Average Shear Stress

While normal stress acts perpendicular to the surface of a material to pull it apart or push it together, Shear Stress acts parallel to the surface. It is the stress component that tends to cause one part of the material to slide or shear past another.

What is Average Shear Stress?

When a force is applied parallel to a cross-sectional area, it creates an Internal Shear Force $V$. The intensity of this force distributed over the area $A$ is called the Average Shear Stress ($\tau$, tau).

Engineering Note: We call this the "average" shear stress because, in reality, shear stress is not perfectly uniformly distributed across the cross-section. However, for common connections like bolts and pins, assuming a uniform distribution is standard and safe engineering practice.

Single Shear vs. Double Shear

One of the most common applications of average shear stress is analyzing connections (like bolts, pins, or rivets). These connections often fail in shear.

Single Shear

In a single shear connection, the applied force $F$ is resisted by a single cross-sectional area of the pin. The internal shear force $V$ is equal to the applied force $F$.

$V = F$ $\tau = \frac{F}{A}$

Double Shear

In a double shear connection, the pin connects three plates, and the force is resisted by two cross-sectional areas. The internal shear force $V$ at each cross-section is half of the applied force $F$.

$V = \frac{F}{2}$ $\tau = \frac{V}{A} = \frac{F}{2A}$

Engineering Design Principle: Using a double shear connection cuts the shear stress on the pin in half compared to a single shear connection of the same diameter, safely allowing the connection to carry twice the load.

Common Mistakes

1. Confusing Normal Area with Shear Area: In normal stress ($\sigma = F/A$), $A$ is perpendicular to the force. In shear stress ($\tau = V/A$), $A$ is parallel to the force.
2. Forgetting to Check for Double Shear: Always draw a Free-Body Diagram of the pin to see if one or two planes are resisting the load. Missing a double shear condition will lead to calculating a stress that is twice as high as reality.