beam, in inche, an pacing of tirrp, in inche. An alternative impler eqation i c 2 f b w ' c o The reqire hear trength to be provie by the teel (vertical web reinforcement): ( φ ) v y c c φ φ A f where f y yiel trength of the teel an pacing of tirrp. When tirrp with inclination θ are e, the contribtion of teel to hear trength become: Af ( inθ coθ ) v y + Contribtion of axial force inimm web reinforcement Shear tranfer o Shear in concrete can cae incline cracking acro a member. It i alo poible that hear tree may cae a liing type of failre along a well-efine plane. Becae of previo loa hitory, external tenion, hrinkage, etc., a crack may have forme along ch a plane even before hear i applie. Upon application of hear force we have the problem of qantifying hear tre tranferre acro the cracke ection. o General hear tranfer mechanim are 1. Throgh till ncracke concrete 3 / 8

4 1.054/1.541 echanic an Deign of Concrete Strctre Spring Direct thrt 3. Dowel action 4. Aggregate interlock Reinforcement provie clamping action. 1. Tranfer of hear throgh intact concrete ch a the compreion region in a beam 2. Direct thrt o oel of hear tranfer: 1. Arch analogy: Beam example 2. Tr analogy (trt-an-tie action): Corbel example Failre mechanim of corbel: Flexral-tenion failre Diagonal plitting failre Diagonal crack an hear force failre Splitting along flexral reinforcement failre Local cracking at pport Local plitting e to cracking 3. Dowel action o Three mechanim of owel action: α l α Flexral 2 l hear Af y 2 Kinking A f coα y 4 / 8

5 1.054/1.541 echanic an Deign of Concrete Strctre Spring 2004 Shear tranfer throgh owel action i approximately 25~30% of the hear reite by the interface hear mechanim. ote that the hear yiel tre may be etermine from von ie yiel fnction: τ y A f 3 y 4. Interface hear tranfer: Aggregate interlock + Dowel action o Simple friction behavior Block B a rebar Block A a a-a crack plane (pre-cracke) o Ame that the movement of Block A i retraint. Upon application of Block B move ownwar an ten to go to rightopening of crack. Crack plane i in compreion. Dowel i in tenion. o Shear force e to imple friction an owel µ A f f y where µ friction coefficient. 5 / 8

6 1.054/1.541 echanic an Deign of Concrete Strctre Spring 2004 o Total hear capacity Af y 1 + f + µ A fy A fy + µ 3 3 A reqire area of the teel 1 f y + µ 3 o oeling of aggregate interlock an hear mol of cracke concrete in R/C element hear iplacement w crack with Crack rface Sfficient hear iplacement hol take place before interlock occr. Crack with will increae with increae hear iplacement. A fnamental theory wa evelope at.i.t. At contact point: Frictional reitance e to general roghne of a crack in concrete, Aitional frictional reitance e to local roghne. (alo involve cyclic hear effect) 6 / 8

7 1.054/1.541 echanic an Deign of Concrete Strctre Spring 2004 hear tre pi w in (o tranvere reinforcement w controlle throgh clamping force) w in w in 500 hear iplacement in Calclation of the eflection e to hear-lip Eqilibrim + Compatibility + Deformation α 1 δ w + β K + + K 0 1 KD K β where δ hear-lip eflection, D α a coefficient repreenting gap proce between aperitie, w 0 initial crack iplacement, K, coefficient relating to owel an normal D K tiffnee, β a coefficient repreenting frictional effect at contact point, an applie hear loa. α increae with the nmber of loaing cycle. β ecreae with the nmber of loaing cycle. 7 / 8

8 1.054/1.541 echanic an Deign of Concrete Strctre Spring 2004 Overall cracke panel hear mol Gcr + h j H w 0 + o Overall effective hear mol i calclate by G cr K G e h + KD βˆ where h 1 itance between two crack, ˆ β a coefficient obtaine from regreion analyi, an G e elatic hear mol. Example of trctral application where inclion of hear tranfer mechanim i important to rece the reqire tranvere reinforcement for contrctability an efficiency o clear containment trctre (R/C, P/C, hybri ytem) o Offhore concrete gravity trctre o Shear wall Deign Example Failre invetigation of a pretree concrete brige girer 8 / 8