What really happens when we cut a cake using a knife? In physics, we could say that the cake experiences stress. Usually when we cut a cake, we hold the knife straight and apply the force perpendicular to the surface area.
So can you guess what type of stress this is? It is normal stress as the force is acting perpendicular to this area. But what about these cross-sectional areas of the cake?
The area on top is not the only area that experiences stress. As we pierce the knife in, this cross-sectional area experiences stress too. It doesn't look too obvious but it does experience stress. We can also see that the force is not perpendicular to this area. It acts parallel to it as we are pushing the knife straight down.
If the force acts parallel to the surface, it exerts shear stress. This stress tries to push the two surfaces away from each other and hence results in plastic deformation. So this is the basic difference between normal stress and shear stress.
Normal stress is where the force is acting perpendicular to the area of contact while shear stress is the force that acts parallel to the area. Let's take another example which explains shear stress better. Here's a beam and assume that it's fixed at its base. If we apply normal force to this cross-sectional area, then we know that the stress experienced by the beam will be normal stress which is simply given by F over A, where F is the applied force and A is this cross-sectional area. This will result in a normal strain in the beam which is given by Delta L over L, where Delta L is the change in length and L is the original length.
Now suppose that we apply a force in this direction, parallel to area A. Again the beam will experience some stress but this time it will be a shear stress. The equation or formula for shear stress is the same as that of normal stress. Stress is simply the applied force per unit area whether it's acting perpendicular or parallel to the area.
What about the deformation in the beam by shear force? Here the deformation will be something like this. The object is stretched to some extent. Note that the beam is fixed to the base.
So this cross-sectional surface will remain where it is whereas the cross sections above it will all get displaced to the right by increasing amounts. Now look at the maximum displacement here. Let's call it delta X. We know that this length is L. It's perpendicular to this.
Also notice that there is an angle formed here. We can call it theta. With this information in place, let us define what shear strain is.
Shear strain is simply equal to tangent of theta. Yes, shear strain is simply the tangent of this angle. But what is tan theta?
We know that it's the opposite side over the adjacent side. Here, the length of the opposite side of theta is delta x and length of adjacent side is L. So it's equal to delta x over L.
So that's how shear strain is defined. Length of the deformation at its maximum over this perpendicular length.