encarta_bridge2

bridge lesson plans


Day 7: Arch Bridges

Warm Up: Can a material become stronger just by bending it?

Activity:

  1. Using strips of poster board (2" x 11") and 8 books, have students make a simple beam bridge
  2. Students place washers on the poster board beam to test strength
  3. Form poster board into an arch shape and again use washers to test strength
  4. Students build the small block arch and describe the shortcomings (things like wobbliness and tendency to splay out at the base)
  5. After discussion, build the model block arch with the foundation supports with student help
  6. Describe the improved stability and strength that is provided by solid foundations.
  7. Suggest that students recall the lessons of the arched poster board and how the book stacks supplied the support to hold up the washers. Arch bridges work by compressing and spreading out the force of weight down to the foundations.
  8. Beam bridges get their strength only from the ability of their materials to resist bending.
  9. Japanese Arch Bridges

Homework:Begin Planning your popsicle stick bridge design.You may visit this web site: http://bellnet.tamu.edu/res_grid/trussb/designs.htm for help


Bridge Building Project Guidelines
Your Bridge Must Be:

  1. made entirely of popsicle sticks and white glue. No other materials are allowed!
  2. able to span a 40 cm gap
  3. have a mass less than 100 grams
  4. have a hole in the middle that is at least 4 cm in diameter so that the testing bar can be inserted

Internet Resources:

Trusses: http://bellnet.tamu.edu/res_grid/trussb/designs.htm to see many more examples of truss designs and actual pictures of truss bridges.

Arches: Pictures and descriptions of how arches work: http://207.99.133.13/science/7th%20Grade/bridges/arch_lessons/arch_lessons.htm

Test your bridges mass by building a balance:

  1. tie two strings to a stick
  2. find the balance point and mark it
  3. tie a bundle of 100g of popsicle sticks to one string
  4. tie a small container to the other string
  5. check to make sure the container is less massive than the sticks
  6. now add pennies or other small objects to the container until the two objects balance when held at the balance point.
  7. set aside the container with the pennies and use it to check that your bridge is less than 100 grams.
..........

View Movie of Bridge Being Broken


Bridge Project Grading Standards

Points = 300: 100 for completing a bridge, 200 according to strength
Letter Grade
Percentage
Strength:Weight Ratio
A+
100%
165:1
A
95%
145:1
A-
90%
132:1
B+
88%
105:1
B
85%
85:1
B-
80%
65:1
C+
78%
45:1
C
75%
25:1
C-
70%
15:1
D
65%
1:1
F
55%
DISQUALIFIED
F
0%
NO BRIDGE


1

Architects in Action--Mathematics/Physical Science lesson plan (grades 6-8)--DiscoverySchool.com


Students will:
1. understand that ratios are used to create scale models of buildings and structures;
2. understand the principles of ratio and apply these principles in the solution of problems; and
3. understand how to calculate scale using ratio.



Materials
Procedures
Adaptations
Discussion Questions
Extensions

Evaluation
Suggested Readings
Background Information


Vocabulary
Academic Standards
Credit

Printable version of the complete lesson plan, including activity sheets. You need the free Adobe Acrobat Reader plugin.


The class will need the following:
0.25-inch graph paper
map(s) of the United States
pencils
ruler (metric or inches)
tape measure
Take-Home Activity Sheet: Home Measurements


Use our Teaching Tools to create custom worksheets, puzzles and quizzes about this topic.
Discovery Channel School video: “Measurement & Scale.”

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1. Begin by introducing the concept of scale. Write the word scale on the board and brainstorm examples of where scales are found and what they measure. For example, we use scales to measure the weight of an object, the temperature of air, the length of an object, and so on.
2. Show students a map of the United States and point out the scale in the map key. Remind them that this map is a smaller, scaled-down representation of the United States, not an actual representation. Explain that sometimes we shrink objects or make them larger so they are easier to work with. The map is a scale model of an object that is too large to represent on paper. Other scale models represent objects that are too small, such as a diagram of an atom or a magnified view of a computer chip. Review the scale on the map. For example, the scale may say that 1 inch is equal to 50 miles. Explain that a scale is a ratio used to determine the size of a model of a real object. In this case, the map of the United States is the model.
3. A ratio is a relationship between two objects in quantity, size, or amount. For example, four quarters are in a dollar, so the ratio of quarters to dollar is 4 to 1. In other words, a quarter is one-fourth the value of a dollar. Have students think of other examples of how money can be turned into a scale, such as dimes to dollars (10:1 or 1:10) or pennies to dollars (100:1 or 1:100).
4. Illustrate how to draw an object to scale. Use a ruler to draw a square on the board with sides that equal 10 inches in length. Ask students how they might use this square to draw another that is half its size. Explain that an object is not simply cut in half when it is scaled down. The whole object is shrunk proportionally, meaning that it doesn’t change shape but is reduced to a smaller size. For example, if you could scale a carrot to half its size, you wouldn’t simply cut the carrot in half. All parts of the carrot need to shrink equally in size.
5. Now measure and draw a second square with 5-inch sides. Explain that when an object is scaled down, the length of its sides must be reduced by the same amount. Compare the corresponding sides of the two squares. The ratio of the small square to the larger is 5:10. Explain that a ratio can be expressed in three ways: 5:10, 5 to 10, or 5/10, which is a fraction that reduces to 1/2.
6. Remind students that the perimeter of an object is the sum of the length of its sides. So if an object has been scaled down proportionally, the perimeter of the object will scale down by the same ratio. For example, the perimeter of the smaller square is 20, or 5 × 4, which is half the perimeter of the larger square, which is 40, or 10 × 4.
7. Explain that students will use ratio to make a scale drawing of the classroom floor plan. First invite students to brainstorm a list of the kinds of people who might use scale drawings. (Examples include architects, construction workers, and cartographers.)
8. Divide students into teams of four. Explain that each team will measure the surface areas of objects in the classroom—the desks, tables, closets, and so on. The class may choose to use either metric or English measurements. Explain to students that their floor plan will show objects in the classroom as seen from above. Each group should have access to a tape measure, pencils, and paper to record their measurements.
9. Construct a class data table on the board with three columns labeled “object,” “measurement,” and “scaled measurement.” Students should copy this table in their notebooks and fill in the answers as they measure the objects.
10. Once teams have recorded all their data, they will decide on the scale of their floor plan. Distribute graph paper. With the class, discuss the proportions that would allow students to draw the entire room on one sheet of 8.5" × 11" graph paper. (For example, if the longest wall in the classroom is 16 feet long, then a scale of 1" = 1’ will not work. But 0.5" = 1’ will work perfectly.)
11. Use the agreed-upon ratio to create the proportion for your classroom. Then have groups convert their measurements into scaled equivalents. For example, if a desktop measures 2 feet in width and the scale is 0.5" = 1’, use the following equation to figure out how large the scaled drawing of the desktop should be.

0.5 inches divided by 1 foot = the scaled down length of the object divided by 2 feet

Or, written as an equation of two ratios:

0.5 inches = y inches
1 foot   2 feet

y = 1 inch

12. Students can determine their scaled equivalents by cross-multiplying. Students should recall that when both sides of an equation are multiplied by the same amount, the equation remains balanced. In cross-multiplication, both sides of an equation are multiplied by the denominators (the bottom numbers in the fractions). The result is the same as multiplying across the “equals” sign diagonally (i.e., the “bottom left” number times “top right” number equal to the “top left” number times the “bottom right” number). Have students consider the following example:




13. Have students use their scaled measurement, rulers, and graph paper to draw the floor plan their team measured. Remind them to include a title, labels, and a scale.
14. As students complete their drawings, encourage them to calculate the perimeter of their classrooms. What is the relationship between the perimeter of the drawing and the perimeter of the actual classroom?
15. For homework, ask students to complete the sheet, asking them to make a floor plan of a room in their home.
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Have students determine the relationship between the area of the drawing and the area of the actual classroom. They should notice that the ratio of these areas is the square of the scale they chose. For example, if a scale of 0.5 inch = 1 foot was used, the ratio of areas of the drawing to the actual room will be (0.5 inches)2 = (1 foot)2 or 0.25 square inches = 1 square foot. Students can also conduct experiments to determine how volume changes with scale.
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1. Using what you have learned about ratios, proportions, and scale models, create four word problems for other students in your class to solve. For example: A square carpet measures 8 feet × 4 feet. Suppose the scale of a drawing containing the carpet is 1 foot to 1/4 inch. What are the dimensions of the carpet in the drawing? The answer: 2 inches × 1 inch.
2. Is it possible to draw scale models that are completely accurate? Why is accuracy important in the creation of maps, blueprints, and other scale models?
3. Compare your classroom floor plan to that of another student. How are they similar and different? Which would be more useful to a construction worker trying to build a classroom in a new school? Why?
4. List other instances in which you use ratio to compare objects in your daily life. Why is it important to maintain the same scale for each measurement you record when making your model?
5. Debate the merits of using the metric system and the English system to measure lengths. Explain how to convert between the two systems.
6. Compare your classroom to a nearby classroom using scale models of each. Explain how you could use estimation to create a scale model. Would the model be more or less accurate?
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You can evaluate students’ work using the following three-point rubric: Back to Top

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Map

Frank Lloyd Wright

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Distance
Brenda Walpole. Gareth Stevens, 1995.
Learn how standardized measurements developed, as early civilizations used parts of the body for measurements like cubits and fathoms, which gradually became inches and feet. Ways of estimating distances and heights are included along with lots of easy measuring experiments you can do with just a few simple objects. A timeline of important measurement “events” shows the progress of standardization to the present.

The Story of Weights and Measures
Anita Ganeri. Oxford University Press, 1996.
An excellent introduction to the concepts of weight and measurement is encompassed in this slim book. Learn about the history of the development of instruments for accurate weighing and measuring. A short timeline and glossary are included, as well as illustrations and short descriptions

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equivalent
Definition: Being the same or effectively the same; equal.
Context: The length of the front wall is equivalent to the length of the back wall in our rectangular classroom.

perimeter
Definition: The boundary, or border, of a closed, two-dimensional figure or area.
Context: We built a fence around the perimeter of our yard to keep the dog from running away.

ratio
Definition: The relation of one part to another or to a whole.
Context: We have twice as many girls as boys in our class. Therefore the ratio of girls to boys is 2 to 1, or 2:1.

scale
Definition: The ratio of the size of a model or other representation, such as a map, to the actual size of the object represented.
Context: By looking at the scale, we could tell that 1 inch represented 1 mile on our map of New York.

symmetry
Definition: A state in which parts on opposite sides of a plane, line, or point display the same size, form, or arrangement.
Context: The butterfly’s wings were exactly alike, displaying perfect symmetry.




Vocabulary Quiz Whiz
 
Create a variety of interesting quizzes to test your students' word power.
Puzzlemaker
 
Send your students home with word searches, crossword puzzles and more. This tool will help you create unique puzzles using the vocabulary words from this lesson plan.
 
Glossary Builder
 
Ten different options let you create a custom glossary out of any list of vocabulary words.
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This lesson plan may be used to address the academic standards listed below. These standards are drawn from Content Knowledge: A Compendium of Standards and Benchmarks for K-12 Education: 2nd Edition and have been provided courtesy of the Mid-continent Research for Education and Learning in Aurora, Colorado.
 
Grade level: 6-8
Subject area: Mathematics
Standard:
Understands and applies basic and advanced properties of the concepts of measurement.
Benchmarks:
Solves problems involving units of measurement and converts answers to a larger or smaller unit within the same system (i.e., standard or metric).

Grade level: 6-8
Subject area: Mathematics
Standard:
Understands and applies basic and advanced properties of the concepts of measurement.
Benchmarks:
Understands formulas for finding measures (e.g., area, volume, surface area)

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Jessi Hempel, communications team member, Bay Area School Reform Collaborative, San Francisco, California; former fourth-grade teacher in New York City Public School 92.2

Lesson Plans -- Stable and Unstable Structures -- (6-8, Technology)


Students will
1. examine the structural flaws that caused three bridges to collapse,
2. determine what factors need to be considered in building a stable structure, and
3. compare and contrast the pros and cons of various bridge building materials.



Materials
Procedures
Adaptations
Discussion Questions
Extensions

Evaluation
Suggested Readings
Links
Background Information


Vocabulary
Academic Standards
Credit

Printable version of the complete lesson plan, including activity sheets. You need the free Adobe Acrobat Reader plugin.


The class will need the following:
Computers with Internet access (optional but very helpful)
Each student will need the following:
Paper
Pencils and pens
Classroom Activity Sheet: Designing Bridges (see printable version)
Structures Fact Sheet (Distribute this to students if they don’t have access to the Internet and need the information in order to complete the activity.) (see printable version)
Take-Home Sheet: Top 10 Construction Achievements of the 20th Century (see printable version)


Use our Teaching Tools to create custom worksheets, puzzles and quizzes about this topic.
Discovery Channel School video: “Collapse: Failure by Design.”

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1. Begin the discussion by showing the class two photographs of the Tacoma-Narrows Bridge, in the state of Washington, in the process of collapsing. You can find these images at the following Web sites:
Photo 1
Photo 2
2. Ask students to brainstorm about the causes that forced this bridge to wobble and then fall apart. (You may want to ask them if certain weather conditions may have contributed to the bridge’s collapse.) Write their suggestions on a piece of newsprint. After discussing students’ ideas, explain that the cause of the collapse was winds of more than 40 miles per hour.
3. Discuss with the class two other bridges that have collapsed:
  • Silver Bridge, Point Pleasant, West Virginia, 1967. In the worst bridge disaster in the history of the United States, 37 trucks and cars fell into the water when this bridge collapsed. The damage was caused by a broken I-bar, a small metal beam that connects the bridge’s different parts. As engineers found out later, one I-bar had a tiny crack at the time of construction; over time the wear and tear of weather and traffic broke the I-bar apart. Once one side of the bridge fell, the other side couldn’t handle the weight, so it collapsed too.
  • Melbourne Bridge, Melbourne, Australia, 1968. When constructing the bridge, engineers and architects made a simple mathematical error that resulted in an instability in the bridge’s steel girder box. When some of the steel expanded from heat, the bridge fell 120 feet to the ground.
4. Using the information about bridge collapses as a starting point for discussion, ask students what variables must be considered when building a bridge. Point out that these include environmental factors, such as wind and temperature, building materials, and shapes used to support the structure. Also, discuss with the class the natural forces with which structures must contend, such as the weight of a building pressing down on the lower columns (compression) and natural stretching of materials (tension). Explain how these factors also must be taken into consideration when designing a bridge.
5. Divide the class into small groups of three or four students. Tell each group to design a plan, or blueprint, for a bridge to cross a gap in your city or town; the bridge could cross a river or join two sections of land. Their goal is to propose the strongest, safest bridge they can with the least expensive materials. As students work, have them answer the questions listed below and record their findings on the Classroom Activity Sheet: Designing a Bridge.
  • What natural forces might affect your bridge? How can you compensate for them?
  • What materials are most suitable for your bridge? Keep in mind wear and tear on the bridge, temperature, wind speed, and expense when making your decision.
  • How much weight can triangles, rectangles, and arches support? Which is most suitable for your bridge? Why?
To guide students in their research, you may want to distribute copies of the Structures Fact Sheet, which provides information on common forces (such as tension and compression), properties of different materials (such as steel and concrete), and how shapes (such as rectangles and arches) affect designs. To conduct the necessary research, have students visit the Web sites listed below.

Forces Lab: squeezing, stretching, bending, sliding
http://www.pbs.org/wgbh/buildingbig/lab/forces.html

Materials Lab: wood, plastic, aluminum, brick, concrete, reinforced concrete, cast iron, steel
http://www.pbs.org/wgbh/buildingbig/lab/materials.html

Shapes Lab: rectangles, arches, triangles
http://www.pbs.org/wgbh/buildingbig/lab/shapes.html

6. Have the groups write down their recommendations and draw their blueprints on the Classroom Activity Sheet: Designing a Bridge. Suggest that each student make a copy of his or her group’s recommendations. Then have the groups present their designs to the class. Give other students a chance to comment on the strengths and weaknesses of each design.
7. Assign the Take-Home Sheet: Top 10 Construction Achievements of the 20th Century for homework. Students will research one of the structures honored by the architectural community in 1999. They will record important facts about the structure and find out how it is reinforced to protect against destructive forces such as high winds, floods, and earthquakes. After students complete the assignment, have them share their findings with the class.
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Students in high school could take this assignment one step further by creating 3-D models of their proposed bridges. Alternatively, they could simulate a famous bridge disaster by first building a small, inexpensive model of a bridge that collapsed, then replicating the forces that caused its collapse. For example, high winds can be simulated using a fan, and an earthquake can be simulated by shaking the table supporting the model. The following Web site on bridge disasters might be helpful in completing this project: http://www.iti.nwu.edu/clear/bridge/bri_dis.html
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1. What are some of the forces that could cause a bridge to collapse?
2. What are the differences between concrete and reinforced concrete?
3. Which of the following shapes would be best able to handle pressure from the top: horizontal rectangle, arch, or triangle? Why? Which would be the weakest?
4. If you were developing a list of safety measure for bridges, what items would you include on your list? Why?
5. In addition to the bridges discussed in this lesson, can you name some other structures, such as dams, tunnels, or buildings, that have collapsed? Why did these structures collapse?
6. In 1979, the Kemper Arena in Kansas City, Mo., Was hit with severe thunderstorms. Because of its poor drainage systems, the roof filled with water. Why do you think this caused the building to cave in?
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Students should be able to work well together, complete the research accurately and thoroughly, develop a reasonable blueprint for a bridge, and clearly present their findings to the class. Use the following three-point rubric to evaluate students’ work during this lesson: Back to Top

To the Rescue!
When a structure collapses, federal, state, and local organizations rush to the aid of any victims. Brainstorm with the class which organizations help during a disaster. Ask them about the role of these organizations. Have students each become a “Disaster Action Kid,” visit the Web site for kids set up by the Federal Emergency Management Agency: http://www.fema.gov/kids/

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Bridges

Wind Tunnels

Notable Bridges (chart)

Technology

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Catastrophe! Great Engineering Failure - and Success
Fred Bortz. W.H. Freeman and Company, 1995.
Good engineers should try to anticipate anything that could go wrong with whatever it is they are designing. Most do, and some unfortunately do not. This book examines six cases where a mistake in design led to disaster. The fascinating details of each incident is described, illustrated in photographs and drawings, and analyzed so the reader can understand what went wrong and why.

Collapse: When Buildings Fall Down
Phillip Wearne. TV Books, 2000.
The author tells the stories of how eleven of the worst structural engineering disasters of the last fifty years occurred. The stories of these disasters are also the stories of the forensic engineers who sifted through layers of debris, studied architectural drawings, and staged reconstructions in order to search for the true cause of each catastrophe.

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Great Engineering Failures: Tacoma Narrows Bridge
The collapse of the Tacoma Narrows Bridge is featured on this web page. The site will lead you to other great bridge disasters.

Resonance
A multimedia demonstration showing that not only can "resonance" destroy a bridge, it can also reduce to rubble your family's favorite glassware and even disintegrate a kidney stone.

Structures
An elementary classroom for the budding civil engineer tells all about structures and what a civil engineer does for a living.

CONTEST: Welcome to the Bridge Building Home Page
The Illinois Institute of Technology invites you to participate in their annual basswood bridge building contest.

Engineering Disasters: Learning from Failure
The engineering department at the State University of New York shares its list of websites on engineering disasters, from falling bridges to Chernobyl.

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Click on any of the vocabulary words below to hear them pronounced and used in a sentence.

  box girder bridge
Definition: A type of bridge made of steel or concrete that is constructed from supporting beams that look like a long box.
Context: Box girder bridges, such as the Melbourne Bridge in Australia, are popular because they are light, strong, and economical.

  collapse
Definition: To break down or fall in.
Context: When the Silver Bridge collapsed in 1967, 37 cars and trucks fell into the river.

  compression
Definition: A pressing force that squeezes a material so that it becomes more compact.
Context: The weight of the building on its lower columns caused a great deal of compression.

  I-beam
Definition: A steel joist or girder with short flanges and a cross section formed like the letter “I.”
Context: A steel joist or girder with short flanges and a cross section formed like the letter “I.”

  tension
Definition: A stretching force that pulls on a material.
Context: The vertical cables of suspension bridges must remain in tension at all times because of the continuous weight of the roadway and cars.

  torsion
Definition: the twisting and wrenching of a structure by the exertion of forces.
Context: In 1940, strong winds created too much torsion, causing the Tacoma-Narrows bridge to collapse.

  unstable
Definition: Characteristic of a structure that collapses or deforms under a realistic load.
Context: The bridge was unstable and collapsed during the earthquake.




Vocabulary Quiz Whiz
 
Create a variety of interesting quizzes to test your students' word power.
Puzzlemaker
 
Send your students home with word searches, crossword puzzles and more. This tool will help you create unique puzzles using the vocabulary words from this lesson plan.
 
Glossary Builder
 
Ten different options let you create a custom glossary out of any list of vocabulary words.
Back to Top

This lesson plan may be used to address the academic standards listed below. These standards are drawn from Content Knowledge: A Compendium of Standards and Benchmarks for K-12 Education: 2nd Edition and have been provided courtesy of the Mid-continent Research for Education and Learning in Aurora, Colorado.
 
Grade level: 6-8
Subject area: Technology
Standard:
Understands the nature and uses of different forms of technology.
Benchmarks:
Knows that construction design is influenced by factors such as building laws and codes, style, convenience, cost, climate, and function.

Grade level: 6-8
Subject area: Technology
Standard:
Understands the nature and uses of different forms of technology.
Benchmarks:
Knows that manufacturing processes use hand tools, human-operated machines, and automated machines to separate, form, combine, and condition natural and synthetic materials; these changes may be either physical or chemical.

Grade level: 6-8
Subject area: Technology
Standard:
Understands the nature of technological design.
Benchmarks:
Knows that the design process relies on different strategies (i.e., creative brainstorming to establish many design solutions, evaluating the feasibility of various solutions to choose a design, and troubleshooting the selected design.

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Jordan D. Brown, a freelance author in New York City, enjoys writing books, magazines, and Web sites for kids and teachers.3


Sources

1.   "bridge lesson plans." http://www.lincoln.smmusd.org/science/7th%20Grade/bridges/bridge.html (08/28/01 22:55:39)

2.   "Architects in Action--Mathematics/Physical Science lesson plan (grades 6-8)--DiscoverySchool.com." http://school.discovery.com/lessonplans/programs/architectsinaction/index.html (08/28/01 23:09:34)

3.   "Lesson Plans -- Stable and Unstable Structures -- (6-8, Technology)." http://school.discovery.com/lessonplans/programs/stableandunstable/index.html (08/28/01 23:10:44)

 




Bibliography


"Architects in Action--Mathematics/Physical Science lesson plan (grades 6-8)--DiscoverySchool.com." http://school.discovery.com/lessonplans/programs/architectsinaction/index.html (08/28/01 23:09:34)

"Lesson Plans -- Stable and Unstable Structures -- (6-8, Technology)." http://school.discovery.com/lessonplans/programs/stableandunstable/index.html (08/28/01 23:10:44)

"bridge lesson plans." http://www.lincoln.smmusd.org/science/7th%20Grade/bridges/bridge.html (08/28/01 22:55:39)