Concrete · Slabs & post-tensioning
Post-tensioned flat slab: load balancing, stresses, punching calculator
Interior panel of a bonded post-tensioned flat plate. The tendon drape balances a chosen share of the self-weight (P = w_bal·L²/8h), giving the strands per metre and the average precompression. Service stresses at the column strip under the unbalanced load, an approximate long-term deflection, ultimate strength with the strand stress σpu from AS 3600 Cl 8.1.8 and the extra bonded reinforcement, and punching shear at an interior column with the precompression term 0.3σcp.
Standard: AS 3600-2018 Sec 8, 9 · load balancing (Lin) · bonded 12.7 mm strand in flat ducts
Inputs in the worked example
The live calculator starts with these values; change any of them and every result, check and diagram updates instantly.
| Input | Value | Unit |
|---|---|---|
| Span (square interior panel) | 8.4 | m |
| Slab thickness | 240 | mm |
| Superimposed dead load | 1.5 | kPa |
| Live load | 3 | kPa |
| Concrete f′c | 40 | MPa |
| Concrete Ec (Table 3.1.2) | 32800 | MPa |
| Strand centroid to top face (at columns) | 45 | mm |
| Strand centroid to bottom face (midspan) | 45 | mm |
| Share of self-weight balanced | 0.9 | |
| Strand area (12.7 mm) | 98.6 | mm² |
| Strand fpb | 1870 | MPa |
| Jacking stress / fpb | 0.8 | |
| Total losses | 20 | % |
| Strands per duct | 4 | |
| Square column size | 600 | mm |
| Bonded reinforcement fsy | 500 | MPa |
| Long-term deflection limit span / | 250 |
Worked example — results
| Result | Value | Unit |
|---|---|---|
| Self-weight | 6.00 | kPa |
| Effective drape h | 150 | mm |
| Balanced load w_bal | 5.40 | kPa |
| Required prestress P = w_bal L²/8h | 318 | kN/m |
| Effective force per strand Pe | 118.0 | kN |
| Strands per metre | 2.69 | |
| Duct spacing (4 strands / duct) | 1,487 | mm |
| Average precompression P/A | 1.32 | MPa |
| Column-strip support M (unbalanced service) | 37.0 | kNm/m |
| Top-fibre stress at column (+ tension) | 2.54 | MPa |
| Bottom-fibre stress at column | -5.18 | MPa |
| Bottom-fibre stress at midspan | 0.22 | MPa |
| Long-term deflection (approx.) | 8.2 | mm |
| Strand stress at ultimate σpu | 1,814 | MPa |
| M* at column strip | 119.1 | kNm/m |
| Strand-only capacity Mu | 90.2 | kNm/m |
| Extra bonded reinforcement | 549 mm²/m → N16 @ 300 | |
| Punching V* / φVuo | 944 / 1,036 | kN |
- ✓ Precompression within 1.0–3.5 MPa — 1.32 MPa
- ✗ Tension ≤ 0.25√f′c (no crack-control steel needed) — 2.54 vs 1.58 MPa
- ✓ Compression ≤ 0.6 f′c
- ✓ Deflection ≤ L/250 — 8.2 vs 33.6 mm
- ✓ Ductility ku ≤ 0.36 — 0.092
- ✓ Punching V* ≤ φVuo — 91 %
Method, formulas and assumptions
- Load balancing: a parabolic drape h exerts an upward load 8Ph/L² (Lin). Effective drape taken as D − ct − cb for an interior span with reversed curvature over the columns.
- Column strip carries 75 % of the negative moment over half the panel width (1.5 × average), wL²/12 support and wL²/24 midspan coefficients on the unbalanced load; secondary moments ignored.
- Deflection: crossing-beam estimate 2.4wL⁴/384EI on the uncracked section with kcs = 2 (×3 long-term) under G + 0.4Q − w_bal.
- σpu = fpb(1 − k1k2/γ), k1 = 0.4 (low-relaxation strand, bonded), φ = 0.85; punching fcv = 0.17(1 + 2/βh)√f′c ≤ 0.34√f′c with + 0.3σcp, φ = 0.7, moment transfer Mv* not included.
Related concrete calculators
- One-way slab — Bending steel, bar spacing and deemed-to-comply span/depth for a one-way slab.
- Two-way slab — Moments in both directions for a rectangular slab simply supported on four edges.
- Composite slab (steel deck) — Positive moment capacity of a composite slab with the profiled deck acting as reinforcement, vs factored…
- Prestressed beam fibre stresses — Top and bottom fibre stresses at transfer and service for a rectangular section with eccentric prestress.
- Slab punching shear (AS 3600) — Critical shear perimeter at dom/2, concrete capacity fcv, and moment-transfer reduction for an interior…
- Post-tensioning friction & draw-in losses — Force along a parabolic tendon from curvature and wobble friction, and the length affected by anchorage…
- Load balancing (parabolic tendon) — Equivalent upward load wp = 8Pe/L², balanced fraction of the permanent load, and average precompression.
For preliminary design and education. Check every result against the current standard and your own engineering judgement before use.