critical flange for continuous beam using AS4100.

[geopat69]

Hi all.

Hoping to get some assistance with an academic issue and continuous beams to AS4100.

CASE: A gravity udl is acting on a 3 span continuous steel I-beam beam. Spans being 2m, 10m , 2m. The 2 internal supports clearly have negative moment but the end spans do not have any positive moment. Ie only the centre span sees some positive moment.

The internal supports are considered as Full restraint.

The outer supports provide only vertical support (i.e no twist or rotational restraints).

QUERY: would the critical flange for the end spans be the top or bottom flange.

caution: its not as straight forward as you might think and the complexity arises on if the end spans are acting as cantilevers.

some insight is appreciated

 

[Trenno]

Taken from this design guide

Is there a chance that this beam is subject to a load reversal? Or pattern loading?

 

[jrbaus]

If the outer supports act as vertical supports only, with tension throughout the entire length of the top flange, I would treat the outer segment as a cantilever with the outside support considered as a load at or below the shear centre of the section:

alpha_m = 1.25 -> 2.25 [Table 5.6.2]
kt = 1 [Table 5.6.3(1)]
kl = 1 (shear centre) [Table 5.6.3(2)]
kr = 1 [Table 5.6.3(3)]

You would then need to consider the 10m interior segment separately, which will probably be treated as 3 "design segments" due to the top flange changing from tension to compression at some point. Have a look at the textbook "Design of portal frame buildings", in particular the section that deals with moment distribution and design segments in rafters. That should help you with the design process for the interior span. I suspect the interior segment between the points of contraflexure will be the critical segment (assuming no intermediate flange restraints).

Regards Jake

 

[geopat69]

Hi jake. Thanks for your post. I initially thought the same way you did for the end span ( ie treating it as a cantilever with top flange being critical)

Then i start to think twice! If at the end supports i introduce twist restraint to the system (everything elese unchanged)...do we suddenly make the bottom compression flange critical?

 

[geopat69]

Hi trenno.
The case i am referring to is not a cantilever.. but a beam unrestrained at one end..and having a vertical support only. Thus i dont think the cantilever clause is as straight forward as we might think.

 

[Trenno]

Refer to pictures and text above.

 

[Trenno]

Sorry, I didn't see your next post which referred to my post.

Can we have some particulars about the situation? How are the tips connected to only provide vertical support? Is the main rafter an I section?

 

[Trenno]

Despite this system not having a cantilever at each end, the bending moment diagram (due to the span layout) does mimic that of the cantilever case.

That's the reason why I am inclined to treat it as the case highlighted in my original post.

But perhaps I'm wrong - keen to hear other people's opinions.

 

[geopat69]

Hi trenno.

Its a hypothetical case really. But i do have case where the end supports are merely providing vertical support only.

This has come from an in-house office discussion regarding a design issue. The as4100 code appears to discuss beams "unrestrained at one end" instead of "cantilevers". Thus, the end supports of a continuous beam (ie supports without twist or lateral restraints...as in my example above) is not a "cantilever", but it could be argued that the top flange rules still apply. BUT....should one simply add in a twist/lateral restraint at the first supports...then suddenly the critical flange flips to the bottom compression side-> and this does not seem to follow logic!

 

[geopat69]

By illogical i refer to the following: consider sheeting screwed to the top flange of the continuous beam. Thus, for the end span, if treated as a cantilever...has continuous lateral restraint at the top flange...YET if adding in lateral+twist restraint at the first support, then suddenly the critical flange is the unbraced bottom flange!

 

[KootK]

The key here Is recognizing where the vertical location of of the centre of LTB rotation is for each case:

1) Ends restrained, no tip sidesway. Here, the point of interest lies between supports and the LTB centre of rotation is at or above the top flange depending on whether or not there is decking. Thus, it makes sense to brace the bottom, compression flange.

2) Ends unrestrained, sidesway permitted. Here, the point of interest is at the first support and [pre][/pre]the LTB centre of rotation is below the bottom flange. Thus, it makes sense to brace the top flange.

Note that case one would have a higher LTB capacity as well. Also, if the end restrain was somehow rotational but not lateral, it would represent yet another case altogether.

I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.

 

[geopat69]

Many thanks kootk.

Am i correct in saying you believe your case 2 is applicable? For my continuous beam case?

 

[KootK]

You're quite welcome and you are indeed correct. I believe that the case you've described matches my case two and is best represented as an unrestrained cantilever.

I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.

 

[jrbaus]

geopat, interesting post. Has me thinking (I now understand exactly what it is you are asking)....

Thanks KootK & Trenno for your input.