Analytical load-deflection equations for beam and 2-D panel with a bilinear moment-curvature model

A simplified bilinear moment-curvature model are derived based on the moment-curvature response generated from a parameterized stress-strain response of strain softening and or strain-hardening material by Dr. Barzin Mobasher and Dr. Chote Soranakom. Closed form solutions are developed for deflection calculations of determinate beams subjected to usual loading patterns at any load stage. The solutions are based on a bilinear moment curvature response characterized by the flexural crack initiation and ultimate capacity based on a deflection hardening behavior. Closed form equations for deflection calculation are presented for simply supported beams under three point bending, four point bending, uniform load, concentrated moment at the middle, pure bending, and for cantilever beam under a point load at the end, a point load with an arbitrary distance from the fixed end, and uniform load. These expressions are derived for pre-cracked and post cracked regions. A parametric study is conducted to examine the effects of moment and curvature at the ultimate stage to moment and curvature at the first crack ratios on the deflection. The effectiveness of the simplified closed form solution is demonstrated by comparing the analytical load deflection response and the experimental results for three point and four point bending. The simplified bilinear moment-curvature model is modified by imposing the deflection softening behavior so that it can be widely implemented in the analysis of 2-D panels. The derivations of elastic solutions and yield line approach of 2-D panels are presented. Effectiveness of the proposed moment-curvature model with various types of panels is verified by comparing the simulated data with the experimental data of panel test.