Post-Tensioned Concrete

What post-tensioning actually does

Concrete is brilliant in compression — 35 to 70 MPa is routine — but feeble in tension, cracking at perhaps 3 to 5 MPa. Ordinary reinforced concrete handles this by accepting cracks and trusting embedded steel rebar to carry the tension that opens them. Post-tensioning is the more elegant solution: never let the concrete crack at all. Squeeze the entire section in compression with stressed steel tendons before the service load arrives, and the load merely reduces the compression instead of pulling the concrete into tension.

The trick is to do the squeezing after the concrete has already cured. A reinforced concrete slab or beam is cast with hollow corrugated ducts — steel tubes about 60 to 90 mm in diameter — embedded inside, snaking from one end of the member to the other. Anchorages are cast into both ends. After the concrete has reached strength (typically 5 to 7 days), high-strength steel tendons are threaded through the ducts, a hydraulic jack at one end stretches the tendon to about 75% of its ultimate 1860 MPa strength, and wedge grips bite into the strand and lock the tension into the anchorage. The duct is then filled with cement grout (in bonded systems) or left greased and sheathed (in unbonded systems). The concrete is now pre-loaded in compression and will stay that way for the life of the structure.

The parabolic profile — load balancing

A tendon following a straight horizontal path applies pure axial compression to the concrete — useful, but not the full story. A tendon following a curved path applies, in addition to that axial force, a transverse force proportional to the curvature. If the tendon sags low at mid-span and rises high at the supports — a parabolic profile — the transverse force points upward all along the span, lifting the concrete. Tune the tendon force and sag so the upward pressure exactly cancels the downward dead load, and the concrete sees no net bending from self-weight at all. This is T. Y. Lin's "load-balancing" method, published in 1963, and it is how every long-span post-tensioned floor and bridge girder is conceived today.

For a parabolic tendon with sag e and prestress force P over span L:

  Upward transverse load per unit length = 8 P e / L²

Set this equal to dead load w:
  8 P e / L² = w
  P × e     = w L² / 8

Same expression as the dead-load bending moment M = w L² / 8, which means:
  the prestress moment exactly cancels the dead-load moment at midspan.

Real designs aim to balance about 60 to 80% of the dead load — full balancing leaves no margin for tendon losses, and slight over-balancing puts the slab into compression-controlled upward camber that can be cosmetically problematic. The remaining unbalanced dead load and the entire live load bend the cross-section like a conventional beam, but the section is essentially unstressed at rest, so the depth required to handle service loads is roughly half that of a reinforced-concrete slab of the same span.

Materials

Component	Spec	Strength	Notes
Seven-wire strand (low relaxation)	ASTM A416 Grade 270	fpu = 1860 MPa	15.2 mm Ø common, area 140 mm², force 260 kN ultimate per strand
Smaller strand	ASTM A416 Grade 250	fpu = 1725 MPa	12.7 mm Ø, area 99 mm², force 171 kN ultimate
Concrete	f'c = 35 to 55 MPa typical	Higher than reinforced concrete	Must resist anchorage zone bursting plus service stresses
Ducts	Corrugated steel or HDPE	—	60 to 100 mm Ø; corrugations bond grout to concrete
Anchorages	Forged steel + wedges	Static + fatigue rated	Castings cast into concrete; wedges grip strand by friction
Grout (bonded systems)	Sand-cement w/c < 0.45	f'c,grout ≈ 25 MPa	Pumped under pressure to fill duct after stressing

A typical "tendon" inside a single duct bundles 4 to 31 strands and is treated as one prestressing unit with a combined force of 800 kN to 6 MN. Multi-strand tendons are stressed simultaneously with mono-strand jacks that pull each wire individually, or with multi-strand jacks that pull the entire bundle. The 250 to 350 mm Ø bearing plate at each end transfers the concentrated tendon force into the concrete through an anchorage zone whose detailing dominates the design at the ends of the member.

Worked example: a 14 m post-tensioned flat slab

14 m × 14 m office floor bay, 225 mm flat slab (no beams), supported on four columns at corners. Dead load: 5.6 kN/m² (slab) + 1.5 kN/m² (finishes) = 7.1 kN/m². Live load: 4.0 kN/m². Target: balance 80% of dead load with parabolic tendons.

Slab depth                  h     = 225 mm
Effective depth to tendon   d_p   = h - 30 cover - 12.5 strand/2 = 188 mm
Tendon sag                  e     = d_p - (h/2 + 25 cover top) = 188 - 138 = 50 mm
                                    (rises from low at midspan to high at columns)
Service balanced load       w_b   = 0.80 × 7.1 = 5.7 kN/m²

For 1 m wide strip, parabolic span L = 14 m:
  P × e = w_b × L² / 8
  P × 0.050 = 5.7 × 14² / 8 = 139.7 kN·m/m
  P        = 2,794 kN/m of slab width

Strand force after losses (≈ 0.62 × f_pu × A_strand):
  F_strand,service = 0.62 × 1860 × 140 = 161 kN per strand
Number of strands per metre:
  n = 2,794 / 161 = 17.4 strands/m  →  18 strands/m

Spacing if strands placed individually: 1000 / 18 = 56 mm — too close.
Use multi-strand tendons of 4 strands each, bundled in 22-strand bands or
distributed banded-uniform layout: bands of 7 tendons (each 4-strand) in
column strips, distributed monostrand in middle strip.

Camber from prestress at midspan (instant, before losses fade):
  Δ_camber ≈ P e L² / (8 E_c I)
           ≈ 2,794,000 × 0.050 × 14² / (8 × 30,000 × 10⁶ × 9.5 × 10⁻⁴)
           ≈ 12 mm upward

Live load deflection (full live + 20% unbalanced dead, with cracked section):
  Δ_LL ≈ 18 mm  < span/360 = 39 mm  ✓
Net deflection after creep ≈ 8 mm sag — acceptable for office floor.

The same slab in reinforced concrete would need to be 350 mm deep with much heavier rebar — about 60% more concrete and a third more cost, plus deeper floor-to-floor stacks. Post-tensioning wins the long-span office floor market in the United States, Australia, and Southeast Asia for exactly this reason.

The stressing sequence

What actually happens on site is a choreographed multi-day operation:

1. Concrete cast. Slab or beam is cast with ducts, anchorages, and conventional rebar in place. Concrete cures normally for 5 to 7 days, until cylinder strength reaches typically 25 MPa.
2. Tendons threaded. Strands are pushed through ducts from one end to the other. In long bonded tendons, the whole bundle is pre-fabricated and pulled in by winch.
3. Anchorages set. Wedge plates and individual wedges are installed at the live (jacking) end. Dead-end anchorages are already cast into the concrete with the strands embedded.
4. Stressing. Hydraulic jack grips the strand, pulls to the target force (e.g. 195 kN per strand for 0.75 f_pu), the jack hesitates, the wedge slides into its tapered hole and locks. Jack is released — a few millimetres of "anchorage seating loss" follow as the wedges bite home.
5. Stressing record. Each tendon's measured elongation is checked against predicted elongation (Hooke's law: ΔL = P L / (A E)). A discrepancy of more than 5 to 7% signals a problem — friction higher than expected, wedge slip, or even a broken strand — and requires investigation.
6. Grouting (bonded systems). Cement grout is pumped into the duct under pressure from the low end, displacing air out vents at the high points. Grout cures and bonds tendon to concrete.
7. Anchorages sealed. Wedge pockets are cut off, the strand stub is capped, and a non-shrink mortar plug protects the anchorage from corrosion.

Cross-section, drawn

POST-TENSIONED BEAM — elevation view (long axis)

  ┌───────────────────────────────────────────────────────────────┐
  │█  ┌───────────────────────────────────────────────────────┐  █│  ← top reinforcement
  │█  │           parabolic duct profile                      │  █│
  │█  │                                                       │  █│
  │█  └─                                              ──┐    █│
  │█   ╲────────                            ──────────╱     │  █│   ← tendon
  │█       ╲╲───── tendon sags toward mid ─────────╱╱       │  █│     (low at midspan,
  │█         ╲╲────                          ────╱╱         │  █│      high at ends)
  │█           ╲╲──── parabolic profile  ───╱╱            │  █│
  │█             ╲╲ ───────────────── ╱╱                  │  █│
  │█               ╲────────────────╱                       │  █│
  │█  ┌─────────────────────────────────────────────────┐    █│  ← bottom reinforcement
  │█  └─────────────────────────────────────────────────┘    █│
  └───┴───────────────────────────────────────────────────┴───┘
       L (span)
      ↑                                                      ↑
  anchorage                                              anchorage
  (live end, jacks here)                            (dead end)

Free body of curved tendon ⇒ uniform upward pressure on concrete
                              along the parabolic span.

The parabolic shape is hand-tuned in design. At interior supports of continuous spans, the tendon profile goes the other way — sagging upward over the support and dipping below mid-depth in the span — because the bending moment over interior supports is hogging (top in tension). The tendon thus follows the moment diagram, lifting upward in span and pressing downward over supports, balancing dead load everywhere.

Bonded versus unbonded, internal versus external

Bonded tendons. Duct is grouted after stressing. Tendon and concrete now act as one composite section — the strand acts like a high-strength reinforcement embedded along its profile. Bonded systems have higher ultimate flexural capacity, span cracks reliably, and are the standard for bridges, water-retaining structures, and external pressure vessels (LNG containment, nuclear). Disadvantage: grouting is a critical operation, voids in the grout lead to corrosion that is invisible from outside.

Unbonded tendons. Each strand is individually greased, coated with corrosion-inhibiting compound, and sheathed in plastic. The strand slides freely inside its sheath after stressing and is anchored only at the ends. Unbonded is the dominant system for building floor slabs: faster install, no grouting, easier to detail. Disadvantage: a single corroded or fractured strand loses force over its full length; bonded tendons lose force only locally.

Internal tendons. Tendons inside the concrete cross-section, the standard for buildings and most bridges. Profile fixed at casting; loss of any tendon requires demolition to replace.

External tendons. Tendons outside the concrete cross-section, running through deflector blocks in the open box-girder voids of segmental bridges. Easy to inspect, replaceable, but with smaller eccentricity and limited profile flexibility. Used in many modern segmental box-girder bridges including the I-35 over Lake Travis (Texas) and the Confederation Bridge (Canada).

Prestress losses in detail

Loss	Mechanism	Magnitude	When
Friction (duct curvature + wobble)	Tendon presses against duct walls along curved path	5 to 15% (worst at far end)	During jacking
Anchorage seating (wedge slip)	3 to 6 mm slip into the anchorage as jack releases	3 to 8% (worst near anchorage)	Instant at lock-off
Elastic shortening	Concrete compresses under prestress; subsequent tendons see shorter concrete	2 to 5%	During stressing
Concrete creep	Sustained compression causes long-term deformation	5 to 12%	Over decades, ~50% in first year
Concrete shrinkage	Concrete dries and contracts	3 to 8%	First few years
Steel relaxation	Steel loses stress at high sustained strain	2 to 4% (low-relaxation strand)	Logarithmic over time

Designers compute each component separately, sum to a long-term loss estimate, and verify the remaining effective prestress at the critical sections. AASHTO and ACI 318 provide formulas; modern practice uses creep and shrinkage models (CEB-FIP, AASHTO LRFD) that account for relative humidity, age at stressing, and member dimensions.

Real-world post-tensioned structures

• Sydney Opera House (Australia, 1973). The precast concrete shell ribs are post-tensioned together with vertical tendons that hold each rib's segments in compression — without post-tensioning, the iconic sails would not stand.
• Confederation Bridge (Canada, 1997). A 12.9 km segmental box-girder bridge with both internal and external post-tensioning, spanning Northumberland Strait between New Brunswick and Prince Edward Island. Box-girder segments are precast and stitched together with longitudinal post-tensioning.
• Burj Khalifa upper-floor slabs (Dubai, 2010). The world's tallest building uses post-tensioned floor slabs throughout to minimise depth and structure weight — critical when every floor adds to gravity load on the spire.
• Apple Park ring (USA, 2017). Curved 1.6 km perimeter has post-tensioned slabs spanning between widely spaced columns, allowing the iconic uninterrupted glass perimeter.
• Nuclear containment vessels. Almost all PWR and BWR containments are post-tensioned concrete vessels with circumferential and longitudinal tendons holding the structure together against design-basis accident pressure.
• Cantilevered hotel balconies, worldwide. The 4 to 6 m projecting balconies common in modern luxury hotels and condos are almost universally post-tensioned — reinforced concrete cannot deliver the slenderness without unsightly tip deflection.

Common pitfalls

• Anchorage zone bursting. The concentrated tendon force at the anchorage spreads laterally over a length of about one section depth, generating bursting tension perpendicular to the tendon axis. Spiral or grid reinforcement in the anchorage zone is mandatory — skipping it cracks the concrete around the anchor and can fail catastrophically.
• Drilling into a tendon. Post-tensioned slabs have hidden, highly stressed tendons inside. Cutting a 25 mm hole for a new fixture and severing a strand can release 200 kN explosively, killing workers. Every post-tensioned floor needs a tendon map and a "no drilling" zone in column strips.
• Insufficient concrete strength at stressing. If concrete has not reached the required strength when the jacks pull, the anchorage zone crushes locally. Standard wait: 5 to 7 days for ambient cure or 1 to 3 days for accelerated cure.
• Corrosion through unsealed anchorages. Water and chlorides intruding through exposed anchorage pockets corrode the strand. Modern unbonded systems use fully encapsulated, factory-greased strand and watertight anchorage caps.
• Re-tensioning live anchorages. The 2018 FIU bridge collapse involved adjustment of cracked diagonals while the bridge was still partially supported. Re-tensioning live anchorages in a damaged structure is extremely dangerous and requires temporary shoring before any adjustment.
• Ignoring secondary moments in indeterminate structures. In continuous spans, the tendon profile generates secondary support reactions in addition to the primary prestress effects. Treating a multi-span beam as a series of simple spans underestimates the moments and can lead to under-design over interior supports.