Elastic shear stress in I-shaped beams
In the odd case where you need a beam to remain elastic under shear (crane structures, lifting devices), you'd calculate the maximum shear stress according to this formula.
I noticed a shortcut when doing this for a symmetric W shape. (I noticed on my own although I'm sure I'm not the first person to notice this).
At the midheight where shear stress is maximum, Q = Z / 2, where Z is the plastic section modulus.
It makes perfect sense, since to calculate Q you integrate y dA over half the section, and to calculate Z you integrate |y| dA over the entire section.
So you can use a tabulated value instead of doing a calculation. It should work for rectangular and square HSS too; anything doubly symmetric.
Posted Jan 25, 2026, 12:27 PM UTC
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