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Current code provisions for slabcolumn connections, such as,for example, ACI 318-11 , JSCE , and the b Model Code2010 [13,14], have been developed for normal concrete structuresand their application to FRC slabcolumn connections is notalways straightforward, particularly for empirical design formulae.To this end, several specic models for punching shear of FRC
takes into account the bre pull-out strength to estimate the contri-bution of the bres and considers the perimeter of the critical sec-tion depending on the quantity of bres and their properties.
2.Punchingshear strengthbasedon thecritical shear crack theory
2.1. Critical shear crack theory
The ultimate punching shear strength and deformation capacityof reinforced concrete slabs can be estimated using the mechanical
Corresponding author.E-mail addresses: email@example.com (L.F. Maya), miguel.fernandezruiz@
ep.ch (M. Fernndez Ruiz), firstname.lastname@example.org (A. Muttoni), s.foster@unsw.
Engineering Structures 40 (2012) 8394
Contents lists available at
lsevier .com/ locate /engstructedu.au (S.J. Foster).4]. A number of alternatives are available for increasing the punch-ing shear capacity, such as the use of closed stirrups, bent-up bars,shear studs or post-installed shear reinforcement. More recently,the use of bre reinforced concrete (FRC) for increasing the punch-ing shear capacity has been studied (e.g. ). These studies haveconrmed an increase in the punching shear strength of FRC slabsas well as an increase in their deformational capacity and thisenhancement is mostly due to the bridging action of the bres afterthe cracking of the concrete matrix (shown in Fig. 1).
posed considers the assumption that yielding of tensile reinforce-ment occurs prior to punching shear failures, which is valid forthin slabs with large span to thickness ratios. The contributions ofcompressive and tensile zones at the critical sectionwere taken intoaccount and the punching shear capacity of both zones was as-sumed to be controlled by tensile cracking, rather than compressivecrushing. More recently, Higashiyama et al.  proposed a designequation based on the JSCE model for assessing the punching shearcapacity of normal concrete slabcolumn connections. The equation1. Introduction
Given their construction and arforced concrete at slabs are commoce buildings, residential buildingssoftmakes the formwork and reinfoallowing for easy placement and install storey heights. The ultimate strengslab is usually governed by the punchcolumn connections. This failure molead to progressive collapses and lo0141-0296/$ - see front matter Crown Copyright 2doi:10.1016/j.engstruct.2012.02.009ural advantages, rein-d in medium height of-rking stations. The att substantially simpler,and offers lower over-reinforced concrete atear capacity at its slabypically brittle and canhe entire structure [1
slabcolumn connections have been proposed over the last decades.Narayanan and Darwish  provided a design equation for thepunching shear capacity of SFRC slab considering the strength ofthe compressive zone above the top of the inclined cracks, thepull-out shear forces on the bres along the inclined cracks andthe shear forces carried by dowel and membrane actions. Harajliet al.  proposed an empirical design equation for the punchingshear capacity of SFRC slabcolumn connections based on a bestt linear regression of the coupled contribution of concrete andbres. Choi et al.  performed a theoretical study to propose adesign equation based on a FRC failure criteria. The formula pro-Design models Crown Copyright 2012 Published by Elsevier Ltd. All rights reserved.Punching shear strength of steel bre rei
L.F. Maya a,, M. Fernndez Ruiz a, A. Muttoni a, S.J. Fa Ecole Polytechnique Fdrale de Lausanne, Station 18, CH-1015 Lausanne, Switzerlandb School of Civil and Environmental Engineering, The University of New South Wales (U
a r t i c l e i n f o
Article history:Received 3 November 2011Revised 24 January 2012Accepted 5 February 2012Available online 28 March 2012
Keywords:PunchingFibre reinforced concreteCritical shear crack theoryVariable Engagement Model
a b s t r a c t
The ultimate strength of rewhich may be increased wshear heads. In addition toforcement has proved to bimproves not only the sheThis paper presents a mecslabs reinforced with steelagainst a wide number of adesign equation for theproposed.
journal homepage: www.e012 Published by Elsevier Ltd. All rorced concrete slabs
), 2052 Sydney, Australia
rced concrete slabs is frequently governed by the punching shear capacity,addition of traditional tments such as reinforcing steel, headed studs orse traditional methods of strengthening against punching, steel bre rein-n effective and viable alternative. The addition of bres into the concreteehaviour but also the deformation capacity of reinforced concrete slabs.cal model for predicting the punching strength and behaviour of concretees as well as conventional reinforcement. The proposed model is validatedlable experimental data and its accuracy is veried. On this basis, a simpleching shear capacity of steel bre reinforced concrete (SFRC) slabs isSciVerse ScienceDirect
84 L.F. Maya et al. / Engineering Stmodel of the critical shear crack theory (CSCT), as has been pre-sented by Muttoni  for slabs without transverse reinforcementand Fernndez Ruiz and Muttoni  for slabs with transversereinforcement. According to the CSCT, the opening of a criticalshear crack reduces the strength of the inclined concrete compres-sive strut carrying shear and eventually leads to the punchingshear failure. Thus, as the opening of the critical shear crack in-creases with slab rotations, the punching shear strength decreases.According to Muttoni and Schwartz , the width of the criticalshear crack (w) can be assumed to be proportional to the slab rota-tion (w) multiplied by the effective depth of the member (d); thatis, w / wd as illustrated in Fig. 2.
A failure criterion for the punching shear strength of reinforcedconcrete slabs without transverse reinforcement was proposed byMuttoni  as
p 3=41 15 wddg0dg
where w is the maximal rotation of the slab; d is the effective depthof the slab; b0 is the control perimeter at a distance of d/2 from the
Fig. 1. Post-cracking behaviour of bre-reinforced concrete. Matrix and brecontributions.face of the column; fc is the compressive strength of concrete; dg isthe aggregate size, and dg0 is a reference aggregate size set to16 mm. The failure criterion of Eq. (1) takes into account the inu-ence of the concrete strength and the crack roughness by consider-ing the maximum aggregate size dg.
To determine the ultimate punching shear strength and thedeformational capacity, the loadrotation relationship of the slab
Fig. 2. Critical shear crack developing through the theoretical compression strut.must be known. As shown in Fig. 3, the intersection between theestimated loadrotation relationship and the failure criterion de-ned by Eq. (1) corresponds to the predicted ultimate failure loadand rotation. For complex cases, this relationship can be obtainedby carrying out a non-linear numerical simulation of the exuralbehaviour of the slab, for instance using non-linear nite-elementanalysis (NLFEA). The loadrotation for axisymmetric cases can alsobe obtained analytically after some simplications considering aquadrilinear or bilinear momentcurvature relationship for thereinforced concrete cross-section . This approach allows takinginto account the contribution of the bres to the exural strength ina simplemanner. To that aim, an effective tensile strength of the FRCat the cross-section can be adopted to calculate the quadrilinearmomentcurvature relationship, as illustrated in Fig. 4.
The expressions for the quadrilinear moment curvature rela-tionship presented in Fig. 4a can be calculated assuming the mate-rial behaviours for the concrete and for the steel presented inFig. 4c and e. Prior to yielding of the exural reinforcement, the ac-tual stress distribution over the cross section in Fig. 4b is idealizedthrough a linear stressstrain relationship for the concrete in thecompressive zone and an average strength is assumed for theFRC in the tensile zone, Fig. 4c. To calculate the ultimate exuralcapacity, the actual stress distribution in Fig. 4c is idealized assum-
Fig. 3. Assessment of punching shear strength and deformation capacity accordingto the CSCT.
ructures 40 (2012) 8394ing an equivalent rectangular compressive stress block and anaverage tensile strength of FRC, Fig. 4e. Following a similar proce-dure as that described in Muttoni  and included in Appendix C,the following expressions are obtained:
EI1 qbEsd3 1 cd
c qb EsEc
mR qd2fy 1 b1qfy fct2;f h=d2accfc fct2;f
1 qfyd=h fct2;faccfc fct2;f
1 qfyd=h fct2;faccfc fct2;f 1 b1