Sandwich Panel Designer BETA
Calculation parameters & Eurocode coefficients
EN 1990 — Partial factors for actions
EN 1990:2002 Table A1.2(B) — STR/GEO persistent and transient design situations. National Annex may modify these values.
ULS — single variable action
Ed = γG,unfav · Gk + γQ · Qk
EN 1990 Eq. 6.10 — governing for snow-only or wind-only load cases.
ULS — two variable actions
Ed = γG,unfav · Gk + γQ · Qk,1 + γQ · ψ0,i · Qk,i
EN 1990 Eq. 6.10 — leading action Qk,1 at full value; accompanying actions multiplied by ψ0 (e.g. snow + wind pressure).
ULS — uplift / suction
Ed,uplift = γQ · Qsuction − γG,fav · Gk (≥ 0)
EN 1990 Eq. 6.10 — used for wind uplift on roof panels and ceiling tension checks. Stabilising permanent load uses γG,fav.
SLS — characteristic combination
Ed,SLS = Gk + Qk,1
EN 1990 Eq. 6.14b — used for deflection and bearing SLS checks. No combination coefficient on the leading action.
EN 1991-1-4 — Wind parameters
Site-independent wind constants and partial factors. Terrain roughness (z₀, zmin) and cpe,10 tables are fixed to EN 1991-1-4 Tables 4.1 and 7.1.
Terrain roughness factor kr
kr = 0.19 · (z0 / z0,II)0.07
EN 1991-1-4 Eq. 4.5 — z0,II = 0.05 m (terrain category II reference). Depends only on site roughness z0.
Roughness factor cr(z)
cr(z) = kr · ln(z / z0)
EN 1991-1-4 Eq. 4.4 — evaluated at reference height z = max(h, zmin). Increases logarithmically with height.
Mean wind velocity vm
vm(z) = cr(z) · c0 · vb
EN 1991-1-4 Eq. 4.3 — vb = basic wind speed from national map. c0 = 1.0 for flat terrain.
Turbulence intensity Iv
Iv(z) = kI / (c0 · ln(z / z0))
EN 1991-1-4 Eq. 4.7 — kI = turbulence factor (default 1.0). Increases with lower height and rougher terrain.
Peak velocity pressure qp
qp(z) = [1 + 7 · Iv] · ½ · ρ · vm2
EN 1991-1-4 Eq. 4.8 — result in Pa, stored as kN/m² (÷1000). Can be overridden by manual qp input.
Net wind pressure we
we = qp · (cpe − cpi)
EN 1991-1-4 Eq. 5.1 — characteristic value. cpi,max = +0.2 for suction zones; cpi,min = −0.3 for pressure zones.
ULS design wind pressure wd
wd,ULS = γF · |we|
Wall panels: γF,wall = 1.30. Roof panels: γF,roof = 1.50. SLS uses |we| directly.
EN 14509:2013 — Panel structural checks
Material partial factors and steel constants used in Annex E calculations. Core material properties (fcv, Gc) are declared per panel variant in the Panel Library.
Face centroid distance e
e = D − t1/2 − t2/2
EN 14509 Annex E §E.1 — D = total thickness, t1 = outer face, t2 = inner face (all in mm).
Bending stiffness Bs
Bs = Es · t1·t2 / (t1+t2) · e2
EN 14509 Annex E Eq. E.1 — per unit width, kN·m²/m. Increases with face thickness and eccentricity.
Core shear rigidity S
S = Gc · e
EN 14509 Annex E §E.1 — per unit width, kN/m. Gc = core shear modulus from DoP.
Shear flexibility parameter k
k = 3 · Bs / (L2 · S)
EN 14509 Table E.10.1 — k→0 = rigid core (beam theory). Larger k reduces moments at internal supports.
Core shear resistance qs
VRd = fcv · e / γM,cv
qs = 2 · VRd / [L · (1+α)]
EN 14509 Annex E §E.2 — fcv = core shear strength from DoP. α = shear factor from Table E.10.1.
Face wrinkling resistance qwr
MRd = fwr · tf · e / (γM,wr · 1000)
qwr = 8 · MRd / (L2 · mfactor)
EN 14509 Annex E §E.3 — fwr = declared wrinkling stress. mfactor = (1−α)² in span or 8/(10+4k) at support.
Deflection resistance qwt (SLS)
qwt = (L/lim) · C · Bs / (L4 · fdefl)
EN 14509 Table E.10.1 — inverted from w = q·L4·fdefl/(C·Bs). lim = deflection limit denominator (e.g. 100 → L/100).
Thermal bow δT
δT = αs · |ΔT| · L2 / (8 · e)
EN 14509 Table E.6 — simply-supported (conservative). Combined with wind: δ = δT + ψ0,wind·δwind or δwind + ψ0,T·δT.
Fastener resistance factors
Characteristic screw resistances (NRk, VRk) are stored per screw type. The partial factor below is applied to obtain design values NRd = NRk / γM,f.
Design resistances per fastener
VRd = VRk / γM,f
NRd = NRk / γM,f
ETA (Etanco / RAPID) — VRk and NRk are tabulated per screw type and panel steel thickness (0.5 – 0.8 mm).
Combined shear + tension interaction
|NSd| / (n · NRd) + |VSd| / (n · VRd) ≤ 1.0
EN 1993-1-8 §3.6 — n = number of fasteners per side. The calculator finds the minimum integer n satisfying this condition (≥ 3 minimum per side).
Wall panel — design forces
VSd = γG,unfav · RG + γQ · Rwind,v
NSd = γQ · Rwind,suction
R = support reactions from beam analysis. Vertical assembly: all gravity shear to bottom support only.
Roof / ceiling panel — uplift tension
NSd,uplift = max(γQ·Rwind − γG,fav·RG, 0)
EN 1990 uplift combination. Ceiling panels additionally include internal pressure as an uplift action with its own partial factor.
1 EN 1990
2 Wind EN 1991-1-4
3 Snow EN 1991-1-3
4 Roof Load Cases
5 Section Properties
6a Single Span
6b Two Spans
6c Three+ Spans
7 Resistances
8 Thermal Bow
9 Bearing
10 Beam Reactions
11 Fasteners
1 — EN 1990:2002 §6.4 — Load Combinations
ULS — single variable action (Eq. 6.10)
Ed = γG,unfav · Gk + γQ · Qk
Used for snow-only, wind-only, and imposed-load-only roof cases.
Gk = permanent load; Qk = leading variable action.
Gk = permanent load; Qk = leading variable action.
ULS — two variable actions (Eq. 6.10)
Ed = γG,unfav · Gk + γQ · Qk,1 + γQ · ψ0,i · Qk,i
Qk,1 = leading action (full); Qk,i = accompanying action (reduced by ψ0).
Used for snow + wind pressure and wind + snow combinations.
Used for snow + wind pressure and wind + snow combinations.
ULS — uplift / suction
Ed,uplift = γQ · Qsuction − γG,fav · Gk (≥ 0)
Wind suction on roof panels and ceiling uplift. Stabilising self-weight uses γG,fav = 1.00.
SLS — characteristic combination (Eq. 6.14b)
Ed,SLS = Gk + Qk,1
Used for deflection and bearing SLS checks. No ψ0 on the leading action.
Sweden — safety class adjustment
γG,unfav = 1.35 · γd γQ = 1.50 · γd
SS-EN 1990 Swedish NA. γd: SC1 = 0.83, SC2 = 0.91, SC3 = 1.00. Applied to γF,wall and γF,roof as well.
Denmark — consequence class adjustment
γG,unfav = 1.35 · KFI γQ = 1.50 · KFI
DS/EN 1990 Danish NA. KFI: CC1 = 0.90, CC2 = 1.00, CC3 = 1.10. Also scales γF,wall and γF,roof.
2 — EN 1991-1-4:2005+A1:2010 — Wind Load
Terrain roughness factor kr (Eq. 4.5)
kr = 0.19 · (z0 / z0,II)0.07
z0 = roughness length for terrain category (Table 4.1). z0,II = 0.05 m (fixed reference).
Roughness factor cr(z) (Eq. 4.4)
cr(z) = kr · ln(z / z0)
z = max(h, zmin) — reference height at building top. zmin from Table 4.1.
Mean wind velocity vm (Eq. 4.3)
vm(z) = cr(z) · c0 · vb
vb = basic wind velocity from national wind map (m/s). c0 = orography factor (1.0 flat terrain).
Turbulence intensity Iv(z) (Eq. 4.7)
Iv(z) = kI / (c0 · ln(z / z0))
kI = turbulence factor (default 1.0). Increases with lower height and rougher terrain.
Peak velocity pressure qp(z) (Eq. 4.8)
qp(z) = [1 + 7 · Iv] · ½ · ρ · vm2
Result in Pa; stored as kN/m² (÷ 1000). ρ = air density, default 1.25 kg/m³. Overrideable by manual qp input.
Net wind pressure we (Eq. 5.1)
we = qp · (cpe − cpi)
Characteristic net pressure. For suction zones: cpi = cpi,max = +0.2. For pressure zone D: cpi = cpi,min = −0.3.
ULS design pressure wd,ULS
wd,ULS = γF · |we| wd,SLS = |we|
Wall panels: γF,wall = 1.30. Roof panels: γF,roof = 1.50.
cpe,10 interpolation for h/d (Table 7.1)
0.25 < h/d ≤ 1: cpe = c0.25 + (c1 − c0.25) · log(h/d / 0.25) / log(4)
1 < h/d ≤ 5: cpe = c1 + (c5 − c1) · log(h/d) / log(5)
Logarithmic interpolation per EN 1991-1-4 §7.2.2 note. c0.25, c1, c5 from Table 7.1.
Wall zone reference length e and widths (§7.2.2 Fig. 7.5)
e = min(b, 2h)
wA = e/5 wB = 4e/5 (or d − e/5 if e ≥ d) wC = d − e
b = crosswind width; h = height; d = depth parallel to wind. Zones D and E span full width b.
Roof zone reference length and zone depths (§7.2.3)
e = min(b, 2h)
depthF = min(d, e/10) depthH = min(d, e/2) − depthF depthI = d − min(d, e/2)
Corner width = min(b/2, e/4). Middle width G = b − 2·cornerWidth. Used for flat and monopitch roofs.
3 — EN 1991-1-3:2003 — Snow Load
Snow load on roof (Eq. 5.1)
s = μ1 · Ce · Ct · sk
sk = ground snow load (kN/m²). Ce = exposure coefficient (default 1.0). Ct = thermal coefficient (default 1.0).
Snow shape coefficient μ1 (§5.3.3 Fig. 5.2)
α ≤ 30°: μ1 = 0.8
30° < α < 60°: μ1 = 0.8 · (60 − α) / 30
α ≥ 60°: μ1 = 0
α = roof pitch angle. Linear interpolation between 30° and 60°.
4 — Roof Load Cases (EN 1990 + EN 1991)
Permanent load G
Gk = gself + glong-term
gself = panel self-weight (kN/m²) = kg/m² ÷ 100. glong-term = additional permanent distributed load.
Snow (leading)
Ed = γG,unfav · Gk + γQ · s
Single variable action. s = roof snow load from EN 1991-1-3 (§3 above).
Wind pressure (leading)
Ed = γG,unfav · Gk + γQ · wpressure
Downward wind pressure on roof (e.g. zone I positive). wpressure = |we| for pressure zones.
Snow + wind pressure (snow leading)
Ed = γG,unfav · Gk + γQ · s + γQ · ψ0,wind · wpressure
EN 1990 Eq. 6.10 two-variable case. Snow is leading; wind pressure is accompanying.
Wind pressure + snow (wind leading)
Ed = γG,unfav · Gk + γQ · wpressure + γQ · ψ0,snow · s
Wind pressure is leading; snow is accompanying.
Wind suction uplift
Ed,uplift = −max(γQ · wsuction − γG,fav · Gk, 0)
Negative = upward. Net uplift only when wind suction exceeds stabilising self-weight.
Concentrated point load Qk — global equivalent
qeq,global = Qk / (bpanel · Ltotal)
EN 1991-1-1 Category H/I. Converts point load to equivalent distributed load over full panel area.
Concentrated point load Qk — local span check
qeq,local = 2 · Qk / (bpanel · Lspan)
Conservative moment-based equivalent on the loaded span only. Factor 2 from simply-supported midspan assumption.
5 — EN 14509:2013 Annex E — Section Properties
Face centroid distance e (§E.1)
e = D − t1/2 − t2/2 [mm]
D = total panel thickness; t1 = outer face; t2 = inner face. All in mm.
Bending stiffness Bs (Eq. E.1)
Bs = Es · (t1 · t2) / (t1 + t2) · e2 [kN·m²/m]
Per unit panel width. t and e converted from mm to m. Es = 210 000 MPa = 210 × 106 kN/m².
Core shear rigidity S (§E.1)
S = Gc · (e / 1000) [kN/m per unit width]
Gc = core shear modulus from DoP (MPa). e in mm ÷ 1000 to get m. S increases with thicker core.
Shear flexibility parameter k (Table E.10.1)
k = 3 · Bs / (L2 · S)
Dimensionless. k → 0: rigid core (beam theory). k > 0: shear-flexible core reduces support moments. Calculated per span L.
6a — EN 14509 Table E.10.1 — Single Span (n = 1)
Shear factor α
α = 0
No internal support — reactions equal at both ends: V = q · L / 2.
Bending moment in span
Mspan = q · L2 / 8
Maximum sagging moment at midspan. Span moment factor = 1.
Midspan deflection
w = 5 · (1 + 3.2k) · q · L4 / (384 · Bs)
The (1 + 3.2k) factor accounts for shear deformation of the core. For rigid core (k = 0) reduces to classical w = 5qL4/(384EI).
6b — EN 14509 Table E.10.1 — Two Equal Spans (n = 2)
Shear factor α
α = 1 / (4 · (1 + k))
k = shear flexibility parameter (§5). α → 1/4 as k → 0 (rigid core).
Shear at internal support B
VB = q · L / 2 · (1 + α)
Higher reaction at internal support. Used to calculate core shear resistance demand.
Sagging moment in span
Mspan = q · L2 / 8 · (1 − α)2
Reduced from single-span value due to continuity at B.
Hogging moment at support B
MB = q · L2 / 8 · 1/(1 + k)
Governs inner-face wrinkling at the internal support under gravity load.
Midspan deflection
w = q · L4 · (0.26 + 2.6k + 2k2) / (48 · Bs · (1 + k))
Deflection at the midpoint of each span.
6c — EN 14509 Table E.10.1 — Three or More Spans (n ≥ 3)
Shear factor α
α = 1 / (5 + 2k)
Applied to every span using 3-span coefficients. α → 1/5 as k → 0.
Shear at internal support
Vint = q · L / 2 · (1 + α)
Governs core shear resistance at every interior support.
Sagging moment in interior span
Mspan = q · L2 / 8 · (1 − α)2
Governs outer-face wrinkling in span under positive (downward) load.
Hogging moment at interior support
Msup = q · L2 / 8 · 8 / (10 + 4k)
Governs inner-face wrinkling at supports under gravity and outer-face under suction.
Midspan deflection
w = q · L4 · (0.83 + 5.6k + 2k2) / (24 · Bs · (5 + 2k))
Interior span deflection. Used to derive SLS resistance qwt.
7 — EN 14509 Annex E — ULS & SLS Resistances
Core shear resistance VRd (§E.2)
VRd = fcv · e / γM,cv [kN/m]
fcv = core shear strength from DoP (MPa). e in mm. γM,cv = 1.50.
Load capacity limited by shear qs (§E.2)
qs = 2 · VRd / [L · (1 + α)] [kN/m²]
Inverted from Vint = qL/2 · (1+α). For single span α = 0, so qs = 2VRd / L.
Face wrinkling moment resistance MRd (§E.3)
MRd = fwr · tf · e / (γM,wr · 1000) [kN·m/m]
fwr = declared wrinkling stress from DoP (MPa). tf = governing face thickness (mm). γM,wr = 1.25.
Load capacity limited by wrinkling qwr (§E.3)
qwr = 8 · MRd / (L2 · mfactor) [kN/m²]
In span: mfactor = (1−α)². At support: mfactor = 1/(1+k) [2-span] or 8/(10+4k) [3+span].
Load direction — governing face
Positive (gravity/pressure): outer face in compression in span → fwr,span,ext
Negative (suction/uplift): inner face in compression in span → fwr,span,int
At internal support the roles reverse: gravity compresses inner face; suction compresses outer face.
Governing ULS resistance qULS
qULS,positive = min(qs, qwr,span,ext, qwr,sup,int)
qULS,negative = min(qs, qwr,span,int, qwr,sup,ext)
Evaluated separately for positive and negative signed loads. The relevant one is selected per wind zone.
SLS deflection resistance qwt
qwt = (L / deflLim) · C · Bs · Dden / (L4 · Dnum)
Inverted from w = q·L4·Dnum / (C·Bs·Dden). C, Dnum, Dden from Table E.10.1 for each span count.
ULS utilisation
ηULS = wd,ULS / qULS ≤ 1.0
Pass when η ≤ 1.0. Evaluated per wind zone and span; governing (maximum) utilisation reported.
SLS utilisation
ηSLS = wd,SLS / qwt ≤ 1.0
wd,SLS = |we| (characteristic, no partial factor). Pass when η ≤ 1.0.
8 — EN 14509 Table E.6 — Thermal Bow Deflection
Thermal bow δT
δT = αs · |ΔT| · L2 / (8 · e)
αs = 12×10−6 /°C. ΔT = temperature difference across thickness. L in m, e in m (converted from mm). Computed for both summer and winter.
Temperature difference ΔT
ΔTsummer = Tout,summer − Tin
ΔTwinter = Tout,winter − Tin
Tout,summer = max outdoor surface temperature (e.g. +80°C for dark cladding). Tout,winter = min outdoor (e.g. −20°C).
LC-a — temperature leading
δcomb = δT + ψ0,wind · δwind,SLS
δwind,SLS = (wd,SLS / qwt) · (L / deflLim) — back-calculated from utilisation ratio.
LC-b — wind leading
δcomb = δwind,SLS + ψ0,T · δT
ψ0,T = 0.60 (EN 14509 Table E.6). Governing = max(LC-a, LC-b) for both summer and winter.
Pass criterion
δgoverning = max(LC-asummer, LC-awinter, LC-bsummer, LC-bwinter) ≤ L / deflLim
deflLim = deflection limit denominator (e.g. 100 → limit = L/100).
9 — EN 14509 Annex E §E.4 — Bearing Check
Bearing resistance ARd
ARd = fc0k · Ls · 1000 [kN/m]
fc0k = characteristic compressive strength of core perpendicular to faces (MPa). Ls = bearing width (m).
Required minimum bearing width Ls,req
Ls,req = REd / (fc0k · 1000) [m]
REd = ULS or SLS support reaction (kN/m) from beam analysis (§10). Decisive = max(Ls,req,ULS, Ls,req,SLS).
Bearing utilisation
ηbearing = REd / ARd ≤ 1.0
Checked at ULS and SLS for every support. If Ls not provided, only Ls,req is reported.
10 — Continuous Beam Reactions — Euler–Bernoulli Stiffness Method
Single span — trivial
RA = RB = q · L / 2
Equal end reactions for uniform load on simply-supported span.
Element stiffness matrix (EI = 1, DOFs: [v, θ])
k = [ 12/L³, 6/L², −12/L³, 6/L² ]
[ 6/L², 4/L, −6/L², 2/L ]
[−12/L³, −6/L², 12/L³, −6/L² ]
[ 6/L², 2/L, −6/L², 4/L ]
[ 6/L², 4/L, −6/L², 2/L ]
[−12/L³, −6/L², 12/L³, −6/L² ]
[ 6/L², 2/L, −6/L², 4/L ]
Standard Euler–Bernoulli beam element. Assembled by direct stiffness for all spans. Vertical DOFs fixed at supports; rotations free.
Consistent nodal load vector for UDL q
f = { q·L/2, q·L2/12, q·L/2, −q·L2/12 }
Equivalent fixed-end forces and moments for uniform distributed load. Assembled into global load vector.
Point load — simply distributed to adjacent supports
Rleft = P · (L − a) / L Rright = P · a / L
a = distance from left support to point load within the span. Used for concentrated live load Qk on roof panels.
11 — Fastener Design — EN 1993-1-8 / ETA (Etanco, RAPID)
Design resistances per fastener
VRd = VRk / γM,f NRd = NRk / γM,f
VRk, NRk = characteristic shear and pull-out resistances from ETA per screw type and panel steel thickness. γM,f = 1.33.
Combined shear + tension interaction (EN 1993-1-8 §3.6)
|NSd| / (n · NRd) + |VSd| / (n · VRd) ≤ 1.0
n = fasteners per side. Minimum n = 3. Calculator increments n until interaction ≤ 1.0. Total count = 2n (both sides).
Wall — horizontal assembly design forces
VSd = γG,unfav · RG + γQ · Rwind,v
NSd = γQ · Rwind,suction
R = beam reactions from stiffness method (§10). V = shear parallel to face (gravity). N = tension perpendicular (wind suction).
Wall — vertical assembly design forces
VSd,bottom = γG,unfav · (Gk + Qv) · bpanel · Ltotal
NSd = γQ · Rwind,suction (all supports)
All gravity shear accumulates at the single bottom support. Wind tension distributed to all supports via beam analysis.
Roof — design forces per support
VSd,governing = γG,unfav · RG + γQ · max(Rsnow, Rservice, Rpoint)
NSd,wind = max(γQ · Rsuction − γG,fav · RG, 0)
VSd,wind-only = γG,fav · RG also checked (stabilising gravity case). Governing V = max of both.
Ceiling — design forces per support
VSd = γG,unfav · RG + γQ · max(Rservice, Rpoint) + γpressure · Rpressure
NSd,uplift = max(γpressure · Rpressure − γG,fav · RG, 0)
γpressure defaults to γQ = 1.50. Internal pressure acts as uplift; self-weight is stabilising.
Country Preset Coefficients (Calculator Start Selector)
These are the coefficient presets applied when you choose a country on the calculator start screen. The active preset shown here is read from local storage.
Fixed: Terrain roughness — EN 1991-1-4 Table 4.1
| Category | Description | z₀ (m) | zmin (m) |
|---|---|---|---|
| 0 | Sea or coastal area | 0.003 | 1 |
| I | Open country, few obstacles | 0.01 | 1 |
| II | Agricultural land, low vegetation | 0.05 | 2 |
| III | Suburban / industrial / forest | 0.30 | 5 |
| IV | Urban area, > 15 m buildings | 1.00 | 10 |
Fixed: Wall cpe,10 — EN 1991-1-4 Table 7.1
| Zone | h/d ≤ 0.25 | h/d = 1 | h/d ≥ 5 |
|---|---|---|---|
| A (corner suction) | −1.2 | −1.2 | −1.2 |
| B (side suction) | −0.8 | −0.8 | −0.8 |
| C (far-side suction) | −0.5 | −0.5 | −0.5 |
| D (windward pressure) | +0.7 | +0.8 | +0.8 |
| E (leeward suction) | −0.3 | −0.5 | −0.7 |
Intermediate h/d values interpolated logarithmically per EN 1991-1-4 note.
Fixed: Flat roof cpe,10 — EN 1991-1-4 §7.2.3 Table 7.2
| Zone | Suction cpe | Pressure cpe |
|---|---|---|
| F (corner) | −1.8 | 0 |
| G (edge strip) | −1.2 | 0 |
| H (interior edge) | −0.7 | 0 |
| I (interior) | −0.2 | +0.2 |
Fixed: EN 14509:2013 Annex E Table E.10.1 — span coefficients
| Spans | α (shear at support) | Span M factor | Support M factor |
|---|---|---|---|
| 1 | 0 | 1 | 0 |
| 2 | 1 / (4(1+k)) | (1−α)² | 1 / (1+k) |
| 3+ | 1 / (5+2k) | (1−α)² | 8 / (10+4k) |
k = 3Bs / (L²·S) — shear flexibility parameter. k→0 approaches rigid-core beam theory.
Fixed: Snow shape coefficient μ₁ — EN 1991-1-3 §5.3.3
| Roof pitch α | μ₁ |
|---|---|
| 0° – 30° | 0.8 |
| 30° – 60° | 0.8 × (60 – α) / 30 (linear) |
| ≥ 60° | 0 |