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An Elementary Derivation of the Maximum Shear Stress in a Three Dimensional State of Stress

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Abstract

The maximum shear stress associated with a 3D stress state is a widely used quantity in solid mechanics. While the expression of this quantity in terms of principal stresses is given in most mechanics classes, its derivation is far less common. In this classroom note, an elementary derivation of the maximum shear stress is given that avoids vector calculus, Lagrange multipliers, and the full framework necessary for Mohr’s graphical derivation.

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Acknowledgements

The author gratefully acknowledges technical input from Roger Fosdick and support from the Office of Naval Research # N000142012484, the National Science Foundation # 1922081, and Sandia National Laboratories # 2304832.

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  1. Cornell Fracture Group, School of Civil and Environmental Engineering, Cornell University, Ithaca, NY, 14853, USA

    Derek H. Warner

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  1. Derek H. Warner
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Warner, D.H. An Elementary Derivation of the Maximum Shear Stress in a Three Dimensional State of Stress. J Elast 152, 179–182 (2022). https://doi.org/10.1007/s10659-022-09948-7

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