Analytical sensitivity of plastic rotations in beam-column elements

Analytical sensitivity equations for the plastic rotation of beam-column finite elements are derived for reliability and optimization algorithms in structural engineering and for the assessment of plastic rotation sensitivity to uncertain design parameters and modeling assumptions. The plastic rotation is defined by elastic unloading of element forces in a basic system, which makes the corresponding sensitivity computations applicable to most material nonlinear beam-column formulations available in the literature. The analytical response sensitivity is verified by finite differences then applied to a first-order reliability analysis of a steel subassemblage where the performance function places a limit on plastic rotation.