Meriam, Kraige & Bolton — Equilibrium of Rigid Bodies: Problem 4_59

⚡ Mecademy AIENG정역학 · ch4  Problem Statement Determine the forces in members AD and DG of the loaded space truss shown in the figure. Three downward vertical loads of magnitude are applied at joints , , and . The vertical distance between the top chords and the bottom chord is . The horizontal spacing between joints is as indicated: between and , and , and , and , and between the support wall and joint . Problem 4/59 (a) Force in member AD ● Calculation Process 1. Present Final Formula: We analyze the equilibrium of Joint . Due to symmetry of the truss and loading, the forces in members and are equal (). The equilibrium equations for joint in the vertical () and longitudinal () directions are: where is the angle the members make with the horizontal plane, and is the component along the -axis. 2. Substitute Values: From the geometry, the coordinates of the joints relative to joint are: The vector . The vertical component ratio is and the longitudinal component ratio is . LADG 0.8d dGDDAHEEBd/2 G A ABACF = AB F AC Azy F = ∑ z 2Fsinθ − ABz L=0 F = ∑ y 2F cosθ + ABy F = AD 0 θ z AB,AC cosθ y y J(0,0,0) A=(0,2.5d,0) D=(0,1.5d,0) B=(x ,2.0d,0.8d) B = AB(x − B 0,2.0d−2.5d,0.8d−0)=(x ,−0.5d,0.8d) B L AB 0.8d L AB −0.5d 2 F − AB ( L AB 0.8d )L=0⟹ = L AB F AB 1.6d L 3. Partial Operations: Substitute the ratio into the -equilibrium equation. The unit vector for member pointing away from is . 4. Final Calculation: The negative sign indicates that member is in compression. ● Final Conclu