Average Shear Stress (τ = V/A)

Where normal stress pulls a section apart, shear stress slides it sideways — the scissors action that cuts a bolt or tears a weld. The formula assumes the stress is spread evenly over the sheared area, which is a fiction (in a round bar under transverse shear the true peak is about a third higher at the centre), but it is the fiction every bolt code is calibrated to. A bolt with 200 mm² of shank carrying 20 kN across a splice sees τ = 20 000 ÷ 0.0002 = 100 MPa.

The detail that gets missed is counting shear planes. A bolt in a lap joint has one plane; the same bolt in a double-shear butt splice has two, and doubling the area halves the stress — so use $A = n \times A_{\mathrm{bolt}}$. The consequences of getting connections wrong are not academic: the Hyatt Regency walkway collapse in Kansas City in 1981 killed 114 people because a shop-drawing change doubled the load on a single rod-and-washer connection, and it tore straight through the box beam. The joint, not the beam, is almost always the weakest link.