Glulam Beam / Transform Section

[structeng2]

Hello All,

I am working on replacing rooftop equipment on an existing single-story building.

The new RTUs are located along the column line in the middle of the building with supports on either side of the column, attached to the glulam member, increasing the negative moment. In 2010, a retrofit was performed on these glulams, bolting an MC10x25 on either side of the glulam centered over the columns. We are calculating the capacity of the transform section and I want to make sure our calculations are accurate - as I haven't done a transform section in a while. I reviewed this thread, but still wanted input on our situation.

The calculation and diagrams are attached, but here are my questions/thoughts:
[ul]
[li]We transformed the glulam to steel, so we ended up with a very slender steel 'plate' between the two channels[/li]
[li]We got the necessary section properties of the transformed section[/li]
[li]Calculated the steel section capacity using FyZx (Aisc F2-1)[/li]
[li]Based on the ry of the transformed section, LTB does not control because Lb < Lp.[/li]
[/ul]
However, the part that I am confused on is that the transformed section has these tall slender elements above and below the channels. Using Table B4.1b, Case 10, the elements are slender. Maybe I should be using AISC F3?

For what it's worth, the channels on their own can support the RTU's. And we are attaching the RTU frame directly to the channels with a saddle that goes over the Glulam and bears directly on the steel. But I still want to verify our methodology on the transfor section.

Thanks for your input. Looking forward to the discussion.

 

[driftLimiter]

The transformed section is only used to check the stress at different points within the beam cross section. you have a composite S and a composite I that are used to find the stress in the composite section then using the modular ratio you can convert that stress back into stress inside the glulam.

The transformed section analysis does not include stability checks like what AISC is doing in section F. Perhaps you could call it a built up section per AISC, but still the rationale behind the local stability checks in AISC don't directly translate to the stability of the local elements in the transformed section.

I think you need to do a sanity check on the stability part of your question, then just compare stresses against allowables for each of the materials in the composite beam. More (perhaps most) importantly is ensuring that the sections are fastened together enough to get a fully composite section. If they aren't you could; add more fasteners to get full composite, use a partial composite section, or just treat the beams as non-composite and have load sharing by stiffness compatibility.

 

[structeng2]

Thanks, driftlimiter. This makes sense and is what I was missing.

So, I can basically take Mc/I (with 'c' to the steel flanges) and compare against steel stress and then Mc/I (with 'c' to the wood extreme fiber) and compare against allowable wood stress (modified by modular ratio).

As far as the composite action, the bolts are epoxied into the glulam (although there still could be mechanical slip at the steel hole). I will probably check full composite, and full non-composite and see where I land.

 

[driftLimiter]

So, I can basically take Mc/I (with 'c' to the steel flanges) and compare against steel stress and then Mc/I (with 'c' to the wood extreme fiber) and compare against allowable wood stress (modified by modular ratio).

@structeng2 That is the way I think the transformed section analogy should be applied.

 

[rb1957]

should you transform the section into both materials ?

you have a beam of two materials, A and B.
transform into material A and extract stresses on components with material A (like the extreme fiber), transforming B components into their equivalent A area doesn't change the geometry of A components;
then transform into material B and extract stresses on B components.

or if you transform into A material, can you extract B component stresses, take stresses in B component from a A-transformed section, then factor by EB/EA ?

I think you need to transform about both axes (X and Y) separately.

another day in paradise, or is paradise one day closer ?

 

[ChorasDen]

Careful when running your transform section analysis. Each ply in a glulam has different stiffness and/or strength. For an unbalanced layup, the bottom 1 or 2 plies has much higher Ft and stiffness than the core plies on the glulam. This may affect the results of your analysis. Would actually have to think about it a bit more if it would be okay to use the global design values for the glulam, or if you would need to go ply by ply.

Edit: for an unbalanced beam, the neutral axis is not half the beam height, due to the offset plies, so be sure to include that when considering the new neutral bending axis.

 

[structeng2]

The glulam is a 24F-V8, so it is a balanced layup. Since we are looking at the extreme fiber for the glulam, I believe the Fbx+ and Fbx- (they are the same in this case) are appropriate to use? Or should I compare the stress demand against Ft and Fc since I am looking at tension/compression in the extreme fibers?

I found this video to be extremely helpful - very simple and straightforward and is very similar to our situation. (They also follow the method outlined by driflimiter)

@rb1957, I believe we effectively do this by using the modulus ratio to convert the stress to the appropriate values. (e.g. after getting the stress at the extreme fiber in the transform section (steel), we multiply back by the modulus ratio to get the stress for the wood)

 

[KootK]

This seems out of whack to me:

1) I don't think that a composite treatment makes sense when you only have connections every 8' oc. Beams in tandem connected at those three locations seems more appropriate to me.

2) I question the efficacy of the reinforcing in the first place. With the glulam being 32" deep and the channels being 10" deep, I'd have to think that you'd snap the glulam tension fibers well before you'd meaningfully engage those channels for anything useful. And that's without considering any potential slip in the bolt holes.

And we are attaching the RTU frame directly to the channels with a saddle that goes over the Glulam and bears directly on the steel.

I'd avoid connection the frame to the channels. Three reasons:

3) You'll force the channels, and their connections, to take all of the load initially rather than share it with the glulam.

4) Unless you grout a gap below the base plates, there will be a gap and all of the load will tend to be delivered to the channels.

5) Cheaper not to bother with it.

 

[structeng2]

Thanks for the input, KootK. I will try to address each of your points..

1) We had planned on adding regularly spaced anchors to create a better composite action.

2) I see your point here, but wondering how to actually calculate/determine this? When we looked at the stresses of each material with the transform section analysis, they were both under the allowable.

3/4/5) We had gone back and forth on this. Sort of to your point on item #1, going directly to the channel ensures that the load from the RTU actually gets to the steel. I am not opposed to just a regular saddle that sits on top of the glulam and is bolted through. Then the load would travel through the glulam and engage both the wood and steel. Would you mount it a different way?

Lastly.. if there is concern about the composite action, would it make sense to add an additional piece of steel welded to the top of the channel and bolted to the glulam? This would get the steel closer to the tension fibers for negative bending.

 

[driftLimiter]

You get the best effect for shear flow by increasing the distance from the centroid to the fasteners. Full composite steel and wood beams are mostly a figment of education I think if you dive into this calc you will find it difficult to get fully composite.

 

[phamENG]

structeng2 - to your question about KootK's number 2, I'd say that a transformed section analysis is inappropriate here. You don't have adequate fastening to make it composite, so they won't be sharing load through their length, only at three discreet points. Therefore, the steel and the glulam are free to deflect independently between the connections. The close the connections are together, the smaller and less consequential that becomes. 8 feet is pretty consequential.

Are you using a 3D analysis program for your design? If so, you might try modeling the glulam and the steel channels as discreet members and connecting them with rigid links at the centroid of each bolt group. It won't be perfect, but it'll give you a pretty good idea of the load sharing that is (or isn't) happening.

If you're doing it by hand, you might try this:

Far from perfect, but I think it would be a decent starting point.

As for the efficacy of the reinforcement...I agree it looks pretty iffy. It's difficult to judge whether or not the bolt holes were drilled small enough to prevent slop in the connection and additional rotation. Even a visual inspection is unlikely to do anything for you since it'll be hidden under the plates, washers, nuts, and bolt heads. It also does little to nothing for you for unbalanced loading. The configuration is dependent upon the glulam on the opposite side not deflecting up to resist the loads.

 

[structeng2]

Thanks,phanENG. Your approach makes sense if not considering a transform section. I am using SAP so I did a quick model following your approach. My D/C for the glulam is 0.85 and my D/C for the channels is 0.32. This makes me feel a little better knowing that I am still under capacity on the glulam, and the load is being shared with what seems like a more reasonable distribution based on stiffness.

Model:

Moment Diagram:

Shear Diagram: (I would assume that the difference in shear at the rigid link joint is the shear being transferred through the bolts?)