Eurocode Design Guide · Part 8 of 9
Serviceability Checks — EN 1992 / 1993 (Eurocode)
Deflection limits for RC (EC2 §7.4) and steel (EC3 §7.2), span-to-depth indirect method, effective stiffness under cracking, long-term deflections from creep and shrinkage, crack width control per EC2 §7.3, and vibration guidance.
1. Why Serviceability Often Governs
For long-span floors, shallow members, and lightly loaded structures, serviceability limit states frequently produce the critical design constraint — not strength. Common governing scenarios:
- Long spans (>8 m): Deflection under quasi-permanent load drives beam depth even when flexural utilisation is low
- Flat slabs: Punching is often secondary to deflection — slab thickness is set by L/d limits
- Brittle finishes: L/500 post-construction deflection limit for partitions can be critical on shallow spans
- Crack control: In XC3/XC4 or XD/XS environments, wk ≤ 0.3 mm may govern minimum reinforcement over ULS requirements
2. RC Deflection — Span-to-Depth Method (EC2 §7.4.2)
EC2 allows verification of deflection by limiting the span-to-effective-depth ratio l/d without calculating explicit deflections:
K Factors (EC2 Table 7.4N)
Simply Supported
K = 1.0
Beam or slab, single span
End Span
K = 1.3
Continuous, end bay
Interior Span
K = 1.5
Continuous, interior bay
Flat Slab
K = 1.2
Two-way; L = longer span
Cantilever
K = 0.4
Governs almost always
Absolute Deflection Limits (EC2 §7.4.1)
- Total deflection under quasi-permanent load: δ ≤ L/250
- Post-construction deflection (affecting partitions): δ₂ ≤ L/500
- Sagging camber to offset long-term: permitted but not required
EC2 vs ACI 318 deflection: ACI Table 9.3.1.1 gives minimum h for beams (l/16 simple, l/21 continuous). EC2's l/d method is more flexible but requires knowing the steel ratio and fck. Both methods are equivalent in intent: avoid explicit deflection calculation for typical spans. For critical applications, EC2 §7.4.3 (direct calculation) is always preferred.
3. Effective Stiffness Under Cracking (EC2 §7.4.3)
Once a RC section cracks, its flexural stiffness drops from the uncracked value (EI₁) toward the fully cracked value (EI₂). EC2 uses an interpolation factor ζ for the intermediate state (tension stiffening):
Deflection is then integrated from the mean curvature. For uniform loading on a simply supported beam: δ = (1/rmid)·L²/9.6 approximately.
4. Long-Term Deflection — Creep & Shrinkage
Creep (EC2 §3.1.4)
Shrinkage Curvature
Long-term deflection often doubles or trebles initial elastic deflection due to creep and shrinkage. For flat slabs and prestressed beams, always calculate explicitly. The span-to-depth l/d method already accounts for typical creep by calibration, but only for standard (ρ, RH) assumptions.
5. Steel Deflection Limits (EC3 §7.2)
EC3 recommends deflection limits in Table 7.1 (informative). National Annexes may modify these. Deflections are computed under the SLS quasi-permanent combination unless noted.
| Member / Condition | Limit (EC3 recommended) | ACI / AISC Equivalent |
|---|
| Floor beam — variable action only | L/300 | L/360 (ACI; live load only) |
| Floor beam — total (permanent + variable) | L/250 | L/240 (AISC, total) |
| Roof — variable only (not accessible) | L/200 | L/180 (AISC) |
| Column / wall — horizontal drift | H/300 | H/400 (AISC typical) |
| Crane runway girder — vertical | L/600 | L/600–L/1000 (AISC) |
For simply supported steel beams under uniform load: δmax = 5·w·L⁴/(384·E·I). Verify that Irequired = 5·w·L⁴/(384·E·δallow) is not larger than ULS-selected section.
6. Crack Width Control (EC2 §7.3)
Maximum Crack Width Limits (EC2 Table 7.1N)
| Exposure Class | Reinforced / Prestressed (bonded) | Combination |
|---|
| X0, XC1 | wk ≤ 0.4 mm | Quasi-permanent |
| XC2, XC3, XC4, XD1, XS1 | wk ≤ 0.3 mm | Quasi-permanent |
| XD2, XD3, XS2, XS3 | wk ≤ 0.2 mm | Frequent |
| Prestressed — XD2, XS2 | Decompression required | Frequent |
Minimum Steel for Crack Control (EC2 §7.3.2)
7. Vibration Checks
RC Floors — Natural Frequency Estimate
Steel Floors — AISC DG11 / SCI P354 Approach
For composite steel floor systems, the walking-induced vibration check compares acceleration response a/g to tolerance limits based on occupancy:
- Offices: a/g ≤ 0.5% (ISO 10137 Category A)
- Hospitals / labs: a/g ≤ 0.25%
- Rhythmic activities (gym, dancing): a/g ≤ 2–5%
Natural Frequency Targets (EC2 §7.4.1 / SCI)
- fn > 4 Hz: generally acceptable for office floors without detailed check
- fn > 8 Hz: generally acceptable for hospital/lab floors
- Pedestrian bridges: fn > 5 Hz (EC1 §1.4.4 / EN 1337)
Practical tip — post-tensioned flat slabs: PT slabs have higher stiffness-to-weight ratio than RC slabs of the same thickness. Natural frequency is typically 1–2 Hz higher, reducing the likelihood of vibration problems on long spans.
Educational use only. Deflection limits and crack width thresholds in this article follow EN 1992-1-1:2004 and EN 1993-1-1:2005 recommended values. National Annexes may specify different limits. Always verify against the applicable NA and current EN text for your project's jurisdiction.