Complete Guide to Concrete Slab Deflection
The Concrete Slab Deflection Calculator predicts immediate and long-term deflection for one-way and two-way slabs under service loads. Includes cracking, creep, and shrinkage per ACI 318. Use with Slab Thickness and Reinforcement tools.
Deflection Components
- Immediate: Elastic + cracking
- Long-term: Creep + shrinkage
Immediate Deflection (One-Way)
\[ \Delta_i = \frac{5 w L^4}{384 E_c I_e} \]
Effective Moment of Inertia Ie
Branson: \[ I_e = \left( \frac{M_{cr}}{M_a} \right)^3 I_g + \left(1 - \left( \frac{M_{cr}}{M_a} \right)^3 \right) I_{cr} \]
Long-Term Multiplier
\[ \lambda_\Delta = \frac{\xi}{1 + 50 \rho'} \]
Step-by-Step
- Compute gross Ig
- Find Ma, Mcr
- Calculate Ie
- Immediate Δi
- Apply λ_Δ for long-term
Example: One-Way Slab
L=5m, h=150mm, w_d=3.5 kPa, w_l=2.0 kPa, ρ=0.8%:
- Δi = 4.2 mm
- Δ_long = 10.5 mm
- L/480 = 10.4 mm → OK
ACI Limits
| Case | Limit |
|---|---|
| Roof (non-sensitive) | L/180 |
| Floor (partitions) | L/360 |
| Long-term | L/240 |
Best Practices
- Min h = L/20 (one-way)
- Use ρ ≥ 0.0018
- Check camber
Common Mistakes
- Ignoring cracking
- Using Ig only
- Forgetting sustained load
Advanced Topics
- Finite element analysis
- Time-dependent creep
- Two-way plate theory
Conclusion
Control concrete slab deflection to prevent cracking and serviceability issues. Our calculator delivers instant, ACI-compliant results. Design durable, flat floors!
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