Institute of Fundamental Technological Research

The relationship between limit analysis and yield-line analysis is investigated. Attention is restricted to simply supported, isotropic slabs subjected to single-point loadings. It is found that conventional yield-line analyses quite often give substantial overestimates of the carrying capacity. A general method is formulated for finding the yield-point load, and various examples are considered.

The yield condition for a rigid-plastic circular cylindrical shell subjected to axially symmetric loading is described in terms of the circumferential hoop stress n and the axial bending moment m. Different yield conditions are obtained depending on whether the shell is of homogeneous or ideal sandwich construction, and on whether the shell material satisfies Tresca's or Mises' yield condition. Previous work has been limited to Tresca's yield condition.

The example of a long shell subjected to a ring of pressure at its midpoint is considered for each of the four shell yield conditions as well as for a simple “limited interaction” approximation. Complete stress and velocity fields are determined, the limit load is found, and the extent of the plastic region is determined. The results are assessed in terms of the theorems of limit analysis.