Critical Softening of Hinges in Portal Frames

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, a_cr, 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 a_cr 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 a_cr are found to be quite accurate. For given frame geometry ``soft points'' at which a_cr is a minimum may be found for each member.