Column buckling of truss structure

[JStephen]

How do you handle Euler column stability in a truss type tower? Examples would be lattice-type crane boom or antenna towers. Design of individual elements wouldn't be a problem, but how do you show that the overall structure won't buckle in classic column failure?

 

[rb1957]

if the individual elements won't buckle, how could the ass'y ? a really tall tower may have tip displacement constraints, which migth be a bit tricky to calculate by hand (tho' no problem for FE).

 

[Drej]

How do you handle Euler column stability in a truss type tower? Examples would be lattice-type crane boom or antenna towers. Design of individual elements wouldn't be a problem, but how do you show that the overall structure won't buckle in classic column failure?

(1) Calculate the buckling load using the Euler method, either by hand or by FE. The buckling equation is given here This gives you the critical load to cause buckling of the structure. You can also do this in FE if you have access to a code.

(2) Carry out a non-linear buckling analysis. Expensive.


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[trainguy]

You need to calculate an effective radius of gyration for the combined cross section. I'm sure classical equations/methods exist to do this, although I can't currently peg down a reference.

Using basic principles, you can calculate the centroid, and moment of inertia of the axial members in your section, and use this to approximate an effective radius of gyration, then check this as a (built-up) column.

I disagree with rb1957- you can certainly get global column buckling even if your truss elements do not buckle locally.

tg

 

[UcfSE]

I would start with the built-up column section of the AISC specification and also check the ASCE 10-97 "Design of Latticed Steel Transmission Structures". Can you model the tower in a 3D analysis program and check for stability issues?

 

[Cardinal177A]

I agree with trainguy. Each individual beam segment has its own moment of inertia, load, length, and boundary conditions. The full tower has a different moment,load, length, and B.C. This gives each a different Euler buckling value.

 

[ssulei]

The buckling of structural members would depend on the slenderness ratio (KL/r). Usually, analysis is carried on the structure and the ultimate forces/stressess are determined. The failure of the members would be either be in inelastic or elastic mode (euler failure). This depends on the KL/r ratio which inturn is set by the member length, end connection details and geometric property. For slender structures, a second order analysis may be needed. It is perfectly possible to design your structures based on the capacity of individual members. Full scale tower tests have been carried on electrical power lattice towers in EPRI which based on ANSI/ASCE 10/97 that validate such approach. Numerous papers on these issues in the journal of structural engineering (ASCE)

 

[Cardinal177A]

Roark and Young's "Formulas of Stress and Strain" has a good section on latticed beams, covering both the global and local buckling issues. Bruhn has a good section for calculating the properties of composite(meaning built up of several metal sections) beams, as does "Advanced Mechanics of Materials" by Seely and Smith. Roark shows that since latticed beams have many joints that each have a small amount of give, a latticed column is not as stiff as one would expect, so a correction factor needs to be applied. Since JStephen asked specifically about crane booms and antenna towers, some of which are 2000' tall, and not relatively short transmission towers which are usually almost as wide as they are tall(at least the ones I have seen), global buckling is very much a major issue, as Roark details. Any tower needs global buckling analysis, even if it is a simple determination of whether or not the tower is tall enough to require global buckling analysis. Any paper stating that global buckling analysis is not required for certain structures, needs to give guidelines for when ignoring global buckling is OK, and when it is not.

 

[SoeSoe]

Here's a vague recollection:
Wasn't a famous bridge collapse around the turn of the century during erection in Canada the result of said buckling? Wasn't the cause the neglect of global shear deformation (Essinger's equation)? Sorry no time to research and see if memory serves correct--have to get back to work.

 

[JStephen]

I remember hearing of one large bridge that collapsed during erection. I think the problem was two-fold. They made the span longer AFTER the design had been done, without re-evaluating. Then also, they may have had laterally unsupported compression trusses- not sure of the terminology- with no way to evaluate.

 

[SoeSoe]

Yes, here it is,

http://www.civeng.carleton.ca/Exhibits/Quebec_Bridge/intro.html

Apparently, "built-up" columns may be approximately analyzed as homogeneous columns, but the shear effect causes the above to happen, which in standard formulae is neglected. The bridge at the time was to be the longest span in the world. I never see anyone calculate anything anyways, just reams of illegible computer output. It seems policy and perception find software superior to understanding, it makes everyone feel warm and comfortable. Must be done right if the software was expensive and created by PHD's. It's just so pretty and professional.