Critical Softening of Hinges in Portal Frames

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Abstract
Softening behaviour, or decrease in bending moment capacity at far advanced curvature, is assumed to occur over a finite hinge length, or discontinuity length, at any point in a single-bay portal frame. The critical softening parameter, acr, is defined as that ratio of falling-arm slope to elastic slope on the moment-curvature diagram for the hinge, at which the structure as a whole cannot sustain increased load, however redundant it may still be. Formulae are derived for acr for the first formed hinge in fixed base portal frames. The critical softening parameter is found to be inversely proportional to the member-length : hinge-length ratio, m. For realistic values of m, appropriate formulae for acr are found to be quite accurate. For given frame geometry ``soft points'' at which acr is a minimum may be found for each member.

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