Direct Analysis of Slender Columns with P‐Delta Effects

A numerical method is introduced for direct analysis of nonlinear behavior of slender beam‐columns. A strain control technique in conjunction with the quasi‐Newton's method was developed to obtain the updated flexural stiffness directly for lateral deflection estimation. Numerical difficulties such as singular problems or softening behavior could be detected beforehand and overcome. This algorithm may also be formulated to trace the $M‐P‐\Phi$ curve and to calculate the current flexural stiffness for sections from very small strain to extremely large strain. Details about the principles and the formulations are given in this paper. Examples include step‐by‐step calculation results for biaxially loaded sections and analyses of slender reinforced concrete and steel columns including uniform or nonuniform cross sections. Further applications can be made to uniaxially or biaxially loaded columns constructed with most engineering materials or to enhance the performance of nonlinear frame analyses.