Minimal cycle bases for analysis of frames with semi-rigid joints

For an efficient force method of frame analysis, special cycle bases should be generated for the formation of localized self-equilibrating systems, leading to sparse flexibility matrices. In this paper, an algorithm is presented using a fundamental cycle basis, where the selected cycles are improved via an algebraic exchange method. Optimal analysis is performed for frames with semi-rigid joints. In this method, flexibility matrices are generated which are highly sparse. An ordering algorithm is also used for profile reduction to acquire an efficient method for the solution of the corresponding equations. Thus a complete force method analysis of semi-rigid frames is formulated and a computer code is developed. Examples are analyzed with the present approach and the results are compared to those of a stiffness method program with semi-rigid joints.