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# How do compression and tension make things strong?

## How does the curve of an arch affect its strength?

### Introduction: (Initial Observation)

Think about bridges, long buildings, tower cranes, airplanes and almost any other large structure. How can they be made so large and so strong with material that don’t seem to have enough strength? The answer to this question by material and structure engineers is compression and tension. In other words these structure are designed in a way that all forces including weight and wind will be converted to tensile and compressive forces on the structural material.

In this project we will try to find out how compression and tension can make a bridge or tall building strong.

Dear

This project guide contains information that you need in order to start your project. If you have any questions or need more support about this project, click on the “Ask Question” button on the top of this page to send me a message.

If you are new in doing science project, click on “How to Start” in the main page. There you will find helpful links that describe different types of science projects, scientific method, variables, hypothesis, graph, abstract and all other general basics that you need to know.

Just to have an idea what is this project about, do some initial experiments. You may already know that a piece of paper does not have much strength. Now get a piece of paper, roll it up to make a tube and pull it in opposite directions. How strong is it? I think it can easily support a 100 Lbs person.

Can you fold a piece of paper and make a column that can hold a plate with 5 pounds of material on that?

### Information Gathering:

In this section we will gather information about strength of material and factors that affects such strength. We do this by studying books related to structure design and physics. We also search the internet for some information.

Following are among the gathered information that we can use:

The Science of Structure
Why Doesn’t it fall down?

Tension and compression are the key forces explaining how structures stay up and why they fall down.

Tension: the pulling force
Tension in structures isn’t the same thing you feel when you forget to study for a test. Tension is a pulling force. It stretches materials. Link your hands together and pull. You feel tension. Stretch a rubber band. You see tension in action. The rubber stretches, and the band gets longer. It’s in tension.
Look for materials in tension in: rope bridges, telephone wires, tents, suspension bridges, inflated stadium domes, steel cables supporting a full elevator, and hair when someone yanks on it.

Compression: the pushing force
Compression is a pushing force. It squashes materials. Put your hands together and push hard. You feel compression. Put a big marshmallow on the counter and push it down with your hand. As you push, the marshmallow gets shorter. It’s in compression.
Look for materials in compression in: pyramids, telephone poles, arch bridges, elephant legs, tree trunks, and your little brother when you sit on him.

Tension and Compression
When a load is placed on a beam, as above, the top half of the beam shortens in compression. The bottom half lengthens in tension.

The different parts of a structure are either in tension, or in compression, or both. So the materials we use to build structures must be strong in tension, in compression, or both. Steel wires bundled together to make suspension bridge cables are one material strong in tension. A steel cable one centimeter in diameter can support 8,000 kilograms–the weight of two full-grown Indian elephants!
Stone would not be a good choice for a tension structure. Stone is, however, strong in compression. Think of the Egyptian pyramids, which are made of stone blocks, some weighing over a tone. The blocks on the bottom support the weight of the upper blocks. The fact stone is strong in compression but weak in tension actually helped the Egyptians cut the huge limestone blocks. They drove wooden wedges into the limestone. The wedges were then soaked with water until they swelled up and split the limestone. The Egyptians used the strengths and weaknesses of stone to their advantage. Pretty smart!
What if we mix two materials, one strong in compression and one strong in tension? Embedding steel rods into concrete makes reinforced concrete, a material stronger in tension than ordinary concrete.

Workers pour cement around steel reinforcing bars. The result will be a reinforced concrete floor. (Photo by Art Makosinski)

All structures–from spider webs to suspension bridges–have to stand up to the loads placed on them.
Live loads are the things a structure supports through regular use. Like “live” things, these loads can change and move. Live loads: snow, rain, people, cars, furniture, wind.
Dynamic loads act suddenly upon a structure. Their effects can be quite disastrous unless the structure is designed to handle their force. Dynamic loads: earthquakes, tornadoes, tidal waves.
When engineers are designing a structure, they must plan carefully for loads. But sometimes it’s hard to plan for every possible load situation: in 1945 a plane hit the Empire State Building while traveling at 400 km/h! The building withstood the force of this dynamic, dramatic load, but the plane’s crew and some people in the building were not so lucky.

Result of the 1994 earthquake in Northridge, California.

What is Arch?

An arch, in construction, is a rigid span curving upward between two points of support. It appears in a variety of structures, such as an arcade, formed by a row of arches, supported by load-bearing arches or a roof or a bridge, or as a single, freestanding triumphal or memorial arch.

### Question/ Purpose:

Problem facing all architects and structural engineers is to come up with designs that provides necessary strength without being too heavy or too expensive.

The purpose of this project is to see how we can use compression and tension to create a strong structure. We will then try to make a tall structure such as Eiffel Tower or any other tall building that can carry 100 times it’s own weight.

Question: What geometrical shapes can be used to divert forces to compressive and tensile forces.

A specific question that can be the subject of this science project and allows completing a research using experimental method is:

How does the curve of an arch affect its strength?

### Identify Variables:

When you think you know what variables may be involved, think about ways to change one at a time. If you change more than one at a time, you will not know what variable is causing your observation. Sometimes variables are linked and work together to cause something. At first, try to choose variables that you think act independently of each other.

Following is a sample variable definition for the question “How does the curve of an arch affect its strength?”

Independent variable (also known as manipulated variable) is the curve of the arch structure.

Dependent variable (also known as responding variable) is the maximum strength of the arch against loads placed on the center of the arch.

Constants are the distance between the supports of the arch, the weight and material of the arch.

Controlled variables are temperature, wind and other environmental factors that may affect the strength of our structural material.

### Hypothesis:

Based on your gathered information, make an educated guess about what types of things affect the system you are working with. Identifying variables is necessary before you can make a hypothesis.

Following is a sample hypothesis:

As the curve of the arch increases, its strength against loads will increase. It seems that arches can divert forces of a load to compressive forces on the material of the arch. My hypothesis is based on my collected information and daily observation of structural designs that normally are a combination of arches and triangles.

### Experiment Design:

Design an experiment to test each hypothesis. Make a step-by-step list of what you will do to answer each question. This list is called an experimental procedure. For an experiment to give answers you can trust, it must have a “control.” A control is an additional experimental trial or run. It is a separate experiment, done exactly like the others. The only difference is that no experimental variables are changed. A control is a neutral “reference point” for comparison that allows you to see what changing a variable does by comparing it to not changing anything. Dependable controls are sometimes very hard to develop. They can be the hardest part of a project. Without a control you cannot be sure that changing the variable causes your observations. A series of experiments that includes a control is called a “controlled experiment.”

### Experiment 1: Does arch form gives additional strength to a structure?

Introduction:
Build an arch bridge (from card board, balsa wood or even paper) to see how much stronger an arch structure can be. (in compare to the same amount of original material). Test the strength of the structure by placing weights on the center.

Procedure:

1. Get a piece of ply wood about 16″ x 24″ for the base of your experiments.
2. Use nails, screws or glue to mount two wooden blocks about 8 inches apart on your base board. Each wooden block must be about 6 inches long. These wooden blocks are the supports for your test bridge.
3. Get a strip of cardboard or construction paper 5 inches wide and 8 inches long.
4. Place the cardboard between two wooden supports.
5. Place some weight to the center of that and record the maximum weight that it can support.
6. Get another piece of cardboard or construction paper 4.7 inches wide and 8.5 inches long.
7. Place the cardboard between two wooden supports. It will form an arch because it is longer than the distance between two supports. Width 4.7 is selected so the area of the bridge and the weight of material will remain constant.
8. Get another piece of cardboard or construction paper 4.4 inches wide and 9 inches long.
9. Place the cardboard between two wooden supports. It will form an arch again with more curve. With 4.4 is calculated by dividing 40 (area) by 9 (length).
10. Place some weight to the center of that and record the maximum weight that it can support.
11. Record your results in a table like this:
 Shape of bridge Maximum weight supported Length of arch Distance Arch length/ Distance Flat/ No arch 8″ 8″ 1 Small curve arch 8.5″ 8″ 1.062 Larger curve arch 9″ 8″ 1.125

12. You may try other arch lengths as well. For example you may also try 9.5″ and 10″ arches.
13. Use the results to determine if arch form does increase the strength.
14. Use the results table to make a graph using the arch length and maximum strength.
15. You may alternatively make a graph to show the relation between arch curve (arch length/distance ratio or arch height/length ratio) and strength.

Following diagrams shows one possible setup for this experiment.

Here you see a wooden frame with two red blocks of wood as supports for your test subject. You may test a strip of cardboard, a strip of balsa wood, a strip of aluminum sheet or any other material that you want to test. Cut the material at a length that can enter the frame and rest on the red supports.

Test the strength of this plain sheet of sample material by placing a weight on the center of the strip.

Then test the arch. Cut a longer strip of the same material in a way that when placed between the supports, it will form an arc.

Test the strength again by placing different weights on it’s center.

Since the arch uses more material, you need to consider that in calculating the strength ratio.

You may perform additional experiments to show how other geometric shapes can distribute the forces and provide additional strength.

Experiment 2:
We build an equilateral triangle (from card board, balsa wood or even paper) to see how much stronger an equilateral triangle structure can be. (in compare to the same amount of original material)

Triangle will have one of the highest strength. Do you know which members of triangle are subject to tensile force and which members are subject to compressive force?

Experiment 3:
We build a rectangle (from card board, balsa wood or even paper) to see how much stronger a rectangle structure can be. (in compare to the same amount of original material)

The weights in this pictures does not represent real strength of the structure. This triangle will probably have the same strength as plain material or even less.

Experiment 4:
Use the knowledge that you collected in the above experiments to build a model of a tall structure. Then test the strength of your structure.

### Materials and Equipment:

You have many choices for material that you may use in this project. Papers, cardboards, toothpicks, Bamboo skewers or fruit skewers found in table top supply stores, discount stores, and the like. For the weight you may use an empty plastic container and then fill it up with sand or gravels to make it heavy. Sand and gravel may be weighed separately using a scale. Other heavy metal pieces may also be used as well.

### Results of Experiment (Observation):

Experiments are often done in series. A series of experiments can be done by changing one variable a different amount each time. A series of experiments is made up of separate experimental “runs.” During each run you make a measurement of how much the variable affected the system under study. For each run, a different amount of change in the variable is used. This produces a different amount of response in the system. You measure this response, or record data, in a table for this purpose. This is considered “raw data” since it has not been processed or interpreted yet. When raw data gets processed mathematically, for example, it becomes results.

### Calculations:

If you do any calculation, write your calculations in this part of your project report. For example you may calculate the ratio of strength to material weight. For example if you use 150 grams of cardboard to make a structure that its maximum strength is 5000 grams, then the ratio of strength to material will be 0.33 or (33%).

### Summary of Results:

Summarize what happened. This can be in the form of a table of processed numerical data, or graphs. It could also be a written statement of what occurred during experiments.

It is from calculations using recorded data that tables and graphs are made. Studying tables and graphs, we can see trends that tell us how different variables cause our observations. Based on these trends, we can draw conclusions about the system under study. These conclusions help us confirm or deny our original hypothesis. Often, mathematical equations can be made from graphs. These equations allow us to predict how a change will affect the system without the need to do additional experiments. Advanced levels of experimental science rely heavily on graphical and mathematical analysis of data. At this level, science becomes even more interesting and powerful.

### Conclusion:

Using the trends in your experimental data and your experimental observations, try to answer your original questions. Is your hypothesis correct? Now is the time to pull together what happened, and assess the experiments you did.

What you have learned may allow you to answer other questions. Many questions are related. Several new questions may have occurred to you while doing experiments. You may now be able to understand or verify things that you discovered when gathering information for the project. Questions lead to more questions, which lead to additional hypothesis that need to be tested.

### Possible Errors:

If you did not observe anything different than what happened with your control, the variable you changed may not affect the system you are investigating. If you did not observe a consistent, reproducible trend in your series of experimental runs there may be experimental errors affecting your results. The first thing to check is how you are making your measurements. Is the measurement method questionable or unreliable? Maybe you are reading a scale incorrectly, or maybe the measuring instrument is working erratically.

If you determine that experimental errors are influencing your results, carefully rethink the design of your experiments. Review each step of the procedure to find sources of potential errors. If possible, have a scientist review the procedure with you. Sometimes the designer of an experiment can miss the obvious.

### References:

Visit your local library and find books related to structural engineering, architecture and civil engineering. You may also try books related to mechanics and material strength. All such books may have information that contribute to the completion of your project. Look for articles that shows how the design affects the strength.

Following are some we resources.

Bookmarks:
The following sites should be bookmarked:

This is an award winning site dedicated to tall buildings. The site has a very clever interface for accessing hyperlinks that simulates an elevator panel in a tall building. The FAQ section provides excellent reference material.

This virtual museum gives a comprehensive history of tall buildings. It provides a list of programs run by museums that can be useful for enrichment program planning. A portion of the site is dedicated to New York City skyscraper architecture.

This site provides information on most of the high-rises of the world listed by country. It contains very nice graphics, including one pictorial comparison of the heights of the tallest buildings in the world. Its features include: a fabulous listing of U.S. high-rises by cities, and a table of the 30 top skyscrapers in the world today.

This site presents an interesting design of a tall building with visual renderings of structure and floor plans. It also contains a description of the design of the building.

This site offers a tour of all of the major buildings of New York City.

This site provides a virtual field trip to one of the world’s most famous skyscrapers, the Empire State Building. The site includes a video camera from the building. It has an extensive section of trivia about the building’s architecture, construction, history, and other important facts.