Meriam, Kraige & Bolton — Equilibrium of Rigid Bodies: Problem 4_114

⚡ Mecademy AIENG정역학 · ch4 In this problem, we analyze a bridge truss to determine the maximum load parameter that can be applied without exceeding the buckling (compression) limits of its members. We will perform a complete truss analysis using the Method of Joints and then apply the given safety constraints to find the governing value of .  Problem Statement A buckling analysis of the bridge section reveals that the vertical truss members can safely support a maximum of 525 kN in compression, the horizontal truss members can safely support a maximum of 300 kN in compression, and the diagonal truss members can safely support a maximum of 180 kN in compression. What is the largest value of L for which no safety requirement will be violated? Problem 4/114 (a) Calculate external reactions and identify member forces 1. Formula: Total downward load: Sum of moments for reactions: By symmetry for equal reactions: 2. Substitution: Total load Reactions: (upward) 3. Calculation: Truss geometry: height = , panel width = . Diagonal length = . Trigonometry: , . Joint A: (Compression) Joint B: . Since AB pushes up with , L L W=P ∑ i M =∑ G 0 A = y G = y W/2 W=3L+L+2L+L+3L=10L A = y G = y 10L/2=5L 3 m4 m = 3+4 22 5 m cosθ=4/5=0.8sinθ=3/5=0.6 F =∑ y A + y F = AB 0⟹F = AB −5L F =∑ y −3L+F − AB,internal F sinθ= BJ 0 5L−3L+5L−0.6F = BJ 0⟹F = BJ 3.333L (Tension). (Compression). Joint J: . Since is tension, it pulls up on J: (Compression). Joint C: . Since JC pushes up with , (Tension). . Since