If a girder's depth is doubled, how many times the weight can it support compared to its original capacity?

When the depth of a girder is doubled, its ability to support weight increases significantly due to the principles of structural engineering and the mechanics of materials. The capacity to support loads primarily depends on the moment of inertia, which is a geometric property of a cross-section that contributes to its strength and rigidity.

The moment of inertia for a rectangular cross-section is proportional to the cube of its depth. Therefore, if the depth is doubled, the moment of inertia increases by a factor of two cubed, which is eight. This means that the girder can support a weight that is four times greater than its original capacity.

This significant change in capacity occurs because increasing the depth enhances the girder's resistance to bending. By doubling the depth, the girder not only becomes stronger in resisting bending moments but also has a more efficient distribution of material, contributing to an overall higher load-bearing capacity.

In contrast, the other options do not account for the correct relationship between depth and weight support. The increase in capacity is not a simple doubling or halving but a multiplication directly related to changes in the geometry, leading to the conclusion that the girder can indeed support four times its original weight.