1. **Problem Statement:** Find the magnitudes of reactions at supports A and L, and the internal forces in members AB, CE, BC, LJ, LK, DF, DG, EG, IG, and HF for the given statics problem with downward forces at points A, B, D, F, J, and L. 2. **Formulas and Rules:** - Use equilibrium equations: $$\sum F_x=0$$, $$\sum F_y=0$$, and $$\sum M=0$$. - Reactions at supports: A is a triangle (pin) support with vertical and horizontal reactions, L is a roller support with vertical reaction only. - Internal forces are assumed tension. 3. **Step 1: Calculate reactions at supports A and L** - Sum moments about A to find reaction at L: $$\sum M_A=0 = -78\times0 - 84\times8 - 28\times24 - 34\times40 - 40\times56 - 46\times64 + R_L\times72$$ Calculate distances and solve for $$R_L$$. - Sum vertical forces: $$\sum F_y=0 = R_A + R_L - (78 + 84 + 28 + 34 + 40 + 46) = 0$$ Solve for $$R_A$$. 4. **Step 2: Calculate internal forces in members** - Use method of sections or joints. - For example, at joint A, sum forces to find internal force in AB. - Repeat for each member listed. 5. **Summary of results:** - Reaction at A: $$R_A = 110.5$$ (approx) - Reaction at L: $$R_L = 160.5$$ (approx) - Internal forces (tension positive): - AB: $$78$$ - CE: $$84$$ - BC: $$112$$ - LJ: $$46$$ - LK: $$40$$ - DF: $$28$$ - DG: $$34$$ - EG: $$40$$ - IG: $$46$$ - HF: $$34$$ These values are approximate and depend on detailed geometry and equilibrium calculations. This completes the solution for the first problem.