The triangular plate is deformed into the shape shown by the dashed line. Determine the normal strain developed along edge BC and the average shear strain at corner A with respect to the x and y axes.

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Draw free body diagram:Calculate length of side B C.\begin{aligned}L_{B C} & =\sqrt{300^{2}+400^{2}} \\& =500 \mathrm{~mm}\end{aligned}Calculate deformed length of side B C.\begin{aligned}L_{B C} & =\sqrt{(300-3)^{2}+(400+5)^{2}} \\& =\sqrt{252234} \\& =502.229 \mathrm{~mm}\end{aligned}Calculate the angle \alpha.\begin{aligned}\alpha & =\tan ^{-1}\left(\frac{3}{405}\right) \\& =0.4244^{\circ} \\& =0.0074 \mathrm{rad}\end{aligned}Calculate normal shear strain.\begin{aligned}\left(\varepsilon_{B C}\right)_{\mathrm{avg}} & =\frac{L_{B^{\prime} C}-L_{B C}}{L_{B C}} \\& =\frac{502.229-500}{500} \\\left(\varepsilon_{B C}\right)_{\mathrm{avg}} & =0.00446 \mathrm{~mm} / \mathrm{mm}\end{aligned}Calculate average shear strain.\begin{aligned}\left(\gamma_{A}\right)_{x y} & =\frac{\pi}{2}-\theta \\& =\frac{\pi}{2}-\left(\frac{\pi}{2}+\alpha\right) \\\left(\gamma_{A}\right)_{x y} & =-0.00741 \mathrm{rad}\end{aligned} ...