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

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...

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Bibliographic Details
Published inJournal of elasticity Vol. 152; no. 1-2; pp. 179 - 182
Main Author Warner, Derek H.
Format Journal Article
LanguageEnglish
Published Dordrecht Springer Netherlands 01.12.2022
Springer Nature B.V
Subjects
Biomechanics
Classical and Continuum Physics
Classical Mechanics
Classroom Note
Derivation
Engineering
Lagrange multiplier
Materials Science
Mathematical Applications in the Physical Sciences
Shear stress
Solid mechanics
Theoretical and Applied Mechanics
Plastic slip
15-01
Stress analysis
Critical plane analysis
Plasticity
Mohr’s circle
Tresca yield surface
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Summary: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.
ISSN:0374-3535
1573-2681
DOI:10.1007/s10659-022-09948-7