Problem 3.154

1. C b B P a 300 mm A 200 mm Problem 3.154 The force P has a magnitude of 250 N and is applied at the end C of a 500 mm rod AC attached to a bracket at A and B. Assuming a = 30o and b = 60o, replace P with (a) an equivalent force-couple system at B , (b) an equivalent system formed by two parallel forces applied at A and B.

2. Problem 3.154 C b B P a 300 mm A 200 mm Solving Problems on Your Own The force P has a magnitude of 250 N and is applied at the end C of a 500 mm rod AC attached to a bracket at A and B. Assuming a = 30o and b = 60o, replace P with (a) an equivalent force-couple system at B , (b) an equivalent system formed by two parallel forces applied at A and B. 1. Replace a force with an equivalent force-couple system at a specified point. The force of the force-couple system is equal to the original force, while the required couple vector is equal to the moment of the original force about the given point.

3. Problem 3.154 Solution C b B P a 300 mm A 200 mm SF : F = PorF = 250 N 60o SMB : M = _ (0.3 m)(250 N) = _75 N Replace a force with an equivalent force-couple system at a specified point. (a) Equivalence requires: The equivalent force couple system at B is: F = 250 N 60o, M = 75 N . m

4. Problem 3.154 Solution C b B P a 300 mm A 200 mm C C y x B B 60o = F 30o 250 N A FB A F FA (b) Require: The two force systems are equivalent.

5. Problem 3.154 Solution C C y x B B 60o = F 30o 250 N A FB A F FA Equivalence then requires: SFx : 0 = FA cos F + FB cos F FA = _FB or cos F = 0 SFy : _250 = _ FA sin F_FB sin F IfFA = _ FB then_ 250 = 0 reject Consequently cos F = 0 orF = 90oandFA + FB = 250

6. Problem 3.154 Solution C y x B 60o 30o 250 N A + C B = F FB A F FA Also: SMB : _ (0.3 m)( 250 N) = (0.2 m) FA orFA = _ 375 N andFB = + 675 N FA = 375 N 60o, FB = 625 N 60o