TABLE OF CONTENTS The basic equation of beam-column theory is a differential equation of the fourth order linking the displacement of the center line w( x) to the axial load P and lateral load q( x). Since the elastic. in-plane beam-column equation can be regarded as a special case of the biaxially loaded, elastic-plastic beam-column equation, we start in this chapter with the derivation of this special equation.
Figure 3.5(a) shows a simply supported straight beam-column of length l which is subjected to an axial compression P at the ends and a lateral load q( x) along the whole length. In order to examine the stability of the column. it is necessary to consider the equilibrium state of the column in the deflected configuration as shown by the solid line. The coordinate x is taken along the initial straight column and the coordinate s is taken along the deflected configuration.
On a cross section at a distance, x, from the end, the generalized stresses or stress resultants as shown in Fig. 3.5(b) are obtained by integrating the axial stress ? x and the shear stress ? xz over the entire area of the section A.
| (3.1) |  |
where z is the vertical coordinate from reference axis of the section. The stress resultants N and Q have directions normal and tangent to the cross...
