Bending is not the only thing happening inside a loaded beam. The two halves either side of any horizontal cut are trying to slide past one another, and something has to stop them — the material itself in a solid beam, the glue or the nails or the welds in a built-up one. The relation is $\tau = \dfrac{V Q}{I b}$, read aloud tau equals V Q over I b.

$\tau$ — the Greek letter tau — is the transverse shear stress at the cut, in MPa. $V$ is the transverse shear force at that section, in N. $I$ is the second moment of area of the WHOLE section, in mm⁴. $b$ is the width of the section AT THE CUT, in mm — for a plate girder that is the web thickness, not the flange width, which is why the web is where shear is checked.

Then there is $Q$, and it deserves its own paragraph because it is the subtlest given in this course. $Q$ is the first moment of the area beyond the cut: take the part of the cross-section on one side of your cut, call its area $A'$, find the distance $\bar{y}'$ from the neutral axis to THAT piece's own centroid, and multiply. $Q = A' \bar{y}'$, in mm³. Two errors live here and both are worth a clean factor of two: taking the whole section instead of the part beyond the cut (whose first moment about its own centroid is zero, by definition), and measuring $\bar{y}'$ to the outer fibre instead of to that area's centre.

For a solid rectangle cut at the neutral axis the algebra tidies up beautifully: $\tau_{max} = 1.5\,\dfrac{V}{A}$. Exactly one and a half times the average. Memorise that as a sanity rail — if your VQ/Ib does not land on it for a rectangle, something upstream is wrong.

Stop one step earlier and you get the shear flow, $q = \dfrac{V Q}{I}$, in newtons per millimetre. It is the same numerator before it is spread over the width, and it is what a joint is actually rated in: force per unit length along the beam. Nail spacing, bolt pitch and fillet weld size all come out of $q$, not out of $\tau$.