TABLE OF CONTENTS Chapter 5 of Volume 1 discussed the in-plane behavior of beam-column segments throughout the entire range of loading up to ultimate load, and developed simple analytical expressions for the moment-curvature-thrust relationship to describe this behavior. This is the basic relationship required in the analysis of any beam-column problems. This chapter attempts to generalize that discussion to the case of beam-column segments subjected to combined axial compression, biaxial bending, and warping deformation. As was seen for in-plane behavior, plastic behavior of beam-column segments is fairly involved and any rigorous analysis which attempts to cover their space behavior is destined to be very complex, even for an elastic-perfectly plastic material. This is due mainly to the fact that it is difficult to determine the elastic-plastic boundary which separates the plastic portion from the elastically remained portion of a cross section. Furthermore, the neutral axis is no longer a straight line. For these reasons, recourse must be had to numerical methods to obtain solutions.
The purpose of this chapter is to describe analytical methods to establish the relations between generalized strains (axial strain ? o, biaxial curvatures ? x and ? y and warping curvature ? ?) and generalized stresses (axial thrust P, biaxial bending moments M x and M y and warping moment or bi-moment M ?). Since plastic state of stress and strain depends highly on the history of loading, the generalized stress-strain relation cannot be obtained directly Step-by-step...
