Which statement about the load-bearing capacity of evenly distributed loads on beams is true?

Which statement about the load-bearing capacity of evenly distributed loads on beams is true?

• A. Twice as much as a concentrated load
• B. The same as a concentrated load
• C. Half as much as a concentrated load
• D. Four times as much as a concentrated load

Answer: (A)

Think in terms of bending moments. The beam’s capacity is governed by the maximum moment it must resist, which depends on how the load is applied. For a simply supported beam: - a uniformly distributed load w over the span gives Mmax = w L^2 / 8. - a single concentrated load P at midspan gives Mmax = P L / 4. If you compare the same total load, W, carried either as a distributed load (W = wL) or as a midspan point load (P = W), the maximum moments are Mmax_udl = W L / 8 and Mmax_conc = W L / 4. The concentrated load produces twice the moment of the distributed load with the same total load. Therefore, to reach a given allowable moment, the total distributed load you can carry is twice that of the concentrated load. That’s why the correct statement says the load-bearing capacity of evenly distributed loads is twice as much as a concentrated load. The other options don’t fit because the moment comparisons don’t support equal, half, or four times the capacity for the same beam and span.

Think in terms of bending moments. The beam’s capacity is governed by the maximum moment it must resist, which depends on how the load is applied.

For a simply supported beam:

• a uniformly distributed load w over the span gives Mmax = w L^2 / 8.

• a single concentrated load P at midspan gives Mmax = P L / 4.

If you compare the same total load, W, carried either as a distributed load (W = wL) or as a midspan point load (P = W), the maximum moments are Mmax_udl = W L / 8 and Mmax_conc = W L / 4. The concentrated load produces twice the moment of the distributed load with the same total load. Therefore, to reach a given allowable moment, the total distributed load you can carry is twice that of the concentrated load.

That’s why the correct statement says the load-bearing capacity of evenly distributed loads is twice as much as a concentrated load. The other options don’t fit because the moment comparisons don’t support equal, half, or four times the capacity for the same beam and span.