Concrete · Materials & serviceability
RC deflection and crack control calculator
Short-term and long-term deflection of a simply supported RC beam or slab strip using Ief, and the service steel stress for crack control.
Standard: AS 3600-2018 Cl 8.5.3 (Branson / Bischoff Ief) · 8.6 steel stress
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 L | 7 | m |
| Width b | 1000 | mm |
| Depth D | 250 | mm |
| Effective depth d | 215 | mm |
| Ast | 1130 | mm² |
| Asc | 0 | mm² |
| f′c | 32 | MPa |
| Ec | 30100 | MPa |
| fsy | 500 | MPa |
| Shrinkage-restraint stress σcs | 0.8 | MPa |
| Service load (short term) | 11 | kN/m |
| Sustained load | 8.4 | kN/m |
| Span / limit | 250 |
Worked example — results
| Result | Value | Unit |
|---|---|---|
| Modular ratio n | 6.64 | |
| Neutral axis kd | 49.8 | mm |
| Icr / Ig | 246.1 / 1,302.1 | ×10⁶ mm⁴ |
| Mcr / Ms | 27.0 / 67.4 | kN·m |
| Ief | 283.0 | ×10⁶ mm⁴ |
| Short-term deflection | 40.4 | mm |
| kcs | 2.00 | |
| Total long-term deflection | 102.0 | mm |
| Limit L/250 | 28.0 | mm |
| Service steel stress fs | 301 | MPa |
- ✗ Deflection ≤ L/250 — 102.0 mm
- ✓ fs ≤ 0.8fsy (crack control) — 301 MPa
Method, formulas and assumptions
- Ief = Icr / [1 − (1 − Icr/Ig)(Mcr/Ms)²] ≤ Ief,max (Cl 8.5.3.1)
- Mcr = (0.6√f′c − σcs)Z
- Δ = 5wL⁴/(384 Ec Ief); long term adds kcs × sustained deflection, kcs = 2 − 1.2 Asc/Ast ≥ 0.8
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For preliminary design and education. Check every result against the current standard and your own engineering judgement before use.