Meriam, Kraige & Bolton — Equilibrium of Rigid Bodies: Problem 4_31

⚡ Mecademy AIENG정역학 · ch4  Problem Statement Determine the force in member BE of the loaded truss. Problem 4/31 (a) Force in member BE ● Calculation Process 1. Geometry Analysis: Establish a coordinate system with joint A at the origin . Based on the provided dimensions: Joint B is at , Joint C is at , and Joint D is at . Joint G is at . The inclined member follows the line equation: . Joint E lies on this line at the same height as C (): . So, . Joint F lies on this line at the same height as B (): . So, . Member connects to . The length is . 2. Method of Sections: Pass a section cut through members , , and . Consider the equilibrium of the upper portion of the truss containing joints and . External loads on this section: at joint directed right. at joint directed right. Internal forces at the cut (assuming tension): acting vertically at . acting along the line from towards . acting from towards . (0,0) (0,2)(0,4)(0,6) (3,0) DGy−0= (x− 0−3 6−0 3)⇒y=−2x+6 y=44=−2x + E 6⇒ x = E 1 mE=(1,4) y=22=−2x + F 6⇒ x = F 2 mF=(2,2) BEB(0,2)E(1,4)L = BE = (1−0)+(4−2) 22 m 5 BCBEEF CD 6 kND(0,6) 5 kNC(0,4) F BC C F EF DGEF F BE EB 3. Moment Equilibrium: Take moments about joint to eliminate the unknown forces and (as their lines of action pass through ). Moment of load at : (Counter-clockwise). Moment of (assumed Tension): The force acts from towards . Vector . Force vector . Equating the moments: 4. Final Calculation: ● Final Conclusion: The force in member is in tension. ✨ Final Answer