Global Buckling of Trussed Tower

[bootlegend]

Hello all,

I am working on the design of the structure shown in the attached sketch. I have modeled the structure and done a second order analysis in RISA 3D. I don't have any issues with the model stability but I am trying to verify the global buckling with a hand check. For each mast I calculated the overall properties of the four columns and treated it as a concentrically loaded column and calculated the Euler buckling capacity based on a fixed base-free top column. However, since the interior columns carry more of the load from the upper truss I want to account for the eccentricity on the built up column shape, along with wind loads, etc. My first thought was to just calculate the bending stress and do an interaction check on the mast. But how do I calculate the critical stress for bending?

Am I making this more complicated than it needs to be? I think for a given load there is some height that the overall mast would buckle before any individual member failures, but is modelling it with a second order analysis the best way to capture the condition. For reference, I copied my model and added about 40' feet to the height of the mast and the P-delta iterations definitely increased based on solution time. But the columns are also failing as local members too due to lateral loads so I would have increased those which would also increase the stiffness.

To summarize, is there a reasonable way to check by hand the global stability of a box truss or lattice structure under axial and bending loads?

 

[human909]

I'd considered getting rid of the eccentric loading. For a small change you can make your life a whole lot easier. Regarding hand calculations you could start by calculating your I and S and for the lattice going from there.

 

[JoshPlumSE]

Am I making this more complicated than it needs to be?

Probably, but you're following a good process. Making sure that the computer output in is in the "ballpark" of what you'd expect. I'm with Human909.... this is just a simplified hand check to make sure that you haven't done something wrong with the model. I'd probably just treat the each leg of the tower as an "equivalent column" with an EI, P, L, and a K.

 

[bootlegend]

I'd probably just treat the each leg of the tower as an "equivalent column" with an EI, P, L, and a K.

I've done that and it's okay. I guess beyond that I'll double check that the bracing meets the AISC bracing strength and stiffness requirements for column bracing. I guess my confusion is whether the second order analysis in RISA captures the global stability under lateral loads. I thought that it did but I am confusing myself the more I think about it.

 

[JoshPlumSE]

I guess my confusion is whether the second order analysis in RISA captures the global stability under lateral loads.

When I worked at RISA (which ended in late 2017), RISA was only capable of doing a P-Large Delta analysis based on joint deflections. So, the P-Little Delta effect (which is related to member curvature between joints) could not be accounted for directly. But, there was a very easy work around..... to add joint along the length of the member. If those joints along the length of the compression member effectively captured the member curvature, then the RISA P-Delta analysis would capture both.

That (when combined with the AISC Direct Analysis Method) will do a very good job of capturing the global buckling of the structure. In fact, if you've modeled a lattice tower like you showed in your image, then RISA will automatically have joints along those compression chords and it will do a BETTER job than it would have for a regular steel moment frame.

 

[JoshPlumSE]

Caveat: I has been awhile since I've looked at any of the newer versions of the program. So, they may have changed the way they handle P-Delta. I know I did a number of write-ups / specifications on how to do this.

Also, I don't have the best relationship with the current RISA management. So, while I didn't intend to include any bias in my response, it may still be there. I say this because they once contacted me through a 3rd party threatening litigation if I were to continue to communicate with their customers through social media. I laughed it off, but am now cautious about what I say and always want to acknowledge my bias (as a disgruntled ex-employee and as an employee of one of their major competitors).

 

[human909]

I've done that and it's okay. I guess beyond that I'll double check that the bracing meets the AISC bracing strength and stiffness requirements for column bracing. I guess my confusion is whether the second order analysis in RISA captures the global stability under lateral loads. I thought that it did but I am confusing myself the more I think about it.

I can't speak specifically about the program you are using or niche circumstances. But in general, buckling analysis of calculation packages is generally quite good at calculating global buckling. And even reasonably good at covering bracing stiffnesses. Though most of the time I'd want to see global buckling at least 2-3x ultimate load.

What most static analysis programs don't capture well is all the other subtle factors such as eccentric connections etc.

 

[bootlegend]

Caveat: I has been awhile since I've looked at any of the newer versions of the program. So, they may have changed the way they handle P-Delta.

Understood and thank you for the feedback.

Though most of the time I'd want to see global buckling at least 2-3x ultimate load.

That seems reasonable and is achievable in my case. Thanks.

 

[BAretired]

To summarize, is there a reasonable way to check by hand the global stability of a box truss or lattice structure under axial and bending loads?

If each tower is treated as a single column with known properties and the applied axial and bending loads are known, the stability could be checked by finding the deflection for increments of load, keeping applied P and M in the same ratio for each increment. Newmark's numerical procedures would be one hand method which could be used. The critical load combination is the point where the column yields or deflection exceeds an acceptable limit.