Simplified Approach for Torsional Analysis of Non-homogenous Tubes with Non-circular Cross-sections

In this paper a method is presented for torsional analysis of non-homogeneous tubes with arbitrarily shaped cross-sections. A previously presented method based on Bredt's theory is extended to achieve formulas for torsional analysis. Shear modulus varies through the thickness according to a power law distribution. To validate the accuracy of the presented formulas for angle of twist and shear stress, calculated results are compared with available analytical and numerical data. Moreover, the effects of thickness, bluntness of corners and cross-sectional shape are investigated. The presented formulas are relatively accurate, simple and applicable to thin to moderately thick cross-sections with constant wall thickness. Based on the method presented herein, one can achieve desirable maximum shear stress and angle of twist for a polygonal non-homogeneous tube using a proper bluntness. The presented formulas quickly converge and can be implemented in optimization programs.