How do I calculate the structural properties of a fiberglass laminated wood panel?

I'm constructing 2.2 meters span, 1 m wide shelf. Want to make it cheap but thin. I'm planning to use 18mm thick OSB board and reinforce it with a layer of stronger material stuck to it's bottom.

My first idea for reinforcement is 2 strips of 60*4 mm steel. I'm not very familiar with the subject. I found OSB modulus of elasticity here , transformed width of the OSB board to it's steel equivalent, that gave me 38mm. Then I ran it through L-beam moment of inertia online calculator, and beam calculator assured me that the sag would be much less than my acceptable 1cm. (The load is under 100kg)

My second idea is to use glass fabric instead of steel. Glass itself is just 3 times less strong than steel, so that makes this option at least worth evaluating.

Hence comes the question: Where do I find properties of the layer I'll get when I put fiber glass and pour epoxy on it? The only thing that's stated for the "structural fiberglass fabric" available on the market is it's ultimate tensile strength.

I'm talking about the glass fabric, not the plastic sheet reinforced with it: • How familiar are you with composites in general, and with manufacturing laminated composites? You say "pour on" but that won't work. You have to completely wet the fibers with the epoxy to have a reasonable transmission of stress and low probability of failure. The fibers also need to be kept as clean as possible to avoid dirt interrupting the interface. Almost all of the properties of composites depend on the interface. Mar 22 '16 at 16:12
• What properties are you looking for? Stiffness? Strength? How much of each? Is there a limit on maximum deflection? Is there a known load? What are the structural supports? You said you compared the strength of glass to steel when considering it, but then when you found UTS for glass that wasn't what you needed. A mechanical diagram of your loading scenario and desired object design would be helpful. Mar 22 '16 at 16:15
• @starrise not familiar at all. I do know this technique is widely used in DIY boat construction, that's where I got the idea of it being doable from.
– Gleb
Mar 22 '16 at 16:17
• @starrise wikipedia quotes glass at 70GPa elasticity modulus. What I couldn't find is this property of the fabric made out of glass.
– Gleb
Mar 22 '16 at 16:20
• I don't know how its done in DIY boat construction, but I would assume at the very least you need clean paint brushes to paint the laminate onto the fiberglass, ensuring that the fibers are thoroughly wetted by applying gentle but firm pressure as you brush. You might try asking "how?" on DIY.SE. Don't just copy the entirety of this question, phrase the specifics of how to do the layup in a way that is sensible for that community. Mar 22 '16 at 16:20

To determine the properties of a composite laminate, the properties of each component and their relative volume fractions must be known.

The properties of glass fiber laminate may be determined using the rule of mixtures. Consider a cross-section of the fiberglass laminate as shown below. White regions are the fiberglass, black regions are the epoxy matrix. The white dots are transversely-sectioned fibers, and the white highly-eccentric ellipses are longitudinally-sectioned fibers. If we consider only the bottom portion of the image, so that all the fibers are aligned into and out of the image, then it appears that about 50% of the volume is occupied by fibers and 50% by matrix, which is a reasonable mix.

From the rule of mixtures:

$$E_c = E_f V_f + E_m V_m$$

where the subscript $c$ denotes composite bulk, $f$ denotes fiber, and $m$ denotes matrix, and $E$ is tensile modulus and $V$ is volume fraction. Then because the tensile modulus of the fibers are $E_f=70\ \textrm{GPa}$ and of the matrix is $E_m=2\ \textrm{GPa}$ (give or take a little), the composite modulus $E_c$ is

$$E_c = (70\ \textrm{GPa})(0.5)+(2\ \textrm{GPa})(0.5) \\ E_c = 35\ \textrm{GPa} + 1\ \textrm{GPa} \\ E_c = 36\ \textrm{GPa}$$

For strength, the situation is a bit more challenging, and depends on elastic compatibility. Since we know the stiffness of the composite, $\sigma_{f,UTS}=2\ \textrm{GPa}$ for E-glass fibers gives the strain at failure by the relationship $\sigma_{f,UTS}/E_f=\varepsilon_f=0.029$. Similarly for the matrix assuming $\sigma_{m,UTS}=0.085\ \textrm{GPa}$ gives $\varepsilon_m=0.043$. Since the strain at failure is lower for the fibers, they fail first, by compatibility. The strength of the composite is then the product of strain at failure and composite modulus, or about $1\ \textrm{GPa}$. This result also assumes the interface doesn't fail before either of the components, hence the need for cleanliness and full wetting of the fibers.

Deflection may be calculated by assuming the shelf is a beam, and using the worst-case, i.e. 100kg centered load and simply supported at the ends, and not supported at the wall. The equation for the deflection is

$$\delta_{center} = \frac{FL^3}{48\sum EI} \\ = \frac{\left(980\ \textrm{N}\right)\left(8\ \textrm{m}^3\right)}{48\left[\left(36\times 10^9\ \textrm{N}\cdot\textrm{m}^{-2}\right)\left(8.4\times 10^{-9}\ \textrm{m}^4\right)+\left(2.5\times 10^9\ \textrm{N}\cdot\textrm{m}^{-2}\right)\left(5.8\times 10^{-6}\ \textrm{m}^4\right)\right]} \\ = \frac{7840\ \textrm{N}\cdot\textrm{m}^3}{7.1\times 10^{5}\ \textrm{N}\cdot\textrm{m}^{2}} \\ = 0.011\ \textrm{m} \\ \approx 1\ \textrm{cm}$$

Which is your desired value, but with no safety factor. I've assumed for simplicity that the neutral axis is at the midplane, which is inaccurate. The actual location is the elasticity-weighted centroid of the laminate area. The neutral axis should be shifted away from the laminate to compensate for its increased stiffness. The effect on the area moment of inertia of the laminate should be to increase it and with its greater stiffness should result in a smaller deflection.

Image comes from aerospaceengineeringblog.com

Hi to the next person to read this,

The preceding appears to be all correct, however, it appears to be for a solid composite beam. If you are using a USB board as a core, you must rather do composite beam calculations.

I landed on this post because I wanted to refresh my memory to calculate composite beams for a snow yatch I am building (like an iceboat but on special skis I have laminated). The cross beam is 12 feet, laminated with 6oz unidirectional ( I presume 140GPA, thanks wwarniner!) and woven 6oz 45 degree twill for torsional rigidity and capping (this is more complex with poisson ratios and that stuff (?). Anyway, I have 400 lbs centre load, simply supported and I will pre-stress for extra stiffness (laminate tensile side flat, then compression side with twice the curvature desired. Loads up the core in compression and adds loads of Stiffness! I am looking to know roughly how many layers Of UD I will need.

The process is as follows:

1. You calculate the total moment of inertia for each rectangular area consdering the distance from the neutral axis that really pays off!!! That is why surface layers in a sandwich make it so light and stiff.

2. You then calculate the contribution of each area multiplied by it's stiffness (E) for the flex. Soft materials and layers near the neutral axis contribute insignificantly, as opposed to surface layers, particularly UD in my case. Note: A honeycomb or foam core as you can imagine contributes insignificantly, all the work is done by the extreme fibres. However, you must be concerned about core shear in this case)

3. You can do the same for strength using UFM or UTS (ultimate tensile strength)

Reminders: Rectangle I = b*h^3/12, Z = I/c. (C is distance to extreme fibre, that is h/2). Right? (This is all from memory, so pls chk 2 b sure)

That is what I remembered from the Gibbs and Cox composite design bible I used many years ago. Once you use it, you ré member the principles for life ;-)

BTW, if anyone would like the most delightful engineering read ever, I strongly recommend a book I read about the development of all this in war times, "The Science of Strong Materials" by a British engineer by the name of J.E.Gordon. Composite calculations came from plywood calculation for aircraft) Bloody good read if I do say so meeself ;-)

Cheers! Paul Isabelle, Industrial designer and tinkerer

• Welcome to engineering.SE! At first glance, this reads more like a blog post about a personal project than an answer to the specific question. Please note that StackExchange is a Q&A site, not a forum in the conventional sense. Jan 3 '20 at 19:36