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(Solved): 1.9 Derive Eqs. (1.12) and (1.13) from the freebody diagram shown in Fig. 1.15b. 1.10 Show that Eq ...



1.9 Derive Eqs. (1.12) and (1.13) from the freebody diagram shown in Fig. 1.15b.
1.10 Show that Eqs. (1.14) and (1.15) are de\( \begin{aligned} \sigma_{x^{\prime}} & =\sigma_{x} \cos ^{2} \theta+2 \tau_{x y} \sin \theta \cos \theta+\sigma_{y} \sin ^{\( \sigma_{x^{\prime}}=\frac{\sigma_{x}+\sigma_{y}}{2}+\frac{\sigma_{x}-\sigma_{y}}{2} \cos 2 \theta+\tau_{x y} \sin 2 \theta

1.9 Derive Eqs. (1.12) and (1.13) from the freebody diagram shown in Fig. 1.15b. 1.10 Show that Eqs. (1.14) and (1.15) are derivable from Eqs. (1.12) and (1.13).


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QRPIn the figure,moment = 0?x(n)×QR×1??x×PQ×1??xy×PR×1=0divided by QR both side we get,?x(n)??x×PQQR??xy×PRQR=0Here PQ/QR = cos?? PR/QR = sin
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