Resource: Columns: Experimenting with Paper Cups

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.

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?