Skończone Ugięcia Sprężysto-Plastyczne Belek o Dowolnym Przekroju

The present paper is concerned with the application of the method of substitute "multipoint sections" described in Refs. 6, 7, 8, 10 for approximate computation of finite elastic-plastic deflection of a beam. This method consists in replacing the given cross-section by a "multipoint section" (Fig. 1) composed of n "concentrated flanges" and an accurate computation of the deflection of the beam thus obtained. A linear relation (which is the simplest possible) between the bending moment and the longitudinal force and the curvature of the beam (cf. (2.1)) can be obtained in this way for a perfect rigid-plastic body and a body with sectionally linear strain hardening independently of the form of the cross-section. The case considered in the present paper is that of any load distributed along the horizontal projection and concentrated forces and moments acting in any manner. As a result sets of differential equations are obtained. Their solutions describe the form of the deflection line. Particularly simple solutions [cf. (4.32) and 4.36)] expressed by tabularized incomplete elliptic integrals and functions are obtained in the case of a constant longitudinal force (n = const) with no distributed load. In the practical case of a cantilever the problem of boundary conditions is considered as well as the range within whitch the external forces should vary So that the beam may remain in the elastic-plastic state. The paper is illustrated by numerical examples.