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A stainless steel member has a three-dimensional state of stress at a critical location where sx = 50,000, sy = -10,000, sz = 15,000. txy = -3500, tyz = -1000, and tzx = 2000 psi. Calculate the first, second, and third stress invariants and solve the characteristic equation for the principal normal stresses. Also, calculate the maximum shear stress and draw the Mohr circle representation of the state of stress at the critical point.

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