Jlambergris
New member
- Joined
- Feb 20, 2020
- Messages
- 1
I'm one of those people that uses scrap pieces or something bought at the box store and welds it together with a thumbs up.
This time I thought I would try doing the math and have a properly constructed cantilever. Wow, not easy.
The project is a simple cantilever with two uprights.
I was thinking 6ft tall with 24in long arms at 3ft and 4.5ft intervals.
Figure 750lbs for each level.
I started at the arms and learned a uniform load of 750lbs on 24in arms would equal a 375lb point load at 12in on a single arm and create a 375lbft moment on the upright.
The beam seems straightforward in properly selecting for deflection/load/length when using beam load tables for structural steel.
The column is problematic
The best I have found is
I am able to substitute P with x for
σmax=P[1A+ecIsec(π2√PPcr)]σmax=P[1A+ecIsec(π2PPcr)]
in a graphing calculator and replicate the Maximum Stress graph.
I assume the usefulness of this is to see how much stress a specific load creates at the corresponding eccenticity.
Although, I need to know the maximum weight at a specific eccentricity. From what I can discern, the Nondimensional Eccentric Buckling graph provides this information. I can follow the example but I am unable to replicate the graph so that I can input my own material specifications.
How is this graph generated?
1.This seems to satisfy a single level load calculation but would not be appropriate for 2 levels. The closest I could find was another example but with a point load on top of the column in addition to the eccentric load.
2.Safety Factor and K for column end factor are absent in this
- These facts lead me to believe I would have an insufficient answer but for this forum basic help with equations and graphs would be enough to satisfy my intrigue.
Bonus question, c-? How is this number calculated? "The maximum bending stress occurs at a point in the cross-section farthest from the neutral axis, i.e., y=c"
Thanks!
This time I thought I would try doing the math and have a properly constructed cantilever. Wow, not easy.
The project is a simple cantilever with two uprights.
I was thinking 6ft tall with 24in long arms at 3ft and 4.5ft intervals.
Figure 750lbs for each level.
I started at the arms and learned a uniform load of 750lbs on 24in arms would equal a 375lb point load at 12in on a single arm and create a 375lbft moment on the upright.
The beam seems straightforward in properly selecting for deflection/load/length when using beam load tables for structural steel.
The column is problematic
The best I have found is
I am able to substitute P with x for
σmax=P[1A+ecIsec(π2√PPcr)]σmax=P[1A+ecIsec(π2PPcr)]
in a graphing calculator and replicate the Maximum Stress graph.
I assume the usefulness of this is to see how much stress a specific load creates at the corresponding eccenticity.
Although, I need to know the maximum weight at a specific eccentricity. From what I can discern, the Nondimensional Eccentric Buckling graph provides this information. I can follow the example but I am unable to replicate the graph so that I can input my own material specifications.
How is this graph generated?
1.This seems to satisfy a single level load calculation but would not be appropriate for 2 levels. The closest I could find was another example but with a point load on top of the column in addition to the eccentric load.
2.Safety Factor and K for column end factor are absent in this
- These facts lead me to believe I would have an insufficient answer but for this forum basic help with equations and graphs would be enough to satisfy my intrigue.
Bonus question, c-? How is this number calculated? "The maximum bending stress occurs at a point in the cross-section farthest from the neutral axis, i.e., y=c"
Thanks!