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Physics 101: Help and Review17 chapters | 212 lessons

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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.

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** 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.

*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

So, we can calculate that the bottom can of your 12-can-high wall is under 1.76 pounds of compressive stress (since the 11 cans on top of it all add 0.16 pounds each) and it will, thus, be 1-3/4 inches shorter due to all the weight on top of it. If you calculate the compressive stress at each level of your wall, you'll see that the compressive stress has made your wall a total of 10.56 inches shorter. That's why your roommate's presence is still able to reach you!

After you figure out that you need a wall that's 14 cans tall to block your annoying roommate, you gleefully place the 14th row of cans on top of each column and sit back, knowing his shenanigans are now completely blocked. However, a sickening creaking sound shortly follows as the cans at the bottom or your wall collapse and send the rest of the wall crashing down, allowing a pent-up flood of roommate to re-invade your previously serene space.

Unfortunately, the compressive stress on those bottom cans exceeded the **compressive stress maximum** for your construction material! The maximum is the point at which any material is taking the most possible stress it can without breaking. In the case of your cans, the material could only handle the weight of 11.9 cans, and the compressive stress of the 13+ cans stacked on top of it, unfortunately, caused a serious collapse.

So, what have we learned (besides the fact that we need another material to block annoying roommates)? We've seen that **compressive stress** is a consideration in understanding how a material performs when under pressure. It's calculated by dividing the force applied to the material by the area it is applied to. A material that's under the most severe stress without breaking is at its **maximum**, after which the material fails and collapses.

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Physics 101: Help and Review17 chapters | 212 lessons

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