A Mechanics-based Analytical Solution for Restrained Beams with Application to Progressive Collapse Behavior

This dissertation presents an axially restrained beam (ARB) model that incorporates axial-flexural interaction throughout the entire static load-deflection curve: the elastic material range, the plastic, flexural dominant range, the range beyond plastic flexure with increasing catenary effect, and the full catenary range. Energy methods are applied to static load-deflection curves to determine dynamic load-deflection relationships. Specifically, this dissertation considers the two conditions; Pinned-Pinned-Pinned (PPP) which has no flexural resistance at the boundaries, and Fixed-Fixed-Fixed FFF (also Pinned-Fixed-Pinned, PFP) condition which provides the beam with flexural resistance at the boundaries equal to flexural capacity of the beam. Behavior is explained analytically for both PPP and FFF conditions based on a static model that explains the dynamic behavior by an energy method. Simplified analytical methods are also presented. While various methods have been presented to model the behavior of restrained beams, explanations are offered for mechanics-based estimation of the complete static and dynamic load-deflection curves. Finally, the results are validated with experimental and finite element modeling. A parametric study that uses OpenSees modeling provides an explanation of the accuracy of the method