CLT floor panel: deflection, stiffness and vibration
Checks a cross-laminated timber (CLT) floor panel spanning one way at the serviceability limit state: deflection with the shear deformation of the cross layers and creep, the floor stiffness under a 1 kN point load, and an empirical span limit for vibration. Every step shows its formula.
Pro EN 1995-1-1
Part of the Pro plan
This module is included in the Pro plan and above, with its calculation note.
About this check
clauses, worked example and questions
Checks a cross-laminated timber (CLT) floor panel spanning one way at the serviceability limit state: deflection with the shear deformation of the cross layers and creep, the floor stiffness under a 1 kN point load, and an empirical span limit for vibration. Every step shows its formula.
What it checks
- Shear stiffness of the lay-up: GAs = k · b · Σ(Gi · di), with G0,mean in the layers along the span and the rolling shear modulus GR,mean in the cross layers.
- Deflection at mid-span: bending part wB = 5 · q · l⁴ / (384 · E · I) and shear part wS = q · l² / (8 · GAs); creep φ applied to the quasi-permanent share of the load only; checked against l / n.
- Floor stiffness: deflection under a 1 kN point load at mid-span, bending and shear, against your limit wG.
- Vibration: span limit LG = 111 · (E·I / 10⁶)^0.293 / m^0.123, an empirical limit on the span rather than a frequency calculation.
What you enter and what you get
You enter the lay-up and the width considered, the moduli E0,mean, G0,mean and GR,mean, the correction on the shear stiffness, the span, the frequent load (g + ψ₁·q) and the quasi-permanent load (g + ψ₂·q), the creep coefficient, the deflection limit, the limit under a point load, and the linear mass of the floor structure.
You get the three checks with their utilisations and every intermediate value. With the Pro plan, it prints as an A4 calculation note.
Assumptions and limits
- Panel spanning one way, simply supported; only the layers along the span carry bending.
- In CLT the shear deflection is not negligible, because the cross layers shear easily; it is always included.
- The vibration check is an empirical span limit, not a frequency or response calculation.
- The strength of the panel (its own module) and the fire situation (its own module) are separate.
Worked example
The five-layer panel 40-20-20-20-40 mm, one metre wide, spanning 4.00 m, with E_0,mean = 11,500 N/mm², G_0,mean = 650 N/mm², G_R,mean = 50 N/mm², a frequent load of 3.73 kN/m, a quasi-permanent load of 2.70 kN/m, φ = 0.8, a limit of l/350, w_G = 0.65 mm and a linear mass of 100 kg/m. These are the module's own results, computed when this page was built.
| Input | Value | Ref. |
|---|---|---|
| Number of layers | 5 | |
| Layer 1, along the span d1 | 40 mm | |
| Layer 1–2, across the span d12 | 20 mm | |
| Layer 2, along the span d2 | 20 mm | |
| Layer 2–3, across the span d23 | 20 mm | |
| Layer 3, along the span d3 | 40 mm | |
| Width considered b | 1000 mm | |
| Modulus of elasticity along the span E0,mean | 11500 N/mm² | |
| Shear modulus G0,mean | 650 N/mm² | |
| Rolling shear modulus GR,mean | 50 N/mm² | |
| Correction on the shear stiffness k | 0.25 | |
| Span of the panel l | 4000 mm | |
| Frequent load, g + ψ1·q qd | 3.73 kN/m | |
| Quasi-permanent load, g + ψ2·q qφ | 2.7 kN/m | |
| Creep coefficient φ | 0.8 | |
| Deflection limit l / n | 350 | |
| Limit under a 1 kN point load wG | 0.65 mm | |
| Linear mass of the floor, structure only m | 100 kg/m |
| Step | Value | Ref. |
|---|---|---|
| Shear stiffnessGAs = k · b · Σ(Gi · di), with G0 along the span and GR across it | GAs = 16,750,000 N |
| Step | Value | Ref. |
|---|---|---|
| Bending deflection per 1 kN/mwB = 5 · q · l⁴ / (384 · E0,mean · I0,net) | wB = 1.3716 mm | |
| Shear deflection per 1 kN/mwS = q · l² / (8 · GAs). In CLT this is not negligible, because the cross layers shear easily. | wS = 0.1194 mm | |
| Deflection at mid-spanwEd = qd · (wB + wS) · (1 + φ · qφ / qd), so creep is applied only to the quasi-permanent share of the load. | wEd = 8.782 mm | |
| DeflectionwEd ≤ l/350 | η = 0.768 · Pass77 % of the capacity used |
| Step | Value | Ref. |
|---|---|---|
| Deflection under a 1 kN point loadwf = P·l³/(48·E·I) + P·l/(4·GAs), with P = 1 kN at mid-span | wf = 0.6083 mm | |
| Floor stiffnesswf ≤ wG | η = 0.936 · Pass94 % of the capacity used |
| Step | Value | Ref. |
|---|---|---|
| Span limit for vibrationLG = 111 · (E·I / 10⁶)^0.293 / m^0.123, an empirical limit on the span rather than a frequency calculation. | LG = 4,680.8 mm | |
| Vibrationl ≤ LG | η = 0.855 · Pass85 % of the capacity used |
How this module is verified
Verified step by step against independent calculations used on real projects, before release.
Questions
Why is creep applied only to part of the load?
Creep acts on the quasi-permanent share of the load. The module scales the deflection by (1 + φ · q_φ / q_d), so the short-term share is not increased.
Is the vibration check a frequency calculation?
No. It is an empirical limit on the span from the stiffness and the mass of the floor; the module says so in the calculation.
Which plan includes this module?
The Pro plan, with its calculation note.
Related
- CLT floor panel: bending and rolling shear
- CLT floor panel — fire situation
- EN 1995: modules and checks
Norm: EN 1995-1-1 · Page updated: 20 October 2026