Columns: Experimenting with Paper Cups

Resource for Grades 3-8

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Columns: Experimenting with Paper Cups (Document)

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Background Essay

Vertical columns are typically paired with horizontal beams to provide the structural framework for most buildings today. Columns become strong under compression, the squeezing produced by the downward force exerted by a load and the counteracting force upward from the ground. A column must manage two types of load: (1) the dead load, or weight of the structure it supports plus any permanent fixtures, and (2) the live load, which includes people, furniture, cars, or other temporary objects whose weight bears down on the structure.

When properly designed and loaded, a column (or grouping of columns) is able to support a lot of weight because it transfers it directly to the ground. A column can fail in two basic ways. A load placed off center subjects the column to bending, or buckling. To prevent this, it is important to center a load squarely over the middle third of the top of the column. The second kind of failure occurs when the maximum strength of a column's material is exceeded by the weight of the load. When this happens, the column crushes, or collapses.

Even hollow, thin-walled columns made of weaker material can be made strong under the weight of a heavy load. A paper cup with its bottom removed, for example, is no match for the weight of a person standing on it. It crushes easily because the paper is weak in compression. Filled with sand, however, the paper cup can withstand the same weight -- and then some. Why is this so? Paper is fairly strong by itself in tension. It resists the sand's outward thrust, preventing it from spreading out. Thus contained, the sand in turn prevents the paper from collapsing by resisting the downward force of the weight and making the column stronger in compression. Engineers can sometimes use an inexpensive filler material that is strong in compression -- like sand or loose rocks -- to reinforce a hollow, thin-walled column, allowing them to build safely and cost-effectively.

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Discussion Questions

How would you go about finding out the smallest number of cups needed to support your weight?

What could you use instead of sand to resist the compressive forces on the bottomless cups?

Why do you think cups are often tapered so they are a little wider at the top than at the bottom?

Is the round shape of the cups important? What do you think would happen if you tried this activity with milk cartons or some other square shape?

When columns are used to support a building, what are the advantages of using hollow columns? What are the disadvantages?

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Transcript

(humming) (gasps) Ooh!

KALEIGH: Mrs. Caballero's second-grade class, in Brookline, Massachusetts, challenged us to use these paper cups and this piece of cardboard to make a platform that's strong enough to support a weight of a person.

GARRETT: If I stand on a cup... it'll get smooshed.

ALL: (laughing)

GARRETT: That's because all of my weight is pushing, or compressing, this one cup.

CAROLINE: When we arrange the cups like this and put the cardboard on top, each cup supported less weight, and there wasn't too much weight on any one cup.

KALEIGH: Ready, Garrett? Yahoo. (chuckling) We still have a few questions, like, do the cups need to have bottoms to make this work?

CAROLINE: Here's what we found out.

ALL: (yelling)

CAROLINE: We wanted the cups to support our weight without any bottoms, so we needed to change something about the cups to make them stronger. We learned that the bottoms of the cups keep the sides apart and keep the cups from smooshing in.

KALEIGH: So if we add sand to the cups without any bottoms in it, the sand would push on the sides of the cup and keep the cup sides from smooshing in. So make that ten—the circle out of nine, and then one in the middle. Ready?

CAROLINE: I bet this will be really strong.

KALEIGH: I know, because the bottom... The bottom worked well at holding it up, but the cup was still hollow. The sand—because it fills up all the area in the cup—will be twice as strong as... Where's the cardboard? Okay. Okay. Okay.

GARRET:: Whoa!

KALEIGH: I bet we could even...

GARRET: You want to get on it?

KALEIGH: Me?=

GARRETT: Yeah, go, try it.

KALEIGH: Hey, it works. I'm not stepping on any cups.

GARRETT: That's all right.

(ALL: (screaming playfully)

GARRETT: Here's why the paper cup supported us when we filled it with sand. There are two things going on. The first thing is that the paper is holding the sand in place. See? If I hold the sand in my hand, it spreads all over the place. But when I put the sand in a cup, the sides of the cup prevent the sand from spreading out.

CAROLINE: To spread out, the sand would have to stretch the paper in the cup. Since the paper in the cup is strong, it's able to stop that. See, when I pull the paper like this, it's really strong. It's called "tension."

KALEIGH: But when Caroline pushes on the paper, like that, it folds in on itself. So the sand inside the cup is pushing on the sides of the cup, preventing it from folding in on itself when we push on the cup.

GARRETT: The cups are like the columns of the building and the cardboard is like the roof. When I stand on the cardboard, I put a heavy load, pressing down, on the columns. This is called "compression." The columns become very strong when they are compressed, and they hold me up. Really cool.

KALEIGH: Try to bounce on it.

GARRETT: All right, hold on.

ALL: Whoa!

(bubbling)