Slope-Deflection for Elastic-Viscoplastic Frames

The conventional slope-deflection method of beam and frame analyses is extended to the case of structural materials that follow an elastic-linear strainhardening, viscoplastic constitutive power law. Slope-deflection equations are derived in an incremental form for the cases of linear power law with strainhardening and nonlinear power law without strainhardening under the assumption that the effect of axial force/bending moment interaction on inelastic deformation is negligibly small. These equations are subsequently used in developing a computerized large displacement/lumped mass frame analysis procedure. Two approximate techniques applicable to shear frame analysis are developed for the general constitutive power law case. Three example problems, i.e., mild steel cantilever beams and shear frames, respectively, subjected to strong blast, impact, and earthquake loadings are presented for demonstration purposes. Importance of inclusion of material strain rate effects in the inelastic analysis of such or similar dynamic problems is emphasized.