Meriam, Kraige & Bolton — Equilibrium of Rigid Bodies: Problem 4_110

⚡ Mecademy AIENG정역학 · ch4 The problem asks for the components of the reaction at support for a 3D space frame. Each connection is treated as a ball-and-socket joint, which implies that the structure acts as a space truss where members support only axial loads. ### Analysis of Geometry and Coordinates We define a 3D coordinate system with the origin at the base of the central vertical pole. Based on the provided dimensions: Support is on the -axis: . Support is on the -axis: . Support is on the -axis: . Joint is on the vertical pole (-axis): . Joint is on the vertical pole (-axis): . ### Forces Applied is applied at the top joint (assumed at for a determinate truss solution) in the direction: . is applied at joint in the direction: . ---  Problem Statement Determine the components of the reaction at for the loaded space frame shown. Each connection may be treated as a ball-and-socket joint. Problem 4/110 (a) Reaction components at A 1. Formula: The reaction at support , , must balance the forces from members and . Since are all in the plane ( ), . We use the method of joints at and to find member forces. 2. Substitution: At Joint : . A O(0,0,0) DxD=(4,0,0) m AyA=(0,1.5,0) m EyE=(0,3,0) m BzB=(0,0,4) m CzC=(0,0,6) m F = 1 6 kNC +yF = C 6j kN F = 2 5 kNB+xF = B 5i kN A AR = A A i+ x A j+ y A k z ABACA,B,Cy−z x=0A = x 0BC CF =∑ x F ( )= CD 52 4 0⇒F = CD 0 F =∑ y F ( )+ CA 1.5+6 22 1.5 F ( )+ CE 3+6 22 3 6=0 F =∑ z −F − BC F ( )− CA 6.185 6 F ( )= CE 6.708 6 0 At Joint : 3. Calcu