EN 16612:2019 worked example 2: Toughened glass, 2000 by 1200 mm, 6 mm, wind and snow
Check 6 mm toughened float glass of 2000 by 1200 mm on four edges under a wind load of 1.60 kPa and a snow load of 0.80 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
- 2000.00 mm
- Short dimension, b
- 1200.00 mm
- Construction
- Monolithic
- Glass
- 6.00 mm toughened
- Surface
- As produced
- Toughening
- Horizontal, kv 1.00
- Wind, characteristic value
- 1.60 kPa (gust, 3 s)
- Snow, characteristic value
- 0.80 kPa (3 weeks)
- Allowable deflection, wallow
- 18.46 mm (span/65)
Calculations
Factors
- Edge factor, ke (Cl 8.1.2)
- 1.00
- Duration factor, kmod (highest of the actions in the combination)
- 1.00
- 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)
- 120.00 N/mm²
- Production factor, kv (Table 7)
- 1.00
- Partial factor, γM;A (Table 1)
- 1.80
- Partial factor, γM;v (Table 1)
- 1.20
- Design strength, fg;d (Eq 6)
- 1.00 × 1.00 × 45.00 / 1.80 + 1.00 × (120.00 − 45.00) / 1.20 = 87.50 N/mm²
Load combinations
- Wind (gust, 3 s)
- 1.60 kPa; kmod 1.00; ψ0 0.60, γQ 1.10
- Snow (3 weeks)
- 0.80 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 1.76 kPa; Fd SLS 1.60 kPa; kmod 1.00; σmax/fg;d 0.27
- Combination 2: Snow
- Fd ULS 0.88 kPa; Fd SLS 0.80 kPa; kmod 0.45; σmax/fg;d 0.21
- Combination 3: Wind leading, snow
- Fd ULS 2.20 kPa; Fd SLS 2.00 kPa; kmod 1.00; σmax/fg;d 0.31
- Combination 4: Snow leading, wind
- Fd ULS 1.94 kPa; Fd SLS 1.76 kPa; kmod 1.00; σmax/fg;d 0.29
- Combinations checked
- 4; strength is governed by combination 3, deflection by combination 3.
- Glass area, A
- 2.40 m²
- Short over long dimension, b/a
- 0.60
- Span of the deflection limit (Cl 9.1.4)
- 1200.00 mm
Strength, wind leading, snow
- Design load, Fd (Eq 1, ULS)
- 1.10 × (1.60 + 0.50 × 0.80) = 2.20 kPa
- Non dimensional load, p* (B.4)
- 8.73
- k1 (Table B.1)
- 0.3108
- Maximum stress, σmax = k1 b² Fd / h² (B.1)
- 27.35 N/mm²
- Design strength, fg;d
- 87.50 N/mm²
- σmax / fg;d
- 0.31
- Load at σmax = fg;d, Fd
- 10.03 kPa
Deflection, wind leading, snow
- Design load, Fd (Eq 2, SLS)
- 1.60 + 0.50 × 0.80 = 2.00 kPa
- Non dimensional load, p* (B.4)
- 7.94
- k4 (Table B.2)
- 0.0559
- Deflection, w = k4 b⁴ Fd / (h³ E) (B.2)
- 15.33 mm
- Allowable deflection, wallow (span/65)
- 18.46 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 24.91 N/mm² (8.9 percent lower), w 16.36 mm (6.7 percent higher).
Maximum stress, σmax. Annex B at Fd = 2.20 kPa. The plate solver is a von Karman plate, simply supported, with E normalised to 70000 N/mm².
Deflection, w. Annex B at Fd = 2.00 kPa, deflection at the center of the glass.
Hand check
Short side 1200 mm, long side 2000 mm, λ = 1200 / 2000 = 0.6000.
Combination wind: Fd (ULS) = 1.1 × 1.60 = 1.76 kPa, kmod 1.00, fg;d = 87.50 N/mm², p* = 6.9841, k1 = 0.3418, σmax = 24.06 N/mm², ratio 0.27.
Combination snow: Fd (ULS) = 1.1 × 0.80 = 0.88 kPa, kmod 0.45, fg;d = 73.75 N/mm², p* = 3.4921, k1 = 0.4398, σmax = 15.48 N/mm², ratio 0.21.
Combination wind leading, snow: Fd (ULS) = 1.1 × 2.00 = 2.20 kPa, kmod 1.00, fg;d = 87.50 N/mm², p* = 8.7302, k1 = 0.3108, σmax = 27.35 N/mm², ratio 0.31.
Combination snow leading, wind: Fd (ULS) = 1.1 × 1.76 = 1.94 kPa, kmod 1.00, fg;d = 87.50 N/mm², p* = 7.6825, k1 = 0.3281, σmax = 25.41 N/mm², ratio 0.29.
Strength is governed by wind leading, snow: σmax / fg;d = 27.35 / 87.50 = 0.31.
Deflection is governed by wind leading, snow: Fd (SLS) = 2.00 kPa, p* = 7.9365, k4 = 0.05590, w = 15.33 mm against 18.46 mm.
- Design load, Fd (Eq 1, ULS)
- Hand 2.20 kPa, GlassLoad.com 2.20 kPa, equal
- Design strength, fg;d
- Hand 87.50 N/mm², GlassLoad.com 87.50 N/mm², equal
- Maximum stress, σmax (B.1)
- Hand 27.35 N/mm², GlassLoad.com 27.35 N/mm², equal
- σmax / fg;d
- Hand 0.31, GlassLoad.com 0.31, equal
- Design load, Fd (Eq 2, SLS)
- Hand 2.00 kPa, GlassLoad.com 2.00 kPa, equal
- Deflection, w (B.2)
- Hand 15.33 mm, GlassLoad.com 15.33 mm, equal
- Allowable deflection, wallow
- Hand 18.46 mm, GlassLoad.com 18.46 mm, equal
The design strength of toughened glass follows Eq 6. The strength ratio is low and the deflection comes near its limit.
Outputs
Strength PASS. Deflection PASS.
Strength: σmax = 27.35 N/mm² ≤ fg;d = 87.50 N/mm²; σmax/fg;d = 0.31.
Resistance: Fd = 10.03 kPa at σmax = fg;d.
Deflection: w = 15.33 mm ≤ wallow = 18.46 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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