Unbonded PT Flexural Strength

[rasaonline]

When we want to find the type of Unbonded PT beam section in flexure, what depth and strain is used to determine if the section is Tension-Controlled / Compression-Controlled / or in Transition?

Since the PT tendons are unbonbed, Their strain can not be found by strain compatibility. and it has to be found from ACI 318-11 EQ. 18-2 devided by Es=29000ksi.

Please clarify if you want to find NET TENSILE STRAIN, do you take Average of Strain in mild steel and PT tendons or just consider either of them? (Question #1)

ACI is not clear about Unobnded PT.

PTI has an example. (at Here on page 51) which I think can not be true! because they used strain compatibility to find strain in Unbonded PT!!! it is Unbonded!! How could it have the same strain as its surrounding concrete??!!

I have sample calculation below. Do you think it is OK for critical section strength? (Question #2)

 

[Ingenuity]

Please clarify if you want to find NET TENSILE STRAIN, do you take Average of Strain in mild steel and PT tendons or just consider either of them? (Question #1)

ACI-318 § 10.3.4 states "...net tensile strain in the EXTREME steel...". So in your example, the rebar.

And in the PTI example you reference, it states the same, on page 43, as follows:

In beams and one-way slabs, the rebar will almost always be the extreme steel.

With regards to the PTI UNbonded PT example, they are using the strain profile at the EXTREME steel to calculate the NET strain for purposes of only determining if the member is TENSION, TRANSITION or COMPRESSION controlled, so the ø-factor can be calculated . It does not represent the actual strain in the UNbonded prestressing.

And note that they use the L/D<35 based equation to calc the UNbonded prestress force, so NOT based upon strain compatibility.

 

[rapt]

Yes, for unbonded you do not assume strain compatibility, just take a guess at a stress increase under strain over the whole length of the tendon and this gives you a tension force in the tendons unrelated to the strain in the concrete at the level of the tendons. But this is only at ultimate strength, there is assumed to be no stress increase at service.

One thing to note relating to another thread about over-stressed tendons is that this ACI rule on stress increase at ultimate is that it would not apply if the tension is over-stressed! It assumes the force in the tendon is in the elastic range and requires the force after jacking to be limited to the ACI limits! If higher, the stress/strain relationship is very different so there would be a significant to very large reduction in this stress increase as the starting force/stress increases.

 

[rasaonline]

Thanks for through answers! Made it clear to me and increased my confidence.

I see in this presentation, the strain at the level of Tendons is calculated by compatibly which does not make sense in this example that there is no Mild Steel at "dp". Then it is concluded the section is Tension-Controlled because 0.0346 is more than 0.005!!
I think this should be revised to

f_se / E_s = ε_pt = 227 ksi / 29000 ksi = 0.0078 > 0.005

What is your thought?

 

[rapt]

Are they talking about the strain in the steel at that level or the strain in the concrete at that level?

Their calculation is correct for the strain in the concrete. If their neutral axis depth is correct for the tension force in the un-bonded prestress based on the code formula (independent of concrete strain) and the compression force in the concrete, then the concrete strain at this level is correct, and I think that is what controls the ductility.

PS you should never have an un-bonded PT section with no bonded reinforcement unless you can guarantee that the concrete will always be fully in compression.

 

[Ingenuity]

rasaonline,

As rapt states, the highlighted/boxed calculation is the strain in the concrete at the location of the extreme steel location (rebar, bonded or unbonded prestress) and is pseudo-fictictious calc on ductility for purposes of calculating the ø-factor only.