Meriam, Kraige & Bolton — Equilibrium of Rigid Bodies: Problem 4_1

⚡ Mecademy AIENG정역학 · ch4  Problem Statement Determine the force in each member of the loaded truss. Explain why knowledge of the lengths of the members is unnecessary. Given: Load at joint is directed vertically downward. Angles at supports and are and respectively. Support is a pin, and support is a roller. Problem 4/1 (a) Determine the force in each member 1. Formula: First, find the support reactions using equilibrium of the entire truss. Let be the distance . Then, use the Method of Joints at and : 2. Substitution: In , the angle at is . Horizontal distance of load from : . Reactions: 3. Calculation: B4000 lb AC30 ∘ 60 ∘ A C L AC M = ∑ A 0, F = ∑ y 0, F = ∑ x 0 AC F = ∑ x 0, F = ∑ y 0 △ABCB180− ∘ (30+ ∘ 60)= ∘ 90 ∘ Ad=(Lcos30)cos30= ∘∘ Lcos30 2∘ M = ∑ A R ⋅ C L−4000⋅(Lcos30)= 2∘ 0⟹R = C 4000⋅cos3 2 R = C 4000⋅ = ( 2 3 ) 2 3000 lb↑ F = ∑ y 0⟹R + Ay 3000−4000=0⟹R = Ay 1000 lb↑ F = ∑ x 0⟹R = Ax 0 Joint A: Let and be tensions. Joint C: Let be tension. 4. Result: , , ● Final Conclusion: The forces in the members are (Compression), (Compression), and (Tension). (b) Explain why knowledge of the lengths of the members is unnecessary 1. Formula: Forces in a statically determinate truss are governed by equilibrium of joints. The equations are: 2. Substitution: The geometry of the truss is completely defined by the angles. The relative positions of the joints (ratios of lengths) depend only on these angles. For example, the reactions depend on the ratio of the horizontal distance