Kinematical compatibility problems in yield-line theory

Abstract

Summary An attempt is made to classify assumptions made in yield-line theory in connexion with the upper-bound theorem of limit analysis. Both classical theory and theory taking into consideration membrane forces are examined for reinforced concrete slabs. The complete set of generalized stresses and strain rates is considered, and compatibility conditions imposed by the associated flow law are discussed, including those for the configuration of yield lines and for internal compatibility of the cross-section. In the case of Johansen's yield-line theory, the general type of fan pattern generated from the envelope line is considered, and some statical restrictions applied in the upper-bound technique are discussed. Considerations are limited to the case of isotropy, unless otherwise specified, but conclusions can be more or less directly extended to the case of orthotropic slabs.