MecMovies 4.0 : M13.6: Principal Stresses from Rosette Data

Having determined ε_x and ε_y, find γ_xy from the equation for gage b:

ε_{b} = ε_{x} \cos^{2} θ_{b} + ε_{y} \sin^{2} θ_{b} + γ_{xy} {sinθ}_{b} {cosθ}_{b}

Gage b makes an angle of 45° with the x-axis; therefore:

{cosθ}_{b} = 0.7071

and

{sinθ}_{b} = 0.7071

Solve the strain transformation equation for γ_xy:

γ_{xy} = \frac{ε_{b} - ε_{x} \cos^{2} θ_{b} - ε_{y} \sin^{2} θ_{b}}{{sinθ}_{b} {cosθ}_{b}}

= \frac{1, 180 με - (770 με) (0.5) - (- 350 με) (0.5)}{0.5}

= + 1, 940 μrad