Hi folks!

Today, allow me to have my continuation of my previous [blog](https://steemit.com/steemiteducation/@josephace135/random-review-problems-in-strength-of-materials) of which there are 4 review problems and I decided previously to present each problem in a separate blog post. With that in mind, without further ado, here is the second review problem.


``A cast iron column with annular cross section supports an axial compressive load of 250 kilo Newtons (kN). Determine the inside diameter of the column if its outside diameter is 200 millimeters (mm) and the limiting compressive stress of 50 megapascal (MPa).``
Choices:
 <center></center> | <center></center>   |  <center></center> |  <center></center>
--- | --- | --- | ---
A.    183.4 mm |  B. 175.98 mm | C. 45.67 mm | D. 123.5 mm

Solution:

For this review problem, the only way to solve this one is just simply remembering that applied stress is always equal to the ratio of the applied load to the cross sectional area of a material. As for the cast iron column, the cross section is the area between the outer circle and inner circle. And the formula goes like this:
<center>![](https://cdn.steemitimages.com/DQmdXkgiH2ffH5JjQgFVmT1PDSBDQP29fkAa5sgKXoWcxMY/blob)</center>
wherein:
- `σ` is the stress, which can be expressed in terms of pound force per square inch (psi) or in kiloPascal (kPa).
- `F` is the applied, which can be expressed in terms of pound force (lb<sub>f</sub>) or in Newtons (N).
- `A` is the cross sectional area, which can be expressed in terms of square inches (in<sup>2</sup>) or in square meters (m<sup>2</sup>) or in square millimeters (mm<sup>2</sup>).

For the aforementioned problem, the cross sectional area of the column can be obtained using this formula for annulus or annular rings.
<center>![](https://cdn.steemitimages.com/DQmPYo7BqAZD5Zu5NDuWWixmvgkYpyu3pngMHJopZXUVP74/blob)</center>
wherein:
- D<sub>o</sub> is the outside diameter of the annulus.
- D<sub>i</sub> is the inside diameter of the annulus.

Since we now have all the formula for obtaining the inside diameter of the column, we can now proceed to the computation which is shown below.
<center>![](https://cdn.steemitimages.com/DQmSFVDGBgzUUqwV8NScaZox2LLxS7Lxf7SBkZhVPDJjGbr/blob)</center>
<sub>In the above computation, we found out that the inside diameter (D<sub>i</sub>) of the column is `183.4 mm` which satisfies to the stress and the load that is being applied to the column.</sub>
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Well, the computation is a bit easy and pretty straightforward. I guess that would be all for today's review problem.
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Thank you for spending your precious time reading my blog.

<br>

Much love and respect.

<br>

Ace | @josephace135

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Presentation of the calculations where made possible using the Equation features of MS Word. All screenshots are made by me and is made  possible by Snipping Tool application.