This paper presents four new approximation formulas for predicting the shear stress in rectangular members subjected to torque loading. The results are developed using a hybrid optimization method applied to a polynomial merit function to predict the maximum shear stress along the center of the shorter side of a rectangular cross section subjected to a torque. The results of this optimization process are shown to be highly accurate and easy to apply. It is believed that this is the first time that this approach has been applied to find this component of the shear stress. This paper includes an example application to illustrate the use of the approximate polynomials developed. The results are shown to be especially relevant to rectangular members that are subjected to combined torsion and bending.

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