Post-tensioning Hyperstatic Moments in RISA 3D 3

[IngeIvan]

Hello,

I am trying to find a good way to model the hyperstatic moments due to post-tensioning in Risa 3D for column design purposes only.

I think if I find a good way to have them in the model, I can just add a new load combination including these hyperstatic moments and the RC column design would be accurate and I would be able to account for P-delta effects automatically when I include my lateral loads.

One possible way I was thinking is to add the balanced dead loads as a new combination but I can't think of a good way to also add the Primary moments due to post-tensioning (Hyperstatic Moments = Balanced moments - primary moments).

Any ideas?

 

[JoshPlumSE]

Keep in mind that I'm not an expert in pre or Post-Tensioned concrece.... meaning that I have never designed real structure with post-tensioning. Back in my college years, I took a class on the subject, so I understand the basics. But, there are likely subtleties of the code or new code developments that I will not be knowledgeable about at all.

That being said, I would think there are two primary ways to do this in RISA.

Option #1: Convert the pre-stress stress loading into equivalent distributed or point loads. This is what we did back in my college projects. Just look at the tension in the cable and the angle changes it goes through and convert that into an equivalent point load or distributed load or such. My guess is that this is a pretty standard practice in the industry and that most books on the subject will have some guidelines on doing this.

Option #2: You could try to model in the tendons themselves. You have to connect them to the beam via rigid links so that there will be force transfer between them. Then you add in some negative thermal loads (see the help file section on Loads - Thermal Loads for more information on this) in order to pre-tension the tendons.

Personally, I think that Option #1 is probably the easier and more reliable option. Option #2 has the possibility of being more accurate if done correctly. But, I would build a few simple models as a proof of concept to make sure it gives you the desired results first.

 

[rapt]

Unfortunately, those solutions only give the total prestress effect, not the hyperstatic effect. In terms of column moments, they are the same thing as there is no primary moment from prestress uplift in the columns, but it is not correct for column reactions.

 

[JoshPlumSE]

I have to admit, I don't really understand what you guys are talking about when you say "hyperstatic" moments. I'm just not enough of a PT guys for that. Maybe it was covered back in my college course, but it doesn't ring a bell. Or, maybe the terms have changed slightly since then. The college course was focused almost entirely on bridge PT work, so maybe there is a different terminology for different industries.

Personally, I would have thought option #2 would have been as accurate as possible within the context of elastic analysis and small deflection theory. Because for option #2, you only introduce tendon tensions into the system. The tension combined with the geometry imparts loads into the beams and columns. I would think that would be accurate.

 

[mike20793]

I've always referred to these as secondary moments (so does ACI). There's plenty of PT software available that will calculate the secondary moments. PTdata and ADAPT are just a couple.

 

[mike20793]

Sorry, I never responded to the question of calculating the secondary effects in RISA. Sorry, but if JoshPlum doesn't know, then I don't think it's possible (unless you calculate and apply the secondary moments manually). Refer to my previous post for software that can handle the calculations.

Is this for a PT slab (one way/two way?) or just beams. If it's a beam, the calculation isn't very difficult.

 

[JoshPlumSE]

Secondary moments are what we referred to them back in my college days. Typical application would be post-tensioning of a two span bridge where the tensioning causes the structure to want to deflect upwards, but it is restrained by the mid span column.

I have a difficult time seeing how that would not be handled with option #2 that I described above (perhaps even for item #1), at least for the types of bridge problems that I'm thinking of. Not sure why rapt disagrees.... Perhaps a simple two span example with a "theoretically correct" solution would solve the disagreement.

Alternatively, I suppose he could be talking about a 2nd order change to the geometry of the structure... where the geometry of the structure and / or tendon profile is assumed to be change significantly during the tensioning process. That could not be handled in RISA. I would think that takes a true non-linear analysis program with incrementally applied loads (and stiffness matrix and load vectors re-formulated for each iteration).

 

[JoshPlumSE]

I just created a simple two-span example from Nawy 4th edition. Section 6.5.2 "Effect of Continuity on Transformation of C-line for Harped Tendons" Example 6.2 and I get roughly the same results as Nawy shows in his calculations.

The top bridge is one without supports just to confirm that I've got my pre-tensioning about right. The lower one models in the support so that the secondary moments will be included.

I get almost exactly the same numbers as Nawy... within about 0.3%. So, method 2 seems to be satisfactory. Granted, it is relatively easy with a harped tendon profile like this. But, for a draped tendon it would be trickier because we'd have to use much more rigid links to connect between tendon and beam.

 

[mike20793]

That's pretty nifty. What load are you applying to the tendon? Is it the equivalent load due to post-tensioning? Would you use a rigid link at the end of the beam for any eccentricities you might have?

 

[JoshPlumSE]

The load applied to the tendons is merely a negative thermal load....i.e. we are thermal loads to shrink the tendons, thereby creating our tension. I had to play around with the thermal load a bit before I got it to create the level of pretension specified in Nawy's example. But, once I did that the rest seemed to fall into place pretty quickly.

Obviously, it gets more difficult if have to model in tension losses due to friction or anchor set or such. I don't have confidence that this method could end up getting into that much detail. But, then again, I'm not sure how much that would affect the overall analysis.

 

[rapt]

I will modify my previous post slightly,

As long as the forces from all of the angle changes are applied and all of the section changes if there are any, including the downward force over the length of the reverse curve, the results from applying equivalent forces will work and will produce the total prestress moments and shears in the slabs and moments and reactions in the columns. This will not predict the hyperstatic prestress effects in the slab as to do this you would have to subtract the P.e from this result.

The hyperstatic prestress moments and reactions in the columns are equal to the total prestress values as there is no primary prestress moment in the columns (P = 0 unless the columns are themselves prestressed) so this method will predict the hyperstatic prestress effects in the columns.

It is important that ALL of the prestress forces are included, not just the uplift forces.

The effects of prestress losses will change this significantly as the equivalent forces also have to reflect the effects of the friction forces and I have found this very difficult to do, so in RAPT, to allow for friction and development length effects (pre-tensioned ends and bonded dead ends) we have changed to applying the curvatures caused by the prestress tendons to determine the hyperstatic prestress effects. This effect is probably relatively minor in unbonded prestress as the friction is fairly small and there should be no dead end loss effects.

 

[JoshPlumSE]

Rapt -

Thank you for the clarification. Your comments make a lot more sense to me now. I knew I had to be missing something or that we had to be talking about different issues.