Engineering Mechanics: Statics & Dynamics (14th Edition)

Published by Pearson
ISBN 10: 0133915425
ISBN 13: 978-0-13391-542-6

Chapter 4 - Force System Resultants - Section 4.7 - Simplification of a Force and Couple System - Problems - Page 176: 112

Answer

$$ \begin{aligned} & \mathbf{F}_R=\{-28.3 \mathbf{j}-68.3 \mathbf{k}\} \mathrm{N} \\ & \mathbf{M}_{R A}=\{-20.5 \mathbf{j}+8.49 \mathbf{k}\} \mathrm{N} \cdot \mathrm{m} \end{aligned} $$

Work Step by Step

$$ \begin{aligned} & \mathbf{F}_{\boldsymbol{n}}=\mathbf{F}_4+\mathbf{F}_2 \\ & --40 \cos 45 \mathrm{j}+\left(-40-40 \sin 45^{\circ}\right) \mathbf{k} \\ & \mathbf{F}_h=|-28 . \mathbf{j}-68.7 \mathbf{k}| \mathrm{N} \\ & \end{aligned} $$ $\left.\mathbf{r}_{A P}=\mid-0.3 \mathbf{i}+0.0 \mathrm{j} \mathbf{j}\right]=$ $$ \begin{aligned} & \mathbf{r}_{A P 2}=-0.3 \mathbf{i}-0.08 \sin 45^{\prime \prime} \mathbf{j}+0.08 \cos 45 \mathrm{k} \\ & -|-0.3-0.0666 j+0.006 f i k| m \\ & \mathbf{M}_{K A}=\left\langle\mathbf{r}_{A F 1} \times \mathbf{F}_1\right\rangle+\left\langle\mathbf{r}_{A F} \times \mathbf{F}_2\right\rangle \\ & -\left|\begin{array}{ccc} \mathbf{i} & \mathbf{j} & \mathbf{k} \\ -0.3 & 0.06 & 0 \\ 0 & 0 & -40 \end{array}\right|+\left|\begin{array}{ccc} \mathbf{i} & \mathbf{j} & \mathbf{k} \\ -0.3 & -0.0566 & 0.0666 \\ 0 & -40 \cos 45^* & -40 \sin 45^* \end{array}\right| \\ & \mathbf{M}_{A A}=|-20.5 \mathrm{j}+8.49 \mathrm{k}| \mathrm{N} \cdot \mathrm{m} \\ & \end{aligned} $$ Also. $$ \begin{aligned} & M_{\text {AA, }}=\mathrm{Y} \cdot \mathrm{M}_{\mathrm{A}} \\ & M_{\text {A. }}-2828(0.0566)+2828(0.0566)-40(0.08) \\ & M_{\text {AA, }}=0 \\ & M_{A_A}=\mathbf{\Sigma} \cdot M_A \\ & M_{\text {KA, }}=-28.28(0.3)-40(0.3) \\ & M_{\hbar A}=-20.5 \mathrm{~N} \cdot \mathrm{m} \\ & M_{B A,}=\Sigma \cdot M_A \\ & \left.M_{E A}=282 \times 0.3\right) \\ & M_{\text {EA, }}=8.49 \mathrm{~N}-\mathrm{m} \\ & \mathbf{M}_{K A}=|-20.5+8.49 k| \mathrm{N} \cdot \mathrm{m} \\ & \end{aligned} $$
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