Meriam, Kraige & Bolton — Equilibrium of Rigid Bodies: Problem 4_45

⚡ Mecademy AIENG정역학 · ch4  Problem Statement Determine the force in member of the loaded symmetrical truss. The truss is supported at joints and . It consists of 6 panels, each with a horizontal width of , for a total span of . The top chord is straight and horizontal. The bottom chord is a circular arc with a radius of . The vertical distance at the ends (between the top chord and joints or ) is . The loads are applied as follows: Vertical downward loads of at the end supports and . Vertical downward loads of at the interior bottom joints and . The truss is symmetrical about the vertical centerline passing through member . Problem 4/45 (a) Force in member 1. Formula: First, determine the support reactions using global equilibrium. Then, determine the geometry of the circular bottom chord to find joint coordinates and member angles. Finally, use the method of joints or sections to find the internal force. Total Load: By symmetry, reactions at and : (upward). 2. Substitution: Establish a coordinate system with origin at the center of the top chord. Let be positive to the right and be positive downward. Top joints (all at ): . Bottom joints lie on an arc: , where . At joint : . Since the arch curves upward, the center is below: . Equation for : . Joint : GK AI 9 ft54 ft 75 ft AI18 ft L/2AI LN,M,L,K,J EL GK F =∑ y + 2 L L+L+L+L+L+ = 2 L 6L AIR = A R = I = 2 6L 3L E xy y=0E(0),F(9),G(18),H(27) x+ 2 (y−y )= c 2 R 2 R=75 ft I(27,18)27+ 2 (18−y )= c 2 75⇒ 2 729+(18−y )= c 2 5625⇒(1