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 4.9 - Reduction of a Simple Distributed Loaded - Problems - Page 197: 146

Answer

$\begin{aligned} & F_R=27.0 \mathrm{kN} \\ & \left(M_R\right)_A=81.0 \mathrm{kN} \cdot \mathrm{m} \text { (clockwise) }\end{aligned}$

Work Step by Step

Equivalent Resultant Force And Couple Moment About Point A. Summing the forces along the $y$ axis, $ \begin{aligned} +\uparrow\left(F_R\right)_y=\Sigma F_y ; \quad F_R & =-\frac{1}{2}(3)(3)-3(6)-\frac{1}{2}(3)(3) \\ & =-27.0 \mathrm{kN}=27.0 \mathrm{kN} \downarrow \end{aligned} $ Summing the moments about point $A$, $ \begin{aligned} C_{+}\left(M_R\right)_A=\Sigma M_A ; \quad\left(M_R\right)_A & \\=-\frac{1}{2}(3)(3)(1)-3(6)(3)-\frac{1}{2}(3)(3)(5) \\ =-81.0 \mathrm{kN} \cdot \mathrm{m}=81.0 \mathrm{kN} \cdot \mathrm{m} \text { (clockwise) } \end{aligned} $
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