Post Tension - Fundamental Theory

[Fevola]

Hi All,

Very new to PT design. I have been reading bits and pieces of theory. I understand P/A, I understand P applied at at distance E from the centroid is P.e. I've read about equivalent load... GREAT.

In order to properly I understand this, I feel I need to go back further into basics and fully understand the unbonded situation. Stressing tendons and then anchoring them at the ends of a beam/slab applies a compressive force (P/A) throughout the length of member. If the anchorage lies above/below the member centroid, there is also a moment applied to the end of the beam. The bit that confuses me is, without grouting, how can there be a transfer of force between tendon and concrete, other than at the end anchorage zones as mentioned above. The only other way I can visualise force being transferred is through catenary action when a draped tendon tries to straighten under applied tension loading - I believe the tendancy of the tendon to straighten is what lifts the beam/slab (or counteracts the applied vertical loads). But nobody ever seems to mention catenary action so I am obviously missing something.
Without bonding the tendons, and neglecting catenary action, I also do not see how the profile/drape plays any part - all that matters is what happens at the anchorage zone because there is no force interaction between tendon and concrete anywhere else.

 

[BAretired]

KootK,

It seems to me that rapt is suggesting more than mere semantic confusion about definitions. I believe he is suggesting that, without As.min, a huge crack could open up at the maximum moment, say midspan, which could not be prevented by the unbonded tendons. A large angle change could occur at midspan, causing concrete strains to increase to the point of failure. If Mattock relied on tests showing this to be the case, I have nothing to add, having not seen the tests. Suffice it to say, it is not what I would have expected.

A large angle change at midspan should have no effect on tendon strength, so that should not be a factor.

The probability of anchorage failure is small but non-zero. That is one good argument against the use of unbonded PT systems, but the provision of As.min does not help that problem.

BA

 

[rapt]

Kootk,

The early 1953 was a very hard read. As is Leonhardt, but it is worth it. I think you will find Lin read Leonhardt before writing his own! Leonhardt talked about the concept of Moment Balancing, which Lin changed to the simplified but more limited Load Balancing concept.

The 1974 Double Volume on Limit State Design is my preference, except I have lost my 2nd Volume. Actually I had lost both, but Ingenuity found a copy of the 1st Volume for me several years ago to replace the 1st.

Great section on anchorage zone design!

 

[KootK]

Thanks Rapt. I have Leonhardt, at your previous recommendation, and thought my collection complete. Now I must have Guyon! They're pricy though so I want to make sure that I get the best one. Looking at the table of contents for the 1953, it seemed focused on elastic behavior and I wondered if the 1974 (Limit States) might include more plastic design concepts. I don't need easy; I want as deep a technical treatment as I can get my hand on.

 

[KootK]

I believe he is suggesting that, without As.min, a huge crack could open up at the maximum moment, say midspan, which could not be prevented by the unbonded tendons. A large angle change could occur at midspan, causing concrete strains to increase to the point of failure.

Interesting. Some thoughts on that below, including the interesting statement in the Mattock article that performance improves when the tendon is made to come in contact with the concrete.

 

[rapt]

Kootk,

Yes it would improve at low levels of load with draped tendons but not a lot. But the final failure/collapse condition is the problem.

I still think Leonhardts book that you purchased is great. After 44 years I still refer back to it. As you know from reading it, you really have to understand engineering before you start reading it. But it is very comprehensive and you understand more about engineering after reading it!

RE Guyon, definitely the 2 part 1970's version. I did not think it was still available. It is still very comprehensive but from a Limit State standpoint. Re The old Guyon, I was probably too young and inexperienced when I tried to read it 40 odd years ago, but definitely a much harder read than Leonhardt. Unfortunately I no longer have access to a copy so do not know if I would change my mind now. Guyon was at the forefront of prestressing development with Eugene Freyssinet in France.

 

[rapt]

Kootk,

Not sure that either will cover unbonded all that well. I cannot remember what Guyon says about it. Leonhardt 's opinion is basically less economic and less safe so why would you do it!

 

[KootK]

Not sure that either will cover unbonded all that well.

Thanks for the heads up on that. I'm equally interested in bonded so it's all good.

RE Guyon, definitely the 2 part 1970's version. I did not think it was still available.

It's slim pickings out there. Managed to find one V2 which, awesomely, only cost me $13. There were a few V1's for $100-ish. So much for supply and demand...

Unfortunately I no longer have access to a copy so do not know if I would change my mind now.

There's actually one floating about on Amazon for $65 + shipping: Link. I very nearly bought that too for its historical significance but, you know, $300 CAD on redundant, antiquated Guyons in one evening seemed a bit frivolous.

 

[KootK]

As long as we're plugging books, some lucky person should buy this: Link. It's a beautifully bound classic by one of Canada's best (UofT Prof). It's geared towards non-code specific fundamentals and is the better of Collins' two books in my opinion. It's also a rare find. So much so that I couldn't find a pic of the cover. I can photograph my own if anyone is intereted.

 

[Celt83]

Are these the right Guyon volumes, images show different covers: Link

1953 Text: Link


My Personal Open Source Structural Applications:

https://github.com/buddyd16/Structural-Engineering

Open Source Structural GitHub Group:

https://github.com/open-struct-engineer

 

[KootK]

Those are the 1974's that I bought.