Elastic Resistance to Lateral Buckling (Appendix H - 3404) 1

[micks87]

Hi,

I am trying to design a warren truss using the elastic buckling method as described in Appendix H of NZS3404. I have heard this method produces more efficient results but I am unsure of how to implement this. Does anyone have an example of how this applies to a truss member?

To add some context, I have attached a simple warren truss below. Assuming all members are 75x3 SHS members.

Thanks for your time.

 

[Agent666]

Micks87, Appendix H is more about lateral torsional buckling under moment. For a truss I am guessing you are more interested in member buckling under axial loads?

If so read on:-

You need to undertake an elastic buckling analysis, most common software in NZ can do this (spacegass/microstran, etc).

From this you get an elastic critical buckling load factor, this factor is a ratio by which the applied loads in your model would need to be increased to cause the first member to buckle.

This load for your critical member embodies the buckling length, in effect takes care of k_e * L in the analysis. You don't have to guess the effective length factor k_e, but the critical buckling load (the load in member times the load factor) does not include the effects of initial imperfections on which the column buckling curve is based (the calculation for slenderness (λ_n) and hence α_c factor). NZS3404 requires the initial imperfections to be considered, typically span/1000, or length/1000. Analysis is obviously typically based on perfectly straight members.

Note this analysis will effectively give you the buckling mode shapes also, so review what members are buckling by viewing the modeshapes, so you make sure you are checking the critical member.

But using the elastic critical buckling load directly, you then apply the requirements in clause 6.3.4, whereas N_om is the value coming out of your buckling analysis. This works out the slenderness (λ_n), use this to work out the alpha_c factor like any other member. Then ΦN_c = ΦN_s * α_c

Also the process was discussed in a few recent threads, so have a read here & here as it might answer a few questions about the approach.

To cement the approach in your mind I suggest making models to which you know the idealised k_e factors from figure 4.8.3.2, then work capacity out like you normally would and then by using clause 6.3.4. For k_e=1.0 you should get the same answer. For other cases the normal way will be conservative because the 0.7 and 0.85 cases are theoretically 0.5 & 0.7 (this is what your buckling analysis should output the equivalent of). Similar for k_e>1.0 cases they will be slightly conservative.

Hopefully you will see that it is effectively working out the same thing but takes the guesswork out determining the k_e effective length factor, because in reality most members have rotational springs at their ends (another member, foundation, etc) and the restraints are never perfectly pinned or fixed, similarly for truss chords that might buckle over several panels the load in the member is varying which improves the buckling vs considering the maximum axial load over the entire member length.

 

[ukbridge]

Agree with everything Agent says

If you don't do an eigenvalue buckling analysis, you need to use the BEF method and model the top chord as a beam on springs representing the U-Frame stiffness of the diagonals (I'm assuming theres no plan bracing). EN 1993-2 has a method of doing this, or you could also use a simple plane frame model.

As a very crude rule of thumb (that does not replace the need for detailed design calculations), Le for the top chord is usually about L/3 for these types of configurations.

 

[micks87]

Thank you for the reply folks. Very helpful posts.

 

[ukbridge]

No worries - one other thing that gets often forgotten, dont provide full lateral restraints at the end of the BEF model as this will overestimate the buckling load factors you calculate. Make sure theyre springs not fixed supports.