**MATH OLYMPIAD (1998)
Grade 7-8: The Bridge Construction Problem**

The Nufrofhtam County Planning Commission has asked for your engineering firm to help them decide how best to replace the Gauss River Bridge that was washed out during the spring floods. The supporting structure is already designed and contracted out. There are two options for the bridge deck: concrete and steel. Now the commission needs bids for these two options:

Here are specifications for a concrete replacement bridge deck:

- The bridge deck must be 4 feet thick, 400 feet long, and 60 feet wide
- The bridge must have a three foot high wall along the side, and the wall must be 2 feet thick.

Here are the specifications for a steel replacement bridge deck:

- The bridge deck must be 4 feet thick, 60 feet wide, and 400 feet long
- Horizontal beams connected together make up the deck
- Each side of the bridge is 2 feet thick and 30 feet high and will run the entire 400 foot length of the deck. The sides will consist of a top and a bottom steel beam with beams forming equilateral triangles connecting the top and bottom beams, as shown in the figure below.
- All steel beams used are of uniform size and length (2 feet wide, 4 feet high, and 60 feet long.
- The ends of the sides should be vertical beam sections.

The bids from the construction suppliers are as follows:

Steel beams as specified: $24.35 per linear foot

Concrete as specified: $99.00 per cubic yard

The labor costs involved in this project are to be paid by an alternate funding source and do not need to be included in your bid.

INSTRUCTION:

Your task is to determine the cost of building the bridge using both concrete and steel beams. Prepare a proposal on the response sheet supplied. Your proposal should include:

- A diagram of the
**steel**bridge you would build - The cost of the
**steel**bridge - The cost of the
**concrete**bridge

Your recommendation about which option is better with a list of reasons justifying your opinion. Include any special considerations or observations you wish the evaluator to consider. Write your recommendation on the Letterhead supplied on the response sheet. (note to Diane--one side of a sheet--so that the total response will fit front and back on the sheet. Additional sheets may be supplied, and proctor has instructions to remind teams to put name and number on the sheet.)

**Grade 7-8: The Bridge Construction Proposal**

__Steel Beam Bridge Diagram:__

__Steel Beam Bridge Cost Calculation:__

__Concrete Bridge Cost Calculation:__

**Figure Right Construction123 St NE, Nufrofhtam WA 98934**

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