Enter the center point load (force), span length, modulus of elasticity, and second moment of area (area moment of inertia) into the calculator to estimate the maximum midspan deflection using a simply supported beam approximation.

Glass Deflection Calculator

Pick your scenario, enter the glass dimensions, and see how much it will bend.

Shelf · point load
Window · wind load

Glass Deflection Formula

The following formula is used to estimate the maximum midspan deflection of a simply supported glass strip/beam with a single center point load. For a full glass plate under distributed wind pressure, plate theory (and glass design standards) should be used instead.

D = (P * L^3) / (48 * E * I)

Variables:

  • D is the maximum midspan deflection (mm)
  • P is the center point load applied at midspan (N)
  • L is the span length between supports (mm)
  • E is the modulus of elasticity (N/mm², i.e., MPa)
  • I is the second moment of area (area moment of inertia) of the cross-section (mm⁴)

To calculate the deflection, multiply the center point load by the cube of the span length. Divide this result by the product of 48, the modulus of elasticity, and the second moment of area. Note: if you use mm for L and mm⁴ for I, then E must be in N/mm² (MPa). (For reference, 70 GPa = 70,000 MPa = 7.0 × 1010 Pa.)

What is a Glass Deflection?

Glass deflection refers to the bending (out-of-plane displacement) of a glass surface under load. This can occur in windows, doors, shelves, or other glass elements when subjected to forces such as wind loading, impacts, or other applied loads. The amount of deflection depends on factors such as glass thickness, span, support conditions, and the type and location of the load. Excessive deflection can increase stress in the glass or cause serviceability issues (like frame or seal problems).

How to Calculate Glass Deflection?

The following steps outline how to calculate the Glass Deflection using the given formula:

  1. Gather the known values among P, L, E, I, and D (you typically solve for D).
  2. Substitute the values into the formula: D = (P * L^3) / (48 * E * I).
  3. Calculate the unknown value using the formula.
  4. Check your answer with the calculator or by comparing it with other known values.

Example Problem:

Use the following variables as an example problem to test your knowledge:

D: deflection of the glass strip/beam (mm) = ?

P: center point load at midspan (N) = 500

L: span length (mm) = 1000

E: modulus of elasticity (N/mm²) = 70,000 (≈ 70 GPa)

I: second moment of area (mm⁴) = 5000

Calculated deflection: D = (500 × 10003) / (48 × 70,000 × 5000) ≈ 29.76 mm