Determine the components of the reactions at A and B, (a) if the 60-lb load is applied as shown, (b) if the 60-lb load is moved along its line of action and is applied at point E.
Fig. P6.87
SOLUTION
Free body: Entire frame:
Analysis is valid for either parts (a) or (b), since position of 60-lb load on its line of action is immaterial.
∑MB = 0: − Ay (5 in.) – (60 lb)(4 in.) = 0 Ay = −48 lb
+↑ ∑Fy = 0: By − 60 − 480 = 0 By = +108 lb
∑Fx = 0: Ax + Bx = 0 (1)
a) Load applied at D.
Since BCE is a two-force member (with forces applied at B and C only), the reaction at B must be directed along CB. We have, therefore,
Bx = 0
The reaction at B is B = 108.0 lb↑
From Eq. (1): Ax + 0 = 0 Ax = 0
The reaction at A is A = 48.0 lb↓
(b) Load applied at E.
Since ACD is a two-force member, the reaction at A must be directed along AC. We have
From Eq. (1): 80 lb + Bx = 0 Bx = 80 lb
Thus, Bx = 80.0 lb ←, By = 108.0 lb ↑
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