Limit Analysis for Punching Shear Design of Compact Slabs and Footings

In this paper, the kinematical theorem of limit analysis is used to obtain the governing failure mechanisms and the corresponding failure load of reinforced concrete footings without transverse reinforcement. To that purpose, a Mohr-Coulomb yield criterion is used for the concrete together with uniaxial rigid-plastic behaviour for the reinforcing bars. Two different mechanisms allowing failures with both rotational and translational movements are used. The results show that various failure modes can develop, associated to clockwise or counter-clockwise rotations combined with translational movements. It is also shown that a flexural-shear regime, representing a transition between pure flexural and punching shear failures may be governing, with a lower load carrying capacity than a pure flexural failure mechanism. Finally, it is shown that the failure mechanism governing in the punching shear regime might be dependent on the amount of top compression reinforcement. A fairly good agreement is found between theoretical and experimental results.