Shear stress in a beam

So far in this pathway, every stress we've looked at has been a normal stress, acting along the member: first from bending on its own, then from axial force and bending together. But a beam also carries shear force, which results from shear stress, which acts across the section rather than along the member. In most beams, shear stress is a secondary concern, because the bending stress becomes critical long before the shear stress does. In a short, heavily loaded span, that isn't the case. So, in this step, we'll see why shear stress is spread so unevenly through an I-section, read it in Structure Bench with the $\tau$ chip, and check the peak by hand.

The model for this step: Shear stress in a short, heavily loaded beam — Shear stress in a short, heavily loaded beam. Orbit, read the results and hover the members; nothing you do here changes the model.

1.0 How shear stress is distributed through the section

Shear stress doesn't spread evenly over the cross-section. To see why, imagine slicing the beam horizontally at some height above the neutral axis, and look at a short length of the beam above that slice. Wherever there's a shear force, the bending moment is changing along the beam. So the bending stresses acting on the part above the slice are bigger at one end of our short length than at the other. Those two end forces don't balance, and the only thing left to keep that piece of beam in equilibrium is a shear force acting along the slice itself.

Where	Quantity	Value
Between the support and the load, at the neutral axis	$\tau$	96.3 MPa
Between the support and the load, in the flanges (from the colour bar: the card gives the web's peak)	$\tau$	22.8 MPa
Under the load, at the extreme fibres	$\sigma$	114.2 MPa

Shear stress in a beam

1.0 How shear stress is distributed through the section

2.0 The model

3.0 What you'll see

4.0 What to take from this step