New Elastoplastic Analysis of Two-Dimensional Frames When Some Plastic Hinges Unload Elastically

Two-dimensional frames are made of elastic and perfectly plastic materials. Frames are analized by using the step by step elastoplastic analysis method where the applied loads are gradually increased at each step until a plastic hinge is developed. Then an equivalent frame model is generated by placing a mechanical hinge at the location of the plastic hinge and the increased external loads and the reduced plastic moments acting at the plastic hinge sections are applied to this model and elastoplastic analysis is performed. This elastoplastic analysis is repeated by incrementally increasing the external loads and applying the new reduced plastic moments, until the next plastic hinge is developed. Then a new equivalent frame model is generated to search for the following plastic hinge. This step by step elastoplastic analysis continues until the frame partially or totally collapses. When a plastic hinge is developed, it means that the section is at a fully plastic stress state. In the following small load increment: if this fully plastic stress state moves to another fully plastic stress state then this movement is called plastic flow. But if this fully plastic stress state moves to an elastic–plastic stress state then this movement is called elastic unloading. During the search of the next plastic hinge if one of the plastic hinges begins to unload elastically then the current equivalent frame model must be revised. For this the frame member which contains the elastically unloading plastic hinge is replaced by the equivalent frame member carrying balancing loads.