# Shear and Bulk Stress and Strain Equations

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• 0:02 Normal Stress & Strain
• 1:32 Shear Stress & Strain
• 3:14 Bulk Stress & Strain
• 4:52 Lesson Summary
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Lesson Transcript
Instructor: Damien Howard

Damien has a master's degree in physics and has taught physics lab to college students.

Discover how to tell when an object is experiencing normal, shear, and bulk stress and strain in this lesson. Then, learn about the basic formulas we use to find shear and bulk stresses, strains, and moduli.

## Normal Stress and Strain

At some point in your life you've probably had the experience of having to pack some of your belongings into a box either due to moving or simply putting some stuff in storage. If you had to move a large heavy box just a short distance to get it out of your way, you might have decided it was easier to push it along the floor than pick it up. In a physics problem, we would view this as you creating a force that pushes the box in the direction of that force. However, is moving the box the only effect the force has on it?

You might have noticed that when you push the box, the side bends a slight amount. The force you are creating is not only moving the box, it's also creating stress in the box. This stress is an internal force per unit area. The deformation the object experiences, in our case the bending you're seeing, is the strain on the box due to stress. From these definitions we can get the basic equations for stress and strain as follows:

There are actually multiple types of stress and strain that depend on how the force is being applied to an object. In our example, we are seeing normal stress and strain, where the force is perpendicular or normal to the box's surface. Along with normal stress and strain, two other common types are shear and bulk stress and strain. In this lesson, we'll go over both shear and bulk stress and strain and the equations associated with them.

## Shear Stress and Strain

While normal stress and strain are the result of a force being applied perpendicularly to the surface of an object, shear stress and strain occur when the force is applied tangentially or parallel to the object's surface. In our previous example, if you put your hands on top of the box to push it across the floor instead of on its side, you would be creating shear stress in the box.

For finding the shear stress equation, the main difference from the general formula is that we've specified the force as a tangential force. This also means that the area we are looking at is the cross sectional area parallel to the tangential force. We get:

Since we are applying a tangential force, for shear strain we are going to have a tangential displacement. So:

If we know both the stress and strain a material is undergoing, we can use them to find something called the shear modulus. This tells us the measure of how well a material resists deformation due to a tangential force. The ratio of stress to strain will give us the shear modulus. In other words:

This is useful because different materials deform to varying degrees when subjected to the same amount of stress. Imagine you had two identically shaped objects, one made of cardboard and the other of granite. If they experienced the same amount of stress, which one would deform more? It's the cardboard object, and the shear modulus is how we represent these different materials' varying ability to resist deformation due to a tangential force.

## Bulk Stress and Strain

Much like before, we differentiate bulk stress and strain from shear and normal stress and strain by how force is being applied to the object. For bulk stress and strain, force is being applied on all sides of the object while pushing inwards. Because of this, bulk stress is commonly associated with pressure.

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