Arch buckling

[ido3778]

Hello,

I need to design a steel pedestrian bridge that the middle span is hanged on an arch that pass over it.

How do I take into account the arch geometry for buckling calculation?

I think I need to reduce the effective length, but I an not sure, and if it is the effective length I do not know the amount of the reduction.

Please advice.

Any reference will be great.

Thanks.

 

[BAretired]

I'm not entirely happy about leaving this discussion where it is because we haven't answered the original question in a manner which the OP can apply to his problem.

I believe that the arch can be designed assuming a straight member with a length of one half the curved length of the centerline. If the arch centerline follows the funicular curve of the bending moment, there is no bending at any point along the arch, so we would have a case of plain buckling.

If the arch centerline does not follow the funicular curve, then we can consider a straight member with combined axial load and bending moment which also can be solved by hand methods.

If one half of the arch is loaded and the other half unloaded, the loaded half may carry pure axial thrust, but the unloaded half would carry combined thrust plus substantial bending moment. It is this condition which I would expect would usually govern the design of the arch.

If a frame analysis is used, it seems to me that, at least for the unbalanced load case, it would not be necessary to model slight geometric irregularities into the arch.

If the arch is circular or any other shape which does not follow the funicular curve, it should not be necessary to model slight irregularities because there are bending moments even in the case of symmetrical loading.

BA

 

[IDS]

I'm happy to agree with BAretired

The critical load case for any arch bridge will be due to assymetrical live loading (not necessarily half the span loaded) combined with wind loading. Even under dead load for a structure that exactly followed the funicular shape for final dead load (which in practice no arch ever does), there will be significant deflections locked in during construction, which should be included in the analysis. The effect of this is that there will be far from the unstable equilibrium position that exits in a straight compression member, so you don't need to add imperfections.

My recommendations would be:

- Analyse the structure with a suitable frame analysis program that allows for a construction sequence analysis and includes geometric non-linearity.

- Use lower bound stiffness values for everything, including foundations.

- Don't forgat to allow for creep, shrinkage and cracking if there is any concrete involved.

- Carry out the analysis at the Ultimate Limit State, i.e. apply load factors to the loads in the analysis, don't scale the output member actions by a load factor.

- Use influence lines to estimate critical load configurations.

- Investigate load conditions around these configurations, since the behaviour is non-linear and the influence lines are not strictly applicable.



Doug Jenkins
Interactive Design Services

http://newtonexcelbach.wordpress.com/

 

[ido3778]

Many thanks guys, your help is really appreciated.
I am about to print this thread and go over it very thoroughly.

Probably a few more questions will pop up.

Thanks again.

Ido