By what factor does the load-carrying capacity of a beam increase when the depth doubles?

The load-carrying capacity of a beam is primarily influenced by its moment of inertia, which is a function of its geometry. Specifically, when discussing the depth of a beam, the moment of inertia increases significantly as the depth increases.

When the depth of a beam is doubled, the moment of inertia increases by a factor of eight, due to the relationship that governs the moment of inertia for a rectangular beam section, which is proportional to the depth raised to the third power (d^3). However, in terms of practical application and the context of this question, the increased capacity in relation to the load-carrying capacity typically refers to common guidelines in structural performance.

Under typical circumstances, when you double the depth of a beam, the load-carrying capacity approximately increases by a factor of four. This is a critical understanding in structural engineering and fire service practice as it helps in selecting appropriate materials and designing beams that will effectively support the intended loads, especially in fire scenarios where structural integrity is paramount.

Thus, the correct answer is that the load-carrying capacity of a beam increases by a factor of four when the depth is doubled.