Question

bench before the top and shelves are added. (see the blueprint.) the specs call for 1 1/4 - in.×1 1/4 - in. square steel tubing for the frame and 3/32 - in. thick sheet metal for the top and shelves. for pricing and shipping purposes, dwayne needs to determine both the amount of materials needed and the weight of each workbench. 1. to simplify his calculations, dwayne decides to convert all fractional dimensions to decimal form. list all fractional dimensions given on the blueprint in decimal form. 2. the designers omitted some crucial dimensions on the blueprint. fill in the missing dimensions a, b, c, d, and e, assuming that there is equal spacing between shelves and between sections of the frame. 3. dwayne next needs to determine the total amount of tubing needed to create this workbench. assume that 18 cuts need to be made and that each cut wastes 1/16 in. of tubing. what is the total number of inches of tubing needed for each workbench?

Explanation:

Step1: Convert fractions to decimals

$54\frac{1}{8}=54 + \frac{1}{8}=54+0.125 = 54.125$, $\frac{3}{4}=0.75$, $40\frac{5}{8}=40+\frac{5}{8}=40 + 0.625=40.625$, $1\frac{1}{2}=1.5$, $1\frac{1}{4}=1.25$, $\frac{3}{32}=0.09375$, $\frac{1}{16}=0.0625$

Step2: Find missing dimensions

The height of the work - bench is $40\frac{5}{8}=40.625$ inches. Since there are two equal - spaced shelves and we consider the top and bottom frame parts of height $\frac{3}{4}=0.75$ inches each and the bottom clearance of $1\frac{1}{2}=1.5$ inches. The available height for the two equal - spaced shelves is $40.625-(0.75 + 0.75+1.5)=37.625$ inches. So $C=\frac{37.625}{2}=18.8125$ inches.
The width of the work - bench is $18$ inches. The frame members are $1\frac{1}{4}=1.25$ inches square. In the top view, if we assume equal spacing between the three sections, $A = B=\frac{18-(2\times1.25)}{3}=\frac{18 - 2.5}{3}=\frac{15.5}{3}\approx5.1667$ inches.
In the front view, the width of the frame members is $1\frac{1}{4}=1.25$ inches. So $D = 54.125-(2\times1.25)=51.625$ inches and $E=40.625-(0.75 + 1.5)=38.375$ inches.

Step3: Calculate tubing length

Count the lengths of tubing

• Vertical tubes: There are 4 vertical tubes of height $40.625$ inches each, total length $4\times40.625 = 162.5$ inches.
• Horizontal tubes in the front and back: In the front and back, for the top and bottom horizontal tubes, there are 4 tubes of length $54.125$ inches each, total length $4\times54.125=216.5$ inches. For the middle horizontal tubes in the front and back, there are 2 tubes of length $51.625$ inches each, total length $2\times51.625 = 103.25$ inches.
• Horizontal tubes in the sides: In the sides, for the top and bottom horizontal tubes, there are 4 tubes of length $18$ inches each, total length $4\times18 = 72$ inches. For the middle horizontal tubes in the sides, there are 2 tubes of length $\frac{18-(2\times1.25)}{3}\times3+(2\times1.25)=18$ inches each, total length $2\times18 = 36$ inches.

The total length of tubing without considering cuts is $162.5+216.5 + 103.25+72+36=590.25$ inches.

Account for cuts

There are 18 cuts, and each cut wastes $0.0625$ inches of tubing. The total waste from cuts is $18\times0.0625 = 1.125$ inches.
The total tubing needed is $590.25+1.125=591.375$ inches.

Answer:

1. Decimal dimensions: $54.125,0.75,40.625,1.5,1.25,0.09375,0.0625$
2. $A\approx5.1667$ inches, $B\approx5.1667$ inches, $C = 18.8125$ inches, $D = 51.625$ inches, $E=38.375$ inches
3. $591.375$ inches