That wall thiccness
2023-07-06
In the last post we determined that no matter what Euler’s critical load formulas determined, we can not load a column beyond the steel’s yield point. Well what’s the yield load for a given pipe size? Since yield is in pounds per square inch, the number of square inches of steel in a pipe determines how much force we can apply to it before things go from happy to snappy. The math is simple; since we’re loading the post vertically, multiple the cross sectional area of the pipe in inches2 by the yield strength of the steel per inch2. Our yield strength is \(25,000\) so if \(a_c\) is cross-sectional area, allowable loading before the steel yields is \(a_c * 25,000\) or column \(l_m\).
| Pipe size, nominal (in) | OD, actual (in) | Wall thiccness (in) | \(r_1\) | \(r_2\) | \(a_c\) | \(l_m\) |
| 1.5 | 1.900 | 0.145 | (\0.8050\) | \(0.9500\) | 0.79946 | 19,986.4 |
| 2.0 | 2.375 | 0.154 | \(1.0335\) | \(1.1875\) | 1.07453 | 26,863.3 |
| 2.5 | 2.875 | 0.203 | \(1.2345\) | \(1.4375\) | 1.70405 | 42,601.3 |
| 3,0 | 3.500 | 0.216 | \(1.5340\) | \(1.7500\) | 2.22847 | 55,711.7 |
| 3.5 | 4.00 | 0.226 | \(1.7740\) | \(2.0000\) | 2.67954 | 66,988.5 |
As we can see the calculated critical load overtakes the yield strength of the material at 2.5″ NPS.
| Pipe size, nominal (in) | Critical load, lb, adjusted |
| 1.5 | \( 11,848\) |
| 2.0 | \( 25,452\) |
| 2.5 | \( 42,601\) |
| 3,0 | \( 55,711\) |
| 3.5 | \( 66,988\) |
Again, this is maximum load assuming perfect load distribution, perfectly vertical column, just the right alignment of the stars, what mood Hephaestus is in that day, etc. Also this is factor of safety of one. Nothing in the real world is designed to exact failure point of a thing.
Next post we’ll compare the above calculated values to industry figures and to wooden posts that are currently holding up my porch roof.