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: 143

Answer

$$ \begin{aligned} & F_R=12.5 \mathrm{kN} \\ & d=1.54 \mathrm{~m} \end{aligned} $$

Work Step by Step

Summing the forces along the $y$ axis $$ \begin{aligned} +\uparrow\left(F_R\right)_y=\Sigma F_y ; \quad-F_R & =-4(2)-\frac{1}{2}(6)(1.5) \\ F_R & =12.5 \mathrm{kN} \end{aligned} $$ Now Summing the Moment about point $O$, $$ \begin{aligned} ↺+\left(M_R\right)_o=\Sigma M_O ; \quad-12.5(d) & =-4(2)(1)-\frac{1}{2}(6)(1.5)(2.5) \\ d & =1.54 \mathrm{~m} \end{aligned} $$
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