The AISC 360-05 Appendix 7 describes a method of analysis, called Direct Analysis, which accounts for the second order effects resulting from deformation in the structure due to applied loading, imperfections and reduced bending stiffness of members due to the presence of axial load.

This is a non-linear iterative analysis as the stiffness of the members is dependent upon the forces generated by the load. The analysis will iterate, in each step changing the member characteristics until the maximum change in any Tau-b is less than the tau_tolerance, If the maximum change in any Tau-b is less than 100*tau_tolerance and the maximum change in any displacement degree of freedom is less than the disp_tolerance; then the solution has converged for this case.