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

• A. P*L/4
• B. P*L/2
• C. P*L
• D. 0

Answer: (A)

When a simply supported beam carries a single point load at midspan, the supports share the load equally, so each reaction is P/2. Between the left support and the center, the shear is constant at P/2, so the bending moment increases linearly from zero at the left end. The moment at a distance x from the left support is M(x) = (P/2) x. At the center, where x = L/2, the maximum moment is Mmax = (P/2) · (L/2) = P L / 4. The moment then decreases symmetrically to zero at the right support.

Thus, the maximum bending moment is P L / 4.