Twin beam lateral restraints at top flange 1

[george69]

HI all

I have 2-900WB simply supported beams spanning 18m. the beams are 1100mm apart. There is a large concentrated load in the middle. There is top flange K-bracing that tie the beams together. The nodes that for this "truss" are at 1m centres.

They have the same bending moment at midspan and are working near their section capacity.

The AS4100 steel code says that lateral restraints need to be able to take 2.5% of the flange compression force at the section considered. Is anyone able to elaborate on how these forces are applied/considered?

For instance, do I treat the top flange and bracing as a truss with discrete point loads along the length? i.e a truss analysis!!, OR, is the 2.5% loading meant to be interpreted as a load for each restraint considered in isolation and ignoring the global effects(i.e ignoring the truss effect)

Cheers

Thanks

 

[paddingtongreen]

The bracing acts as a horizontal truss, apply your stability, and any other horizontal loads to it. Make sure that the bracing is up close enough to the top flange to be effective.

Michael.
Timing has a lot to do with the outcome of a rain dance.

 

[BAretired]

Your code is slightly more conservative on that point than the NBC which requires 2% of flange compression in each brace unless a more detailed analysis is performed. When a detailed analysis is performed, the bracing requirement is, in my experience, always less than 2%.

Bracing forces are acting alternately in opposite directions, i.e. if Braces 1, 3, 5 and 7 act east, then Braces 2, 4 and 6 act west. Thus you do not include these forces in your truss design.



BA

 

[george69]

Thanks for your response.

BAretired is your suggestion that the global truss effect is ignored?

I have attached a rough sketch to elaborate

 

[TXStructural]

I have designed similar members, which were closely spaced wide flange beams, and using Vierendeel configuration cross connections. Model the top flange as a truss for out of plane deflection resistance (stiffness of the truss is primary), using your code-required bracing forces.

Also, look at whether the loads will be eccentric, causing warping of the top flanges, and brace in cross section if needed to prevent rotation.

 

[BAretired]

The top flange of each beam must be connected to the truss for a force 2.5% of the compression in it, but the forces are not cumulative as you show on your sketch. That would make no sense at all. If you had elected to space panel points at 0.5m instead of 1m, by that reasoning, you would need to design the truss for twice as many forces of the same magnitude. Or, if you had opted to space them at 2m, you would need to provide only half as much lateral load.

The required force, Pb in a brace can be determined in another way. This is the expression in the NBC:

Pb =[β]([Δ]o + [Δ]b)Cf

Pb = the force used to design the bracing system. When two or more points are braced, the forces Pb alternate in direction.

I believe it would be conservative to design your truss for one midspan force F = 2.5% of the combined maximum compression in the two top chords plus wind pressure if applicable.



BA

 

[BAretired]

The relevant page from NBC is attached.

BA

 

[apsix]

The 2.5% restraint force is required at spacings equal to the effective length which results in the member capacity you require.
If the restraints (panel points) are at closer centres the restraint force can be averaged out to achieve the same overall force. (That's how I interpret AS4100 Cl.5.3.4.1)

 

[BAretired]

Can you post a copy of the clause in question?

BA

 

[paddingtongreen]

George, I misunderstood the question. That is not "K" bracing!

When you said K bracing, I thought it would be short span with a single K bracing with a strut in the middle, local and global would have been the same.

I defer to BA who didn't misunderstand.

Michael.
Timing has a lot to do with the outcome of a rain dance.

 

[apsix]

BA, as requested. Enjoy.

5.4.3.1 Restraint against lateral deflection The lateral restraint at any cross-section considered to be fully, partially or laterally restrained in terms of Clause 5.4.2 shall be designed to transfer a transverse force acting at the critical flange (see Clause 5.5) equal to 0.025 times the maximum force in the critical flanges of the adjacent segments or sub-segments, except where the restraints are more closely spaced than is required to ensure that M* equals Mb.
When the restraints are more closely spaced, then a lesser force may be designed for. The actual arrangement of restraints shall be assumed to be equivalent to a set of restraints which will ensure that M* equals Mb. Each equivalent restraint shall correspond to an appropriate group of the actual restraints. This group shall then be designed as a whole to transfer the transverse force of 0.025 times the maximum force in the critical flanges of the equivalent adjacent segments or sub-segments.

 

[george69]

apsix

Thanks for posting the AS4100 reference. And you are correct, if the restraints are closer, then you don't need to design them for the full load - obviously a pro-rata and easily done.

The question, which I believe BA correctly answers via Canadian approach, is that the "restraining" forces are in opposing directions and NOT all in the one direction - which I thought. Clearly the opposing directions would eventually cancel out. Refer to the attached. I suppose, if the number of braced sections is even, there could be a nett effect in one direction.

Paddingtongreen - sorry to confuse you but I do have K bracing. The sketch I attached was to just show an example of "bracing" (i.e any bracing configuration), to the top flange.


cheers

 

[BAretired]

george69,

I believe your sketch with opposing forces is more in keeping with the NBC approach for bracing members generally.

When the bracing forces are being provided by a truss in the horizontal plane and when there are other lateral forces on the truss such as wind, the lateral deflection of the truss plays a role in stability. If the truss deflects [Δ] under wind pressure, for example, the top flanges become more critical in lateral buckling because of the eccentricity.

I don't believe the clause cited by apsix contemplated that problem and I don't think NBC considered it either. If the lateral deflection of the truss is significant, it will assuredly affect the buckling capacity of the top flanges.

Need more time to think about it.

BA

 

[george69]

BA retired

OK - FYI In this instance there is no lateral wind. Just pure vertical point load at midspan.

As you've seen from the AS4100, it specifically refers to "THE lateral restraint" which I take to mean individual elements need to restrain 2.5% of flange force taken laterally. But it does not specify alternate directions like the canadian approach.

This is ultimately my dilema. Reading the AS4100 blindly - one could be orientating all the lateral loads in one direction and have serious lateral load at the supports to deal with. Whereas, using the canadian approach, the loads are more or less cancelled out along the span.

I'm not familiar with the canadian code, but I gather from your doubt, that clause 9.2.6 of the canadian code is for compression members that have lateral restraints? If that is the case then I believe there is no difference as the top flange, is in essence, a compression member.


I look forward to hearing your reply.

 

[BAretired]

I'm not sure that what I have said is the singular "Canadian approach". While I do not have AISC standards at my disposal, I believe from what I have gleaned from previous posts on this forum, that AISC has a similar approach to ours.

The requirement for lateral bracing of a compression flange comes from theoretical considerations based on an assumed initial misalignment of the member due to accidental eccentricities during the fabrication or delivery process. These limits are specified in our code as L/1000 or L/500 or other. Based on this rather debatable starting position, the requirement for lateral bracing may be determined using somewhat simplified assumptions first proposed by George Winter.

The value of 2% in my code or 2.5% in your code is conservative in the extreme. It refers to the capacity of an individual connection which can act in either direction, but to add these together in a cumulative lateral load would be totally wrong.

BA

 

[OzEng80]

George - I imagine that the alternate bracing directions is due to the sinusoidal deflected shape of the compression member (picture a buckled member over multiple supports). It would be nice if the codes were explicit enough to cover all scenarios but there should be enough here to piece together a valid design approach.

 

[apsix]

The 2-2.5% value may be conservative but the idea that you can alternate the direction as a rule seems questionable to me.

If the member has an intial imperfection curvature in the horizontal plane all the restraint forces will tend to be in the one direction, especially for relatively flexible braces such as the truss.

Of course, if designing to AS4100 all the forces must be taken to be cumulative.

 

[OzEng80]

apsix - AS4100 requires the design of a cumulated bracing force for parallel restrained members (ie a series of beams) - it doesn't give any guidance to alternating restraints 'along the beam'. It dictates that the two beams can buckle in the same direction at a restraint but nothing beyond that. I believe that as a compression member, restraints would be required on alternating sides due to the sine wave deflected shape. This seems to be supported by the Canadian code. There is probably some Euler derived formula that describes this?

 

[apsix]

OzEng80
The fact that there is no guidance isn't a reason to take an overly optimistic view.

If the restraints are provided by a roof or floor diaphragm it doesn't make any real difference.

If you are relying on a flexible restraint, such as the truss discussed here, it would be brave to assume alternating directions.

 

[hokie66]

apsix,
Why would you consider a horizontal truss to be a flexible restraint? I can't see the alternating direction approach, but the truss would provide bracing approaching that of a diaphragm. Think of how it would compare with typical roof bracing for the compression flange of rafters.