Lower bound equilibrium element and submodel for shear joints in precast concrete structures

This paper is concerned with the shear capacity of keyed joints reinforced with overlapping U-bar loops in the transverse direction. The layout of the loop reinforcement affects the capacity and failure mode, and currently it is not accounted for by standards or previous theoretical work. A multiscale approach to the issue is proposed: An equilibrium element for finite element limit analysis representing keyed joints is coupled with a suitable submodel, which handles the complex stress states within the joint. The submodel is based on several modified stringer models, which makes it possible to account for local mechanisms in the core of the joint. The element and submodel are validated by comparison to a detailed model based on finite element limit analysis and experimental data. The joint element and submodel lead to a small optimisation problem compared to the detailed model and the computational time is reduced by several magnitudes.