Meriam, Kraige & Bolton — Equilibrium of Rigid Bodies: Problem 4_14

⚡ Mecademy AIENG정역학 · ch4  Problem Statement Determine the forces in members and of the loaded truss. Problem 4/14 (a) Reaction Forces and Truss Geometry Analysis 1. Formula: Due to symmetry of the truss and loading, the total vertical reaction is distributed equally between the supports at and . 2. Substitution: 3. Calculation: Determine the angle of member : Since the horizontal distance from to the vertical through is (from total span minus middle span divided by 2) and the length , the angle is . Determine the coordinates relative to : , , . Angle of member : Horizontal distance , Vertical distance . Length . Sine and cosine of angle (with horizontal): , . 4. Result: , , . ● Final Conclusion: The reaction at is upward, and the truss geometry establishes member at and member with a slope of . BCBG AF F = ∑ y 0⟹R + A R = F P + C P + D P G R + A R = F 3 kN+3 kN+2 kN=8 kN R = A R= F = 2 8 kN 4 kN↑ ABA B1 m6 m4 m AB=2 mθcosθ= ⟹ 2 1 θ= 60 ∘ A(0,0)B (1, ) m 3C (2,2 ) m 3 G(3,0) m BGΔx=3−1=2 m Δy=0− = 3 − m 3L = BG = 2+( ) 2 3 2 m 7αsinα= 7 3 cosα= 7 2 R = A 4 kNθ= AB 60 ∘ sinα = BG 3/7 A4 kN AB60 ∘ BG 2 3 (b) Force in Member 1. Formula: Apply the equilibrium equation at joint in the vertical direction. Due to symmetry, the vertical components of forces in and must balance the external load at . 2. Substitution: 3. Calculation: 4. Result: (Tension) ● Final Conclusion: The force in member is in tension. (c) Force in Member 1. Formula: First, find the force in member from joint ,