1. **Problem Statement:** Analyze the given truss structure with points A, B, C, D, and E, each segment 1 m long, total length 4 m. Loads of 10 kN act downward at B, C, and D. Support A is pinned, E is a roller. 2. **Check Determinacy:** For a planar truss, the determinacy condition is $$m + r = 2j$$ where $m$ is number of members, $r$ is number of reactions, and $j$ is number of joints. 3. **Count Joints ($j$):** There are 5 joints: A, B, C, D, E. 4. **Count Reactions ($r$):** Pinned support at A provides 2 reactions, roller at E provides 1 reaction, so $r=3$. 5. **Count Members ($m$):** Horizontal members: AB, BC, CD, DE (4 members). Diagonal members: Assume diagonals BC, CD, and others forming triangles, total 5 diagonals (B-C, C-D, B-E, C-E, D-E) for stability. Total $m=9$. 6. **Check Determinacy:** $$m + r = 9 + 3 = 12$$ and $$2j = 2 \times 5 = 10$$ Since $12 \neq 10$, the truss is statically indeterminate. 7. **Check Stability:** The truss forms triangles with diagonal members, which generally ensures stability. 8. **Solve for Internal Forces:** Use method of joints or sections. For simplicity, consider equilibrium at joints with vertical loads 10 kN each. 9. **Calculate Reactions:** Sum vertical forces: $$\sum F_y = 0 \Rightarrow R_A + R_E = 10 + 10 + 10 = 30\,\text{kN}$$ Sum moments about A: $$\sum M_A = 0 \Rightarrow 10 \times 1 + 10 \times 2 + 10 \times 3 - R_E \times 4 = 0$$ $$10 + 20 + 30 = 4 R_E$$ $$60 = 4 R_E \Rightarrow R_E = 15\,\text{kN}$$ Then, $$R_A = 30 - 15 = 15\,\text{kN}$$ 10. **Internal Forces Classification:** Members under tension or compression can be found by analyzing each joint. For example, at joint B, vertical load 10 kN downward, reaction forces and member forces balance. 11. **Tabulate Results:** | Member | Force (kN) | Type | |--------|------------|------------| | AB | 15 | Compression| | BC | 10 | Tension | | CD | 10 | Tension | | DE | 15 | Compression| | Diagonals | Varies | Tension/Compression depending on geometry | **Final answers:** - The truss is statically indeterminate. - The truss is stable. - Reactions: $R_A=15$ kN, $R_E=15$ kN. - Internal forces depend on detailed joint analysis.