Post-Tension Tendon Elongation and Jacking Force

Which is why it catches what a pressure gauge cannot. A gauge reads what the jack is pushing; it says nothing about whether that force reached the far end. A tendon binding in a crushed duct, or one strand of a bundle not gripped, shows up as elongation short of theoretical while the gauge reads exactly the specified pressure -- and the gauge is the instrument people trust. THE FRICTION TERMS ARE WHAT MAKE THE THEORETICAL NUMBER NON-TRIVIAL. Force decays along the tendon with the total angular change of its profile and with unintended wobble, so a draped tendon in a long slab develops noticeably less force at its far end than at the jack. The elongation follows the AVERAGE force along the length, not the jacking force, and the average of an exponential decay is its integral -- one minus the decay ratio, over the exponent. Using the jacking force directly overstates the expected elongation, and on a seven percent tolerance that overstatement is most of the allowance: it makes a perfectly good tendon look like a failing one, and the crew chases a problem that is in the arithmetic. THE TOLERANCE IS TWO-SIDED and both sides mean something. Elongation short means the force is not getting there -- a crushed or blocked duct, or a strand the wedges did not grip. Elongation long means the strand is stretching more than it should, which can mean a wrong strand area, a wrong modulus, or slip at the anchorage. Both require investigation before grouting, because after grouting nothing can be corrected and the tendon is permanent. Anchor set, the seating loss when the wedges bite, is subtracted from the theoretical stretch to give the number the crew should actually measure at the tail. Theoretical elongation from properties the reader supplies. The friction and wobble coefficients belong to the specific duct and tendon system and come from the post-tensioning supplier, not from a general table; the strand area and modulus come from the mill certificate for the reel actually installed, and using catalogue values where a certificate exists is one of the ways a tendon appears out of tolerance. This treats the tendon as one prismatic member at a single average force, which is the standard field method and not a stressing analysis: it does not compute the force profile along the length, elastic shortening, relaxation, creep and shrinkage losses, the sequence effects of stressing multiple tendons, or anything about grouting, duct filling, or corrosion protection. It does not evaluate the structure. The post-tensioning supplier's stressing calculations and elongation tables, ACI 318 and the PTI manuals, the mill certificates, and the engineer of record govern.

theoretical elongation = average force x length / (area x modulus), with force decaying along the tendon as exp(-(mu x alpha + K x)) and the average taken as the integral (1 - decay ratio) / exponent; the expected measured value is that less the anchor set, checked at an entered tolerance.

The post-tensioning elongation relation by name, with about 7% as the usual two-sided acceptance. Friction and wobble coefficients belong to the specific duct and tendon system and come from the post-tensioning supplier; strand area and modulus come from the mill certificate for the reel installed. The supplier's stressing calculations and elongation tables, ACI 318 and the PTI manuals, the mill certificates, and the engineer of record govern.

One exponential and one division on properties from a mill certificate; no supplier elongation table is reproduced.

Estimate. AHJ and licensed professional govern.

Field names used by the API: strand_area_in2, modulus_psi, tendon_length_ft, jacking_stress_ksi, curvature_friction, angular_change_rad, wobble_per_ft, anchor_set_in, measured_elongation_in, tolerance_pct, jacking_force_lb, far_end_force_lb, average_force_lb, theoretical_elongation_in, expected_measured_in, elongation_difference_pct

• Friction and wobble are entered they belong to the specific duct and tendon systemthe post-tensioning supplier
• Strand area and modulus from the mill certificate catalogue values where a certificate exists is a way tendons appear out of tolerancethe mill certificate for the reel installed
• One prismatic member at a single average force no force profile, elastic shortening, relaxation, creep or sequence effectsthe supplier's stressing calculations