School Projects
To assist students working on school projects
on the Golden Gate Bridge, a number of resources are available through this
website that can be used for research. We encourage you to start your learning experience by reading the entire Research Library section right here on this website.
Suspension Bridges
The
following links are not owned by or affiliated with the Golden Gate Bridge, Highway and Transportation District, but we think they will be helpful to you in learning more about suspension bridges.
NOVA Online - Build a Bridge
BridgePros
Discovery School (grades 6 to 8)
Buildings and Bridges for Kids and Teens
This website provides software to design a bridge: http://bridgecontest.usma.edu/.
Teacher Curriculum
The American Experience website includes a includes a Teacher Curriculum with lesson topics including civics, economics, and more. Find the link to this at the bottom left on this page: http://www.pbs.org/wgbh/americanexperience/features/introduction/goldengate-introduction/
Making a Model of the Golden Gate Bridge & Downloadable Golden Gate Bridge Diagram
Bridge dimensions and measurements are here: Construction Data. There are a variety of Golden Gate Bridge model kits available when doing an online search.
Click here for a diagram of the Golden Gate Bridge that includes basic dimensions.
Common GGB Math Questions
Hyperbola: The main span of
the Bridge (section between main towers) is effectively part of a hyperbola or the
"top" part of a hyperbola. To make a graph of it, here are three
points on the curve to use:
North Tower,
Point 1: (0, 746)
Middle of the
Bridge, Point 2: (2100, 246)
South Tower,
Point 3: (4200, 746)
Parabola: Each side (north
and south) of the main towers (they are called side spans) is a parabola. The total distance on the x-axis of each parabola is 1,125 ft and the change in height on the y-axis is 500 ft. One
can be shown as an increasing exponential and the other as a decreasing
exponential.
If you wanted to
represent the Bridge as one single curve, it would be a "4th order"
curve, or something similar to this: y=Ax^4+Bx^3+Cx+D
Using Math for Arches Geometry and Load
There are two kinds of arches in bridge: tension and compression. Tension arches are typically seen in suspension bridges like the Golden Gate Bridge where two main cables form the arch shape. The vertical deck load carried by the structure is transferred to a tensile force in the cable. Compression arches are typically seen in truss bridges where steel or concrete form the arch shape. Similarly, the vertical deck load carried by the structure is transferred to a compressive force in the steel or concrete.
The general mathematical formula that determines the shape of both the tension and compression arches is parabolic, meaning the formula has the typical form: y = k* x ^2.
The inherent property of arches and how they support vertical load determines the parabolic formula in calculating their shape. For a given arch, the formulas relating the geometry and the resultant loads in the members are as follows: H = F*b/S = w*a^2 / (2*S)
"b" is half the horizontal distance from the lowest point of the arch to the highest point (or 1/4 of the total span).
"S" is the vertical distance from the lowest point to the highest point.
"F" is the total weight supported by the deck section between the lowest point and the highest point or "w*a".
"H" is the horizontal component of tension in the arch.
"w" is the unit load supported by the arch.
"a" is the horizontal distance from the lowest point of the arch to the highest point or half the span typically for a suspension or arch bridge.
To determine the arch shape for a particular bridge, engineers and architects can use the formula above and adjust the parameters of "S" and "H" to determine the optimum shape of arch for the span the bridge is intended to serve. For example, if the bridge is to span 100 feet and the unit weight on the deck is 10 lbs/ft and the cable can only support 500 Lbs maximum horizontal force, the arch height "S" is determined as follows:
500 lbs = (10 lbs/ft) * (100 ft / 2)^2 / (2*S)
500 lbs = 25,000 lbs-ft / (2*S)
S = 25,000 lbs-ft / 500 lbs / 2 = 25 ft.
Therefore, the arch will be 100 feet in length and 25 feet high with a parabolic shape. If this shape does not serve the purposes of the engineer or architect (for example if it is too tall and interferes with the views of neighbors or if the tower supporting the cable is in the flight path of incoming airplanes), the engineer can use a stronger cable so that the height may be reduced. The other parameters such as the span and unit weight are typically fixed by the constraints of the site and the weight of the vehicles the bridge is intended to support. Try using a 1000 lbs horizontal capacity cable and see what the height of the arch is now... (answer is 12.5 ft).
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