TABLE OF CONTENTS In the previous chapters, the behavior of elastic and plastic beam-columns was investigated by formulating the governing differential equation in terms of either the deflection or the curvature and then obtaining the solution either exactly or numerically. However, in some instances, solutions obtained by the deflection method or the curvature method are not very efficient in terms of computer time, storage space or the number of cycles required for a convergence. Other methods of analysis are therefore needed as suitable alternatives. The other methods presented in this chapter include the moment method, the method of finite differences, and the modified deflection method.
Consider now a laterally loaded beam-column AB of length l which has an initial deflection w io( x) as shown in Fig. 12.1. An additional deflection w( x) will be produced when end moments M A, M B and a distributed load q( x) together with an axial thrust P are applied. The end reaction forces R A and R B are obtained directly from the considerations of equilibrium of moment.
| (12.1) |  |
| (12.2) |  |
in which
| (12.3) |  |
The bending moment M( x) at a distance x from the left support is related to the additional deflection w( x) by the equilibrium consideration of the left half portion of the beam-column shown in Fig. 12.2.
| (12.4) |  |
in which Eq. (12.1) is substituted for R
