Dip and strike angles method for yield line analysis of reinforced concrete slabs

Abstract

Yield line analysis is a useful method for design of reinforced concrete slabs, but has been limited to slabs of simple geometry, because up to now there has been no generally applicable and fully automatic computational procedure for complex-shaped slabs. Herein, a new yield line method that can be applied to any convex polygonal-shaped slab is developed. In this method, the deflections of the slab regions divided by yield lines are measured in terms of the dip and strike angles of the slab surfaces, which can define the geometry of all kinematically admissible collapse mechanisms or yield line patterns. The external work done and the internal energy dissipation at yield lines are evaluated as functions of the dip and strike angles, and the principle of virtual work is used to determine the corresponding load factor. The final solution is obtained by minimising the load factor with respect to the dip and strike angles. A computer program based on this method has been produced. Its correctness is verified by checking against results obtained by others for simple cases, and its versatility is demonstrated by applying it to complicated slabs subjected to point, line, patch and uniformly distributed loads.