Meriam, Kraige & Bolton — Equilibrium of Rigid Bodies: Problem 4_125

⚡ Mecademy AIENG정역학 · ch4  Problem Statement A space truss consists of two pyramids on identical square bases in the horizontal plane with common side . The truss is loaded at the vertex by the downward force and is supported by the vertical reactions shown at its corners. All members except the two base diagonals are of the same length . Take advantage of the two vertical planes of symmetry and determine the forces in and . (Note that link prevents the two pyramids from hinging about .) Problem 4/125 (a) Force in member 1. Formula: From equilibrium of the entire structure and joint analysis, the relationship between the force in and the applied load is derived using the method of joints and symmetry. The coordinate system is set with the common edge along the - axis. Vertices are at and . The force is obtained from the horizontal equilibrium at vertex : Combining this with equilibrium at other joints, we find: 2. Substitution: Substituting the geometric constants derived from the condition that slant members are of length : 3. Calculation: First, determine the support reactions. From and , we get at and at . At Joint , vertical equilibrium gives . At Joint , vertical equilibrium gives , thus . x−y DGAL b ABDAAB DG AB ABL DGy A(b/2,b/2,b/ ) 2B (−b/2,b/2,b/ ) 2 F AB B F = ∑ x F − AB 2F cosθ + BCx 2F cosφ = BDx 0 F = AB − 2 2 L b F = AB − 2 2 L F =∑ z 0M =∑ DG 0 R = 1 3L/8E,FR = 2 L/8C,H DF = DA −F DB BF = BC −F BD F = BC F AD At Joint , horizontal equilibrium along the -axis