Meriam, Kraige & Bolton — Equilibrium of Rigid Bodies: Problem 4_4

⚡ Mecademy AIENG정역학 · ch4  Problem Statement Calculate the forces in members and of the loaded truss. The truss is supported at joints and against a vertical wall and carries a downward load at joint . The dimensions of the truss panels are by , as indicated in the diagram. Problem 4/4 (a) Force in member 1. Formula: Joint equilibrium equation for vertical forces, . 2. Substitution: Analyze joint . The members connected at joint are (horizontal), (horizontal), and (vertical). There is no external load applied at joint . 3. Calculation: Since no other vertical forces (loads or member components) act at joint , the vertical member must carry zero force to maintain equilibrium. This is a characteristic of a zero-force member where two collinear members ( and ) meet a third non-collinear member with no external load. 4. Result: ● Final Conclusion: The force in member is , making it a zero-force member. (b) Force in member 1. Formula: Method of joints starting from the free end , and equilibrium equations and . 2. Substitution: Joint : Load is down. Member has a slope of ( vertical / horizontal). BEBD CD4 kNA 3 m3 m BE F =∑ y 0 EEAE EDBE E F = ∑ y F = BE 0 EBE AEED F = BE 0 BE0 BD A F =∑ x 0F =∑ y 0 A4 kNAB45 ∘ 3 m 3 m F = ∑ y F sin45− AB ∘ 4 kN=0⇒F = AB = sin45 ∘ 4 4 kN (Ten 2 Joint : Members are ( slope), (vertical), (horizontal), and ( slope down-right). 3. Calculation: Substitute known values and into the vertical equilibrium at : 4. Result: ● Final Conclusion: The force in m