It can be easily proved that the collapse load associated with mechanism 2 is the correct limit load. This is done by constructing an equilibrium set of bending moments and checking that they are not violating the plastic moment condition.

2.11.13 Hinge-by-Hinge Analysis

Instead of finding the collapse load of the frame, it may be useful to obtain information about the distribution and redistribution of forces prior to reaching the collapse load. Elastic-plastic hinge analysis (also known as hinge-by-hinge analysis) determines the order of plastic hinge formation, the load factor associated with each plastic hinge formation, and member forces in the frame between each hinge formation. Thus, the state of the frame can be defined at any load factor rather than only at the state of collapse. This allows a more accurate determination of member forces at the design load level.

Educational and commercial software are now available for elastic-plastic hinge analysis (Chen and Sohal 1994). The computations of deflections for simple beams and multistorey frames can be done using the virtual work method (Knudsen et al. 1933; Beedle 1958; ASCE 1971; Chen and Sohal 1994). The basic assumption of first-order elastic-plastic hinge analysis is that the deformations of the structure are insufficient to alter radically the equilibrium equations. This assumption ceases to be true for slender members and structures, and the method gives unsafe predictions of limit loads.

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