Transfer Length in Prestress Concrete

[Perception]

Hello everyone,

PCI has a formula to calculate transfer length as follows (section 5.2.3):

Transfer Length = Effective Prestress/3 * strand diameter

Does anyone know where this formula came from? Conceptually, I don't understand why a stress computed considering total losses (service level) is used to calculate transfer length. My understanding is the transfer length is the required distance from the end of a beam, that is needed for the friction force between the concrete and strands to transfer the prestressing force into the beam.

In the PCI design examples, at the release stage stresses are checked at the transfer points, and again these transfer points are calculated using a service level stress. It would make more sense to me if the transfer length was computed considering initial losses instead of total losses.

I've looked for an explanation to this in PCI, ACI, and prestressed concrete textbooks to no avail. Hopefully somebody can enlighten me to the errors of my way.

Thanks

 

[rapt]

It is explained perfectly well in ACI.

There are 2 lengths involved which added together give you ld, but the 2 segments are at different force/distance slopes.

The Transfer Length is the bond length at initial transfer of the forces to the concrete and is based on fse because that is the stress in the tendon at transfer.

Then the second part of ld is defined based on fpe - fse and this covers the increase in stress from transfer caused by strain in the member under load.

 

[Perception]

I am aware that the development length has two distinct stages in prestress concrete. The formula for just the transfer length part is 1/3*fse*(strand diameter)

According to PCI, the definition of fse is as follows (pg. 2-7, 7th edition):

fse = effective stress in prestressing steel (after allowance for all prestress losses) (ACI)

Based on that definition, fse is calculated considering losses at transfer (elastic shortening) and losses at service (shrinkage, creep, relaxation, etc.). This is in keeping with the PCI design examples. For example, see a portion of example 5.2.2.5 on cracked section analysis below, where fse is calculated based on total losses.

fpu = 270 ksi
Initial prestress level = 0.75fpu
Estimated loss = 20%
fse = 270 (0.75)(1 – 0.2) = 162 ksi

Estimate decompression force:
Elastic shortening loss ES is approximately 40% of total loss.
TL-ES = 20 – 0.4(20) = 12%

This issue I have is understanding why all the losses need to be considered at the time of prestress transfer, when the only losses that occur at that time are elastic shortening and maybe some anchor loss due to the chucks.

 

[cooperDBM]

Perception, yes the effective prestress, after all long-term losses, is used for the transfer length. It's a simplification that works as part of the bilinear development length curve, where the effective prestress is appropriate. Immediately after transfer the initial prestress is higher by the amount of the long-term losses (REL, CR, SH). The transfer length equation isn't precise enough to worry about the difference and in most cases is sufficient based on tests. When checking concrete tensile stresses at transfer near the ends having a shorter transfer length is slightly more critical. You're still using the initial prestress for the stress calculation.

There would be no anchorage loss with pretensioning. The strands are often over-tensioned a bit to achieve 0.75 fpu after lock-off.