On the use of linearized yield conditions for combined stresses in beams

Abstract

Yield criteria expressed in terms of stress resultants are obtained for typical engineering structures, using the first fundamental theorem of limit analysis. These yield criteria, which are often non-linear, are then replaced by inscribed piecewise linear approximations. The complete solutions based on these approximate yield criteria provide lower bounds ; the corresponding values for the upper bound can be obtained by multiplying the lower bound values by a suitable factor. A few examples are worked out to illustrate the simplicity achieved in determining the collapse load.