Meriam, Kraige & Bolton — Equilibrium of Rigid Bodies: Problem 4_27

⚡ Mecademy AIENG정역학 · ch4  Problem Statement Determine the force in member . Truss diagram for problem 4/27 Given: - Loads: downward at joints , , and . - Horizontal dimensions: between each vertical panel (). - Vertical dimension: Height of the truss is . - Supports: Pin support at joint and a roller support at joint . Problem 4/27 (a) Determination of the force in member 1. Formula: First, we determine the external reactions. Since the truss is in equilibrium, the sum of moments about support must be zero: Then, we use the method of sections by cutting through members , , and and applying vertical equilibrium to the right-hand portion: 2. Substitution: Calculate the vertical reaction at joint by taking moments about (with as origin , at , at , at , and at ): After finding , consider the section to the right of the cut (containing joints , , , and ): The external loads on this section are at and at . The internal force has a vertical component , where (since horizontal and vertical dimensions are both ). CG 5 kipsBCD 10 ftHG=GF=FE=10 ft 10 ft AG CG A M = ∑ A 0 GFGCBC F = ∑ y 0 G y G AA(0,0)B(10,0)C(20,0)D(30,0)G (10,10) M = ∑ A G (10)− y 5(10)−5(20)−5(30)=0 G y FC ED5 kipsC5 kipsD F CG F sinθ CG θ=45 ∘ 10 ft F = ∑ y,right section F sin(45)− CG ∘ 5−5=0 3. Calculation: Reaction at : Vertical equilibrium of the right section: Direction: Since must pull upward on the right section to balance the downward loads, it is in tension. 4. Result: ● Final Conclusion: The force in membe