Meriam, Kraige & Bolton — Equilibrium of Rigid Bodies: Problem 4_34

⚡ Mecademy AIENG정역학 · ch4  Problem Statement Calculate the forces in members , , and . Solve for each force from an equilibrium equation which contains that force as the only unknown. Problem 4/34 To solve for the requested member forces using only one equilibrium equation for each, we use the Method of Sections. We first define a coordinate system with joint at the origin . Based on the provided dimensions, the coordinates of the relevant joints are: (since and is at ) We pass a section through members , , and and consider the right-hand portion of the truss, which consists of joints and a downward external load of at joint . (a) Force in member To isolate , we sum moments about joint because the lines of action of the other two unknown forces, and , both pass through point . 1. Formula: 2. Substitution: Assuming is in tension (pulling left from the right section), its moment arm to is the vertical distance . The load of at has a horizontal moment arm to of . 3. Calculation: BCBEEF G(0,0) G=(0,0) A=(0,3) F=(3,0) B=(3,3) E=(6,1)CE=2 mCy=3 C=(6,3) D=(9,3) BCBEEF C,D,E14 kND BC F BC E F BE F EF E M =∑ E 0 F BC E(6,1)3 m−1 m=2 m 14 kND(9,3)E9 m−6 m=3 m (F ⋅ BC 2 m)−(14 kN⋅3 m)=0 2F = BC 42 4. Result: (Tension) ● Final Conclusion: The force in member is in tension. (b) Force in member To isolate , we sum moments about joint because the lines of action of and both pass through point . 1. Formula: 2. Substitution: The load at has a horizontal arm to of . For at , let's assume tens