What does the deflection of a beam depend on?

The deflection of a beam primarily depends on the modulus of elasticity and the moment of inertia of the beam's cross-section. When considering how a beam bends under load, it is crucial to recognize that a higher modulus of elasticity indicates that the material is stiffer, which reduces the beam's deflection. Similarly, a larger moment of inertia, which is a geometric property related to the shape of the beam, helps in resisting bending. Thus, greater values of both these parameters result in less deflection for a given load.

Understanding these relationships is critical in beam design to ensure that structures can support the required loads without excessive deformation. The correct answer underscores that both the modulus of elasticity and the moment of inertia play a vital role in determining deflection under load, ultimately influencing the beam's overall performance and safety.

In contrast, other choices propose relationships that do not accurately reflect how deflection behaves in bending scenarios. For instance, stating that deflection is inversely proportional to the modulus of elasticity and moment of inertia does not capture the correct mechanical relationship where an increase in these properties results in a decrease in deflection.