Generalized Nonuniform Torsion of Beams and Frames

Abstract

The general torsional boundary conditions are considered for the steel beam‐frame structures with I‐ and C‐shaped cross sections. The algorithm is originated for the stress analyses of beams with generalized torsional boundary conditions and torsional loadings. This algorithm is utilized for analyses with microcomputers. In addition to the first degree of deformation compatibility (so‐called “effect of framing participation”), the second degree is introduced—compatibility of warping deformations for the frame joints. The numerical example of the frame in bending shows significant discrepancies in the normal and shear stresses calculated by existing standard computer programs and by exact solution for this frame. Along with the exact method of frame analysis which involves the generalized slope‐deflection method, an approximate method of frame analysis, the method of identical joint rotations (MIJR), is proposed and compared with the exact solution. MIJR can be used with the existing standard computer programs.