post-tensioned ordinary concrete moment frame beam design

[Roger2017]

Hi,
I am working on a post-tensioned concrete parking garage and using PT moment frames for lateral load system. When I design the PT beam under gravity loads alone, it only needs 3#10 for negative moment at face of column which is per the minimum mild steel reinforcing requirement. When I run the lateral moment frame analysis as ordinary reinforced concrete frame, I will need 8#10 for negative moment at the column if I use full dead load, live load, and wind load with load combinations. Since the post-tensioned tendons already provide uniform balancing load of 80% dead load, I would think I only need 20% of dead load, live load, and wind load for the moment frame analysis, which shows I need 4#10 for the negative moment.

Is this approach reasonable for the PT lateral beam design? How do you take care of the PT lateral beam design?

Thanks,

 

[Ingenuity]

Since the post-tensioned tendons already provide uniform balancing load of 80% dead load, I would think I only need 20% of dead load...

Thanks,

That is not how it works, there is no 'free lunch'.

[SCARCASM ON] Maybe if we provide more PT and 'balance' 125% of DL we could design for -25% of DL [SCARCASM OFF]

You must design for 100% of your dead loads, etc., with appropriate strength factor.

Extending your logic, you would only have to design the PT beams under gravity load too for 20% of the DL. That is NOT correct, but an often misunderstood concept even by 'experienced' PT designers.

 

[Roger2017]

If the mild steel provides full design capacity, the contribution from tendons is very limited except for deflection and crack control. I saw two sets of parking deck design drawings with similar layout, they did not have heavy mild steel reinforcing in the PT moment frame beams. I just wonder how they designed the PT moment frame beams.

 

[EZBuilding]

You can consider your tendons at the top to contribute to your negative moment flexure capacity. I do think there are some good arguments to be made that you should have all of your capacity for your lateral demand load cases come from mild reinforcement.

Likely to be the bigger impact, is the possibility for moment reversal due to the lateral moment frame behavior. You likely have positive moments at your columns, for which in a gravity load combination you would have no continuous mild reinforcement or tendons at the bottom of your beam.

 

[Roger2017]

EZBuilding,
Thank you for your reply. From the post-tensioned design under gravity loads, I only need 3#10 top bars for negative moment (actually per Asmin=0.004Act) at face of column in the beam. When I use RAM Elements for the lateral frame analysis, I will need 7#10 top bars for negative moment and 2#10 bottom bars for positive moment at the face of column under 1.2D+1.0W+1.0L and 0.9D+1.0W, respectively. The concern here is that RAM analysis does not consider the effect of post-tensioned tendons. The mild steel bars are used for all loads, including full dead load which is balanced by the tendons uplift load up to 80%. I do not have issue to use mild steel for full wind or seismic moments, just want to make sure I do not overly design the beam (7#10 vs 3#10).

Thank you.

 

[KootK]

That is not how it works, there is no 'free lunch'.

I think that it is how it works. At least, it is if I understand @Roger2017's intent.

I don't believe that OP is trying to double dip by using both the PT balancing load and the the PT contribution to sectional flexural capacity additively. Rather, I believe that he is simply acknowledging that the flexural capacity of a PT beam comes from two sources that are additive:

1) The PT contribution to sectional flexural capacity for which the balancing load, combined with axial prestress, can be used as a proxy and;

2) The mild rebar contribution to sectional flexural capacity.

That said, it surely is simpler to assess the combined PT + rebar flexural capacity in the normal way, as additive contributions to section flexural capacity. That way one does not have to faff about with safety factors / equivalency with respect to the balancing load.

Maybe if we provide more PT and 'balance' 125% of DL we could design for -25% of DL

Indeed we could. You'd just have to provide some wasteful rebar on the opposite side of the beam for that -25%

 

[KootK]

You can consider your tendons at the top to contribute to your negative moment flexure capacity.

I somewhat disagree with that and feel that, fundamentally, this is probably the best reason not to use the PT for the moment frame.

 

[EZBuilding]

@KootK

I was primarily considering an interior condition when I made my statement, and should have clarified. In an end span condition, I would assume that the tendons would be lowered from the top of the beam to the center of gravity of the T-Beam section - reducing their efficacy in providing top flexural capacity..

I would think that in your graphic, the flexural capacity is not "turning a corner" but is provided by the column reinforcement being hooked/developed at the beam/column joint. If you replace the tendons with rebar - you still have the same need for column flexural reinforcement development into that joint. In your graphic, I have not questioned the development of tendons in the same manner that one would hooked flexural reinforcement. Probably remains as a point against utilizing PT for lateral moment frame behavior.

 

[KootK]

I was primarily considering an interior condition when I made my statement, and should have clarified.

I was too. I just showed the end condition because it elucidates the concept more convincingly.

I would think that in your graphic, the flexural capacity is not "turning a corner" but is provided by the column reinforcement being hooked/developed at the beam/column joint.

I'm afraid that's fundamentally incorrect EZ. The moment capacity absolutely does need to turn the corner, as the moment demand does. It's only a matter of how you accomplish that. At an exterior, roof condition, you've really got no choice but to literally run your reinforcement around the corner. At joints where the column or beams are continuous pass the joint, you've got the clamping mechanism shown which is sort of a "cheat" that allows hooking/developing to be enough. This tends to create understandable confusion amongst designers about how it all works.

 

[EZBuilding]

When I use RAM Elements for the lateral frame analysis, I will need 7#10 top bars for negative moment and 2#10 bottom bars for positive moment at the face of column under 1.2D+1.0W+1.0L and 0.9D+1.0W, respectively.

From my understanding RAM Elements does not have any post-tensioned design features. I would assume that RAM Elements is performing the analysis assuming your beam is a conventionally reinforced concrete beam. It appears that you are utilizing a PT analysis tool (RAM Concept?) to design for your gravity load cases and RAM elements for your lateral analysis. In this consideration, you could use hand calculations to check your flexural moment capacity accounting for both your mild reinforcement and PT. As discussed further in the thread; there are a number of different thoughts to be given in using PT as a reinforcing element for a LFRS. You should be considering your cracking factors for your columns, PT delta, detailing, etc...

 

[Celt83]

If you are using RAM Elements you would need to figure out the hyperstatic moments from the PT and apply those as loads to be included at the ultimate level.

one method of accomplishing this would be to apply the equivalent loads of the PT to the structure then at each joint find the delta between the joint moment and the P*e moment the result would be the hyperstatic joint load. once you find all the joint loads moments and shears apply them as nodal loads and include them in all load combinations with a 1.0 load factor or other load factor if your code requires it. Do not apply the balance loads when checking the ultimate limit states the P*e moment is included in the cross-section capacity and should not be included in the loading as well that would be double dipping.

 

[Roger2017]

Thank you, EZBuilding and Celt83,
I am using old post-tensioned software, POSTEN, for post-tensioned design and RAM Elements for lateral analysis since the ramp beams per frame are not in the same elevation.

Are the hyperstatic moments from the PT same as the secondary moments?
Are the equivalent loads of the PT same as the balancing loads?
If yes, I assume that the joint loads moments are the secondary moments (balancing moments-P*e) in which P is effective post-tensioned force. Before your recommendations, I thought I might just need to add balance loads (uniform uplifting loads) to the frame which would reduce the gravity loads and make the beam negative moments smaller. It looks like that the secondary nodal moments play the same role. The secondary moments would reduce the gravity load moments at the beam end.

Thank you again.

 

[Ingenuity]

I think that it is how it works. At least, it is if I understand @Roger2017's intent.

I don't believe that OP is trying to double dip by using both the PT balancing load and the the PT contribution to sectional flexural capacity additively. Rather, I believe that he is simply acknowledging that the flexural capacity of a PT beam comes from two sources that are additive:

1) The PT contribution to sectional flexural capacity for which the balancing load, combined with axial prestress, can be used as a proxy and;

2) The mild rebar contribution to sectional flexural capacity.

That said, it surely is simpler to assess the combined PT + rebar flexural capacity in the normal way, as additive contributions to section flexural capacity. That way one does not have to faff about with safety factors / equivalency with respect to the balancing load.

With this statement: "Since the post-tensioned tendons already provide uniform balancing load of 80% dead load, I would think I only need 20% of dead load..." the OP implied intent to use only 0.2D on the DEMAND side for seismic and not 1.0D (excluding factored loads etc.), which is clearly wrong. On the CAPACITY side then any mild steel and PT reinforcement combination can be used within the prescriptive allowances of the code, taking into account secondary moments due to PT using a LF of 1.0.

Ingenuity said:​

Maybe if we provide more PT and 'balance' 125% of DL we could design for -25% of DL​

Indeed we could. You'd just have to provide some wasteful rebar on the opposite side of the beam for that -25%

What? Your DEMAND loading would be totally incorrect.

 

[KootK]

With this statement: "Since the post-tensioned tendons already provide uniform balancing load of 80% dead load, I would think I only need 20% of dead load..." the OP implied intent to use only 0.2D on the DEMAND side for seismic and not 1.0D (excluding factored loads etc.), which is clearly wrong.

I don't believe that it is wrong. Consider it reworded something like this, as I believe OP intended it:

Since the post-tensioning system is designed to resist 80% of the dead load, then the mild reinforcing system need only resist 20% of the dead load.

100% of the dead load is still in play, OP is just considering how much of that needs to be resisted by the mild reinforcing system.

What? Your DEMAND loading would be totally incorrect.

All I was getting at is that you can over balance and just design for it. This happens often in precast, prestressed beam design where the pre-stressing produces negative flexure at the plank ends prior to install that has to be addressed by installing top side rebar or strand. Obviously, one does not do this just for sport.