Show in two dimensions that the maximum shear stress m = {[(xx yy)/2]2 + (xy)2}(1/2) is invariant

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Show in two dimensions that the maximum shear stress τm = {[(σxx − σyy)/2]2 + (τxy)2}(1/2) is invariant under a rotation of the reference axes and is equal to one-half the difference of the major and minor principal stresses in the considered plane.
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Shigleys Mechanical Engineering Design

ISBN: 978-1121345317

9th edition

Authors: Richard G. Budynas, J. Keith Nisbett

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