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

To determine the bolt diameter to the nearest 1/8 inch for a factor of safety of 1.5, the calculated diameter of 2.4183 inches should be rounded up to the next 1/8 inch increment, resulting in a diameter of 2.500 inches.

Step-by-step explanation:

The given problem involves the sizing of a bolt diameter that is loaded in shear. According to the student's calculations, a bolt diameter required to achieve the specified factor of safety of 1.5 is 2.4183 inches. However, the question is asking for the size of the bolt to the nearest 1/8 inch. To solve this, we need to round the calculated diameter to the nearest 1/8 inch increment. An inch is divided into eight 1/8 inch increments, so we can list some 1/8 inch increments around the calculated value: 2.375 inches (2 3/8 inches), 2.500 inches (2 1/2 inches).

Comparing the calculated diameter (2.4183 inches) with these values, 2.375 inches is the nearest diameter that is lower than the calculated value, and 2.500 inches is the smallest diameter higher than the calculated value. However, because we are seeking a factor of safety, we must round up, not down, to ensure that the bolt is not undersized. Therefore, the correct diameter for the bolt is 2.500 inches to the nearest 1/8 inch increment.

Answer 2

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 /(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