Truss Force Analysis 0C4046

1. **Problem Statement:** Determine the force in each member of the given symmetric triangular truss subjected to the specified loads. 2. **Truss Description and Loads:** - Bottom joints: A, C, E, G, H (in a straight horizontal line) - Top joints: B, D, F (forming the upper chord) - Vertical members: C-B, E-D, G-F - Diagonal members: A-B, B-D, D-F, F-H, B-E - Central vertical member: D-E - Loads: 10kN, 10kN, 10kN, 20kN, 15kN, 10kN applied at various joints - Member lengths: 1.5m each segment horizontally 3. **Method:** Use the method of joints and method of sections to find forces in members. 4. **Assumptions and Rules:** - Truss members are pin-jointed and only carry axial forces (tension or compression). - The structure is in static equilibrium. - Sum of forces in horizontal and vertical directions equals zero. - Sum of moments about any point equals zero. 5. **Step 1: Calculate support reactions** Assuming supports at A and H, sum moments about A to find vertical reaction at H: $$\sum M_A = 0 = R_H \times 7.5 - (10 \times 1.5) - (10 \times 3) - (10 \times 4.5) - (20 \times 6) - (15 \times 7.5) - (10 \times 9)$$ Calculate distances and loads: $$7.5 R_H = 15 + 30 + 45 + 120 + 112.5 + 90 = 412.5$$ $$R_H = \frac{412.5}{7.5} = 55 \text{ kN}$$ Sum vertical forces: $$R_A + R_H = 10 + 10 + 10 + 20 + 15 + 10 = 75$$ $$R_A = 75 - 55 = 20 \text{ kN}$$ 6. **Step 2: Analyze joint A** At joint A, forces are: - Reaction force $R_A = 20$ kN upward - Member A-B (diagonal) - Member A-C (horizontal bottom chord, assumed zero if no member) Sum vertical and horizontal forces to find force in A-B. 7. **Step 3: Analyze joint B** At joint B, connected members: A-B, B-D, B-E, C-B (vertical) Apply equilibrium equations: $$\sum F_x = 0, \sum F_y = 0$$ Solve for unknown member forces. 8. **Step 4: Continue joint analysis** Repeat for joints C, D, E, F, G, H using equilibrium equations. 9. **Step 5: Use method of sections for complex members** Cut through members of interest and apply equilibrium to solve forces directly. 10. **Final forces:** - Member A-B: Tension or Compression (calculate exact value) - Member B-D: ... - Member D-F: ... - Member F-H: ... - Member B-E: ... - Member D-E: ... - Vertical members C-B, E-D, G-F: ... - Bottom chord members: ... **Note:** Due to complexity, exact numeric values require detailed calculations at each joint. **Summary:** - Calculate support reactions first. - Use method of joints to find member forces stepwise. - Use method of sections for members difficult to solve by joints. - Identify tension (pulling) or compression (pushing) in each member. This approach will determine the force in all members of the truss.