Meriam, Kraige & Bolton — Equilibrium of Rigid Bodies: Problem 4_112

⚡ Mecademy AIENG정역학 · ch4  Problem Statement Determine the forces in members CH and CF. Horizontal distances: , . Vertical distance: . Loads: downward at joint , downward at joint , and downward at joint . Support at is a pin, support at is a roller on a vertical wall. Problem 4/112 (a) Force in member CF 1. Formula: Apply the method of joints starting from the right end of the truss. At Joint , the sum of vertical forces must be zero: . Then, analyze Joint for vertical and horizontal equilibrium. 2. Substitution: For Joint : . So, . At Joint : Horizontal equilibrium gives . Horizontal component at : . Thus, . At Joint (coordinates (6,1)): vertical force balance is . Horizontal balance is . 3. Calculation: From horizontal balance at : . From vertical balance at : . Substitute: . AB=BC=CD=DE=2 mIH=HG=2 m AI=2 m 24 kNG24 kNF24 kN E IA EF =∑ y F sinθ− FE 24=0 F Esinθ= = 2+1 22 1 5 1 F = FE ( 5 1 )24 kN DF = CD F DE EF = DE −F cosθ= FE −24 = 5( 5 2 )−48 kNF = CD −48 kN F F − 5 1 FE F + 5 1 GF F − 5 1 CF 24=0 F − 5 2 FE F − 5 2 GF F = 5 2 CF 0 FF − FE F − GF F = CF 0⇒F + GF F = CF 24 5 F24− F + 5 1 GF F − 5 1 CF 24=0⇒ F = CF F GF 2F = CF 24 ⇒ 5F = CF 12 5 . 4. Result: ● Final Conclusion: The force in member is (Tension). (b) Force in member CH 1. Formula: Use the Method of Sections. Cut the truss vertically through members , , , and . Analyze the right portion (joints ) and take moments about joint to find . Then use Joint equilibrium to find . 2. Substitution: Right portion mome