Partially Prestressed Moment Capacity by Strain Compatibility 2

[shp6]

I am looking for a good source of equations needed to evaluate the moment capacity of a partially prestressed section using strain compatibility. I am specifically looking at unbonded post-tensioning. The ACI method is simple and efficient use of section equilibrium, but I need something more rigorous. Any ideas? Thanks for your help!

 

[Polecat]

Shp6:

It sounds like you would find the PCI Design Handbook very useful. It has many design aids that address the calculation of the flexural strength of a prestressed beam based on Whitney's rectangular stress block and strain compatability.

The 4th Edition or later is available from PCI Hq in Chicago, 312/786-0300,

http://www.pci.org

.
Look thru their publications section also: Technical Journals JR-351 and JR-312 both contain equations and iterative solutions using stress-strain compatibility.

http://www.spiraleng.com

If you wish to visit my website, we can discuss these or other issues further.

 

[Ingenuity]

shp6,

Since you have UNbonded PT, the final stress (and final strain) in the tendon is more difficult to determine accurately since the tendon is NOT bonded to the concrete.

If you are using "standard equations" be careful and aware that strain compatability approaches like those that are used for RC and bonded PT or pretensioned sections (all of whick are BONDED situtations) are NOT directly applicable for UNbonded PT.

HTH

 

[shp6]

Thank you for your comments. They were very helpful!

 

[austim]

Hi, shp6.

You might give thought to a procees along the following lines (design strategy invented on the spur of the moment, with no textbook justification, so user beware ):

A. Calculate the section moment capacity by conventional means, including the compression caused by the total prestress, but excluding the tension capacity of all unbonded tendons.

B. Then verify that the moment provided by the unbonded tendons will be adequate to provide the difference between your applied moment and the partial moment calculated as above.

 

[Ingenuity]

hi austim,

I think that your idea will unfortumately mix-up stress calculations with strength calculations, and most especially ultimate strength calculations, where, at overload (ultimate!) prestressed sections will behave very simlar to RC sections.

At ultimate, the effect of the axial prestress (P/A) on the section do NOT enter into Mu calculation, (except for small effect in bonded prestress where we need to know the very small initial compressive strain in the concrete to eventually calculate the total strain in the strand at ultimate).

I would suggest that the value for fps (stress in the unbonded prestressing) be calculated from the empirical ACI318 (same as AS3600 essentially) formula. This will be a constant value depending on the span-to-depth ratio of the element. Then with this value undertake strain compatibility as you would with RC design, ensuring that equilibium is maintained. Take moments about any point on the section to calc Mu.

This will work with almost any section shape. Could even use parabolic concrete stress block if you wanted to get fancy! Probably an iterative process is best depending if compression and tension mild steel are present, and how complex the section shape is.

If you only have tension rebar with unbonded PT, assume the steel yields, use fps value (ACI etc), calc neutral axis position (at ultimate - assuming conc strain 0.003) ie C=Ts+Tp, check that steel does indeed yield, then calc Mu.

The above is no different to usual Mu calcs, except we already have the value of the force in the unbonded tendon, all be that this calculaton is approximate (very approximate)!!!


HTH