Consider a beam subjected to an arbitrary loading, where the loads are only present in the plane of bending. The x-y plane is the plane of bending.
If I take a stress element in the beam, there will be normal stresses and transverse and longitudinal shear stresses acting on it as shown.
I'm interested in knowing whether shear stresses appear on the shaded face and on the face opposite to it. The books that I've been following say that there will be no stress on this face, and the state of stress will be a plane stress one.
However, I feel like there will be a tendency of vertical layers slipping past each other (as shown below) when the loads will be applied and that should result in a shear stress on the shaded face.
Why the stresses on the shaded face and the face opposite to it ignored?
Best Answer
Regarding your first diagram, the convention upon viewing is to assume that the loads are applied to the entire top width (in and out of the page). This, along with a few other assumptions, allows straightforward application of Euler-Bernoulli beam theory to obtain closed-form expressions for the stress, deflection, slope, and curvature, for example.
In this sense, "point load" is a misnomer because those loads appears as a point only in the side view. (Alternatively, we might idealize the beam as a 2D object, and then certain loads would appear as points.)
In real life, true point and line loads do not exist, but Saint-Venant's principle tells us that a distributed load can look like an idealized point or line load as we move farther away.
If you choose to specify that the loads are true 3D point loads that are applied only in the plane you show in your second image, then a shear stress would indeed arise on the plane you shaded. Solving this problem is much more complex, which may be why you haven't found an associated discussion in the references you're consulting.