Fiberglass Calculations

Discussion in 'Materials' started by Fanie, Oct 2, 2014.

  1. Fanie
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    Fanie Fanie

    I made a few measurements regarding the strength of fiberglass, but I still need a bit of help please if someone can check this for me. I'm not sure if one can measure the actual strength of a profile this way.

    I measured the breaking strength of a single strand of 450g fiberglass. It pulled apart at over 17kg. This is a dry strand so a wetted out cured strand should be stronger.

    The spacing of the 450g strands are 3mm apart.

    If I make a beam with a 200/250mm dia,
    ....-------
    ./..............\
    |...............|
    .\............../
    ....--------
    then one layer around the beam would have 250 strands. If I make 15 such glass layers...
    15 layers x 17kg/strand x 250 strands = 63750kg
    Devide by pi to compensate for the round shape = 20290kg ?
    If the beam is 6m long then the beam ratio is 200mm/250mm dia to 6000mm long
    This equates to 20290kg x 250 / 6000 = 845kg in the 250mm direction,
    And 20290kg x 200 / 6000 = 676kg in the 200mm direction

    Assuming there is no point loading or deforming of the profile.

    Can this be right ?
    Thanks for checking...
     
  2. rxcomposite
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    rxcomposite Senior Member

    Fanie, what you are doing is similar to filament winding but there are several ways you are doing it wrong.

    First, strength is a unit of measure and is thus measured as force/area such as PSI or N/mm2. True that some fiberglass manufacturer do publish "breaking strength" in force but it is always accompanied by the width of the speciment tested and the "dry" thickness of the fiber (glass in this case). This has no practical use at the moment as laminating it with a resin will alter its mechanical property.

    A roving (a collection of fiber strands) is usually assigned a cross sectional area, say E glass type 30, CSA 0.289 mm2 (44.73 x 10-5 in2). So if you take a several rovings and bundle it, you then have to multiply the CSA by the number of rovings.

    To be practical and reduce errors, take several rovings and bundle it, then wet it with resin. At this stage, it will be soft and easy to form. Sandwich it between two mylar sheet and apply a low even pressure so that you get a relatively flat and uniform thickness. Aim for a 12' long x 1"+ wide laminate. After curing, the edges would be tapered or not consistent. Sand it down so you get a nice edge. Do not sand the face. What you will get is a nice rectangular cross section.

    One inch might be too strong for you to test. What you can do is Dog Bone the shape, that is sand the middle edge until it is down to 1/2" or 1/4" wide. Keep the ends wide at around 1". Now measure the smallest part (the waist) with a caliper. Note the width and thickness.

    Clamp the top edge to a secure beam and glue a reinforcing plate on the other end with a hook to suspend some iron weights. I find barbell plates work well with me.

    Keep adding weights untill you see the laminate crack. This is the yield strength (weight/cross sectional area). You might need a magnifying glass for this if your eye is no longer that sharp.

    Continue adding weights until the laminate breaks. Note the total weight used and again compute weight/CSA.

    Published Ultimate Strength for E glass uni tested in this longitudinal method is 1020 Mpa (150 x 1000 lbs/in2). Note that yield point is more important. A fractured laminate is of no use to us.
     

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    Last edited: Oct 2, 2014
  3. groper
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    groper Senior Member

    If your looking to engineer a Composite beam or tube fanie, the section modulus formula is typically used. So first you need to calculate the section modulus or 2nd moment of area for your proposed section. Eliptical sections should have an equation you can use to find it. Once you know that, you have to select the correct loading equation in which to use it. If it were an unstayed mast for example , you need to use the cantilever type load case equation. Use the material properties published in earlier thread for the elastic modulus of eglass.

    Once you find the ultimate stress = ultimate strength of the material, then the beam breaks. So you apply safety factors by dividing the ultimate number by at least 2 or often upto 3 or more, which then puts you under the fracture limits for composite as per rx composite comments.

    These equations can be found here http://www.engineersedge.com/beam_calc_menu.shtml
    There's also online calculators and some download able applications which can also help or at least speed up the process so you don't have to longhand the math every time. But you need an understanding before using them so you don't lead yourself up the garden path by accident. ..
     
  4. Fanie
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    Fanie Fanie

    Thanks Rx and Groper.

    Groper, the calculator(s) means absolutely nothing because I don't know what I'm calculating, for instance this one here -
    http://www.engineersedge.com/beam_bending/calculators_protected/beam_deflection_2.htm
    I looked up the modulus of elasticity of e-glass... seems you have to calculate it, I found someone's calculation being 6 480 000 psi ? One would think this should be a standard for e-glass ?

    Moment of Inertia... has what to do with something not moving ? LOL even the bent beam in the picture is not moving. Explain to me what this means please.

    I assume the load is the pressure or force on the beam, distance is how far from one end and the length of the beam. This is fine.

    Then the results shows stresses, no idea what it is showing there and no units ?

    It also shows some deflection values, again what does it mean ?

    Then it have a section modulus value. Again it doesn't say anything.

    Nice calculator, but what am I calculating there ? (LOL, math... ?)

    There's nothing that tells the calculator how many strands/layers, or what profile, or the diameter, how is this of any use ?

    I am up the garden path smelling the roses...

    Klaas Vakie het nou sand in my oe gegooi. Hoyte can translate for you ;)
     
  5. PAR
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    PAR Yacht Designer/Builder

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  6. rxcomposite
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    rxcomposite Senior Member

    Filament winding and mast/spar design is one of the most difficult thing to do. Let us start with the basics so you can get a handle on it.

    Determining the number of bundles required for a given profile (area). Let us call one strand or tow as spool to be consistent with the book. The (arbitrary) width of the bundle is called bandwidth, the thickness is equivalent to one ply. To find the number of spools needed, the formula is;

    N.S. (number of Spools)=(Thickness of ply x bandwidth) / Cross Sectional area

    Again, to be consistent with the books explanation, we use Imperial system and known values provided in the data sheet.

    The cross sectional area of a T40-12k graphite roving is 3.8 x 10-4 in2. When wetted with resin and wound on a mandrel at the specified tension, the resulting thickness (when flattened) would be 0.0058". This is a very tight wound, resulting in a fiber volume fraction of 0.65. Don't worry, as volume fraction of 0.55 is only 0.0061".

    Sample computation would be; (for a desired band width of 0.25")

    N.S.= (0.0058 x 0.25)/3.8 x 10-4
    = 3.8 spools (round off to 4)

    Thus you need 4 strands of roving to produce a cross sectional area of 0.0058" thick x 0.25" wide.

    If you don't know the CSA of the strand/tow you are using, collect a bundle of 20 or more and tightly wound a strip of paper around the middle. Measure the diameter and compute the cross sectional area (deduct 2x the thickness of paper from the diameter). Use Pi/4 x diameter. Just divide the computed area by the number of strands to get the CSA of the individual strand. Not very accurate but a practical way of doing it.
     
  7. rxcomposite
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    rxcomposite Senior Member

    Modulus of Elasticity or Young's modulus is the tendency of an object to deform along an axis when opposing forces are applied along that axis. This is simply called elastic modulus. In order for the computation to be accurate, the modulus is measured along the linear portion of the graph. It can be computed or a straight line drawn along the straightest portion of the graph.

    As you can see from the illustration, the graph is not linear. It starts as a straight line first then fall of after being elastically linear. Where it falls off or where it yields is of no concern to us as that is the point where it fractures.
    This elastic modulus varies for every type of fiber and resins or any combination thereof. It also varies if the oppposing force is shifted along the axis. I will explain that later in another post.

    Note that the vertical numbers are measured in pounds and in small letters, the width and thickness of the specimen is indicated. To convert, it is Force/Area or lbs./in2.

    Sorry for mixing up the units of systems in my explanations. I just want to be consistent with the illustrations provided.
     

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  8. rxcomposite
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    rxcomposite Senior Member

    Varying the modulus of a laminate

    The modulus of a laminate is given/published with a set of constraint. That is given the type of fiber weave, fiber volume content, type of resin, and orientation of the load test. Varying any of the property will alter the predicted modulus.

    For example, increasing the fiber content will increase the modulus (makes it stiffer), reducing the modulus of the resin will make the laminate more stretchable. The combination of the stiffness of the fiber and the resin is dependent on each other. See illustration.

    Another factor which greatly influence the modulus is the type of weave and the angle of force applied. Unidirectional fibers are very strong/stiff when oriented along the axis (or along the length of the mast), but lay it up at an angle, say 45 degree, and you lose about 90% of the strength/stiffness.

    Make a test, pull a bundle of fibers along the ends and you will see it is very strong. Pull it along the sides and it just splits into individual strands. Carbon and Kevlar fibers are notorious for losing the strength at off axis loads.

    WR is more forgiving. Pull it at the ends and it will be half as strong as the uni because half of the fiber orientation is lying at standby. Pull it along the sides and half of the fibers oriented across the weave takes the stress. Pull it at 45 degree and the weave closes in but still give you enought strength because of the mutual influence of the fibers tugging at each other. This mutual influence is increased if a resin is added to the fibers.

    The modulus can be predicted by using what is known as Engineering Constant (see illustration 2). This is a factor that reduces the strength/modulus of the laminate when the fiber orientation is laid up at an angle along the axis. LR and BV have published these formula.

    Thus when laying up a mast, all the longitutudinal fibers will have the strength/modulus as predicted and all fibers laid up off axis will have a corresponding reduction in materail properties. The WR laid up at 45 degree finishes the lay up in order to have a more consistent tortional characteristics aided by the mutual influence.

    This need to be tabulated.
     

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  9. groper
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    groper Senior Member

    If you need definitions, then Wikipedia the stuff you not familiar with... all of the explanations are there. The section modulus will change when you change the beams dimensions ... So if you design a rectangular beam, 200x250mm with a wall thickness of 4mm, then you plug it into the equation or use the online calculator, and it will give you a number. Usually 2 numbers actually, one is about the x axis Ix, and one is about the y axis, Iy.The greater number will be about the beams dimension which is larger and of course results in stiffer performance when loaded in that axis. Think of a floor joist... You use them stood on edge so they are stiff and you don't end up with a springy floor. If you lay them flat, you would have a weak and flexible floor. This reflects the vastly different moment of inertia about the 2 different axis you can load the same physical dimensioned floor joist...

    You can then use this number in the beam bending equations which will can then tell you how much flex it will have, how strong it will be, what deflection will result from a specific load, etc etc... If the beam doesn't meet your design goals, then you can either change its dimensions (section modulus) or change the material the beam is made from -which changes the E (elastic modulus) in the beam bending equations.

    I approach things a little differently compared to rx, I simply divide the total wall thickness of the beam, by the ply thickness, to give me the number of layers I need for that particular fabric. This if course varies depending on your process, a vacuum bagged layup will be thinner for the same tex weight compared to a hand layup etc. This is compensated for by adjusting the elastic modulus and strength numbers based on the fiber volume fraction. I gave you a chart showing typical numbers for eglass uni and wovens in your other thread, it also gave the typical ply thickness for it @ quoted fiber volume fraction. Use these numbers in your equations for modulus of elasticity.

    When using the equations, keep all the units compatible. As we are metric here, everything is in ISO standard units, ie, meters, seconds, newtons, pascals, etc. you can't mix up the units and use imperial units such as psi , lbs, inches etc with metric units in the same equation of it will be completely wrong. Rx composite is obviously heavily influenced by American methods being in the Philippines, that's fine so long as everything is imperial and thus compatible.

    You also have to pay attention to the scientific notation. If the units are meters, then you will have to apply scientific notation to get the units down to mm for certain things, such as a wall thickness for example. So a mm is x10^-3 meters for example. Same goes for pascals... The elastic modulus is in giga pascals, so you need to apply x10^9 to anything given in Gpa as another example.
     
  10. rxcomposite
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    rxcomposite Senior Member

    Groper. That is true the Americans have greatly influenced us on the Imperial system but It has been a long time that Philippines has since changed to metric. As I emphasized, I am using the Imperial system as illustrated in the book. Most of my books are written in the Imperial system because that is where I sourced it out. From the U.S.

    That is why I have to explain it exactly how it was written. Sorry for the confusion. I do think in the Imperial system, it is second nature to me but when I do calculations, it is strictly Metric or SI.
     
  11. Fanie
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    Fanie Fanie

    Thanks Par and again RX !

    I must say the non metric terms are confusing and make it difficult. I have to convert everything to get a grasp of it's size. The guy who came up with these imperial measures must have had one hell of a sense of humor. He also belongs in a nuthouse :D

    How much of a difference does it make ?

    I can go on the internet and there are quite a few calculators that can calculate the forces in round tubing and square tubing for steel etc, but nothing on fiberglass. I understand the direction these shapes could be layered up in, but there could be ratio's for orientation.


    Please RX, if you can find the time and the patience, do continue please.
     
  12. Fanie
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    Fanie Fanie

    There is of course another way to do a beam like this.

    You make it and test it. You invite all your fat friends, give each 50 bricks to hold and they line up on the beam side by side for a beer. You can then measure with a vernier how much the beam bends.

    If it's less than what you expected then you glass over that. From the load you should be able to form an idea of how much more is needed. Since the outer layer encapsulates the inner there's no chance of it going anywhere. You can even add a sandwich layer.

    After that you can simply use the right amount of glass off the bat.
     
  13. rxcomposite
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    rxcomposite Senior Member

    I will draw some methods for you but I will limit myself to composite methodology. My training is on wing spar and wing design as applied to aircraft. Similar, close enough, and some practices are shared in marine and aerospace.

    Eric Sponberg here is the mast design guru and have posted a lot of information on mast design. I see that you are having a hard time with the non metric system. Be prepared to get a nosebleed though as he is an American and all his values are quoted in the English system.
     
  14. Fanie
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    Fanie Fanie

    I e-mailed Eric but he may be busy, he's probably tired of all the noobs pestering him for help.

    Since your field of expertise is wings, why do these racing cats have bent dagger boards... and I see the dagger boards are very thin.
     

  15. SukiSolo
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    SukiSolo Senior Member

    There are a few free tools on the web which allow simple beam loading calculations. Such as for tubes, round and rectangular where you can enter some of the material properties Gpa, e, and then 'load' it appropriately. The tools can give the deflection expected, for example a box section 200X200mm with 4mm wall section suporting 500Kg at 3 meters from one end.

    So you need to find the data of the material and the forces you will be applying, or will be applied (by sea/wind etc) to get a meaningful result. TBH I find the SI system a lot easier than Imperial but you get used to the conversions on some of the data. Important thing is that the input data is good quality from trusted sources ie materials that have been properly tested.

    Yes, you may have to make a test sample and load it if you have a unique layup. rxcomposite has kindly shown you one way to do this, which is most gratifying to see - real test engineering. When you start pushing at the edges not all is fully known, it must be learned. Just like the mathematical models have to be verified by physical test data (and developed), before you can use the maths to predict pretty accurately what will happen with different cases.

    The beam loading, column, truss stuff has been used for a very long time and developed for all kinds of materials. Concrete, timber, metals etc so this is part of the basis of testing newer materials. As it happens,carbon composites have been around certainly from the 1960s' but there are lots of small develoments in their characteristics which have made changes to the physical performance of such fibres.
     
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