Building A Bridge

Rebuilding the Gerald Desmond Bridge

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Objective Given the current bridge dimensions, the student will be able to estimate a plan for a higher bridge to accommodate future container ships.

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Algebra 1 Standards 5.0 Students solve multistep problems, including word problems, involving linear equations and linear inequalities in one variable and provide justification for each step. 8.0 Students understand the concepts of parallel lines and perpendicular lines and how those slopes are related. Students are able to find the equation of a line perpendicular to a given line that passes through a given point.

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Bridge Background

Structural Type: Arch bridge / suspended deck Function/usage: Road bridge connects the Ports of Long Beach and Los Angeles with the I-710. Span: 5,134 Ft. Built: 1968 (replacing the previous pontoon bridge) Length: 1,053 feet long Highest point: 250 feet ***157 feet of clearance above the water 4

157’ Clearance

250’ to top

5134’ span (runs off of the photo)

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The Challenge Currently there are new vessels, or “Mega Ships,” being produced, but they are too large to clear the Gerald Desmond Bridge. As ships get larger, the infrastructure of the port - namely the bridge height, width/depth of waterways and docks/wharves - needs to keep up. How can we plan a new bridge that will accommodate shipping and traffic needs? 8

250 feet at highest point 157 feet at road level

Ground Level

Ground Level

5134 feet 9

A grade (or gradient) is the pitch of a slope, and is often expressed as "rise over run". It is used to express the steepness of slope of a hill, stream, roof, railroad, or road.

This is especially important in trucking becaus fully loaded “big rigs” can’t make it up a grad that is too steep! 10

157 feet at road level 2567 feet

-2567 feet Ground Level

Ground Level 2567 run

Because the bridge is symmetrical, let’s put it in a coordinate plane! Then we can look at the average slope of one side of the bridge. Because we need to calculate slope, we need to know the length of the base of the triangle. 11

157 feet at road level 2567 feet

-2567 feet 157 rise 2567 run

Rise Slope = Run

157 rise = 0.06116 2567 run

0.06116 Change to percent by moving the decimal two places to the right

6.116% grade For our purposes, we will use the decimal form (0.06116) because it is equal to the fraction and we are writing an equation. 12

Considering very heavy trucks use this bridge, we will need to build a new bridge with the same grade (or slope).

Same slope

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we raise the height of the bridge but keep he same slope, what will happen to its span?

250 feet at road level 250 rise

Same slope Same slope x run

0.06116 =

250 rise x run 14

we raise the height of the bridge but keep he same slope, what will happen to its span?

0.06116 1

250 = x

0.06116 x = 250 0.06116 0.06116

Cross multiply

Solve for “x”

x = 4087.6 feet 15

we raise the height of the bridge but keep he same slope, what will happen to its span?

x = 4087.6 feet span = 2 (4087.6 feet) span = 8175.2 feet 250 feet at road level 4087.6 feet

-4087.6 feet

x

x 8175.2 feet

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250 feet at road level 4088 feet

-4088 feet Ground Level

Ground Level

8175 feet 17

If we raise the height of the bridge to 275 feet?

275 feet at road level 275 rise

Same slope Same slope x run

0.06116 =

275 rise x run 18

we raise the height of the bridge but keep he same slope, what will happen to its span?

0.06116 1

275 = x

0.06116 x = 275 0.06116 0.06116

Cross multiply

Solve for “x”

x = 4496.4 feet 19

we raise the height of the bridge but keep he same slope, what will happen to its span?

x = 4496.4 feet span = 2 (4496.4 feet) span = 8992.8 feet 275 feet at road level 4496.4 feet

-4496.4 feet

x

x 8992.8 feet

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275 feet at road level 4496 feet

-4496 feet Ground Level

Ground Level

8993 feet 21

If we raise the height of the bridge to 300 feet?

300 feet at road level 300 rise

Same slope Same slope x run

0.06116 =

300 rise x run 22

we raise the height of the bridge but keep he same slope, what will happen to its span?

0.06116 1

300 = x

0.06116 x = 300 0.06116 0.06116

Cross multiply

Solve for “x”

x = 4905.2 feet 23

we raise the height of the bridge but keep he same slope, what will happen to its span?

x = 4905.2 feet span = 2 (4905.2 feet) span = 9810.4 feet 300 feet at road level 4905.2 feet

-4905.2 feet

x

x 9810.4 feet

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300 feet at road level 4905 feet

-4905 feet Ground Level

Ground Level

9810 feet 25

Current ½ span: 2567 feet What new problem can you now see that limits the height of the bridge? 26

2567 feet 250’

1.6 times the blue length 27

2567 feet 275’

1.75 times the blue length 28

2567 feet 300’

2 times the blue length 29

Written Reflection

• What limits the height of a future bridge? • What solutions can you imagine for that problem? • Are the ideas you have realistic? 30