Elasto-Plastic Analysis of Steel Framed Structures Based on Rigid Body Rule and Plastic-Hinge Concept

Aimed at its elegance, the rigid-body-based procedure for geometric nonlinear analysis is extended to including the plastic-hinge concept for elasto-plastic analysis of framed structures. To this end, the rigid body test for initially stressed elements is first briefed, followed by derivation of the tangent stiffness of the 2D elasto-plastic beam element using the initial and full yield surfaces to consider gradual yielding of the cross-section. Of theoretical importance, the tangent and geometric stiffnesses are jointly tested by the rigid body rule for initially stressed elements. The above concepts are contained in the global and local strategies, respectively, for tracing the load–deflection curves and for performing the trial-and-error iterations. The former can deal with the formation of multi plastic hinges, in addition to multi-critical points, whereas the latter is strongly rooted in the rigid body rule and thus is free of fictitious forces (source of slow convergence). The accuracy and efficiency of the solutions obtained are confirmed by comparison with the existing ones. In conclusion, the procedure proposed in its entity makes the elasto-plastic analysis simpler and faster. The more complicated the problem is, the greater the saving in computation time using the proposed procedure. Since only minimal mathematical operations are required, this procedure has the potential of being widely accepted by structural engineers in routine analysis.