PROBLEM 3.87
Three control rods attached to a lever ABC exert on it the forces
shown. (a) Replace the three forces with an equivalent force-couple
system at B. (b) Determine the single force that is equivalent to the
force-couple system obtained in part a, and specify its point of
application on the lever.
SOLUTION
(a)
First note that the two 90-N forces form a couple. Then
F = 216 N
where
and
θ
θ = 180° − (60° + 55°) = 65°
M = ΣM B
= (0.450 m)(216 N) cos 55° − (1.050 m)(90 N) cos 20°
= −33.049 N ⋅ m
The equivalent force-couple system at B is
F = 216 N
(b)
65.0°; M = 33.0 N ⋅ m

The single equivalent force F′ is equal to F. Further, since the sense of M is clockwise, F′ must be
applied between A and B. For equivalence,
ΣM B : M = aF ′ cos 55°
where a is the distance from B to the point of application of F′. Then
−33.049 N ⋅ m = − a(216 N) cos 55°
a = 0.26676 m
or
F ′ = 216 N
65.0° applied to the lever 267 mm to the left of B 
PROPRIETARY MATERIAL. © 2013 The McGraw-Hill Companies, Inc. All rights reserved. No part of this Manual may be displayed,
reproduced or distributed in any form or by any means, without the prior written permission of the publisher, or used beyond the limited
distribution to teachers and educators permitted by McGraw-Hill for their individual course preparation. If you are a student using this Manual,
you are using it without permission.
248