Compressive Stress: Definition, Formula & Maximum

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  • 0:03 Introduction to…
  • 0:49 Compressive Stress Defined
  • 1:48 Compressive Stress Formula
  • 3:19 Compressive Stress Maximum
  • 4:14 Lesson Summary
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Lesson Transcript
Instructor: Benjamin Truitt
Compressive stress is a consideration in understanding how a material performs when under pressure. In this lesson, learn what compressive stress is as well as the formula necessary for calculating it.

Introduction to Compressive Stress

One morning you decide you're going to build a wall out of soda cans to shield you from your annoying roommate. Each can is 6 inches tall, and you calculate that the only way to block off the annoying roommate is to build a wall that's 6 feet high. You get to work and, using a lot of cans, you are able to build a wall that is 12 cans high, but, your annoying roommate is still annoying!

You measure your wall and discover that despite your careful construction, it's actually less than 6 feet tall! How is this possible? Well, it's possible thanks to the nature of compressive stress, the force that causes materials to flatten under pressure.To ensure your wall is tall enough, you'll need to calculate the impact of compressive stress on the cans.

Compressive Stress Defined

Compressive stress is the pressure on a given material when force or weight is applied to it. It's a key formula in designing any structure, since materials will become shorter under different amounts of weight. Think of a ball of clay that you press with your palm. The sides of the clay push out as it yields to the pressure, and the ball becomes flatter and wider as a result. In constructing a building, like a skyscraper, calculating compressive stress becomes essential to ensure that the building is constructed correctly and safely.

Compressive force is not just a consideration in how material is used, it also serves an important function in making structures that utilize this stress for design and purpose. The arch is a feature that takes advantage of the compressive stress on the material between the columns to hold it and keep it stable (as well as anything it's supporting). Thus, compressive stress makes possible designs like the arch, which allow bridges and cathedrals to be stable.

Compressive Stress Formula

Stress = Force/Area

The formula for calculating compressive stress is simple. It's computed by dividing the force applied by the area it is applied to. This formula is then used to understand how a given material will behave under the pressure it's expected to be under. So, if you take one of your cans for the wall down and calculate how many units of force is subject to the area of the top at each stage of the wall and divide that by the area of the can, you'll know the compressive stress each can is under.

For example, let's say that each can is known to compress 1-inch shorter for every pound of stress it is under, and each can weighs 1/2 pound and has a 1-inch radius. Now we can figure out the compressive stress:

stress = 0.5 pounds/(Pi)1^2 (since our can tops are circles, not squares)

stress = 0.5/3.14

stress = 0.16 pounds of stress for every can you stack on your wall

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