In structural engineering, beam stiffness is a beam’s ability to resist deflection, or bending, when a bending moment is applied. A bending moment results when a force is applied somewhere in the middle of a beam fixed at one or both ends. It will also occur if a torque is applied to the beam, although this is less common in real-world applications. Beam stiffness is affected by both the material of the beam and the shape of the beam’s cross section.
The motivation for designing a beam that resists deflection is easy to appreciate in the case of a bridge. For example, concrete is great for its compressive strength, but a bridge made solely of concrete would be a poor choice. Concrete is not strong when it is bent; a bridge made of concrete will sag in the middle due to gravity and likely will fall apart. The bridge could be much stronger if it had some sort of foundation, or skeleton, to keep it from deflecting in the middle too much.
Beam stiffness can be calculated using two factors. The first factor is the elastic modulus. This is a material property that relates to the material’s tendency to deform, or stretch out, when stress is applied. If the beam is made of stainless steel, it will have a higher elastic modulus than, say, aluminum. This is because if the same forces are applied to the same shape of both steel and aluminum, the steel object would deform less. Even though metals don’t deform much compared to rubber bands, they behave in the same way; they stretch out proportionally to how hard a force pulls on them. So, a beam made from a material with a high elastic modulus will have a high beam stiffness, making it less likely to bend.
The other factor in beam stiffness is the area moment of inertia of the beam’s cross section. This has to do with the vertical distribution of material close to or away from the center of the beam. An often-used beam design in civil engineering with a high area moment of inertia is the I-beam. It is called the I-beam because of its cross section, which is shaped like the letter ‘I’. This shape focuses much of the material toward the bottom and top of the cross section with only enough material in the central regions to connect the outer parts. The reason for this shape is that it maximizes the area moment of inertia for a given amount of material. The most common material used in I-beams is steel, which provides a high elastic modulus. These two properties of the I-beam give it a very high beam stiffness.