Elastic-Plastic Analysis of Frameworks

A general matrix-network procedure is formulated for tracing the load-deflection characteristics of frameworks loaded through the elastic range and inelastically to the plastic collapse stage. An iterative incremental analysis procedure is employed, with the load-displacement characteristics of the structure piecewise linearized over finite loading increments. Consecutive nonproportional loading systems comprised of any arrangement of concentrated member and joint loads are considered. The classical plastic hinge concept is extended to incorporate the interaction of flexural and torsional moments and axial force. The force and plastic deformation increment vectors at each plastic hinge are constrained to remain perpendicular and parallel, respectively, to the yield surface normal vector during finite loading increments. A procedure is developed for periodically drawing the force vector at any plastic hinge an arbitrarily specified distance back from the yield surface tangent plane, while maintaining equilibrium and compatibility in the structure. The analysis procedure incorporates provision for distinguishing between partial and total collapse mechanisms.