Meriam, Kraige & Bolton — Equilibrium of Rigid Bodies: Problem 4_3

⚡ Mecademy AIENG정역학 · ch4  Problem Statement Determine the force in each member of the loaded truss. Problem 4/3 (a) Support Reactions ● Calculation Process 1. Present Final Formula: To find the reactions at the supports and , we apply the equilibrium equations for the entire truss as a rigid body. We assume joint is a pin support (providing reactions and ) and joint is a roller support against the vertical wall (providing a horizontal reaction ). 2. Substitute Values: Taking moments about point (counter-clockwise is positive): Summing horizontal and vertical forces: 3. Partial Operations: From the moment equation: (acting to the left against the wall). From : (acting to the right). From : (acting upward). 4. Final Calculation: The reactions are , , and . AB A A x A y B B x M = ∑ A 0, F = ∑ x 0, F = ∑ y 0 A M = ∑ A B ⋅ x (2 m)−(3000 N)⋅(4 m)=0 F = ∑ x A − x B = x 0 F = ∑ y A − y 3000 N=0 2B = x 12000⇒B = x 6000 N F =∑ x 0A = x B = x 6000 N F =∑ y 0A = y 3000 N A = x 6000 NA = y 3000 NB = x 6000 N ● Final Conclusion: The support reactions are successfully determined. These will now be used for the method of joints. (b) Analysis of Joints B and D ● Calculation Process 1. Present Final Formula: We apply and at each joint. 2. Substitute Values: Joint B: The external reaction is to the left. Joint D: The external load is downward. The member is at . 3. Partial Operations: From Joint B: (Tension) and . From Joint D: (Tension). Substituting into the -equation at D: . The negative s