Course · lesson 2 of 7

Post-tensioned slabs

How an unbonded post-tensioned flat slab strip is designed with the STATIX PT slab calculator on its SANS 10100-1 + ACI 318-19 route: the tendon profile and load balancing, losses, transfer and service stresses, ultimate bending, punching with prestress and deflection.

1. Learning outcomes

After this lesson you can:

lay out a tendon profile and find the balanced load;
follow the losses from the jacking force to the effective prestress;
check the stresses at transfer and in service;
check ultimate bending with unbonded tendons and the bonded bars;
check punching with prestress and the deflection, and say which code each check comes from.

2. Before you start

Lesson 1 (flat slabs, frames and punching).
The PT slab calculator.
A pocket calculator and about 60 minutes.

3. The idea

Why post-tension a slab. A tendon draped low in the spans and high over the columns, then stressed, pushes up on the concrete along its curve. Chosen well, that upward load balances most of the self-weight, so a thinner slab spans further with little deflection and few cracks.

Unbonded monostrands. Most SA flat slabs use single greased strands in plastic sheaths. They are not bonded to the concrete: the strand force acts only at the anchors and along the curve. The PT slab calculator models unbonded monostrands; grouted, bonded tendons are not on the page.

The tendon profile. Each span is made of parabolas: high over the interior columns, low at mid-span, with a short reverse curve over the column so the tendon has no kink. The drape a sets how much it can lift. The calculator lays out the profile from the covers and takes the reverse curve as 0.1 of the span, a practice value it flags.

Load balancing. A parabolic tendon with force P and drape a over a span L pushes up with 8Pa/L². The number of strands per metre is chosen so that this balances most of the self-weight; the calculator starts at 0.8 of the self-weight (a practice target it flags) and the stress and deflection checks decide.

4. Losses and stresses

Losses. The jacking force P₀ (0.75 f_pk A_p, 5.8.1.1) drops at once by friction, wedge draw-in and elastic shortening to P_i, then over time by creep, shrinkage and relaxation to P_e. The calculator works each one from SANS 10100-1 section 5 and uses the average force along the unbonded tendon.

Stresses. The slab is checked uncracked, as P/A ± M/Z with the prestress moment included, twice: at transfer when the prestress is highest and only the self-weight acts, and in service with all the loads. Class 1 allows no tension; class 2 allows a little, with bonded bars near the tension face.

5. Strength, punching and deflection

Ultimate bending. An unbonded strand does not reach its full strength at failure: SANS 10100-1 eq.(15) gives the stress f_pb from the effective prestress and the tendon length. The design moment includes the secondary (hyperstatic) prestress moment at a factor of 1.0 (5.1.4.2, and ACI 318-19 5.3.11 on the page). Bonded bars add to the resistance.

Bonded steel. Unbonded slabs need ordinary bars too: over the columns to control cracking and ductility (ACI 318-19 8.6.2.3, on the page), in the spans where the tension is high, and enough in total for SANS 10100-1 5.9.2.2. The calculator designs them with the strength they add.

Punching with prestress. SANS 10100-1 leaves flat slabs to specialist literature, so the page checks interior columns by ACI 318-19 22.6.5.5, where the precompression f_pc raises the shear strength, on a perimeter at d/2. Edge columns, which ACI excludes from that rule, go to the SANS reinforced-concrete punching check with the prestress ignored (on the safe side). f_pc is the mean P/A of the two directions: the page knows this strip’s own, and you give the other in the input “P/A in the other direction”. Left blank, it takes the 0.862 MPa minimum and warns you.

Deflection. With the prestress balancing most of the weight, the slab may hardly move, or even lift. The calculator works the strip deflection with creep from the specific creep of 5.8.2.5, and checks the final, the after-partitions and the upward limits of SANS 10100-1 3.2.3.2.

Two codes on one route. SANS 10100-1 section 5 covers prestressed concrete, but says flat slabs follow specialist literature. The page's SANS route therefore uses SANS 10100-1 where it speaks and ACI 318-19 for the flat-slab rules, and every row names its clause. Practice values with no code source (draw-in, the reverse curve, the balance target) are flagged.