Analysis of frames with non-prismatic members

Abstract

This paper presents a more realistic and comprehensive static analysis technique for structures having non-prismatic members. In the proposed method a general stiffness matrix for non-prismatic members that is applicable to Timoshenko beam theory has been derived. The stiffness coefficients have been determined for constant, linear, and parabolic height variations of members, employing analytical and (or) numerical integration techniques. Uniform, triangular, and trapezoidal distributed loads over the entire member or along any part of it, concentrated loads, moments at points on the member, and any of these load combinations are taken into consideration to determine the fixed-end forces. A computer program has been coded in Fortran which analyses two-dimensional frames using the proposed stiffness matrix and fixed-end forces for a wide range of external loads. The fixed-end forces may include the effect of shear deformations. The importance of the shear deformations in non-prismatic members with high depth-to-span ratios is shown using numerical examples. The accuracy of the proposed analysis technique is verified by comparing the results of the numerical examples with those obtained from the general analysis program SAP90 using a large number of subelements.