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 198: 153

Answer

$\begin{aligned} & F_R=1.80 \mathrm{kN} \\ & d=2.33 \mathrm{~m}\end{aligned}$

Work Step by Step

Equivalent Resultant Force. Summing the forces along the $y$ axis, $ \begin{aligned} +\uparrow\left(F_R\right)_y=\Sigma F_y ;-F_R & =-400(3)-\frac{1}{2}(400)(3) \\ F_R & =1800 \mathrm{~N}=1.80 \mathrm{kN} \downarrow \end{aligned} $ Location of Resultant Force. Summing the moment about point $A$ $ \begin{aligned} ↺+\left(M_R\right)_A=\Sigma M_A ; \quad-1800 d & =-400(3)(1.5)-\frac{1}{2}(400)(3)(4) \\ d & =2.333 \mathrm{~m}=2.33 \mathrm{~m} \end{aligned} $
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