Secondary Moments Prestressed Concrete 4

[ChiEngr]

Hi Everybody,

I am currently studying for the SE exam in Illinois, and I am reviewing indeterminate prestressed concrete structures. I am trying to grasp the concept of secondary moments, but I am having difficulty doing so. Are these moments completely irrespective of the applied loads? Are they only due to stressing and applied at the load transfer stage? Any help or resources to better understand this topic would be greatly appreciated.

 

[Celt83]

Watch the Dirk Bondy youtube series linked from the FAQ: Link

 

[bones206]

I'm reading Bondy's textbook right now and just finished the section on secondary moments. I find it to be quite straightforward and readable:

http://www.senecastructural.com/products.asp

My basic understanding is that the tensioning induces a certain deflected shape in the member. When there are external supports that restrain that deflected shape, internal stresses are induced in the member by the external actions of the supports/restraints. These internal stresses are then superimposed with those caused by the applied loads.

 

[rapt]

They are purely from the effect of the PT loading.

Assume a weightless member with all interior supports removed.

A profiled tendon will induce upward and downward forces (nett zero for the whole member) on the concrete causing upward and/or downward deflection at different locations.

If the deflected position at any internal support location is not 0, then there will be a reaction at that support to bring it back to zero deflection.

The moments caused by these secondary reactions are the secondary prestress moments.

If the upward and downward forces produce zero deflection at all internal support locations then you have a "Concordant Profile" and there are no secondary moments. This is not usually the most cost effective profile.

The easiest way to calculate it is to determine the bending moment diagram from the upward and downward forces from the prestress. Then subtract the P * e diagram for the tendon. The result is the secondary prestress moment diagram.

This works well if the prestress force is constant over the full length which is not quite correct due to the force losses along the tendon.

 

[centondollar]

rapt,

If one calculates in a detailed manner (accounting for exact tendon force due to losses accumulated to any given point along the beam), the procedure you mention is also easy to implement, at least in FE software. The upward or downward load due to prestress can be divided into several sections in each span, with the upward/downward load due to prestress multiplied by the factor of remaining prestress in the centroid of each section.

 

[RattlinBog]

Here's a short article. Dr. Schokker chairs the upcoming ACI 319 committee.

 

[rapt]

Centondollar,

If you have ever tried to develop the logic theoretically, it does not work by applying loads as you suggest.

You can believe what you like about the numbers you get from a FEM analysis by applying upward/downward loads. The results are not correct.

The only way to do it is to apply the changes in curvature as a loading.

 

[centondollar]

rapt,

You're right. How would you approach the problem, though, assuming that prestressing force is to be taken as the "exact" (as predicted by loss estimations) force in many (say, 5 or 10) parts of one span of a continuous member?

The "balancing load" is a constant line load for each parabolic tendon section where change of sign of curvature does not occur, but it is determined from the tendon force at the ends of this segment (almost entire span for continuous beams). How would one then drape the tendon to achieve load balancing versus self-weight without using an average (or minimum) value of prestress? This is not something I've found discussed in textbooks.

 

[rapt]

To do load balancing calculations, which are just an aid in preliminary profiling and initial tendon requirements, I would just use the average force over the length of each curve segment. You are not worried about being a little inaccurate at that stage as you are not relying on those calculations for your main capacity calculations etc.

To do the real calculations in RAPT we now apply the change in moments moments as a loading, effectively giving an M/EI or change in curvature loading.

I have no idea how other programs do it, but we found that when we allow for large reductions in tendon forces due to strand development (pretensioned ends or bonded dead ends especially), the approximate methods could be a long way out in the areas of the large force losses. But I do not think most of the FEM programs consider those force losses any way.

I know we have a lot of trouble justifying a lot of precast pretensioned designs when they are modeled in RAPT. The tend to miss out on strand development at the ends as they assume constant prestress force full length of the strand, and also longitudinal tension force requirements for shear. When you have a 100-200mm seat for a precast member, and the strand force at 100mm from the end of the precast is effectively 0, there is no tension force capacity there. So there are a lot of precast members out there that violate some very important code requirements.

 

[ChiEngr]

Rapt,

When you mentioned the concordant profile, this is something that has been confusing me in my reading. How does this profile create no secondary actions?

 

[rapt]

P * e = Mp at every point.

If you go back to my initial post, if the result of the upward forces and downward forces from the tendon profile result in zero deflection at the internal support locations, then the secondary reactions equal 0 as the level is already at 0. If there are no secondary reactions required to bring the level back to 0, there are no secondary moments. So the Mp diagram is exactly the same as the P.e diagram.

If you were able to create a profile shape where the tendon eccentricity at every location e = Mp / P, then you would have a concordant profile and there would be no secondary reactions or moments.

But as I also said, it is not something that is necessary or economical, especially with partial prestressing, as you cannot use the full tendon drape available so you waste some available capacity.

 

[centondollar]

To do the real calculations in RAPT we now apply the change in moments moments as a loading, effectively giving an M/EI or change in curvature loading.

Could you expand on this? I do not have previous knowledge on details of actual prestressed designs and as I previously mentioned, most textbooks don't touch on this, so I have a hard time imagining how to most easily recover total moments and secondary moments (direct moment from tendon and eccentricity M=p*e is simple) from an analysis (not load balancing, evidently) that allows considering stepped changes (due to anchoring slip and friction) of tendon force in spans of indeterminate beams.

 

[slickdeals]

Came across this article in the PTI journal that I just received.

 

[IDS]

slickdeals - Interesting article, but I'm not sure that his chosen example 1 is really a good way to "provide a deeper understanding of where this approach came from", and reading the note from the editors, it looks like they had their doubts as well.

Possibly a more useful paper (referenced in this one) is Complete Secondary (Hyperstatic) Effects by Alan Bommer, which available to all at the Bentley site:

https://communities.bentley.com/products/ram-staad/m/structural_analysis_and_design_gallery/272215

Doug Jenkins
Interactive Design Services

http://newtonexcelbach.wordpress.com/

 

[rapt]

I think both of these papers are mixing the effect of secondary effects in the structure due to restraint of prestress forces and other internal effects from cracking, reinforcing etc with Hyperstatic prestress actions which are simply the difference between the prestress effect P * e and the resulting moment diagram caused by this prestress effect.

That is not to say that the other secondary effects do not need to be considered, but there are many other secondary effects on structures that are commonly ignored and they involve much more significant moments and actions, eg, shrinkage and temperature effects. And these other effects affect all structures not just those with PT.

Alan Bommer has also skipped over the problem I mention where he suggests that balanced forces from the prestress using variable prestress forces can be used in a single sentence without justification.

This can be easily shown to be incorrect by calculating the Mp diagram from balanced forces in a simply supported member. The result should be zero at all points in the member. It is not. In the simple cases I checked with a linearly varying prestress force, it was correct at midspan, but not at quarter points. As the prestress force change gets more variable, due to development in pre-tensioning, drawin at anchorages and where friction rate changes due to different changes in profile (eg much tighter reverse curve radius zones), I expect the results to be worse.

I tried to correct this by considering

- the balanced forces are actually perpendicular to the tendon at each location, not vertical, so there are horizontal components are different depths along the member.

- The friction that reduces the tendon force along the tendon induces longitudinal forces in the concrete at the level of the tendon at the slope of the tendon which have to be applied as another set of loadings

None of these fully resolved the issue.

So I reverted to the basic logic that the curvature induced by the prestress forces and profile, P * e causes the hyperstatic moments when the supports will not allow that curvature to occur by restraing uplift at each support location.

 

[centondollar]

rapt, could you detail how what you describe could be implemented in practice? The prestress varies along a continuous member due to prestress losses and unless an "average" or minimum prestress value is used in each section with constant sign for curvature (for a parabolic tendon supporting uniform load e.g., near supports and at midspan extending quite close to supports), the concept of load balancing seems unusable if accurate results are desired. What is the alternative?

 

[rapt]

Calculate M/EI for the full member where M = P * e at all points along the member.

Calculate Fixed End Moments from that M/EI diagram.

Distribute the moments.

That gives you the Msec diagram.

Add the P * e diagram to get the full prestress moments.

Read a good book on PT theory. Not one that thinks Load Balancing is basic theory. e.g. F Leonhardt Prestressed Concrete - Design and Construction section 11.4 and for indeterminate members section 11.43.