Admissible Loads of Gable Frames

The mechanism method and the statical method have been presented in standard texts for plastic analysis and design of gable frames. AISC5 devised charts for both calculating plastic moments and locating plastic hinges of various gable frames subjected to uniform forces with or without wind load. It is understandable that those charts cannot be applied to frames subjected to concentrated loads, simply because the collapse load computed under the concentrated forces is a lower bound on the collapse load of the same structure with equivalent distributed force. Pincus discussed a generalized super-position method in plastic analysis of gable frames for which tedious procedures similar to that of the mechanism method are used to search for cancellation of plastic hinges.In this report, two domains of admissible loads of general gable frames are presented, in which the concentrated forces are independent and the structural dimensions are arbitrary. For given numerical values of structural dimensions and forces of a particular problem, the plastic moment and collapse mode can be simply determined from the appropriate domain; or for the given numerical values of structural dimensions and the magnitude of plastic moment, the possible collapse load of the frame may also be found. It is interesting to note that the condition of a structural collapse may be studied from the relationship of magnitude as well as direction of the independent forces in the domain.