Yield Line Analysis of Reinforced Concrete Slabs with Openings by Dip and Strike Angles Method

Abstract

Using the dip and strike angles method of representing the geometry of yield line pattern in terms of the dip and strike angles of the deflected slab segments, the yield line analysis of reinforced concrete slabs had been successfully computerized. In this study, the dip and strike angles method is generalized for applications to slabs with any number of arbitrary-shaped openings subjected to point, line, patch and uniformly distributed loads. As before, the external work done by applied loads and the internal energy dissipation along yield lines are evaluated as functions of the dip and strike angles, but to allow for the presence of openings, the external work done and internal energy dissipation within the openings are discounted. Based on the principle of virtual work, the load factor is evaluated in terms of the dip and strike angles and the yield line pattern is determined by minimizing the load factor with respect to the dip and strike angles. Examples of slabs with openings under various boundary conditions and loading patterns are presented to illustrate the applicability, efficiency and accuracy of the generalized method.