For a simply supported beam with a center point load P, what is the maximum bending moment?

• A. P*L/8
• B. P*L/2
• C. P*L/4
• D. P*L

Answer: (C)

The maximum bending moment occurs at midspan because the load is centered and the beam is symmetric. The supports share the load equally, so each reaction is P/2. On the left side, the shear is constant at P/2, so the bending moment increases linearly with distance from the left support: M(x) = (P/2) x. At the center, x = L/2, giving M = (P/2)(L/2) = P L/4. By symmetry, the right side mirrors this, and the moment returns to zero at the right support. Therefore, the largest moment is at midspan with value P*L/4.