Why Is the I-Beam Shape Optimal for Moments of Inertia?

[joe tomei]

I recall that the shape of an i-beam is near optimal because of its moment of inertia. Does any have a reference that shows this, with explanation?

 

[brewnog]

Well, if you think about it, you want to have as much material as possible as far away as possible from the centroidal axis, without a risk of the web buckling.

A structural engineer once told me to imagine a square-section wooden beam, supporting it at both ends, and standing on it. He asked me where the maximum tensile and compressive forces were, and I told him; on the bottom and the top respectively. He then led me to conclude that the beam could be optimised by removing material from the areas where there was not much stress, and putting more material where the stresses were high. Not very scientific, but the reasoning is sound.


Efunda has some nice pages relating to moments of inertia of various sections. If you want to prove this for yourself, just plug in some numbers and see how it affects your second moment of area.

 

[joe tomei]

Thanks for your help.