Rafter without fly brace? 22

[fourpm]

I am designing rafters to AS4100 and wondering what if I don't use fly brace. I understand that with fly brace it will give you full restraint. But if I don't use fly brace, will the purlin above be considered as lateral restraint for rafter under uplift? If so. can I take the purlin spacing as segment and the only factor that changes without fly brace is kt?
I have the same question when it comes the continuous steel floor beam design where Z/C floor joints sit on top of the beam. What segment should I take for the beam near the support? Can I take the floor joists spacing as segment with lateral restraint? Can anyone give me some examples? I have read some manuals but the examples they have are simply supported beams only. Thank you.

 

[Tomfh]

A purlin only provides lateral restraint when connected to the critical flange. Under uplift the bottom flange becomes critical, and thus purlins alone do not provide restraint. Hence the need for fly braces.

Under gravity load in continuous members the bottom flange can be critical too, i.e. you can need fly braces for gravity loading.

You should familiarise yourself with AS4100. It's all spelled out there.

 

[fourpm]

HI Tomfh. Thank you for your reply. So if I have a two spans continuous floor beam (6m+8m) supporting Z section floor joints above. The segment length under gravity for the beam will be 8m (the longer span) without any lateral restraint for checking negative moment near the support considering the critical flange will be at the bottom flange? If this is the case, why would people still use continuous beams instead of two simply supported beam of which the critical flange will be on top (under gravity) and lateral restraint will be provided?

 

[Tomfh]

Only a portion of the bottom flange is critical in continuous beam, so it's not nearly as bad as an 8m long beam with the whole bottom flange in compression.

 

[fourpm]

Sorry but I don't quite understand. Does that mean I should take the length of the bottom flange in compression (say L/3 max = 2.7m) as the segment length?

 

[jayrod12]

When you run the analysis of your beam, the critical flange is the one in compression. We can't tell you from here how much of the bottom or top flange that is.

 

[fourpm]

Thanks jay. I understand the critical flange is in compression but I have problem understanding how long should the segment length be. For a continuous beam with floor joists on top under gravity load, which means joists can not provide restraint for negative moment area. Can I take the length from the column below to the point where moment becomes 0 (negative to positive) as the segment length to check if the bending capacity is okay for the negative moment at supports?

 

[jayrod12]

Generally speaking, I would take from inflection point to inflection point because I do not feel that the column to beam connection is a brace point unless the joint is detailed for out of plane moment. Otherwise it's technically a hinge in my eyes.

Edit: I do not consider inflection points as brace points per se. I do feel that if I design a beam for the maximum negative moment, assuming an unbraced length of inflection point to inflection point, while also being conservative with my loading, analysis, lengths, and unity checks, that the beam is adequate. I would bet my house on the answer being the same as if I took it from the first brace point past the inflection point as others have described below but was less conservative on the rest of my numbers.

 

[Agent666]

When you run the analysis of your beam, the critical flange is the one in compression

It's actually defined in As4100 as the flange that laterally deflects the furthest. Usually the compression flange though, but not always.

The inflection point isn't a point of restraint (see this blog post I wrote as an an example demonstrating this aspect). It's something I see people doing from time to time, and it's the wrong way to think about the restraint issue.

The next purlin past the inflection point is possibly an 'L' restraint, possibly 'F' depending on your connections to the top flange. Keep in mind the fly brace braces the beam by preventing the twist (if your purlin meets the stiffness required) so is able to increase the capacity without needing to support the 2.5% flange force by some external horizontal support. For an 'L' type restraint the 2.5% force turns into an axial load in the purlin, so you need some external load path to support this force to achieve the requirement to prevent lateral deflection of the critical flange.

 

[Tomfh]

It’s a bit murky. The floor joists can be counted as a lateral restraint once the top flange becomes the critical flange. As agent666 says, the critical flange is defined as the one which will deflect the furthest in the absence of restraint, which is typically though not necessarily the compression flange. In practice people often just take the compression flange as the critical flange, which allows you to take the first restraint past the point of contraflexure as a restraint (or indeed the point of contraflexure itself as a restraint). I’m don’t know how conservative/unconservative that approach is. Maybe it’s close enough in practice.

 

[fourpm]

Many many thanks guys. I will take the first floor joist outside each injection point in positive moment area as the segment length for negative moment capacity check.
Just one more question regarding the 2.5% force that Agent666 mentioned. As it is a beam instead of a column, how do I work out the equivalent force? (the compressive stress times the area of critical flange?) Can you please give me an example? (I have read Agent666's reference but it is regarding column too).

 

[Tomfh]

how do I work out the equivalent force? (the compressive stress times the area of critical flange?)

Yes the force in the flange. The flange is akin to a horizontal column. It's under compression and wants to buckle (sideways) same as how a column wants to buckle, so you need to grab it to restrain it. 2.5% is a commonly accepted figure, although as agent666 points out, buckling is more to do with stiffness, not strength. The idea is that if something can carry 2.5% of the load it's probably stiff (and strong) enough to prevent buckling.

 

[Agent666]

Often in calculations it's simplified as restraint force = F* = M*/(d-t_f) x 2.5/100.

Don't forget about parallel restraint forces and tracking the cumulative force to something that is stiff/can take the load. Typically for say a roof because of this requirement I'd only say the purlins that align with the roof bracing system are actually effective. Older AS1250 steel standard used to have the provision at the end of my link relating to stiffness. So basically span/400.

In reality you can do a buckling analysis to see at what point (i.e. What stiffness) something that's providing the bracing/restraint forces a higher mode of buckling.

 

[KootK]

I will take the first floor joist outside each injection point in positive moment area as the segment length for negative moment capacity check.

I object strongly to this approach unless:

1) you've got fly bracing in play or;

2) your joist to beam connections provides real rotational restraint to the beam.

Instead, I recommend that you:

3) use the beam span between supports (8m) as your effective, lateral torsional buckling length for the negative moment.

4) Use stiffeners, fly braces, or whatever the heck you've gotta do to call the beam to column connection a point of full restraint for lateral buckling.

The key to understanding the appropriate unbraced length lies in the concept shown below. Think of your bottom flange as:

5) A strut/column whose lateral, buckled shape will have no inflection points between beam support points.

6) A strut/column whose axial load is a funky, linearly varying thing rather than just end loads.

When looking at column Euler buckling, the [L] value is squared. In comparison, the axial load is linear. As result, the length of the buckling mode shape between inflection points matters vastly more than does the particular axial load being applied. So the fact that your axial load in your beam flange is distributed, linearly varying, and sometimes tension does not offset the impact of the buckling mode between beam supports not having any inflection points.

 

[KootK]

Generally speaking, I would take from inflection point to inflection point because I do not feel that the column to beam connection is a brace point unless the joint is detailed for out of plane moment.

If the interior column cannot be considered to LTB brace the beam, then I believe that your effective length for negative moments is actually the full length of the two span beam, outer column to outer column. At which point the moral of the story becomes find a way to make the interior column an LTB brace point.

 

[Tomfh]

Instead, I recommend that you:

3) use the beam span between supports (8m) as your effective, lateral torsional buckling length for the negative moment.

4) Use stiffeners, fly braces, or whatever the heck you've gotta do to call the beam to column connection a point of full restraint for lateral buckling.

This is certainly a safe approach, however quite conservative as it ignores the restraining effect of the floor against lateral torsional buckling.

My reading of AS4100 is that you can treat restraints on the compression flange as lateral restraints, which reduces your effective length.

 

[Agent666]

My reading of AS4100 is that you can treat restraints on the compression flange as lateral restraints, which reduces your effective length.

I concur, this is the intent of the 'L' restraint, provided you are preventing via external means deflection of the critical flange. It can rotate, but no lateral deflection of the flange.

 

[Tomfh]

provided you are preventing via external means deflection of the critical flange.

What I find a bit murky is AS4100 initially defines the critical flange as the flange which will deflect the furthest if the beam was fully unrestrained, however it also allows you to simply take the compression flange as the critical flange.

In our example here the bottom flange will deflect the furthest in the unrestrained situation, but at the middle of the beam the top flange is in compression, thus you could take either the top flange or the bottom flange as the critical flange in the middle portion of the beam.

Is that the intent you think? Is it saying that in such a location you can happily restrain either top or bottom and achieve an L restraint?

 

[hokie66]

I have known other engineers to use full depth stiffeners both sides, along with a 4 bolt cleat connection to the purlin, all in lieu of fly braces. This was apparently because a client or architect objected to the fly braces. It might work, but is not as good, and is more expensive.

 

[Tomfh]

Hokie,

Yes we do that on occasion.