If you have an 'I' cross section cantilever beam and you want to make it stiffer, do you increase the height or width?

If you have an I ‘i’ cross section cantilever beam and you want to make it stiffer. Do you increase the height or width

Making a cantilever beam stiffer involves reducing deflection. Deflection depends on the following equation:

(Load)*(Length) / (Modulus of Elasticity) * (Area Moment of Inertia)

The cross section relates directly to the area moment of inertia. As such, looking at the following equations below, an “I” cross-section relates to a square, just without the excess material. Increasing the height would have a factor of 3 as opposed to the width, which has a factor of 1.

I-beams are used very commonly in structural applications since you’re able to optimize the strength-to-weight ratio of the cross-section.

This is a good answer, I just wanted to add on to it a bit in a simpler way. Generally speaking, the more mass you can get farther away from the bending axis, the stiffer the material will be. I beams are already optimized to do this. If you wanted to make it even stiffer, you could just add more thickness to the top and bottom flanges of the beam; or you can increase the height to shift the mass you do have farther away.


This question doesn’t dictate the direction the stress is being applied. It really depends if the beam is being bent vertically or horizontally. This should be stated up-front before diving into calculations.