# Calculating Glass Thickness for Aquariums

Author: Warren Stilwell
First published in Aquarium World February 2001

### Introduction

For too long now the thickness of glass required to make an aquarium has been a mystery. There are various tables and guidelines that specify the thickness of glass for a given size aquarium. The major drawback with the information is there is no indication of safety factors for the specified glass thickness or any indication of how the suggested thickness was calculated.

This article is intended to help those people who are serious about aquarium design to calculate the correct thickness of glass based on what is an acceptable safety factor for them. There are other points to consider as well as the formula that will also be covered.

This information is intended as a guide only, and is in no way a guaranteed formula for success. It is based solely on proven stress calculation methods and does not account for manufacturing defects or construction faults.

### The Nature of Glass

Glass is a totally brittle substance. It will bend a very small amount, but has no capacity like most metals to deform. It will bend to a point and then break. It is this bending stress that is the focus for calculating the thickness.

Glass also has a wide variability in strength. Testing samples of uniform manufacture has proved this (see specifications for glass, – Tensile Strength 19.3 to 28.4MPa).

Glass is weak in tension, is elastic up to its breaking point, and has no ductility. It is not capable of being permanently deformed, and does not give any pre-warning of impending failure by showing a permanent set after an excessive load has been removed.

An important characteristic is its ability to carry an impulse load approximately twice its rated load (i.e. banging the aquarium with your hand quite hard). This is inevitably what saves many aquariums when they are accidentally knocked.

The variability of the strength of glass due to limitations of the manufacturing process means a suitable safety factor must be used when calculating glass thickness. The factor commonly used is 3.8. While not a perfect guarantee, it will remove all risk bar that of damaged or very poor quality glass. The main damage that will cause failures is scratches and chips. Also a point load on the glass surface will cause it to fail. For this reason a soft packer like polystyrene is used under aquariums to stop the point loading of dirt and grit.

Also when manufacturing an aquarium, the joining compound (commonly silicone) must have a minimum thickness (0.5-1mm) to allow for irregularities along the glass edge. When glass is cut it is not flat along its edge unless it has been specially ground.

It is possible to use a lower safety factor if the glass is of excellent quality and has no internal stress. It is at the designers risk however to lower the safety factor.

Toughened glass is considerably stronger than standard glass. It cannot however be cut. If toughened glass is to be used it must first be cut to size, have its edges finished and then be send away for toughening. The thermal resistance properties of glass are also improved by toughening. Standard 6mm glass will rupture if plunged into water at 21°C if the temperature of the glass is more than 55°C hotter or colder. Toughened glass will rupture at approximately 250°C difference. Toughened glass also has a tensile strength greater than 5 times that of standard glass. Standard glass has a very important advantage when used on aquariums. It tends to fail in a non-spectacular manner, – typically a vertical or diagonal crack. Toughened glass however will fail completely, much like the old style car windscreen (100% shattering).

Glass has a much lower coefficient of linear expansion that most metals. This is important if a metal frame is to be used as part of the structure of the aquarium. If so, the aquarium should be built and stored at a temperature similar to that which it will run at. The length of the aquarium will decide how much elasticity will need to be accommodated by the sealing compound used. Silicone Rubber is the most common sealing compound today. The thickness of the sealing layer needs to be changed as the seal length increases. A general rule of thumb is to allow 2-3mm per meter of joint length. This allows the silicone to take up the stretching forces between the glass and steel.

### Glass Physical Characteristics:

 Density: approx 2.5 at 21°C Coefficient of linear expansion: 86 x 10-7m/°C Softening Point: 730°C Modulus of Elasticity: 69GPa (69 x 109 Pa) Poisson’s ratio: Float Glass 0.22 to 0.23 Compressive Strength: 25mm Cube: 248MPa (248 x 106 Pa) Tensile Strength: 19.3 to 28.4MPa for sustained loading Tensile Strength (toughened glass): 175MPa.

### Design Considerations:

The calculations that follow expect the glass to be supported around its perimeter on all four sides. The calculation is the same regardless of whether the perimeter join is in compression or tension. Typical all glass aquariums have all their joins in either tension or shear or both. This method of construction relies 100% on the strength of the silicone holding it together, and is also the weakest join type when using silicone. Steel frame aquariums have the silicone under compression. The silicone is not required to have any strength for this type of aquarium and serves only as a sealer and packer.

The thickness of the bottom glass is covered by the second set of calculations, but does not cover an aquarium which has a bottom glass that is well supported from below the aquarium in an even uniform manner. The surface must be very level. On very large aquariums this can be difficult to achieve and self-leveling filler may be needed between the polystyrene and the base. This should be applied just prior to fitting the aquarium to the base so that the aquarium’s weight levels out imperfections. Significant time must be allowed for the filler to fully cure before the aquarium is filled. If the bottom glass is only to be supported by all four edges then use the second set of calculations. The same thickness glass can be used on a uniformly supported bottom as well and this will significantly improve the safety factor. If the aquarium is to be supported from below in a uniform distributed manor, then the same thickness glass that is used for the largest side panel may be used. To do so requires the supporting base to support part of the load so therefore it must be VERY strong.

NOTE: The calculations only consider the water to the top edge of the glass. If the glass is a window below the surface then it is outside the scope of this article.

### Calculations

Terms Used:

 Length in mm (L): The length of the aquarium. Width in mm (W): The width of the aquarium from front to back. Height in mm (H): The overall depth of water that is in contact with the glass, but does not exceed its upper edge. Thickness in mm (t): The thickness of the Glass. Water Pressure (p): The force in Newton’s (N). Allowed Bending Stress (B): Tensile Strength / Safety Factor Modulus of Elasticity (E): Elastic Strength

The length to height ratio effects the strength of the glass. The table below lists alpha and beta constants to be used based on with the length to height ratio.

### Table of Alpha and Beta Constants used in the Calculations

 For Side Panels For Bottom Panels Ratio of L/H Alpha Beta Alpha Beta 0.5 0.003 0.085 0.666 0.0085 0.1156 1.0 0.022 0.16 0.077 0.453 1.5 0.042 0.26 0.0906 0.5172 2.0 0.056 0.32 0.1017 0.5688 2.5 0.063 0.35 0.111 0.6102 3.0 0.067 0.37 0.1335 0.7134

When the ratio is less than 0.5, use Alpha and Beta values for 0.5.
When the ration is greater than 3, use Alpha and Beta values for 3.
Note: For bottom panel, use Length to Width ration (L/W).

The water pressure (p) is directly proportional to the Height (H) x the force of gravity (approx 10 (9.81 for people who want to be exact)).

p = H x 10 in N/mm2

The bending stress allowed (B) is equal to the Tensile Strength of glass / safety factor.

B = 19.2 / 3.8 = 5.05N/mm2 (Safety factor = 3.8)

### Calculations for Front and Side Glass Panels:

The thickness of the glass (t) is proportional to the (square root of width factor (beta) x height (H) cubed x 0.00001 / allowable bending stress (B)).

so; t = SQR (beta x H3 x 0.00001 / 5.05) in mm.

Select beta and alpha from the previous chart based on the length to height ratio.
The deflection of the glass is proportional to

(alpha x water pressure (p) x 0.000001 x Height4)
(Modulus of elasticity (E) x Thickness (t) cubed).

Deflection =

(Alpha x p x 0.000001 x H4) / (69000 x t3) in mm.

Example: (Warren’s new tank)

Aquarium Length = 3000mm
Aquarium Height = 950mm
Safety Factor = 3.8 L/H >3 therefore Beta = 0.37 and Alpha = 0.067

p = 950 x 10 = 9500N/m2

Side Thickness:
t = SQR (0.37 x 9503 x 0.00001 / 5.05)

= 25.06mm

Deflection = (0.067 x 9500 x 0.000001 x 9504) / (69000 x 253)

= 0.48mm

### Calculations for Bottom Glass Panel:

There is a small difference when calculating the bottom panel thickness. Beta is now calculated from the Length/Width (where the length L is the larger dimension – therefore L/W is always >=1). The Height is still used to calculate the pressure. Be sure to use the Bottom Panel Alpha/Beta values.

The thickness of the bottom glass (t) is proportional to the square root of width factor (beta) x height (H) cubed x 105 / allowable bending stress (B), – the same as the side panels.

t = SQR (beta x H3 x 0.00001 / 5.05) in mm

Select beta and alpha from the previous chart based on the length to width ratio.

The deflection of the glass is proportional to (alpha x water pressure (p) x 10-6 x Height4) / (Modulus of elasticity (E) x Thickness (t)cubed).

Deflection = (Alpha x p x 0.000001 x H4) / (69000 x t3) in mm.

Example: (Warren’s new tank)

Aquarium Length = 3000mm
Aquarium Width = 900mm
Aquarium Height = 950mm

Safety Factor = 3.8 L/W >3 therefore Beta = 0.7134 and Alpha = 0.1335

p = 950 x 10 = 9500N/m2

Bottom Thickness:

t = (SQR (0.7134 x 9503 x 0.00001) / 5.05)

= 34.8mm

Deflection = (0.1335 x 9500 x 0.000001 x 9504) / (69000 x 34.833)

= 0.355mm