Critical Buckling Load?

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Orion66
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Critical Buckling Load?

Post by Orion66 »

I have been looking into some important equations for designing a tower, and found Euler's Critical Load formula (https://en.wikipedia.org/wiki/Euler%27s_critical_load). While this equation is straightforward enough, it applies only to purely axial loads. With the slanted legs of our towers, however, the load is NOT axial. That being said, how should I apply/modify the equation given side/angled loads? I've asked elsewhere and been told that "Non axial load is resolved into axial load and a moment. Axial load creates additional moment if the column is slender." Unfortunately I have only a foggy idea what that means.

Can anyone explain/clarify?
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Balsa Man
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Re: Critical Buckling Load?

Post by Balsa Man »

Orion66 wrote:I have been looking into some important equations for designing a tower, and found Euler's Critical Load formula (https://en.wikipedia.org/wiki/Euler%27s_critical_load). While this equation is straightforward enough, it applies only to purely axial loads. With the slanted legs of our towers, however, the load is NOT axial. That being said, how should I apply/modify the equation given side/angled loads? I've asked elsewhere and been told that "Non axial load is resolved into axial load and a moment. Axial load creates additional moment if the column is slender." Unfortunately I have only a foggy idea what that means.

Can anyone explain/clarify?
If you take the time to read what's here- Towers thread, and Wood thread, you'll find a lot of discussion and information on exactly what you are wondering about. I just posted a pretty lengthy discussion on applying and using Eulers formula earlier this morning in the Wood thread. If you go back to the 2017 archive of the towers forum, you will find pages and pages of detailed discussion.

Sorry, but you are wrong about the legs of a tower not being axially loaded. The force put on by the load block is transferred axially along the legs to the base. Also, the statement "axial load creates additional moment" is also wrong. It is non-axial loading would do that. Example- a ladder brace glued across the outward facing sides of an adjacent pair of legs. If/as the legs start/try to bow inward toward each other. they are pushing the ends of the ladder toward each other, but that push is being applied to/along the edges of the ladder. As you noted, the forces are 'resolved' into- which means what's happening, what's going on is that some of the force acts along the axis, and some of the force goes into/acts to try to bend the ladder- bowing it outward, away from the tower. That's why. btw, ladders lap jointed onto the sides of legs are weaker than the same strength ladder butt-jointed between the legs.
And the column being "slender" is simply a condition on the applicability of Euler's equation. The equation describes the theoretical behavior of a slender column of an elastic, homogeneous material. There is not a....hard cutoff for a wooden column to be 'slender', but suffice it to say, at the dimensions we're using in towers, 1/8" legs behave as slender columns. Wood, as discussed at length, is not a homogeneous material (you can have two pieces with same weight and cross section, with significantly different buckling strengths)- we account for that/deal with that fact by applying safety factors.

So, do your homework. Understanding Euler buckling is absolutely critical to understanding how to design a good tower, so you've started down the right path. Sure you'll have more questions as you come to understand more.
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Re: Critical Buckling Load?

Post by Random Human »

Orion66 wrote:I have been looking into some important equations for designing a tower, and found Euler's Critical Load formula (https://en.wikipedia.org/wiki/Euler%27s_critical_load). While this equation is straightforward enough, it applies only to purely axial loads. With the slanted legs of our towers, however, the load is NOT axial. That being said, how should I apply/modify the equation given side/angled loads? I've asked elsewhere and been told that "Non axial load is resolved into axial load and a moment. Axial load creates additional moment if the column is slender." Unfortunately I have only a foggy idea what that means.

Can anyone explain/clarify?
Balsa Man just posted a page worths of buckling strength analysis on the "wood thread". Do some further digging into last years forums, and you have yourself the "explanation" or "clarification"
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