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: 145

Answer

$$ \begin{aligned} & F_R=15.4 \mathrm{kN} \\ & \left(M_R\right)_o=18.5 \mathrm{kN} \cdot \mathrm{m} \text { (clockwise) } \end{aligned} $$

Work Step by Step

Summing the forces along the $y$ axis $$ \begin{aligned} +\uparrow\left(F_R\right)_y=\Sigma F_y ; \quad F_R & =-\frac{1}{2}(3)(1.5)-5(2.25)-\frac{1}{2}(5)(0.75) \\ & =-15.375 \mathrm{kN}=15.4 \mathrm{kN} \downarrow \end{aligned} $$ Now Summing the Moment about point $O$, $$ \begin{aligned} ↺+\left(M_R\right)_o=\Sigma M_O ; \quad & \left(M_R\right)_o=-\frac{1}{2}(3)(1.5)(0.5)-5(2.25)(1.125) \\ & -\frac{1}{2}(5)(0.75)(2.5) \\ & =-18.46875 \mathrm{kN} \cdot \mathrm{m}=18.5 \mathrm{kN} \cdot \mathrm{m} \text { } \end{aligned} $$
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