Strength in Numbers?
AbstractEver try to tear a telephone book in half? Even though you can easily rip one or a few pages to shreds, the entire phone book has strength in numbers and holds together. This project is an introduction to measuring and comparing the strength of materials. Does spaghetti get extra strength if you bundle it together, or does strength simply increase proportionally with the number of strands? If you are interested in materials testing, get cracking!
Andrew Olson, Ph.D., Science Buddies
Edited by Ben Finio, Ph.D., Science Buddies
ObjectiveThe objective of this experiment is to measure the bearing capacity of beams of different thicknesses made from uncooked spaghetti. Does the bearing capacity/strand increase, decrease, or stay the same as spaghetti is bundled together? You can also explore different fabrication methods to see which has the best strength-to-weight ratio.
IntroductionEngineers have many good reasons for testing the materials used to build structures and devices. Each of the following questions can be answered with well-designed materials tests:
- How do you choose which material to use for a particular purpose?
- How do you know that manufactured materials meet the advertised specifications?
- How do you know that the finished products have been fabricated properly?
- How long will the finished product last?
- For research and development of new materials, how do you measure progress?
Materials testing often involves deliberately breaking things, which can be fun, as we all know. In order to get good information about the strength and other properties of the material under study, it's important to carefully control the conditions of the test. Any applied force must be measured, for example. Engineers measure stress in a material, or force divided by unit area, and strain, or the percentage change in a material's length. The "Stress, Strength and Strain" resource in the Bibliography goes into these topics in more detail.
In this project, you will measure the strength of beams made from strands of spaghetti. You will place a beam of spaghetti across a gap and hang weights from it. This puts some parts of the beam in compression (pushed together) and other parts in tension (pulled apart), as shown in Figure 1.
Figure 1. When weights pull down on the spaghetti beam, the bottom of the beam is in tension, and the top of the beam is in compression.
One strand of spaghetti snaps pretty easily, because spaghetti is brittle, meaning it will break suddenly rather than stretching or bending slowly like ductile materials. What happens when you bundle spaghetti together? Does the bundle gain extra strength from numbers, does strength simply increase proportionally with the number of strands? Does it actually get weaker per strand of spaghetti? You can find out by calculating the strength to weight ratio, or the weight the beam can support divided by the weight of the spaghetti. You can test this with a simple experiment by hanging weights from a beam of spaghetti suspended between two equal-height tables or chairs.
Terms and ConceptsTo do this project, you should do research that enables you to understand the following terms and concepts:
- Strength-to-weight ratio
- What is the difference between compressive stress and tensile stress?
- When you hang a weight from the center of a beam which is supported at both ends, what stress(es) do you induce on the beam, and where?
- A good place to start is this Science Buddies resource written by Stanford Mechanical Engineering Professor Beth Pruitt and her students:
Stress, Strain and Strength.
- This PBS website has great information on structural engineering, including online labs where you can learn about forces, materials, loads and structural shapes:
WGBH, 2001. Building Big: Bridges, Domes, Skyscrapers, Dams and Tunnels, PBS Online. Retrieved February 17, 2004.
Materials and EquipmentTo do this experiment you will need the following materials and equipment:
- 1 (or more) 16 oz packages of uncooked spaghetti (exactly how much you need will depend on the size of beams you test)
- String or thread
- Plastic or paper cup
- Nail, pin, or sharp pencil/pen for poking holes in the cup
- Paper clip (for hanging cup from weaker, slender beams)
- Optional materials if you want to test stronger, thicker beams:
- Plastic bucket
- "S" hook from hardware store
- Rope or cord (something stronger than string)
- Water, or a large number of coins or small rocks like gravel (something you can use as weights to put in the cup and bucket)
- Measuring cups (if you are using water)
- Postal scale, such as the digital pocket scale from Amazon.com
- Test stand (two supports at equal height, such as tables, chairs, or large cardboard boxes, with a gap between them)
- Lab notebook
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- Create a data table like Table 1 in your lab notebook. Exactly how you format the table will depend on the size of the beams you want to test. For example, for small beams, it may be easy to just count the number of individual strands of spaghetti, so you can label the first column "# of strands of spaghetti." For large beams (with dozens or hundreds of individual strands), it may be too difficult to count. So, it will be better to measure the weight of the entire beam and record that instead. Whichever method you choose, just make sure you are consistent throughout your experiment.
|Maximum Weight Supported|
|# of Spaghetti Strands||Trial 1||Trial 2||Trial 3||Average||Strength to Weight Ratio|
- Set up your test stand for supporting your spaghetti beams, as shown in Figure 2.
- If you will be using water as a weight, set up the experiment outside, or in an area where it will be easy to clean up spills when the cup falls.
- Place two equal-height tables, chairs, cardboard boxes etcetera next to each other. Leave a gap in between them that is slightly shorter than a single piece of spaghetti.
- For adding small amounts of weight (single or a few spaghetti strands), use a plastic cup, some string and a paper clip.
- Punch two holes near the top edge of the cup with a nail or a push pin.
- Tie a loop of string through the holes to make a "handle".
- Bend a paperclip into a C or S-shaped hook, and attach one end to the loop of string. Hang the other end from your spaghetti beam for testing weight-bearing capacity.
- For adding larger amounts of weight to thicker beams, get a sturdy S-hook from the hardware store, and hang a plastic bucket from it by the handle. The experimental setup will be similar to what you see in Figure 2, but bigger.
Figure 2. The experimental setup.
- Make your first spaghetti beam. To bundle together multiple pieces of spaghetti, use string, rubber bands, or tape to hold them together at both ends.
- Place your beam of spaghetti across the gap between the two supports.
- Hang the cup from your beam.
- Slowly start adding weight to the cup. If you are using water, you will need to pour it in in measured increments (using measuring cups) since the water will spill when the beam breaks. If you are using coins, rocks, or dirt, support the cup with your hand as you add them, then gently lower the cup to let the string pull taut. If you just drop or throw rocks or coins into the cup, this may cause the spaghetti to break more easily.
- Keep slowly adding weight, a little bit at a time, until the beam breaks. If the beam bends and falls through the supports before it breaks, you need to start over with your supports closer together.
- Record the weight that caused the beam to break (be sure to include the weight of the cup itself) in Table 1. If the cup spills when it falls, you may need to collect spilled coins, or re-measure the amount of water you added, to do this accurately.
- Repeat steps 4–9 two more times with beams of the same size, for a total of three trials.
- Repeat steps 4–10 for each size beam in your table. You should have three trials for each size beam.
- Calculate an average maximum weight supported for each size beam, and record these values in your data table.
- Calculate the average strength to weight ratio for each size beam, by dividing the average weight the beam could support by the weight of the beam (Equation 1). The units will use will depend on how you measured the size of the beam (whether you weighted it or counted spaghetti strands) and what units you used on your scale. As long as you are consistent for each calculation, the exact units do not matter.
- Make a graph of your results, with beam size on the x-axis and average weight the beam could support on the y-axis.
- Make another graph with beam size on the x-axis and strength to weight ratio on the y-axis.
- How does the strength to weight ratio change with beam size? Does it stay the same, get bigger, or get smaller? Does spaghetti have "strength in numbers" by getting relatively stronger as you bundle more strands together, or is that not the case?
- From your observations of beam failure, does spaghetti perform better, worse or about the same under compression vs. tension?
Ask an Expert
- How much can you increase the strength of your beams by binding with string or thread at closer intervals?
- What happens if you vary the width of the gap on your test stand?
- Instead of lashing spaghetti beams together with string or thread, explore the strength of beams held together with white glue.
- Does the strength improve? Does the strength-to-weight ratio improve?
- Try gluing at successively closer intervals along the length of the beam. After testing, examine the broken beams carefully. Are the glue joints stronger, weaker, or about the same strength as the spaghetti strands? Is the relationship the same for beams with different gluing intervals?
- Use a ribbon-like pasta (like linguine) to explore the effect of geometry. Linguine I-beams might prove hard to make because of rounded edges, but you could compare beams with square cross-section vs. equilateral triangle cross-section, for example. Again, examine the broken beams to determine whether glue joints or pasta fail first.
- Use these methods to investigate the strength of materials other than spaghetti. For example, see: Stressed Out? Take a Break with this Project!.
- If you'd like to try building something more elaborate with spaghetti, see: The Leaning Tower of Pasta.
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