Gale Schools - Sci Try

Structures and Shapes

From Experiment Central, published by U·X·L

Humans have been busy building structures for almost as long as we have existed. The structures that we build, however, have changed dramatically over the last thousand years. We have learned to construct buildings that extend thousands of feet up, and we can build bridges that safely support tons of weight over immense stretches of water. What have we learned that enables us to build what our ancestors would have thought impossible?

The answer lies mainly in concepts about the nature of force and motion that Sir Isaac Newton (1642--1727) developed over three hundred years ago. Newton proposed a set of "laws" that clearly explain why and how objects move or remain still. These laws apply to the planning of structures like buildings and bridges because they must be designed to remain fixed in place and not be moved by the forces that act upon them.

Different forces can act upon one object

One of Newton's laws tells us that different forces can act on a single object at the same time, as when two soccer players kick the ball at the same time. One has exerted force on the ball toward the goal; the other has exerted force in another direction. If the two players kick with precisely the same energy in exactly opposite directions, then the ball will remain motionless. Two kicks that are not equal in energy and not opposite in direction, however, will send the ball flying sideways off the field. This combined force is called a resultant.

Standing a single playing card on its edge is nearly impossible. Two cards, however, can be stood on edge quite easily. This is because the two cards can be made to exert two equal and exactly opposite forces upon each other. As long as this force stays balanced, the cards will remain standing. When different forces add up to a resultant of zero, this state is called equilibrium. If you increase the force on one side without increasing the force on the other, the resultant is no longer zero; equilibrium has been disrupted, and the cards will fall in the direction exerted by the stronger force.

The science of architecture and engineering is largely the analysis of force: how to distribute and direct the many forces acting on a structure to ensure that it remains in equilibrium.

The arch redistributes forces to maintain equilibrium
One early development in architecture that uses the principle of distribution of force is the arch. The arch directs the downward force of the supported weight around the arch and into the ground. In a stone arch, for example, each stone has slightly tapered sides. The weight on the top stone causes it to push out and down on the next stone, and so on around the curve of the arch until it reaches the ground. An arch can support greater weight than a straight beam across an opening, even when the beam and arch are built of the same materials. This is because the force in an arch squeezes, or compresses, the material in the arch, rather than bending it the way it does in a beam. Most materials are stronger in compression than they are in bending. The greatest bending force in a beam takes place in the center, where it is unsupported. Over time, the bending force on the beam could cause it to crack.

The same principle applies to bridges. The platform of a bridge, the flat surface over which vehicles travel, can be supported either by a beam or by an arch. A simple beam bridge can extend only a limited distance before its weight and the weight of the traffic upon it would cause the beam to fail. An arch bridge more effectively transfers the force of this weight out to the ground. Many large bridges today use arches as part of their design.

In the first project, you will construct two bridges---one using a beam and one using an arch---and determine whether the arch can support more weight. In the second project, you will see if you can increase the strength of the beam design by increasing the vertical height of the beam.

Words to Know

Arch: A curved structure that spans an opening and supports a weight above the opening.
Beam: A straight, horizontal structure that spans an opening and supports a weight above the opening.
Compression: A type of force on an object where the object is pushed or squeezed from each end.
Equilibrium: A balancing or canceling out of opposing forces, so that an object will remain at rest.
Force: A physical interaction (pushing or pulling) tending to change the state of motion (velocity) of an object.
Platform: The horizontal surface of a bridge on which traffic travels.
Resultant: A force that results from the combined action of two other forces.
Rigidity: The amount an object will deflect when supporting a weight. The less it deflects for a given amount of weight, the greater its rigidity.

Project 1

Arches and Beams: Which is strongest?

Purpose/Hypothesis

In this project, you will construct one bridge using an arch and one using a beam. The bridges will use the same vertical supports and platforms, and the arch and beam will be of identical thickness. You will test the bridges to determine how much weight each one can support.

Level of Difficulty

Easy/moderate.

Materials Needed

1 sheet of red poster board, 14 x 22 inches (36 x 56 cm)
1 sheet of white poster board, 14 x 22 inches (36 x 56 cm)
scissors
ruler
10 iron fishing sinkers, 0.5-ounce (14-gram) each
4 stacks of textbooks, each approximately 5 inches (12 cm) tall

Approximate Budget

$15 for poster board and sinkers.

Timetable

Approximately 40 minutes.

How to Experiment Safely

Use only iron fishing sinkers for weights in this experiment. If only lead sinkers are available, substitute coins or some other easily measurable form of weights. Lead is toxic and should not be handled without proper protection.

Step-by-Step Instructions

Cut two pieces of white poster board, 14 x 4 inches (36 x 10 centimeters). These will be the platforms of your bridges.
Cut two pieces of red poster board, 14 x 5 inches (36 x 12 centimeters). These will be the support designs (beam and arch) of your bridges.
Place two stacks of textbooks about 8 inches (20 centimeters) apart. Do the same with the other two stacks. These will be the vertical supports of your bridges.
Bend one piece of red poster board into an arch and place it between one pair of vertical supports. This will be the arch of one bridge. The peak of the arch should be the same height as the vertical supports. Adjust the distance between the vertical supports until the peak of the arch is even with the top of the two stacks.
Lay the other red piece across the second pair of vertical supports. This will be the beam of the other bridge. Adjust the distance between the vertical supports until it is the same as the distance on the arch bridge.
Measure and mark the centers of the two pieces of white poster board. Lay each of the white pieces across a pair of vertical supports so that the center mark is halfway across the opening. These will be the platforms of your bridges. The weights must be placed on or near the centerpoints you marked on the platforms. Your bridges should look like the illustrations.
Measure the height of the platforms (at the center) and record this height on a data chart. Place one weight on the center point of each bridge. Measure any distance the center of the platform has dropped. Record this on your data chart. Add another weight as close to the first as possible and measure the height again.
Continue adding weights to the bridges. Measure and record the distance each platform drops after each new weight is added. Repeat this process until both of the bridges have collapsed.

Summary of Results

Examine your data and compare the results of the tests for the two designs. Did your predictions prove true? Which design proved to be the sturdier one? Summarize your results in writing.

Troubleshooter's Guide

Here is a problem you may encounter during this project, some possible causes, and ways to solve the problem.

Problem: One of the bridges tends to twist and dump its weight before collapsing.

Possible causes:

Your weights are off center. Place your weights as close to the center mark as possible.
Your poster board is not rigid enough. Use thicker poster board.

Change the Project

By altering the project, you can investigate other questions about bridges. How does doubling the thickness of the arch or the beam affect its strength? What if you construct the arch bridge with two arches instead of one? Also consider changing the materials. Is rigidity always a good thing? See which supports more weight, a slightly flexible design made of cardboard, or an identical design made of wooden hobby sticks.

Project 2

Beams and Rigidity: How does the vertical height of a beam affect its rigidity?

Purpose/Hypothesis

Rigidity is a measure of how much an object, such as a bridge, will deflect when supporting a weight. Bridges must not only be strong, but they must also be fairly rigid to keep the platform level without sagging. In this project, you will construct three beam-support bridges using beams of different vertical heights. You will test each one and compare the results to determine whether increasing the height of a beam can make this bridge design more rigid.

Level of Difficulty

Moderate.

Materials Needed

1 sheet of red poster board, 14 x 27 inches (36 x 68 centimeters) or the equivalent with 2 sheets
1 sheet of white poster board, 14 x 22 inches (36 x 56 centimeters)
scissors
tape
ruler
10 iron fishing sinkers, 0.5-ounce (14-gram) each
6 stacks of textbooks, each approximately 5 inches (12 centimeters) tall

Approximate Budget

$15 for poster board and sinkers.

Timetable

Approximately 40 minutes.

How to Experiment Safely

Step-by-Step Instructions

Cut three pieces of white poster board, all 14 x 4 inches (36 x 10 centimeters). These will be the platforms of your bridges.
Cut three pieces of red poster board, 14 x 6 inches (36 x 15 centimeters), 14 x 9 inches (36 x 23 centimeters), and 14 x 12 inches (36 x 30 centimeters). These will be used to make the beams of your bridges.
Place the stacks of textbooks in three pairs. The stacks should be about 10 inches (25 centimeters) apart. These will be the vertical supports of your bridges.
On the 14 x 6-inch piece of red poster board, measure and mark the board so the 6-inch (15-centimeter) width is divided into six 1-inch (2.5-centimeter) segments. Fold the board carefully along these marks so it looks like the illustration.
Divide the 14 x 9-inch poster board into six 1.5-inch- (3.8 centimeter- ) wide segments and divide the 14 x 12-inch poster board into six 2-inch- (5 centimeter- ) wide segments. Carefully fold each one into an accordion shape.
Lay the three folded red pieces across the three pairs of vertical supports. These will be the beams of the bridges.
Measure and mark the centers of the three pieces of white poster board. These will be the platforms of your bridges. The weights must be placed on or near the centerpoints you marked on the platforms.
Attach the platforms to the beams using tape. Place the beam/platform assemblies across the three pairs of vertical supports with the beam-side down. Your bridges should look like the illustration.
Measure the vertical height of each bridge, from the bottom of the folded beam to the top of the platform. Record this information on a data chart.
Measure the height of the platforms at the center and record this height on your data chart. Place one weight on the center point of each bridge. Measure the distance the center of the platform has dropped. Record this on your data chart. Add another weight as close to the first as possible and measure again.
Continue adding weight to the bridges. Measure and record the distance each platform drops after each new weight is added. Repeat this process until both of the bridges have collapsed.

Summary of Results

Examine your data and compare the results of the tests for the three beams. Did your predictions prove true? How much does each increase in vertical beam height increase the beam's ability to support weight? Summarize your findings in writing.

Troubleshooter's Guide

Here is a problem you may encounter, some possible causes, and ways to solve the problem.

Problem: The accordion folds of the beams tend to flatten out, decreasing the vertical height of the beam.
Possible causes:

Your tape is not holding. Try folding the edges of the white platform around the beam and then taping the assembly.
Your poster board is not rigid enough. Use thicker poster board.

Change the Project

By altering the project, you can determine whether it is preferable to construct a wide bridge with a low vertical height or a narrow bridge with a greater vertical height. Which is stronger, a bridge 4 feet (1.2 meter) wide and 2 feet (0.6 meter) high, or a bridge 2 feet (0.6 meter) wide and 4 feet (1.2 meter) high? Also consider changing the materials. Is rigidity always a good thing? See which supports more weight, a slightly flexible design made of cardboard or an identical design made of wooden hobby sticks.

Design Your Own Experiment

How to Select a Topic Relating to this Concept

Watching the way your bridge designs reacted to the weight placed on them may have already given you ideas for improving them. Architecture and design engineering encompasses a wide range of structures and products you see and use every day. Can you think of a way to make something work better or keep people safer? Testing ideas in miniature is a vital tool for trying out new ideas.

Think about combining the ideas and designs used in these projects. Can you think of a way to use the strongest beams in the second project to make a stronger arch? Can you build a bridge that uses both a beam and an arch? If you are doing a project as a group, try holding a competition for bridge designs.

If you want to do an experiment or a project, check the For More Information section and talk with your science teacher or school or community media specialist to start gathering information on structure and shape questions that interest you.. As you consider possible experiments or projects, be sure to discuss them with your science teacher or another knowledgeable adult before trying them. Some of them might be dangerous.

Steps in the Scientific Method

To do an original experiment, you need to plan carefully and think things through. Otherwise, you might not be sure which question you are answering, what you are or should be measuring, and what your findings prove or disprove.

Here are the steps in designing an experiment:

State the purpose of---and the underlying question behind---the experiment you propose to do.
Recognize the variables involved, and select one that will help you answer the question at hand.
State a testable hypothesis, an educated guess about the answer to your question.
Decide how to change the variable you selected.
Decide how to measure your results.

Recording Data and Summarizing the Results

In the projects included here and in any experiments or projects you develop, you can look for ways to display your data in more accurate and interesting ways. For example, can you think of a better way to measure the weight sustained by the bridge? Should you test the structures by distributing the weight across the span?

Remember that those who view your results may not have seen the experiment performed, so you must present the information you have gathered in as clear a way as possible. Including photographs or illustrations of the steps in the experiment is a good way to show a viewer how you got from your hypothesis to your conclusion.

Related Projects

To develop other experiments or projects on this topic, take a look at the structures and shapes of things you see around you every day. Take different design options and test them in miniature. Consider ways you could reinforce the bridges you built to enable them to hold more weight. Can you think of a better way to construct new models?

For More Information

Gibson, Gary. Making Shapes. Brookfield, CT: Copper Beech Books, 1995. Demonstrates a variety of structural shapes and how they are applied in construction.

Hawkes, Nigel. .Structures: The Way Things are Built. New York: MacMillan Publishing Company, 1990. Looks at ancient and modern structures and describes how they were built.

Stevenson, Neil. Architecture: The World's Greatest Buildings Explored and Explained. New York: DK Publishing, 1997. Examines in depth the history, design, and construction of fifty buildings and structures from around the world.

The Visual Dictionary of Buildings. New York: DK Publishing, 1992. Clearly illustrates and provides terminology for numerous architectural features from ancient to modern times.

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