Meriam, Kraige & Bolton — Equilibrium of Rigid Bodies: Problem 4_66

⚡ Mecademy AIENG정역학 · ch4  Problem Statement Determine the components of all forces acting on each member of the loaded frame. Problem 4/66 (a) Analysis of the components of forces acting on each member 1. Formula: First, consider the entire frame to find the support reactions at and . Due to symmetry of the geometry and the loading, we have: Next, consider member individually and take moments about the pin joint at to find the horizontal reaction : 2. Substitution: Substitute and into the moment equation for member : 3. Calculation: Divide by and solve for : Since is positive, it acts to the right. From global equilibrium: Meaning acts to the left. Now, find the internal force components at pin for member : AB F = ∑ y 0⟹A + y B − y 2P=0⟹A = y B = y P F = ∑ x 0⟹A + x B = x 0⟹A = x −B x ACC A x M = ∑ C 0=A (R)− y A (R)− x P(Rsin45) ∘ A = y Psin45= ∘ 2 1 AC P(R)−A (R)− x PR = ( 2 1 )0 RA x P−A − x = 2 P 0 A = x P1− ≈ ( 2 1 )0.2929P A x B = x −A = x −0.2929P B x C AC By Newton's third law, the forces on member at pin are equal and opposite to those on member : 4. Result: For member : At : At : For member : At : At : ● Final Conclusion: The frame is a three-hinged arch. By leveraging symmetry and equilibrium of the individual members, we find that the horizontal thrust at the supports is acting inward, and the vertical reactions are both acting upward. The joint at carries only a horizontal shear force of and zero vertical force due to the symmetric loading. ✨ Final Answer Summa