In Fig. 3.91, the empirical limit-state response of a frame is compared with response curves generated in four different types of analyses: first-order elastic analysis, second-order elastic analysis, first-order inelastic analysis, and second-order inelastic analysis. In a first-order analysis, geometric nonlinearities are not included. These effects are accounted for, however, in a second-order analysis. Material nonlinear behavior is not included in an elastic analysis but is incorporated in an inelastic analysis.
In most cases, second-order and inelastic effects have interdependent influences on frame stability; i.e., second-order effects can lead to more inelastic behavior, which can further amplify the second-order effects. Producing designs that account for these nonlinearities requires use of either conventional methods of linear elastic analysis (Arts. 3.29 to 3.39) supplemented by semiempirical or judgmental allowances for nonlinearity or more advanced methods of nonlinear analysis.