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Insulating glass unit to EN 16612

This calculation looks at deflection and stresses in a double glazed glass unit, subject to wind loading.

First page of the Insulating glass unit to EN 16612 sample calcsheet in Maths Explore
The first page of the calcsheet as it appears in Maths Explore.

What this calculation covers

Inputs

  • Pane short side a
  • Pane long side b
  • Outer pane thickness, annealed
  • Inner pane thickness, annealed
  • Cavity width
  • Modulus of elasticity of glass
  • Poisson's ratio of glass
  • ULS wind pressure, factored
  • SLS wind pressure, characteristic
  • Wind gust duration
  • Characteristic bending strength
  • Material partial factor, annealed

The bending stress and deflections coefficients

Annex B include coefficients for deflection and maximum tension stresses in a single glass pane supported on four sides. These coefficients describe fitted curves that capture effects of large out-of-plane deformations, relative to the glass thickness.

  • Fit z₂, printed beneath Table B.1
  • Fit z₃, printed beneath Table B.1
  • Fit z₄, printed beneath Table B.1
  • Stress coefficient k₁(λ, p*), Table B.1
  • Fit z₁, printed beneath Table B.2
  • Deflection coefficient k₄(λ, p*), Table B.2
  • Volume coefficient k₅ at p* = 0, Table B.3
  • Non-dimensional load p*(h, F_d), Annex B

Characteristic geometry and stiffness shares

  • Aspect ratio, short over long side
  • a is the shorter side, as the formulas need
  • Pane area
  • Stiffness share of the outer pane
  • Stiffness share of the inner pane

Load sharing through the sealed cavity

EN 16612 Annex C describes how wind load is shared between the front and rear panes in the unit. The gas in the hermetically sealed cavity acts like a spring.

  • Characteristic length of the unit, EN 16612 Annex C
  • Insulating unit factor
  • ULS pressure carried by the outer pane
  • ULS pressure carried by the inner pane
  • The two shares make up the whole wind
  • SLS pressure carried by the outer pane
  • SLS pressure carried by the inner pane

Bending stress

The bending stress induced by the ULS wind is checked against the glass's capacity.

  • Non-dimensional load, outer pane (ULS)
  • Stress coefficient, outer pane
  • Maximum bending stress, outer pane (ULS)
  • Non-dimensional load, inner pane (ULS)
  • Stress coefficient, inner pane
  • Maximum bending stress, inner pane (ULS)
  • Edge strength factor, four edges supported
  • Surface profile factor, float glass

Design bending strength

EN 16612 builds the design strength of annealed glass from its characteristic bending strength and three factors.

  • Load duration factor by the formula, t in hours
  • Load duration factor adopted, not above 1.0
  • Design bending strength, annealed glass
  • Outer pane: stress within the design strength
  • Inner pane: stress within the design strength
  • Strength utilisation, governing pane

Deflection

Deflections are checked under the SLS wind, each pane under its own share. Deflection limits vary but span/65 is fairly common.

  • Non-dimensional load, outer pane (SLS)
  • Deflection coefficient, outer pane
  • Centre deflection, outer pane (SLS)
  • Non-dimensional load, inner pane (SLS)
  • Deflection coefficient, inner pane
  • Centre deflection, inner pane (SLS)
  • Deflection limit, short span over 65
  • Outer pane within the deflection limit
  • Inner pane within the deflection limit
  • Deflection utilisation, governing pane

Results summary

  • Each 10 mm pane holds half the unit's stiffness (δ₁ = δ₂ = 0.5). The cavity's characteristic length, a^* = 574 mm, is well below the 1200 mm short span, so the trapped air passes the load across almost in proportion to stiffness: φ = 0.050, the outer pane carrying 52 % of the wind (1.57 kPa at ULS) and the inner 48 % (1.43 kPa). At λ = 0.48 and p^* = 1.27 the Table B.1 formula gives k₁ = 0.608, and the outer pane's centre stress is 13.79 MPa against a design strength of 25 MPa (all three strength factors 1.0, 45 MPa over 1.8): 55 % utilised, pass. Under the 2 kPa serviceability wind it deflects 3.63 mm at the centre, 20 % of the 18.5 mm (a/65) limit — pass. The deflections stay near a third of the thickness, so the coefficients sit close to their linear values; a thinner or larger unit drives p^* up and the k factors down as membrane action takes over.

Try changing…

  • Use 6 mm panes — h₁ := 6 mm and h₂ := 6 mm — p^* jumps to 9.4 and membrane action cuts k₁ to 0.433, but the stress still climbs to 26.24 MPa and the strength check fails at 105 %; the deflection, 12.24 mm, stays within the limit (66 %). The gust alone rules out 6 mm annealed glass here.
  • Shrink the unit to a_g := 1000 mm and b_g := 1200 mm — a^* (675 mm) is now comparable to the span, so the air keeps more of the load on the outer pane (φ = 0.172, 59 % against 41 %); at p^* = 0.23 the coefficients sit on their linear values (k₁ = 0.358), the stress falls to 6.29 MPa (25 %) and the deflection to 1.07 mm (7 %): 10 mm glass is heavy for a small unit.
  • Let the wind blow for ten minutes — t_w := 600 s — the formula gives k_{mod} = 0.742, in line with the 0.74 EN 16612 lists for a storm; the design strength drops to 18.54 MPa and the utilisation rises to 74 %, while the deflection, a matter of stiffness, doesn't move.

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