Meriam, Kraige & Bolton — Equilibrium of Rigid Bodies: Problem 4_111

⚡ Mecademy AIENG정역학 · ch4  Problem Statement Determine the force in each member of the loaded truss. . Problem 4/111 (a) Support Reactions and Truss Geometry ● Calculation Process 1. Geometry Analysis: From the given dimensions, the span of the truss is ( ) and the height at the peak (joint ) is . The angle of the top chord members ( and ) with the horizontal is: Thus, and . Given , joints and are the midpoints of the segments and , respectively. 2. Equilibrium for Support Reactions: The truss is loaded symmetrically with three loads. By symmetry: 3. Horizontal Reaction: Since there are no horizontal external forces and joint is a pin while is a roller: ● Final Conclusion: The support reactions are (up) and (up). The geometric parameters are and . (b) Member Forces at Joint A and Joint B ● Calculation Process =AB=BC=CDDE 30 ft 15 ft+15 ftC10 ftθ ACCE θ= tan = −1 ( 15 10 ) tan ≈ −1 ( 3 2 )33.69 ∘ sinθ= = 2+3 22 2 13 2 cosθ= 13 3 = AB = BC = CD DEBDACCE 5-kip F = ∑ y 0⟹R + A R − E 5−5−5=0⟹R + A R = E 15 kips R = A R = E = 2 15 7.5 kips (upward) A E F = ∑ x 0⟹A = x 0 R = A 7.5 kipsR = E 7.5 kipssinθ= 2/ 13cosθ= 3/ 13 1. Joint A Analysis: 2. Joint B Analysis: At joint , we have forces from members , , , and the external load. Note that member has an angle with the horizontal. (where is the compression magnitude pushing in). Solving the system: ● Final Conclusion: The forces are: (c) Member Forces at Joint F and Symmetry ● Calculation Process 1. Joint F Analysis: Member forces an