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Re: Difference between Initial Prestressing and Stressing Force

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When calculating the stress in a tendon to use in determining the ultimate moment strength of a member, ACI 318 - Section 18.7.2 states that

"as an alternative to a more accurate determination of fps based on strain compatibility, the following approximate values of fps shall be permitted to be
used if fse is not less than 0.5fpu:

      Eqn 18-3 (Bonded tendons)
      Eqn 18-4 (unbonded beam tendons)
      Eqn 18-5 (unbonded slab tendons)

Admitedly, the part about unbonded tendons doesn't make sense, but much of Chapter 18 does not make sense.  In particular, the sections pertaining to post-tensioning appear to have been written by free association,  which makes for hours of entertaining reading.

As a practical matter, the final effective stress, fse, will never be less than 0.5 fpu in an unbonded tendon, so equations 18-4 and 18-5 can be used.  You may end up with fse less than 0.5fpu in bridge work where you have a tendon that is 700 or 800 feet long, but these would be bonded.

Most p-t suppliers in the US use  28.9 kips as a lock-off force (jacking force minus losses due to friction and seating) for an unbonded tendon.  The actual force in the strand will vary along the length of the strand, due to friction losses.  28.9 kips (189 ksi), is 0.7 times the ultimate strength of the strand and is taken to be a reasonable average of the values along the strand.  (The strand will have been stressed to 0.8 times its ultimate strength.)

Using the equations developed by Zia et al,  you will always end up with 2 or 3 kips as the long term prestress losses.  The major factor in long term losses is the loss due to shrinkage.  The age at stressing, i.e. 2 days versus 4 days has only a minor effect in post-tensioned construction.  It is more significant in precast members where you are dealing with a discrete amount of concrete.  There was a recent NCHRP study that revisited the issue of long term losses but the focus was more on the losses in preast members using higher strength concretes.  The Zia study didn't look at anything greater than 6000 psi concrete,  precast currently is moving to 8000 and 10,000 psi concrete, sometimes higher.

Neither the lock-off force of 28.9 kips, nor the Zia equations have anything to do with strain compatibility.  As far as I know.  They are just approximations that are typically used.  To a certain extent,  the question is not how accurate any of these numbers are, but how accurate they need to be.

In particular, the prestressing force actually supplied will seldom match what the structural engineer has required.   Consider for example, a design that says 200 kips (final effect force) is required in a beam.  Assuming a final effective force of 27 kips per tendon,  this requires 7.4 tendons.  What will actually be supplied is 8 tendons,  thus the force in the beam will be 216 kips.   If you have assumed a final effective force of 26.8 kips per tendon, you will still get 8 tendons, but the force in the beam will be 214 kips.  

Given all the other approximations involved, the inability to account for restraint with any accuracy, etc.,  it is really not worth worrying about whether you have 200, 214 or 216 kips of force in the beam.

Gail Kelley