Automatic design of tapered member gabled frames

Abstract

A program for calculating member sizes to yield a minimum with grabled frame with tapered members has been developed. The design produced satisfies in all respects the requirements of Appendix D to the 1969 AISC specification which governs the design of tapered members. The frame design is symmetrical about the vertical centerline, although the loading need not by symmetrical. The rafter can have no, one or two changes of taper within its length, at the designer's option. The matrix force method is used to do the analyses necessary in the design process. The problem is solved by finding a design which minimizes frame weight subject to constraints imposed by the design specification,such as maximum stress and maximum width/thickness ratios, to minimum or interior penalty function approach using the variable metric method of Davidon, Fletcher and Powell. A number of example penalty function design are given to show the versatility of the technique, as well as demonstrating the effect parmeters such as purlin spacing, member length, rafter slope and member depth to width ratio have on resulting designs.