TABLE OF CONTENTS In the previous discussions of solution of beam-column, the basic differential equation of beam-column and its boundary conditions are generally expressed in terms of the lateral deflection w as can be seen from Eq. (3.155) and Eqs. (3.157). A solution is obtained by solving the differential equation either exactly or numerically or approximately for the deflection function. Once the deflection function is obtained, the other physical characteristics of the beam-column such as slope and curvature can then be calculated by proper differentiation of the deflection function. This approach of analysis is called herein as the deflection method.
The analysis of beam-column by the deflection method is well known. Analytically exact solutions in the elastic range can be obtained in most cases. Analyses of the solutions and theories are described in detail in Chaps. 3 and 4. It is natural to expect that solutions could be obtained in a similar manner when the beam-columns are stressed beyond the elastic limit. Unfortunately, such attempts have not been successful in obtaining analytical solutions to plastic beam-column problems composed of common structural sections. In part, this difficulty is caused by the inability to obtain a relatively simple moment-curvature-thrust relationship for commonly used structural sections. In addition, the direct solutions to the differential equation of deflection are generally impossible to obtain because of the high nonlinearity of the basic equation. With the aid of the generalized moment-curvature-thrust expressions as given by Eqs. (7.68) (for detailed discussion, see Chap. 5),...
