Composite section design - Why and how? 2

[youngstructural]

Hello All;

The production of a composite section used to be second nature to a Structural Engineer. When I worked as a Bridge Maintenance Engineer, I reviewed or inspected the condition of numerous bridges with sections made up of various typical shapes (plate, angle, tee, etc). I am very comfortable with the application of Tau = VQ/It and q = VQ/I for most situations, but am not sure what to do for the situation I am looking at now...

To take a simple example, say we have an rolled I section to which we would like to attach two plates, top and bottom, to increase the I of the section. In the calculation of the shear flow (taking q = VQ/I from above) we consider the maximum shear load which the beam will have to support (V), multiply that by the first moment of area of the plate being attached(Q) and divide by the overall resulting composite section's second moment of ares (aka Moment of Inertia).

My question relates to flinch beam situations, where you have vertical plates being connected together to create a composite beam, or perhaps back to back channels with (or without) a plate in between. In this case, what is our Q? I would think that we would calculate the Q for the portion of the composite section which will be above the fixing location. This would seem rational to me, as the shear flow is present at an elevation, and the orientation of the fixings should not affect the shear present. Am I correct?

In determining WHEN we are required to create a composite section, I have always followed the advice I received from a very senior engineer at one of the first firms I worked at. He said, quite simply, that if you have a load applied to a beam, the overall stiffness of the beam bears the load. However, if you have a beam made up of multiple parts which you are considering to be sharing a common load, the difference in the relative stiffness could cause problems and as such the section must be made composite so that as one part of the beam takes load, the others are forced to assist. Is there any more formal guidance or design examples that anyone knows of? I'm curious to know what you all think...

I've read through

http://www.eng-tips.com/viewthread.cfm?qid=124984&page=12

but it doesn't address this question...

Thanks,

YS

B.Eng (Carleton)
Working in New Zealand, thinking of my snow covered home...

 

[JAE]

For cases with "flitch" beams where you have multiple beam sections side by side there really isn't any composite action taking place. Each individual part of the built-up section takes its own share of load in direct relation to its stiffness relative to the other sections in the shape.

There is no shear flow between them if they are all loaded directly.

 

[youngstructural]

I can see your argument, and agree.... If they are all directly loaded. But take the case of two back to back 400 deep channels, with a 380 deep flat plate between them. The channels are loaded, not the plate, with the plate receiving load through the connections to the channels. Would there not be shear flow in this situation?

B.Eng (Carleton)
Working in New Zealand, thinking of my snow covered home...

 

[JAE]

Yes, but not based on VQ/I.

The shear flow would simply be the linear transfer of load along the length of the member equal to the share of the load that the plate takes.

Example: Take your overall shape properties and apply a uniform load to it. The overall I value determines the deflection, [Δ] of the beam.

Now, with that deflection, take the I value of the plate only, and back calculate the amount of uniform load that would induce that plate to deflect [Δ].

That is the load that is transfered from the two channels to the plate. Divide by two and that is the uniform load transfered from one channel to the plate.

 

[UcfSE]

You may need some minimum fastening to insure that your side by side section will act composite in the case of buckling. Two channels are not as stable as a single I-section. You may be able to find minimum fastening requirements in the material code you're under.

 

[youngstructural]

Thanks for that JAE; It seems obvious after someone says it... After all, that's what it's all about these days (P-Delta, Stiffness attracting load, etc, etc).

Good point UcfSE, it's something I've thought about, but do not believe will govern in my case...

One further question: What if the middle plate we've been talking about does not connect to the support, but rather is used to increase the section modulus (and thus bending capacity) of the beam in only a local area? So, for example, the two channels are a simply suppored span of 8 meters, with the bending moment in the middle being 20% greater than they are able to handle. A plate is introduced in the middle third which boosts the strength by the required 20%. In that case, we would have load transfered as outlined by JAE, but towards the end we would have the full load taken by the channels alone. Any thoughts on further issues from that arrangement? I don't think there would be an issue, unless we were to try and determine the actual deflection of the resulting beam. I don't think that would be trivial, however with regard to bending strength, I don't see any issue. In this case I see the fastening being accomplished by a simple force couple in simple shear.

B.Eng (Carleton)
Working in New Zealand, thinking of my snow covered home...

 

[JAE]

There would be a point on the moment diagram where your two channels alone could theoretically take the bending without the plate. Call that point A.

I would suggest that you extend the plate beyond point A, towards each support some distance - similar to how a cover plate on a beam is extended. AISC's specification (which is a free download) discusses this in chapter B. Then, at the end of that plate, I would think the interconnection should be increased at bit to ensure a tight termination of the plate.

Then, beyond the interior plate, I think you have some lateral buckling concerns per UcfSE above....two channels with a gap between them.

 

[UcfSE]

I agree with JAE. You will just have a non-prismatic beam, no big deal but it takes a little extra work since you are dealing with different cross sections along the length of the beam.

If you get really bored (or excited) you could graph the moment capacity of your beam wrt length and superimpose that on the bending moment diagram to see where you are with design requirements. You can go back and do the same with the shear force, and then again for required moment of inertia and provided moment of inertia.

 

[jen4950]

"If you get really bored (or excited) you could graph the moment capacity of your beam wrt length and superimpose that on the bending moment diagram to see where you are with design requirements. You can go back and do the same with the shear force, and then again for required moment of inertia and provided moment of inertia. "

Well- that is what I would recommend if you want to do the job correctly.

Of course, if you have access to SAP2000 or equivalent, this becomes a 10 minute exercise-

My little drivel of a thought on the subject: Think of what is actually happening in the beam with your applied force and resulting moment- it's a Tension and Compression force with the associated couple provided by the steel structure. If the elements are side by side, it's just a function of proportioning the load based upon stiffness (section modulus)

If you transition thru a weld or other connection, without direct bearing on the element, you need to figure out what that internal transfer of force is, i.e. you coverplate the flanges, the original D for the section was 24 inches and the new D is 26.

 

[VoyageofDiscovery]

Keep in mind any existing stresses prior to introducing the plate to pick up the "20%". Locked in stresses will not transfer to the new plate tacked.

In some cases the beams are shored prior to installation of new plates.

Regards

VOD