Load Distribution on Precast Double Tee

[JohnRwals]

Hello!

Let's assume two single stem Tees (independent L1xW1 and L2xW2) are combined rigidly into one double tee
along the stitch line.
I wonder how a load will be distributed to each stem.
Do you think a load will be transferred according to the stiffness (k1, k2) of each stem?
Also, how can I find the maximum deflection points?
I guess the largest deflection points will be different from the midpoints, L1/2 and L2/2.

 

[KootK]

Do you think a load will be transferred according to the stiffness (k1, k2) of each stem?

What kind of load? Applied where on the system?

In general, tees suck at load sharing between members on account of their significant torsional flexibility. And single tees are even worse that double tees in this regard as they can't even get the bi-moment thing going that you get with two tees on an integral unit.

For most problems, I'd be inclined to design each tee separately for the loads applied too it and then do a sanity check on the amount of differential that predict between adjacent tees.

 

[driftLimiter]

If you had a rigid line load that spanned across the entire width of each T-beam then I think you could justify enforcing displacement compatibility. However the beam stiffness could be taken at each point, for example if you are near a support of one beam and away from the support of another beam, their is a different level of load sharing. In fact with this model if you placed the rigid line load on the support of one of the beams , that support would take the entire load probably not realistic to have that rigidity in your loading so not sure this model would serve you well.

 

[JohnRwals]

Let's assume this double tee will support parking load, LL=40psf.
W1=W2=6ft, L1=60ft, L2=40ft, 12DT30.

 

[Brad805]

Is there a topping? What are the connections? If something like a JVI vector they do not have a lot of stiffness for this.

 

[BridgeSmith]

Alot depends on what is meant by "combined rigidly". A rigid shear connection, or a full moment connection? The load sharing will be significantly different between those 2 cases.

Rod Smith, P.E., The artist formerly known as HotRod10

 

[JohnRwals]

This could be either field-topped or factory-topped.
Note: This is one piece double tee with connections to adjacent double tees using Vector Connectors, for example.

 

[Brad805]

I think in reality there would be a notable difference in stiffness between the pre-topped and CIP topping wrt load sharing due to the stiffness of that connector style. If one wanted to make a complex model this can be solved, but I think the number of assumptions needed for the spring analogy will lead to dubious results.

 

[KootK]

wrt load sharing due to the stiffness of that connector style.

I feel that your focus on the connectors is spurious and that the load sharing capabilities of a tee framed deck are neutered by the lack of torsional stiffness that those members possess. See the clip below from this paper: Link

 

[Brad805]

I assume we are talking about a 3" or so topping and a section that is along the lines of the second image. I agree a hollow core in the paper will not have any transverse stiffness, but a 4" slab will be very different than a 1 1/4" skin with zero transverse reinforcement.

 

[KootK]

I agree a hollow core in the paper will not have any transverse stiffness, but a 4" slab will be very different than a 1 1/4" skin with zero transverse reinforcement.

The salient information in the paper is not about core transvers capacity but, rather:

1) That hollow core slabs possess tons of torsional stiffness and strength and that's why they distribute loads well and;

2) Tee sections possess very little torsional stiffness and strength and that's why they distribute loads very poorly.

Getting the load across the tee flanges is just one part of the overall, load sharing picture. The larger issue is whether the member of which the flange is a part possess the torsional strength and stiffness required to resist any load that might cross the flanges.

 

[Brad805]

Koot, after re-reading, yes, I see your point. I will mock up a model for my own interest. I never have spans that need DT's so it is interesting.

 

[Brad805]

I created a basic 3D solid model to study the question asked. The cross section was simplified a little to reduce the analysis time and prevent poorly shaped solid elements. To study the differences I used three different analysis cases. The loads applied in each case were the same. All analyses are non-linear using material models noted included in the 2010 model code. I did not include an interface between the topping and the slabs. This is not quite correct because this will results in a perfect solid when it is added to the model.

1. NL1: The topping is excluded from the analysis, but its mass is applied to the cross-sections.
2. NL2: The topping was added to the model after the prestress and dead loads were applied.
3. NL3: This analysis is the same as NL2, but restraints were added in the YY direction to reflect topping continuity or lateral restraint.

Below are a few images from the model. I have included more images in the .pdf attached.

Analysis model:

Cross Section Properties:

Deflected Shapes due to Prestress:

NL1 Moments and Shears:

Deflected Shape from NL2: This shows the torsion mentioned.

Model Summary Forces:

The model suggests that the 60'-0" section does share some load with the 40'-0" section, but it does not seem significant to me. Given the moments in the 40'-0" section remain basically the same in each analysis, the force seems to be transferred locally to the 40'-0" section. Both NL2 and NL3 show a torsion at the end of the 40'-0" section.

 

[JLNJ]

It seems to me that you are just asking for God to put a crack right down the line between the two tees.

Just the unknowns of the camber and the patterned loading would give me pause.

 

[JohnRwals]

Brad807,

Your modelling shows interesting points.

So, is self-weight of this DT 45kips? (150psf ocncrete assumed)
Did you use different strand layouts between 60ft and 40ft long stems? (5 vs. 7 strands?)

JRW

 

[BridgeSmith]

Having one stem with a shorter span doesn't gain you much in terms of capacity, and produces quite a bit of shear stress that the flange doesn't normally see. It would also be significantly more expensive to cast than a standard double tee for the longer span. Is there some reason why you absolutely can't extend the shorter stem to be the same length?

Rod Smith, P.E., The artist formerly known as HotRod10

 

[JohnRwals]

This odd shape double tees often happen at the parking structures.
For example, near stairs, vent and elevator shafts.

 

[JohnRwals]

If my interpretation is correct, short stem bearing load is much higher
than other bearing points. (I assume bearing points are close to the end of each stem.)
This makes sense, but I thought short stem will take much less bearing load like the other end, 96 vs. 83.
What about bearing position (vertical)?
As long stem deflects upward more due to prestressing after erection, isn't this stem bearing position higher than other three bearings?
Doesn't this leveling difference impact actually applied bearing load?

 

[Brad805]

The material model I used in this case uses a concrete self = 156pcf. I have a script to create this material in the model, so I used that. For the strands, I used the PCI detail below.

I believe the load transfer between the longer and shorter tee will be related the stiffness of the assembly and load applied after the topping is cured. Deflected upwards or not, they will undergo deflection due to the application of live load. As the longer tee tries to deform, its neighbor is stiffer and will want to be a supportive buddy. There were some simplifications in the model, so it could be the topping will debond locally before that happens. A small amount topping debond would likely relieve some portion of the load transfer you see in the model. I can apply an interface between the topping and the cross section, but there are a number of variables to get that to work correctly and it would take some time to figure out. In the delegated design world the topping design does not seem to get a great deal of attention. It seems likely that the topping ends up being thinner at this point due to the difference in elevations. I believe that will affect this as well. I drew some general conclusions from this analysis, but it would take an academic to study this further.

 

[JohnRwals]

Brad,

You would like to design one single double tee as combined two single tees (40, 60ft long)...
That's interesting.
As your model shows, the whole load cannot be transferred to two single tees by 50:50 ratio.
I am not sure this method is good.
In fact, because many pieces are produced at the same mold,
strand layout is based on the most critical condition.

JRW