YaleNew Haven Teachers Institute  Home 
by
Michael Golia
 Opening Statement
 History of Bridges
 Bridges
 School Description
 At Risk Students
 Geometry
 Research on the Internet
 Materials used for a Bridge
 Mathematical Scaling
 Field Trips
 Conclusion
 Lesson Plan I
 Lesson Plan II
 Lesson Plan III
 Bibliography
 Student Reading List
 Teacher Reading List
 Links
The earliest primitive bridges, formed from beams, stones, and ropes, evolved into more complex structures fashioned by highly intuitive, often anonymous hands. The Roman domination of the known world was in part attributable to their particular genius for engineering, manifested in their singular masonry arch bridges, many of which still stand today. Lesser known in the West are the exceedingly fine and innovative crossings constructed by the Chinese. Construction methods employed in the sixthcentury Anji Bridge in Zhaoxian predate any thing similar in the West by several hundred years. In the medieval world the construction of bridges fell to the religious orders and were funded by the faithful.
The Renaissance saw the rise of the inhabited bridge exemplified by the Ponte Vecchio in Florence and the Rialto Bridge in Veniceand the Palladian bride, which would not gain widespread currency until the eighteenth century, when Palladio's bridge designs were embraced by English landscape designers. The covered bridge, that most romantic of bridge types, is found throughout the world, but was particular popular in a rapidly expanding young America, where wood was plentiful and time was a premium.
The unassuming poetry of bridges reveals itself to those who would see them. Whether a simple crossing or an intricate labyrinth of steel, each of these structures has much to say about the extraordinary lives, effort, ingenuity and wonder that come together on a bridge."
Arch BridgeA type of bridge in which its weight is carried outward along the curve to supports at each end.
 Arch Bridge
 Beam Bridge
 CableStayed Bridge
 Cantilever Bridge
 Simple Truss
 Suspension Bridge
Beam BridgeA simple type of bridge composed of horizontal beams supported by vertical supports.
 Fixed Arch
 Onehinged Arch
 Twohinged Arch
 Threehinged Arch
CableStayed BridgeA bridge in which the roadway deck is suspended from cables anchored to one or more towers.
Cantilever BridgeA projecting structure supported only at one end, much like a shelf bracket or a diving board.
Simple TrussA triangulated structure based on the theory that all loads can be carried by simple tension and compression members whose axis is the line of force and all forces may be resolved into stable static equilibrium at points where triangulated lines of force intersect.
Suspension BridgeA bridge in which the roadway is hung from strong cables that pass over two towers.
Teamtaught classes promote teamwork, problem solving and active learning, with an emphasis on writing and literacy. Teachers are willing to work with students and their families and to be advocates for the student, when necessary.
Some terms in physics will also need to be discussed:
 1. LinesA line extends forever in two directions
 Types of lines:
 ____a. A ray extends forever in one direction
 ____b. A line segment is a line between two points
 ____c. Parallel lines are lines that do not intersect
 ____d. Perpendicular lines are two lines that intersect at a right angle
 2. AnglesAn angle consists of two rays that meet at the same point, which is called the vertex.
 Types of angles:
 ____a. Acute anglemeasures between 0° and 90°
 ____b. Right anglemeasures 90°
 ____c. Obtuse angle measures between 90°and 180°
 ____d. Straight angle measures 180°
 3. Symmetry:
 Symmetry is when a figure can be divided by a line and both resulting halves are equalmirror images of the other.
 4. TrianglesA polygon with three sides
 Types of triangles:
 ____a. Scalene triangleall sides have different lengths
 ____b. Isosceles triangleat least two sides have the same length
 ____c. Equilateral triangleall three sides have the same length
 Triangles identified by their angles
 ____a. Acute triangle has three angles that are acute
 ____b. Obtuse triangle has one angle that is obtuse
 ____c. Right triangle has one angle that is a right angle
 5. QuadrilateralsA polygon with four sides
 Types of quadrilaterals
 ____a. Parallelogram is a quadrilateral with opposite sides parallel
 ____b. Rectangle is a quadrilateral with four right angles
 ____c. Square is a rectangle with sides of equal lengths
 ____d. Rhombus is a parallelogram with sides of equal length
 ____e. Trapezoid is a quadrilateral with only one pair of parallel sides
 ________1. A trapezoid is isosceles if its non parallel sides have the same length
 6. Regular polygons have sides that are the same length and angles that have the same measurement.
 7. Polyhedronis a solid that is bounded by polygons, which are called faces. The segments where the faces meet are edges, and the points where the edges meet are vertices
 Types of polyhedrons and solids:
 ____a. Prisms
 ____b. Pyramids
 ____c. Sphere
 ____d. Cylinder
 ____e. Cone
Compression, tension, live load, and dead load.
The Netscape Navigator is an easy program to use. With this tool one can read text and view pictures of bridges on pages known as web pages. You can use the scroll bar on the left side of the page to review the screen, or use page up and page down to move up and down on the page. To move around the web, you can use the hyper link, choose one of your previously defined bookmarks, or type a new URL into the location box on top of the screen. The net will be used in the first assignment to look up different types of bridges.
Student will:
1. Understand that there are different types of bridges.
2. What is the purpose of the bridge (vehicular or pedestrian).
3. Why was the bridge built.
Materials: The use of computers, and reference material from the library. Butcher block paper and some markers.
Procedures: Students will work in pairs. The types of bridges will be introduced before the students do this research. Students will research a bridge and will answer questions about the bridge. Who, What Where, Why, When and sometimes how. Students will draw this bridge on white butcherblock paper, using a scale to draw the bridge.
Homework: The students will describe a bridge that is close to their home, an answer: why was it built, what was it built of, when was it built, why do you think it was built there, and how do you think it was built. Included in their homework will be a sketch of the bridge.
Materials Needed: Two pieces of 8 ½ by 11inch paper, weights and two books
approximately 1in. thick.
Procedure: Have students work in pairs, make them record what they have tried and
what has happened. They will also have to draw what they are doing so they will get use to drawing as well as writing. As they try each experiment their success or failure will help them think differently. The reason for this lesson is to show the student that by changing the materials into a different form it will hold up weight.
Check for understanding: Have each group report on what they have tried. They will need to tell why something has worked or not. The students will see that in some cases they have tried the same procedures, and in other cases the students will be the only ones that have tried it. There should be some discussion on each of the student's reports. This will help the students try to understand why each of the experiments works.
Tower Criteria
 Coffee can
 75 uncooked spaghetti noodles
 2m (6.5ft.) masking tape
 Standard set of weights (fishing sinkers work well)
 6 strips of corrugated cardboard:
 ____8cm x 30 cm (3in x 12in)
 ____8cm x 50 cm (3in x 20in)
 ____8cm x 80 cm (3in x 31in)
 ____8cm x 100 cm (3in x 39)
 ____8cm x 120 cm (3in x 47)
 ____8cm x 150 cm (3in x 59)
The structure must
 Balance the longest road possible
 Support the most weight possible
 Prevent twist and turns
Design Guidelines:
Procedure
 The base of the coffee can must be 30 cm (about one foot) above the floor or your desktop.
 The base of the structure should be no wider than the diameter of the can.
 The spaghetti can be cut to any length.
 The spaghetti can be taped at the top and the bottom only.
 The coffee can must be positioned with the open end facing up so you can add weights to it.
 1. First, look at your material and think about how you will design your bridge to meet the challenge. Draw your design on a separate sheet of paper.
 2. Using the spaghetti noodles and tape, build a structure that will support the coffee can. Record the number of noodles used.
 3. After you have completed the structure, find the maximum length of cardboard road that can balance on top of the coffee can. Record the road length.
 4. Next, find the maximum amount of weight the structure can support. Remove the road (cardboard) and slowly add the weights inside the can. Record the maximum weight the structure can support before collapsing. Stop adding weights when it starts to wobble.
 5. Retest the road with the maximum amount of weight in the can and record your results. Does the length of the road, that the bridge is able to carry, increase or decrease when there is weight in the can? Explain.
 6. On a separate sheet of paper, sketch your design and point out its strengths and weaknesses. After comparing your design with others in your class, write down two things you would do to improve your bridge.
Billington, David P., Robert Maillart's Bridges, Princeton University Press, Princeton, NJ, 1997. Ropert Maillart is a Swiss bridge designer who is not only a civil engineer but also a structural artist
Day, Christopher, Places of the Soul, Architecture and Environmental Design As a Healing Art, Harper Collins, Hammersmith, London, 1995. How architectural environments make an impact.
Hawkes, Higel, Structures: the Way Things Are Built, Macmillan Publishing Co., New York, 1993.
Man made structures and how they are made.
Kaner, Etta, Bridges, Kids Can Press, 1997. A guide to handon building of models.
Macaulay, David, Building Big, Houghton Mifflin Co. 2000. Wonders of the construction world: dams, domes, skyscrapers, tunnels and bridges.
Petroski, Henry, Engineers of Dreams: Great Bridge Builders and the Spanning of America, Vintage Books, 1996. A history of five engineers who have built bridges.
Gottemoeller, Frederick Bridgescape: The Art of Designing Bridges, John Wiley & Sons, 1998 This book defines line, form and placement in a site.
Technology & Bridges Design http:projects.edtech.sandi.net/pbmiddle/bridges
Building minds: SpanIt Game http:lsb.sur.edu/projects/structures/resources.html
West Point Bridge Designer http:bridgecontest.usma.edu
Bridges: Bridge Project Menu http://cl.k12.md.us/bridges/bridgept.htm
Truss Bridge Laboratory http://www.ce.ufl.edu/activities/trusslab/trussndy.html
The Bridge Challenge http://www.pbs.org/wgbh/buildingbig/bridge/challenge/index.html
NOVA Online Bridge Activity http://www.pbs.org/wgbh/nova/bridge/build.html
Contents of 2001 Volume V  Directory of Volumes  Index  YaleNew Haven Teachers Institute
