Pinko commie Europeans
2023-06-11
What is the point of these series of posts? Like everything else on there internet, there is no point. All of this stuff is covered in engineering courses and the web is full of much more rigorous treatments. My goal is to explain it to myself. To paraphrase Michael Scott, you can’t claim to understand something if you can’t explain it. This is my attempt at just that.
According to Wikipedia, Euler’s basic formula for calculating critical column loads is: $$ P_{cr} = \frac{\pi^2EI}{(KL)^2} $$ where:
\(P_{cr}\) – the critical load of the column
\(E\) – Young’s modulus of the column material
\(I\) – Minimum second moment of area of the cross section of the column
\(L\) – Unsupported length of the column in inches
\(K\) – Column effective length factor
We’re going with the worst case scenarios for everything. We will assume lowest quality steel, most janky implementations and so forth.
\(K\) is a modifier for column length. Under certain conditions it can reduce the “apparent” length of a column and increase critical load, but due to the preceding we will leave \(K\) at 1. \(K\) is not \(1\) if the ends of the column are fixed, for example. If the ends of the column are fixed in all directions, \(K\)Becomes \(0.65\). For now thought, we’re going with \(1\).
\(E\) Young’s modulus (modulus of elasticity) is something we look up in a table since we’re using standard ASTM A53 pipe.
\(L\) is the length of the column. This is dependent on the design.
\(I\) is actually very interesting and will be covered in its own post.
For purposes of this discussion, below is a list of material properties we will be using. These are all collected from the Internet. I don’t have access to ASTM specs directly 🙄. It’s classified as need to knowpay. On one hand hurray for the capitalist system and everyone charging everyone for everything. On the other hand I can’t help but think that the knowledge that modern life is built around should have some provisions for non-commercial usage. And those commie pinko Europeans are no better. Try to get something out of ISO for nothing. To everyone keeping this sort information under lock and key 🖕🖕🖕🖕🖕🖕
| Tensile strength | 45 ksi | https://amerpipe.com/products/carbon-pipe/a53/a53-specifications/ We’re going with the lowest numbers since my specification at the supplier is “give me the cheapest stuff you have!” |
| Yield strength | 25 ksi | https://amerpipe.com/products/carbon-pipe/a53/a53-specifications/ |
| Modulus of elasticity | 30,000 ksi | This is identical to ASTM A36 steel. Fun story. Most of the websites I checked get this wrong. They list it as 30ksi (rather than 30,000ksi) which results in a critical load of ~12 pounds for an 88″ tall column made out of 1.5″ NPS pipe. That right there is hilarious. |