Which of the following combinations is true regarding decreasing the deflection of a steel beam?

To understand why the combination of options I and IV is the correct choice for decreasing the deflection of a steel beam, it's important to examine these strategies in the context of structural engineering principles.

First, addressing the implications of increasing the moment of inertia (I) of a beam: The moment of inertia is a measure of a beam's resistance to bending. When the moment of inertia is increased—either by selecting a different beam shape or size, or by adding material to the beam’s cross-section—this resists deflection under an applied load. Thus, increasing the beam’s cross-sectional dimensions or utilizing a more efficient shape, such as an I-beam instead of a rectangular beam, can significantly reduce deflection.

Next, considering the effect of using a stiffer material (IV): Steel has a high modulus of elasticity, which means that when using steel, the beam already has substantial resistance to deformation. However, when a designer opts for grade variations of steel that offer a higher modulus or uses reinforced steel composites, it enhances the beam’s ability to resist loads without excessive deflection. Essentially, using more robust materials contributes to lowering deflections.

The other strategies represented in options II and III, while also relevant to beam design and performance, do