Method Of Joints For Truss / Roof
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This document shows a structural frame with 6 members (AB, BC, CD, DE, EF, and BF) and 6 external forces (3 kN, 1.5 kN, 1.5 kN). It performs static equilibrium calculations on each member to solve for the internal forces using the equations of equilibrium. The internal forces are: FAB = -2.12 kN, FBC = 2.12 kN, FCD = 2.12 kN, FDE = -2.12 kN, FEF = -1.5 kN. Members BF and FD are determined to have zero force.
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Method Of Joints For Truss / Roof
- 1. 3 kN C 2m B D 2m 1.5kN 1.5kN E A F 2m 2m 2m 2m MA + =0 -VE (8) + 3(4) + 1.5(8) = 0 VE = 3Kn + Fy = 0 VA + VE - 1.5 3 1.5 = 0 VA = 3kN + Fx = 0 HA = 0 Zero Force Member = BF and FD
- 2. FAB 1.5 kN . A FAF 3 kN + Fy = 0 3+FAB sin 45 - 1.5 = 0 FAB = -2.12 kN + Fx = 0 FAF - 2.12 cos 45 = 0 FAB = 1.5 kN FBC . B 2.12 + Fx = 0 -2.12 cos 45 + FBC 2.12 sin 45 = 0 FBC = 2.12 kN
- 3. 3kN . C 2.12 FCF FCD + Fx = 0 -2.12 cos 45 +FCD cos 45 = 0 FCD = 2.12 kN + Fy = 0 -2.12 sin 45 FCF -2.12 sin 45 3 = 0 FCF = 1.5 kN 2.12 .D FDE + Fx = 0 2.12 cos 45 +FDE cos 45 = 0 FDE = - 2.12 kN
- 4. 2.12 1.5 . EF FEF E EF 3 kN + Fx = 0 FEF + 2.12 cos 45 = 0 FEF = - 1.5 kN FREE BODY DIAGRAM