EN 16612:2019 worked example 1: Annealed glass, 1500 by 1000 mm, 8 mm, wind and snow
Check 8 mm annealed float glass of 1500 by 1000 mm on four edges under a wind load of 1.00 kPa and a snow load of 1.00 kPa.
EN 16612 prints no complete example of a check. This one was worked by hand from the formulas of the standard, step by step, and then run in GlassLoad.com. Both are shown.
Inputs
- Support
- Four edges supported
- Long dimension, a
- 1500.00 mm
- Short dimension, b
- 1000.00 mm
- Construction
- Monolithic
- Glass
- 8.00 mm annealed float
- Surface
- As produced
- Wind, characteristic value
- 1.00 kPa (gust, 3 s)
- Snow, characteristic value
- 1.00 kPa (3 weeks)
- Allowable deflection, wallow
- 15.38 mm (span/65)
Calculations
Factors
- Edge factor, ke (Cl 8.1.2)
- 1.00
- Duration factor, kmod (highest of the actions in the combination)
- 0.45
- Surface factor, ksp (Table 4)
- 1.00
- Modulus of elasticity, E
- 70 000 N/mm²
- Poisson's ratio, ν
- 0.23
- Characteristic strength of annealed glass, fg;k
- 45.00 N/mm²
- Characteristic strength of prestressed glass, fb;k (Table 6)
- not used
- Production factor, kv (Table 7)
- not used
- Partial factor, γM;A (Table 1)
- 1.80
- Partial factor, γM;v (Table 1)
- not used
- Design strength, fg;d (Eq 4)
- 1.00 × 0.45 × 1.00 × 45.00 / 1.80 = 11.25 N/mm²
Load combinations
- Wind (gust, 3 s)
- 1.00 kPa; kmod 1.00; ψ0 0.60, γQ 1.10
- Snow (3 weeks)
- 1.00 kPa; kmod 0.45; ψ0 0.50, γQ 1.10
- Eq 1 (ULS)
- Fd = γG × permanent actions + γQ × (leading action + ψ0 × other variable actions)
- Eq 2 (SLS)
- Fd = permanent actions + leading action + ψ0 × other variable actions
- Combination 1: Wind
- Fd ULS 1.10 kPa; Fd SLS 1.00 kPa; kmod 1.00; σmax/fg;d 0.32
- Combination 2: Snow
- Fd ULS 1.10 kPa; Fd SLS 1.00 kPa; kmod 0.45; σmax/fg;d 0.72
- Combination 3: Wind leading, snow
- Fd ULS 1.65 kPa; Fd SLS 1.50 kPa; kmod 1.00; σmax/fg;d 0.48
- Combination 4: Snow leading, wind
- Fd ULS 1.76 kPa; Fd SLS 1.60 kPa; kmod 1.00; σmax/fg;d 0.51
- Combinations checked
- 4; strength is governed by combination 2, deflection by combination 4.
- Glass area, A
- 1.50 m²
- Short over long dimension, b/a
- 0.67
- Span of the deflection limit (Cl 9.1.4)
- 1000.00 mm
Strength, snow
- Design load, Fd (Eq 1, ULS)
- 1.10 × 1.00 = 1.10 kPa
- Non dimensional load, p* (B.4)
- 0.54
- k1 (Table B.1)
- 0.4703
- Maximum stress, σmax = k1 b² Fd / h² (B.1)
- 8.08 N/mm²
- Design strength, fg;d
- 11.25 N/mm²
- σmax / fg;d
- 0.72
- Load at σmax = fg;d, Fd
- 1.54 kPa
Deflection, snow leading, wind
- Design load, Fd (Eq 2, SLS)
- 1.00 + 0.60 × 1.00 = 1.60 kPa
- Non dimensional load, p* (B.4)
- 0.78
- k4 (Table B.2)
- 0.08419
- Deflection, w = k4 b⁴ Fd / (h³ E) (B.2)
- 3.76 mm
- Allowable deflection, wallow (span/65)
- 15.38 mm
Strength and deflection: EN 16612 Annex B closed forms (B.1, B.2, B.4; Tables B.1 and B.2).
Plate solver: σmax 8.14 N/mm² (0.7 percent higher), w 3.82 mm (1.7 percent higher).
Maximum stress, σmax. Annex B at Fd = 1.10 kPa. The plate solver is a von Karman plate, simply supported, with E normalised to 70000 N/mm².
Deflection, w. Annex B at Fd = 1.60 kPa, deflection at the center of the glass.
Hand check
Short side 1000 mm, long side 1500 mm, λ = 1000 / 1500 = 0.6667.
Combination wind: Fd (ULS) = 1.1 × 1.00 = 1.10 kPa, kmod 1.00, fg;d = 25.00 N/mm², p* = 0.5395, k1 = 0.4703, σmax = 8.08 N/mm², ratio 0.32.
Combination snow: Fd (ULS) = 1.1 × 1.00 = 1.10 kPa, kmod 0.45, fg;d = 11.25 N/mm², p* = 0.5395, k1 = 0.4703, σmax = 8.08 N/mm², ratio 0.72.
Combination wind leading, snow: Fd (ULS) = 1.1 × 1.50 = 1.65 kPa, kmod 1.00, fg;d = 25.00 N/mm², p* = 0.8093, k1 = 0.4661, σmax = 12.02 N/mm², ratio 0.48.
Combination snow leading, wind: Fd (ULS) = 1.1 × 1.60 = 1.76 kPa, kmod 1.00, fg;d = 25.00 N/mm², p* = 0.8632, k1 = 0.4651, σmax = 12.79 N/mm², ratio 0.51.
Strength is governed by snow: σmax / fg;d = 8.08 / 11.25 = 0.72.
Deflection is governed by snow leading, wind: Fd (SLS) = 1.60 kPa, p* = 0.7847, k4 = 0.08419, w = 3.76 mm against 15.38 mm.
- Design load, Fd (Eq 1, ULS)
- Hand 1.10 kPa, GlassLoad.com 1.10 kPa, equal
- Design strength, fg;d
- Hand 11.25 N/mm², GlassLoad.com 11.25 N/mm², equal
- Maximum stress, σmax (B.1)
- Hand 8.08 N/mm², GlassLoad.com 8.08 N/mm², equal
- σmax / fg;d
- Hand 0.72, GlassLoad.com 0.72, equal
- Design load, Fd (Eq 2, SLS)
- Hand 1.60 kPa, GlassLoad.com 1.60 kPa, equal
- Deflection, w (B.2)
- Hand 3.76 mm, GlassLoad.com 3.76 mm, equal
- Allowable deflection, wallow
- Hand 15.38 mm, GlassLoad.com 15.38 mm, equal
Snow alone governs strength: its kmod of 0.45 gives the lowest design strength. The wind and snow combinations govern deflection.
Outputs
Strength PASS. Deflection PASS.
Strength: σmax = 8.08 N/mm² ≤ fg;d = 11.25 N/mm²; σmax/fg;d = 0.72.
Resistance: Fd = 1.54 kPa at σmax = fg;d.
Deflection: w = 3.76 mm ≤ wallow = 15.38 mm (span/65).
Notes
More examples are on the EN 16612:2019 page and on the examples page. Open the calculator to run your own check.
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