University:
Angelo State University
Course:
ENGR 2301 | Engineering Mechanics - Statics
Academic year:

2024
Views:

173

Pages:

6
Author:

Ean Mason

Problem 3.154 C A B β α 300 mm P 200 mm 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 α = 30o and β = 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. Problem 3.154 Solving Problems on Your Own C A B β α 300 mm P 200 mm 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 α = 30o and β = 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. Problem 3.154 Solution C A B β α 300 mm P 200 mm Replace a force with an equivalent force-couple system at a specified point. (a) Equivalence requires: ΣF: F= P or F = 250 N Σ MB : M = _ (0.3 m)(250 N) = _75 N The equivalent force couple system at B is: F = 250 N 60o, M = 75 N . m 60o Problem 3.154 Solution C A B β α 300 mm P 200 mm (b) Require: The two force systems are equivalent. C 60o B A y 30o 250 N B = A C x Φ FB Φ FA Problem 3.154 Solution C y 60o B 30o A B = 250 N A If FB Φ 0 = FA cos Φ + FB cos Φ FA = _ FB Σ Fy : Φ FA Equivalence then requires: Σ Fx : C x _ cos Φ = 0 or 250 = _ FA sin Φ _ FB sin Φ FA = _ FB Consequently then _ 250 = 0 reject cos Φ = 0 or Φ = 90o and FA + FB = 250 Problem 3.154 Solution C y 60o B 30o A B = 250 N A C x Φ FB Φ FA Also: + Σ MB : _ (0.3 m)( 250 N) = (0.2 m) FA or and FA = 375 N FA = _ 375 N FB = + 675 N 60o, FB = 625 N 60 o