Glass Thickness Calculators

Discussion in 'Do It Yourself (DIY)' started by Grassman, Sep 3, 2009.

  1. Grassman

    Grassman Learning on the fly!

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    Here's a few ways to figure out how thick of glass you need if you building your own tanks.

    1.In the table below, the top row indicates the length of the tank, the left vertical column indicates the depth (height) of the tank. To determine the glass thickness to use for constructing your tank, find the length of the tank in the top row (indicated in feet and cm - centimeters), then follow that column down until you reach the height of the tank (indicated in inches and cm). Glass thickness is indicated in mm (millimeters), with the number in parenthesis below indicating the Safety Factor. There is an inches to millimeters calculator below the Glass Thickness Calculator.


    [​IMG]

    2. Glass Thickness Calculator

    By Warren Stilwell 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°CCoefficient of linear expansion:86 x 10-7m/°CSoftening Point:730°CModulus of Elasticity:69GPa (69 x 109 Pa)Poisson's ratio:Float Glass 0.22 to 0.23Compressive Strength:25mm Cube: 248MPa (248 x 106 Pa)Tensile Strength:19.3 to 28.4MPa for sustained loadingTensile 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 FactorModulus 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 PanelsFor Bottom PanelsRatio of L/H

    AlphaBetaAlphaBeta0.50.0030.0850.6660.00850.11561.00.0220.160.0770.4531.50.0420.260.09060.51722.00.0560.320.10170.56882.50.0630.350.1110.61023.00.0670.370.13350.7134

    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 0.9503 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

    3. Use the attachment if you have Excel or OpenOffice to open it. It's the easiest.
    :bowdown:

    Attached Files:

    Grassman, Sep 3, 2009
    #1
    project5k likes this.
  2. Grassman

    yote Ceritfied Mantis Hunter Moderator

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    That'll come in handy Grassman.For those that might want to build their own tank and for those that need to replace a panel because the drilling went wrong.
    yote, Sep 3, 2009
    #2
  3. Grassman

    Grassman Learning on the fly!

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    Thanks Yote. I did was doing it the long way at work since friends of mine where coming tot he shop to buy glass so they could build there own. Then Warren put the xls file up. Makes it a lot faster, but it can kinda be confusing. I suggest reading the long version before using the file, makes it easier to understand what it's asking for....or I may just have been looking into something hard that was really easy. :frustrat:
    Grassman, Sep 3, 2009
    #3
  4. Grassman

    dcantucson

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    Thanks Grassman.
    dcantucson, Sep 3, 2009
    #4
  5. Grassman

    project5k

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    oh, now thats some #'s i can sink my teeth(and graphing calculator) into!
    project5k, Sep 3, 2009
    #5
  6. Grassman

    Grassman Learning on the fly!

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    Tillsonburg, Ont. Canada
    Sorry, I didn't notice the alpha and beta charts didn't come threw correct so I'll post the again here.

    ~~~~~~~~~~~~~~~~~~Sides~~~~~~~~~~~~~~ Bottom
    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

    Also I attached a more refined version of Warren's Calculator. You can enter sizes in inches and it will give you the sizes in both millimeters and inches since not everyone uses the retarted metric system.:mrgreen:

    Attached Files:

    Last edited: Sep 9, 2009
    Grassman, Sep 9, 2009
    #6
  7. Grassman

    jahel318

    Joined:
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    Montana
    I'm building a 6 .5 gallon glass sump for my small cabinet. Is it true that I need some type of rim on the top and bottom for structural support? Or am I OK going rimless?
    jahel318, Feb 2, 2013
    #7

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