This physics problem tests your understanding of fundamental physical laws and their applications. The step-by-step solution below breaks down the problem using relevant equations and physical reasoning.
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To solve question number 2, we need to determine the reactions at the supports, and then draw the Shear Force Diagram (SFD) and Bending Moment Diagram (BMD). The beam is simply supported at W (pin support) and C (roller support). The loads are: • 10 kN at 2 m from W • 15 kN at 5 m from W (2 m + 3 m) • 20 kN at 7 m from W (2 m + 3 m + 2 m) The total length of the beam is 8 m (2 m + 3 m + 2 m + 1 m). Step 1: Determine Reactions at Supports Let R_W be the vertical reaction at W and R_C be the vertical reaction at C. Apply the equilibrium equations: 1. Sum of vertical forces equals zero ( F_y = 0): R_W + R_C - 10\, kN - 15\, kN - 20\, kN = 0 R_W + R_C = 45\, kN (1) 2. Sum of moments about W equals zero ( M_W = 0, taking clockwise moments as positive): (10\, kN × 2\, m) + (15\, kN × 5\, m) + (20\, kN × 7\, m) - (R_C × 8\, m) = 0 20\, kN·m + 75\, kN·m + 140\, kN·m - 8R_C = 0 235\, kN·m - 8R_C = 0 8R_C = 235\, kN·m R_C = (235)/(8)\, kN R_C = 29.375\, kN Substitute R_C into equation (1): R_W + 29.375\, kN = 45\, kN R_W = 45\, kN - 29.375\, kN R_W = 15.625\, kN The reactions at the supports are: R_W = 15.625\, kN $R_C = 29.