Ultimate Bearing Capacity of Reinforced Concrete Slab Carrying Concentrated Load

Abstract

Yield-line theory is accepted as a method for the design of reinforced concrete structures in many codes. Many guidelines have been provided to find the most possible failure mechanism and the lowest upper solution. Slabs equally reinforced in two normal directions, which fail in a fan mechanism under concentrated load, have been studied and ultimate bearing capacity for this kind of slab has been presented. Up to date, the ultimate bearing capacity of unequally reinforced slabs under concentrated load, so-called orthotropic slabs, has not been solved. This paper made an effort to solve this problem. Expression for ultimate bearing capacity of orthotropic reinforced concrete slab under concentrated load is derived in a polar system according to the principle of virtual works. On the basis of the variation principle, the equation of negative yield line is established, which gives the lowest upper solution. The equation of negative yield line for orthotropic reinforced concrete slab under concentrated load is found to be a symmetric and closed curve with determinate shape but indeterminate radius. The ultimate bearing capacity is dominated by bending or punching shear of slab, depending on the depth and the reinforcement ratio of the slab.