MAT 271 SU18Steel Drum Project

Problem Statement:

A 55-gallon Tight Head Steel Drum is constructed by attaching 18 gauge (i.e. 0.0478 inches thick) steel disks to the top and bottom of a cylinder created by rolling up a 20 gauge (i.e. 0.0359 inches thick steel sheet as in the figure below.

The vertical seam on the cylinder is welded together and the top and bottom are attached by a pressing/sealing machine.The pressing/sealing process requires some extra material from the sides and discs to be curled together, which is lost in the final dimension.The pressing/sealing process requires approximately 13/16 inches from the top and bottom cylinder and inches from the edge of the disc to be curled together and hence these are lost in the final dimensions.In addition, the top and bottom are set down 5/8 inches into the cylinder to allow for a lip to the drum for ease of movement. The interior has a diameter of 22 in and the exterior has a height of 34 in. For clarification, refer to the diagram below, which is a side view of the drum.

Side view of can:

Inset, 5/8 in top and bottom

Note: The 55 gallon drum above actually has an interior volume of 56.80 gallons, but we will still call it a 55 gallon drum.

Steel is usually purchased in coils (rolls) of specific heights, but for this project, you can consider that the steel is purchased in rectangular pieces of any size convenient for the production process. Construction costs can be summarized as follows:

18 gauge steel is 68 cents per square foot.

20 gauge steel is 51 cents per square foot.

Welding and pressing/sealing cost 15 cents per foot.

Cutting steel costs 3 cents per foot.

Note:Since you must use rectangular pieces of steel to begin with, you must purchase the full sheet, even though there will be waste, and cut your top and bottom discs from the rectangular piece.

Your group will turn in an electronic copy of your word processed report that discusses each of the following points. You mustinclude all relevant mathematical calculations.

1.Compute the cost of the drum specified in the drawing above.

2.Given the same costs for material, cutting, etc. above, find the optimum dimensions of a 55 gallon drum (interior volume of 56.80 gallons) that minimizes the cost to build the drum.

Total points possible

Points earned

Intro/Conclusion/Presentation

10

Point 1

40

Point 2

50

Total Points

100