## Related questions with answers

Question

(a) Prove that the expression

$σ_{x'}σ_{y'} - τ^2_{x'y'},$

where

$σ_{x'}, σ_{y'}, and τ_{x'y'}$

are components of the stress along the rectangular axes x' and y', is independent of the orientation of these axes. Also, show that the given expression represents the square of the tangent drawn from the origin of the coordinates to Mohr's circle. (b) Using the invariance property established in part a, express the shearing stress

$τ_{xy}$

in terms of

$σ_x, σ_y,$

and the principal stresses

$σ_{max} and σ_{min}.$

Solution

VerifiedStep 1

1 of 8Strategy

Using the given Mohr's circle, we can determine the required expressions.

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