Unformatted text preview: PROBLEM 3.90 Three control rods attached to a lever ABC exert on it the
forces shown. (a) Replace the three forces with an equivalent
forcecouple system at B. (b) Determine the single force that
is equivalent to the forcecouple system obtained in Part a,
and specify its point of application on the lever. SOLUTION A
(a) First note that the two 20—lb forces formA couple. Then “x; g
F = 48 lb 41 6 {55°
where 9 = 180° —— (60° + 55°) = 65°
and M = 2MB
= (30 in.)(48 lb) cos 55° ~ (70 in.)(20 lb) cos 20°
= —489.62 lb  in
The equivalent forcecouple system at B is
F=48.0 lb 465° ’ M=4901b~in.)<
(b) 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.
2MB: M=—aF’cos 55°
Where a is the distance from B to the point of application of F’. Then —489.62 lb  in. = ~a(48.0 lb) cos 55° or a=l7.78 in. F’=48.0 lb A650" 4
and is applied to the lever 17.78 in. V
To the left of pin B ‘ , 4 ...
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 Fall '08
 Jenkins
 Statics

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