Meriam, Kraige & Bolton — Equilibrium of Rigid Bodies: Problem 4_5

⚡ Mecademy AIENG정역학 · ch4  Problem Statement Determine the force in each member of the loaded truss. The truss consists of four main joints: A, B, C, and D. The horizontal distance between joints A and B is 6 m, and the horizontal distance between joints D and C is also 6 m. The slanted member AD has a length of 5 m and makes an angle of 45° with the horizontal at joint A. The slanted member BC also has a length of 5 m. A vertical downward load of 5000 N is applied at joint C. Support A is a pin, and support B is a roller. Member BD is an internal diagonal member. Problem 4/5 (a) Determination of member forces 1. Formula: First, find the external reactions at supports A and B using the equilibrium of the entire truss: Then, find the internal member forces by applying the method of joints: 2. Substitution: From the geometry, the height of the truss . Horizontal projection of member AD is . Assigning coordinates: , , , and . Calculate reaction at B by taking moments about A: Calculate reaction at A: 3. Calculation: Analyze joints to find member forces (using positive for Tension (T) and negative for Compression (C)): Joint A: M = ∑ A 0, F = ∑ y 0, F = ∑ x 0 F = ∑ x 0, F = ∑ y 0 at each joint. h=5sin45= ∘ 3.5355 m5cos45= ∘ 3.5355 m A(0,0)B(6,0)D(3.5355,3.5355) C(3.5355+6,3.5355)=(9.5355,3.5355) M = ∑ A B (6)− y 5000(9.5355)=0⟹6B = y 47677.5⟹B = y F = ∑ y A + y B − y 5000=0⟹A = y 5000−7946.25=−2946.2 F = ∑ x A = x 0 Joint C: Joint B: Angle of member BD with horizontal (from B to