In a text I'm reading on Euler-Bernoulli beam theory it is said that as the beam is assumed to be thin, the effect of transverse shear stress is ignored. If the beam is thick, we need to use Timoshenko beam theory which accounts for transverse shear.
Let's consider a simple loading case:
For the same load F, if the beam is thin, the normal stress distribution inside the cross section of the beam is bigger since the smaller cross sectional area has to be in higher state of stress to counter the moment caused by the load. If the beam is thicker, the same moment is spread across a larger area and the stresses across the cross section are smaller.
But these same normal forces also cause the transverse shear:
Transverse shear is caused by the fact that since the moment felt by the beam is higher when we move to the left, the normal forces inside the beam when considering a small box inside the beam (as in the above picture) are at imbalance and thus a transverse shear has to be present to maintain equilibrium. But if the beam is thick and the normal forces are smaller, why does the transverse shear now become relevant? Shouldn't the situation be the other way around: Thicker the beam, smaller the transverse shear?
