# Metals 101-6 What is Strain

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Video Transcript

Strain is the comparison between how much an object is stretched and how long it was originally. Let’s take a closer look at what that means.

Take this steel welding wire for example.  It’s about five inches long. When I pull on it with my hands, it doesn’t seem to stretch at all.  But it actually is stretching a little bit — I’ll show you. You see, if I take a longer piece of the same wire, and pull on it with the same amount of force (about 20 pounds), you can easily see it stretch.  Even though one wire stretched more than the other, Both wires experienced the same amount of stress, and the same amount of strain.

Strain is the change in the length of an object divided by its original length.

The longer wire is 500 inches long.  By pulling on it with 20 pounds of force, I can stretch it about ½ inch.  Since we know the change in length and the original length, we can calculate the strain. Strain is the change of length over the original length.   We’ll use these symbols to clean things up…. The strain was about .5 inches divided by 500 inches. .5 divided by 500 is equal to .001. So the strain was .001.

But what about the units?  You might expect the units to be inches, but when we divide inches by inches, the inches cancel each other out, and the value becomes unitless.  We sometimes write in/in or mm/mm behind strain values to remind us what happened to the units, but strain is strain, no matter what units of length we use.

Let’s do the same experiment with metric units.  The long wire is about 13 meters long. When we apply a force of about 90 newtons, the wire stretches .013 meters or 13 millimeters.  .013/13 is equal to .001 meters per meter or millimeters per millimeter or inches per inch. The strain is the same because it is unitless.  Just be sure to use the same units for the change of length and the original length.

So, you might be asking — how much did the short wire stretch?  If we assume the strain happens equally along the wire then we can rearrange the formulas to find out.  Strain is the change of length divided by the original length. If the strain is .001 in/in and the original length was 5 inches, then the strain times the original length equals .005 inches. This means that when I stretched the  short wire, it only stretched about as much as the thickness of a piece of paper.

Now, just for fun, and as a way to review our Stress video, how much stress was I able to develop in the wire?  Remember that stress is force per unit area. The force was 20 pounds, and the area of the .03 inch diameter wire was .0 0 0 7 square inches.  20 over .0 0 0 7 is almost 29 thousand PSI.

Understanding the relationship between stress and strain is actually pretty important in the world of engineering and design.  We’ll take a closer look at that in the next video.