PT Slab Design

[cecil123]

I am designing a PT Slab with unbonded tendons.Now, I have determined the post-tensioning forces required in each span based on the considerations of:

1)Permissable Tensile stress
2)Minimum and maximum Precompression
3)Percentage of Dead load balanced
4)Maximum spacing of tendons.

Now, as mentioned I have determined the post-tensioning forces required in each span.Once the manufacturer details regarding the tendon material are given we can calculate the number of tendons in each span which will furnish the required force.

Now,I want to determine the ultimate moment of resistance of the section, which according to the British code is given by:

Mu=fpbAps(d-dn)--------- Eqn A

where:

fpb=design tensile stress in the tendons
Aps=area of prestressing tendons in the tension zone.
d=effective depth to the centroid of steel area
dn=0.45*x
x=neutral axis depth.

For unbonded tendons,the equation for fpb in the code is given by:

fpb=fpe+ 7000/(l/d)(1- 1.7fpuAps/ fcu b d)--- Eqn B

MY QUESTION IS:
1)Since I have determined only the post-tensioning force,I do not have the area of tendons available yet.right?
2)So,in the eqn A, above can I take the product of
"fpu * Aps" as the force I have determined in that span/location.
3)Am I violating the code in any sense?

Please, please help!!!

 

[csd72]

I havent done much PT, but I think you need to determine friction losses in the tendon prior to using this formula. Or have you done that already?

 

[cecil123]

Awaiting some response!!
Please help!!!

 

[AllanBommer]

Hi Cecil,

I assume this is your first PT slab design. Your question is only the tip of the iceberg of questions and construction issues that you are going to run into.

Unless this slab is just a tiny isolated piece, I would suggest you consult with (or partner with) an experienced PT designer to make your first project a success. You will learn enough to do your next PT job by yourself and you will avoid some huge risks. If you do not know of any experienced PT designers, ask your local PT suppliers for some recommendations.

In response to your posted question - you can NOT just take Aps * Fpu as your effective post-tensioning force. That value may be too large by as much as 50%.

You will need to consider friction losses, elastic shortening and long-term losses to calculate a "final effective stress". This stress value can be used conservatively to calculate the ultimate moment capacity. However, you will likely want to use "Eqn B" to get a less conservative stress to use in your capacity calcs.

Hope this helps,

Allan Bommer
RAM Concept, Bentley Solutions Center

 

[cecil123]

If the final effective force, I have is after the consideration of losses, then can this force be use as the product of (fpu * Aps)?

 

[Taro]

In my experience, the "effective force" refers to a service-level force. I think you are asking about a strength-level force for computing the flexural capacity. I'm not familiar with the British code, but from your original post, the code seems to explicitly define how to determine this force. If this is unclear, you should follow Allan's advice and seek out a mentor.