Meriam, Kraige & Bolton — Equilibrium of Rigid Bodies: Problem 4_124

⚡ Mecademy AIENG정역학 · ch4  Problem Statement The lengthy boom of an overhead construction crane, a portion of which is shown, is an example of a periodic structure—one which is composed of repeated and identical structural units. Use the method of sections to find the forces in members and . Problem 4/124 (a) Analysis of Truss Geometry and Loading ● Calculation Process 1. Equilateral Units: The problem states that . This indicates that the basic structural units are equilateral triangles. Since the structure is periodic and composed of identical units, all corresponding triangles in the web are equilateral with side length . 2. Truss Height (): The height of the truss is the altitude of an equilateral triangle with side . 3. Joint Coordinates: Let the bottom chord lie on the -axis. Based on the given horizontal spacings ( for bottom bays, for the offset at the tip): Joint is at . Joint is at (assuming a end bay). Joint is at , and Joint is at . Joint is at . Joint is at , Joint is at , and Joint is at . Joint is at , and Joint is at . 4. Total Load (): The mass is . Using : This downward force acts at Joint . FJGJ = BC = BD = CD2 m s=2 m h 2 m h=ssin(60)= ∘ 2⋅ = 2 3 m≈ 31.732 m x 2 m1 m D(0,0) A(2,0)2 m G(−2,0)J(−4,0) B (1, ) 3 E (0, ) 3H (−2, ) 3K (−4, ) 3 C (−1, ) 3F (−3, ) 3 W5000 kgg= 9.81 m/s 2 W=mg=5000 kg× 9.81 m/s= 2 49050 N=49.05 kN A ● Final Conclusion: The truss height is and the applied load at the tip is downward. (b) Force in Member ● Calculation Process 1. Met