Let me first say that I am impressed! Your writing is generally very clear and ordered, and shows decent flow and clarity. While I have little to no direct experience with technical writing, I have done what I can. I cleaned it up a bit, edited for grammar and flow, but otherwise your work remains unchanged. I have not attempted to revise your concept or general ideas. I am not well versed enough in the subject matter to undertake a re-write. I hope this helps:
Shear stress refers to the amount of shear force per unit area over a given cross section. Shear force is defined by the equation \tau= V/A, where V is the shear force and A is the cross-sectional area parallel to the shear force vector. Direct shear stress is shear stress that is caused by an applied force, rather than from a torque. Shear stress is important because it is often the cause of mechanical failure in many types of connections such as pins, bolts, and hinges.
Fig. 1 is a simple bolt connection between members A and B.
After the cut, the internal forces are exposed and it is clear that the shear force (V) is equal to P.
Fig. 2 is an example of what is called “double shear”. Double shear occurs after the internal forces are exposed. When this happens, we find that there are two locations where shear force is present. The term “double shear” comes from the fact that shear stress is present in two locations. By using the equations for static equilibrium (a sum of forces in the y = 0 here), we find that 2V=P or V=1/2P.
To best understand direct shear stress, one must first understand what shear force is. Shear force is the action that causes two sections of a material to slide over one another. To showcase this, visualize the action of rubbing two hands together. The friction between one’s palms makes it necessary to push one hand alongside the other. This “push” is what is called a force in physics. The word shear describes the direction of the force being parallel to the surfaces which want to slide against one other. In the example of rubbing one’s hands together, the shear force takes place between one’s hands. However, shear force can also happen inside a solid object and cause it to “slip” into two separate pieces.
Direct shear stress is simply the amount of shear force per unit of area. When one rubs one’s hands together, the area would refer to the area of the palm. Shear stress is an important topic because it can cause breakage or mechanical failure in many sorts of connections, such as bolts and hinges. For example, the bolt in fig. 3 will break if the pull on the connection is too great. Because shear stress is inversely proportional to area, we can increase the size of the bolt to prevent it from breaking.
Fig. 3 is a simple bolt connection. The arrows represent a force pulling on both sides of the connection. The figure indicates where shear stress is present, as well as the point at which the bolt wants to split in two directions.
Fig. 4 shows a tree on a slope. The black arrow represents the weight of the tree pushing straight down. Because the tree is on a slope, a portion of its weight is directed down the hill. This concept is represented by the red arrow. The red arrow denotes a shear force, as it is parallel to the hill. This tree is experiencing a shear stress. If the tree’s roots are not strong enough, or the shear force is too great, the tree will give way and slide down the hill.