ANGLE AND Z BEAMS IN BENDING: TENSOR MATRIX METHOD FOR SPREADSHEETS

This paper presents the generalized classical flexure formula for unsymmetrical bending in a matrix format. The new formula is presented as a product of three matrixes: a matrix of all the moments of inertias of the beam or the inertia tensor; the coordinates; and the applied bending moment matrices. Presented as such, the solution to a problem generally regarded as tedious is greatly simplified and is suited for computations using spreadsheets. The calculations for effective bending moments, effective loads, deflections, and principal moments of inertia are made easy. A uniform computational format for all types of unsymmetrical bending problems is provided. The application of the procedure is described for the analysis of hot-rolled or cold-formed angle and Z unsymmetrical steel sections. This paper should be of interest to civil, structural, mechanical, and aeronautical engineers.