Shear stresses due to bending
I am really confused on this topic of transverse and longitudinal shear in a beam and would appreciate some help. I’ve looked through a few textbooks but haven’t had any luck clearing this up in my mind.
So my practical understanding is that bending forces cause longitudinal shear stresses. And the transverse loading on a beam cause transverse shear forces. And we usually design a beam for the maximum transverse shear. And we might consider longitudinal shear in composite beams to ensure no slipping.
But now in theory though, say in a SS beam with a uniform distributed load, the beam is in pure bending in the middle because shear force V = 0. Per textbooks I have read, our shear stress t is also 0 here, which makes sense given our equation for shear stress is t = VQ/It.
But if we’re acknowledging that bending cause longitudinal shear stresses, and on any single discrete solid element, transverse and longitudinal shears are always equal for equilibrium, wouldnt you have shear stresses in your middle portion of the beam even though V = 0?
When we look at the part of the beam near support, where V is maximum, we would use VQ/It to find our shear stress. This implies that longitudinal and transverse shears are directly related and equal since we are using Q whose derivation is based on longitudinal shear due to bending. And this part totally makes sense to me. What doesn’t make sense is why we would now turn to the pure bending portion of the beam and say « no there are no shear stresses here »