How do you calculate the deflection of glass?

For a pane supported on four edges under a uniform load, y = α · q · b⁴ / (E · t³), with b the short side, D = E·t³ / 12(1 − ν²) the plate stiffness (E = 70 GPa, ν = 0.23) and α from the ratio of the sides (0.00406 square, up to 0.01302 very long).

How much does 8 mm glass deflect?

A 1000 × 1500 mm pane of 8 mm glass supported on four edges deflects 2.45 mm under 1 kPa, with a bending stress of 7.6 MPa.

Does thicker glass deflect less?

Yes, with the cube of the thickness: going from 6 to 10 mm takes the same 1000 × 1500 mm pane from 5.8 to 1.25 mm under 1 kPa.

What is the Young's modulus of glass?

About 70 GPa (70 000 N/mm²) for soda-lime glass, with a Poisson's ratio of about 0.23 (the value EN 16612 uses). Tempering does not change it: it changes strength, not stiffness.

Why do standards give less deflection than this formula?

Because a pane that bends more than about half its thickness starts to carry load by stretching, like a membrane. ASTM E1300 and EN 16612 use non-linear analysis that accounts for it; the linear formula is on the safe side.

Glass · Structural

Glass deflection calculator

A glass pane supported on four edges deflects y = α · q · b⁴ / D at its centre, b the short side and α from the ratio of the sides: a 1000 × 1500 mm pane of 8 mm glass under 1 kPa bends 2.45 mm, with a stress of 7.6 MPa. The same pane held only on its two long edges bends 4.1 mm. Deflection goes with the cube of the thickness: 6 mm bends 5.8 mm and 10 mm 1.25 mm.

—

Deflection

— mm

Span / deflection

—

short span divided by the deflection

Bending stress

— MPa

Load used

— kPa

The glass deflection formula

four edges: y = α · q · b⁴ / D σ = β · q · b² / t² two edges: y = 5 · q · L⁴ / (384 · D) σ = 0.75 · q · L² / t² D = E · t³ / (12 · (1 − ν²)) E = 70 GPa (glass) ν = 0.23 b = short side L = span t = thickness

α and β come from the ratio of the long side to the short one (Timoshenko’s table for a plate simply supported on four edges, the same as the wind load page): α runs from 0.00406 for a square pane to 0.01302 for a very long one, β from 0.287 to 0.750. For 1000 × 1500 mm the ratio is 1.5, so α = 0.00772 and β = 0.4872. With D = 70 000 × 8³ / (12 × (1 − 0.23²)) = 3153486 N·mm: y = 0.00772 × 0.001 N/mm² × 1000⁴ / D = 2.45 mm.

1000 × 1500 mm pane under 1 kPa, four edges

Thickness	Deflection (mm)	Stress (MPa)	Half the thickness
4 mm	19.58	30.5	beyond
5 mm	10.03	19.5	beyond
6 mm	5.80	13.5	beyond
8 mm	2.45	7.6	within
10 mm	1.25	4.9	within
12 mm	0.73	3.4	within
15 mm	0.37	2.2	within
19 mm	0.18	1.3	within

Nominal thicknesses. Standards check with the minimum thickness (5.56 mm for 6 mm glass in ASTM C1036), which bends a little more.

What this page does not do

It does not pass or fail a pane. Once the deflection passes about half the thickness, the glass carries part of the load by stretching and the linear formula overestimates the deflection and the stress. ASTM E1300 and EN 16612 use non-linear analysis; the thickness under wind load page applies EN 16612’s design strength.
It does not model point supports, clamps or one free edge. Those change the result a lot; use a structural program for them.

Questions people ask

How do you calculate the deflection of glass?: For a pane supported on four edges under a uniform load, y = α · q · b⁴ / (E · t³), with b the short side, D = E·t³ / 12(1 − ν²) the plate stiffness (E = 70 GPa, ν = 0.23) and α from the ratio of the sides (0.00406 square, up to 0.01302 very long).
How much does 8 mm glass deflect?: A 1000 × 1500 mm pane of 8 mm glass supported on four edges deflects 2.45 mm under 1 kPa, with a bending stress of 7.6 MPa.
Does thicker glass deflect less?: Yes, with the cube of the thickness: going from 6 to 10 mm takes the same 1000 × 1500 mm pane from 5.8 to 1.25 mm under 1 kPa.
What is the Young's modulus of glass?: About 70 GPa (70 000 N/mm²) for soda-lime glass, with a Poisson's ratio of about 0.23 (the value EN 16612 uses). Tempering does not change it: it changes strength, not stiffness.
Why do standards give less deflection than this formula?: Because a pane that bends more than about half its thickness starts to carry load by stretching, like a membrane. ASTM E1300 and EN 16612 use non-linear analysis that accounts for it; the linear formula is on the safe side.