To find the stress area of a [tex]\( \frac{5}{16}-18 \)[/tex] UNC-2A fastener, we refer to standard engineering tables that provide this information based on the dimensions and thread specifications of the fastener. The stress area is critical for calculating the strength of the threaded section of the fastener under load.
Here are the steps to determine the correct stress area:
1. Identify the thread size and type: For a [tex]\( \frac{5}{16}-18 \)[/tex] UNC-2A fastener:
- The nominal diameter of the fastener is [tex]\(5/16\)[/tex] inches, which is equivalent to 0.3125 inches.
- The thread pitch is 18 threads per inch.
2. Refer to standard engineering tables or resources: Standard tables like the ones in engineering design handbooks or machinery handbooks provide the stress area for common fasteners based on their size and thread type. These values have been pre-calculated using precise formulas and measurements.
After referring to such a table for a [tex]\( \frac{5}{16}-18 \)[/tex] UNC-2A fastener, we find that the stress area (At) is approximately [tex]\(0.077 \, \text{in}^2\)[/tex].
Therefore, the correct stress area for a [tex]\( \frac{5}{16}-18 \)[/tex] UNC-2A fastener is:
[tex]\[
0.077 \, \text{in}^2
\][/tex]
Given the options provided:
1. [tex]$0.077^{\prime \prime}$[/tex]
2. [tex]$1.25^{\prime \prime}$[/tex]
3. [tex]$0.77^{\prime \prime}$[/tex]
4. [tex]$0.3125^{\prime \prime}$[/tex]
The correct answer is the first option, [tex]\(0.077 \, \text{in}^2\)[/tex].
