Skończone Ugięcia Sprężysto-Plastyczne Belek o Dowolnym Przekroju - Orkisz, J.; Życzkowski, M. (Engineering Transactions, 1966)
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.