Shear stress is an essential concept in engineering and physics. Shear stress measures the response of a material when forces are applied in different directions. Shear stress is sometimes called “tangential stress.”
If you’re working in manufacturing, you’ll want to understand shear stress, because it tells you how all sorts of materials, including fluids, will respond when you are doing different processes with them, and when they are going to reach some sort of deformation or breaking point. We’ll explain everything below.
What is Shear Stress?
Shear stress is a way of depicting just how much force material can take before it – simply – has had enough. Shear stress is the point at which internal sliding or deformation of a material begins when a force is applied parallel to the surface.
One could also think of this as the level of resistance to stress for that material. To break it down further, think of materials as being made with layers (which they are, on a microscopic level).
When forces (what we call “shear forces”) are applied, the layers of the material will be squished together, but eventually will begin moving, or sliding past each other in different directions as a deck of cards would. The point of sliding is the shear stress.
Therefore, it would be on an engineer’s agenda to learn everything about shear stress (as well as how to calculate it) when designing products such as buildings and bridges and of course, many commercial and personal products.
Knowing shear stress will provide engineers with very clear details regarding exactly how strong and stable a material is, as well as the total load (or weight) a material can take.
This way our structural components, like beams or columns, can withstand wind loads, earthquakes, and many not so predictable forces. In the design for aircraft, vehicles, and spacecraft, components need to withstand the potential forces of wind, acceleration, or braking.
In manufacturing, the knowledge of shear stress will indicate whether a material can go through certain processes such as drilling, cutting or bending.
Most materials, when subjected to too much shear stress, will deform, warp, or bend, which will affect material performance, stability, and reliability.
Accordingly, some materials including ceramic, glass and often other brittle materials are more susceptible to this sort of material failure, and are likely to crack and quickly break into pieces.
Shear stress is not used just with solid materials. In pipelines, hydraulic systems, and any other means of transporting liquids (and commonly gas), knowing the shear stress of many liquids (such as water) and gases with all sorts of viscosities and moving or flowing in varied pattern will assist manufacturers in creating systems that are mechanically sound and do not leak easily or wear prematurely.
For example, in a river, the water exerts shear stress on the river bed and the water eventually will erode, which will create a significantly changing landscape over time.
However, shear stress does not begin and end with material failure. Almost every day to day activity we take part in will create some form of shear stress.
When you use scissors to cut paper or fabric, or a knife to cut various foods, the blades apply shear stress to the item being cut. When we walk on a surface, our feet push against the surface – in a car, the car pushes against the surface.
Shear Stress Formula
In order to supply you with the shear stress equation (it’s a long equation, as there are different equations for different circumstances), we’re first going to need to go through what each of the symbols mean, which will hopefully help you to start understanding it a bit.
The table below is going to help explain what each of the symbols means (we’re going to include shear stress again for quick reference).
| Symbol | Meaning | Measured in |
|---|---|---|
| τ | Shear stress | Pa (pascals) or N/m² (newtons) |
| F | Force (or “shear force”) applied parallel to the material’s surface | N (newtons) |
| N | Number of forces (sometimes used for the “normal force”) | N (newtons) |
| A | Cross-section of the material that the force is applied to | m² |
| V | Internal force within the beam | N (newtons) |
| Q | First (static) moment of an area | m³ or mm³ (can vary) |
| t | Thickness of the particular area | m or mm |
| I | The moment of inertia (the material’s resistance to deformation) | m⁴ or mm⁴ |
| μ | dynamic viscosity of the fluid | Pa·s (pascal-seconds) or poise (P) |
| du/dy (or ∂u/∂y) | Velocity gradient (u = parallel to the direction of flow, y = perpendicular distance) | 1/s (per second) |
Shear Stress Formula Breakdown
Now, let’s look at the different equations to use to find the shear stress of a material:
Shear Stress of Steel
There can be some variation in the shear stress of steel depending on the type of steel, since this would be determined by the composition of the steel, grade, and treatment of the steel. Here is a good reference to shear stress for some of the more common steels.
| Steel Type | Shear Strength (N/mm^2) |
|---|---|
| Low-carbon HR steel | 345 |
| Low carbon C.R. sheet | 276 |
| ASTM A-36 | Depends on grade |
| 45-50 carbon HR sheet | 552 |
| Spring steel 1074, 1095 hardened to spring temper | 1,380 |
| COR-TEN Steel | 379 |
Shear Stress vs. Other Stresses
Shear stress is only one of many kinds of stress that could cause a material to change, deform, or react in some way. For example, bending stress causes a material to bend and tension stress causes a material to stretch. Below, is an illustration of how different kinds of stresses may impact a material:
