Question

you are asked to size the diameter of a bolt loaded in shear to the nearest 1/8 inch with a factor of safety of 1.5. you find that bolt diameter that yields this factor of safety is 2.4183 inches. what is the diameter of the bolt you should use (in units of inches to 3 decimal places).

Answer 1

Answer:

2.375 inches

Step-by-step explanation:

Main Steps

1. Identifying important parts of the question

2. Solving the problem

Step 1. - Identifying important parts of the question

In the question, there is some extraneous information.  For instance, the question introduces the terms "diameter" and "loaded in shear" and "with a safety factor of 1.5".  However, given the information in the problem, and the question asked, it isn't necessary to know that it is "loaded in shear" means, or to know what a diameter is (since everything stays with diameters, and doesn't involve another dimension), and the problem gives the result that will satisfy "a safety factor of 1.5".

Sifting through the problem/question, these are the important parts:

- "to the nearest 1/8 inch" (meaning round to the nearest 1/8th of a unit)

- with "units of inches to 3 decimal places"

- The number to round is "2.4183 inches

Step 2. - Solving the Problem

To round to the nearest 1/8 inch, we can divide the number 2.4183 by 1/8.  

$2.4183 \div(1/8)$

Recall that dividing by a fraction is the same as multiplying by the reciprocal

$2.4183 * 8$

19.3464

So, there are approximately 19, one-eighth-inches in the measurement.  (Note that 19.3464 is closer to 19 than it is to 20).  To find the final rounded measurement, multiply 19 by 1/8

$19 * (1/8)$

2.375 inches

So, the diameter of the bolt that should be used (if rounded to the nearest 1/8 inch, to allow for a factor of safety of 1.5) is 2.375 inches