MECHANICS  THEORY



Shear Stress

Shear Loading on Plate
 
In addition to
normal stress that was covered
in the previous section, shear stress is an important form of stress that
needs to be understood and calculated. Most structures need to be designed
for both normal and shear stress limits.
Similar to average normal stress (σ = P/A),
the average shear stress is defined as the the shear load divided by the
area.




Shear Loading on Bolt 

Shear loads are generally identified by the symbol V and shear stress by the
greek symbol tau, τ. However, this is not a fixed rule.
Another way to express the same concept is to define the total surface parallel
load V as




Shear Loading from Hole Punch 

where A is the area of the surface.
One confusing issue with shear stress is direction. Unlike normal stress with
compression or tension, shear stress is the same if it shears left to right or
right to left. The magnitude of shear stress is the important parameter that needs
to be considered.




Shear Loading on Lap Joint 

It is important to remember that V/A is only the "average" shear
stress. In actual shear stress distribution, it is not uniform and the maximum
shear stress will be higher than the average shear stress. However, for this basic
solid mechanics course, it is assumed that the shear load is uniformly distributed
across the shear surface. 





Bearing Stress

Bearing Stress Due to a Bolt
Actual Bearing Stress on Plate


The average bearing stress is the force pushing against a structure divided by the area. Exact bearing stress is more complicated but for most applications, the following equation works well for the average,
This relationship can be further refined by using the width and height
of the bearing area as
Experiments have shown that the bearing stress distribution is more
elliptical shaped and not uniform but due to calculation difficulties, a rectangular approximation is assumed, dt.



