Meriam, Kraige & Bolton — Equilibrium of Rigid Bodies: Problem 4_119

⚡ Mecademy AIENG정역학 · ch4  Problem Statement The truss shown consists of equilateral triangles. If the magnitude of tensile or compressive force in the aluminum members must be limited to 42 kN, determine the largest mass which can be supported. The cable attaches to the pin at A. Problem 4/119 (a) Determination of the largest mass ● Calculation Process 1. Analyze Geometry and Assumptions: The truss is composed of equilateral triangles, meaning all internal angles are and all member lengths are equal to . Based on the diagram, there is an angle of between member and the vertical. For the truss to consist of equilateral triangles while maintaining this orientation, the entire truss must be tilted. If member is tilted from the vertical, it makes an angle of with the horizontal (tilting to the left). Since triangle is equilateral, member makes an angle of with the horizontal. The cable is routed from the mass , passes over a pulley at , then over a pulley at , and is anchored to the pin at . Thus, the tension in the cable is . 2. Determine Support Reactions: Using the whole-body equilibrium of the truss and cable system, the only external vertical load is the weight . Let . Then and . Summing moments about the pin support : m m 60 ∘ L=7 m 5 ∘ AB AB5 ∘ 90+ ∘ 5= ∘ 95 ∘ ABD AD95− ∘ 60= ∘ 35 ∘ mC BAT= mg W=mgA=(0,0) D=(7cos35,7sin35)≈ ∘∘ (5.734,4.015)C≈(6.954,9.932) D M = ∑ D 0⇒R (x )− AD mg(x − D x )= C 0 R (6.344)− A mg(6.344−6.954)=0⇒6.344R + A 0.610mg=0 R ≈ A −0.0962mg (Downwar