laminate calculations

[haus]

Hi all !

Newbie here, but a long time lurker....

A little background: I am an engineer and I primarily work on vintage racecars....however, I have always had a fond love for boats. While working
on my degrees I completed several composite type courses. Lately I decided to play around with some boat calculations, but I have found some discrepancy's between the formulas that I am familiar with when I compare them to the limited amount of "boat design formulas" that I have found.

I recall calculating centroids, moment of inertia and section modulus back in school. At that time we used these formulas on structures/materials like beams, tubes, pilings...etc etc. Now I would like to apply these equations to a laminates, but it seems as thought some of the terminology is different.

From what i have found:

-The moment of inertia (2nd moment of inertia) = I=bd^3/12 for rect. cross sections.
-SM=Z=I/Y

Question: wouldn't you need the final dimensions of a laminate in order to solve for these parameters ? especially the neutral axis (centroid) ?

I would like to screw around with these equations just for fun...if anyone can give me an example of how they are used for simple laminate boat design I would be more than grateful !

Thanks-

[Guest625101138]

The basic principles apply but the formulas you have for homogenous sections are not applicable. In a foam laminate you have a soft core that separates the main stress carrying fabric. Usually these are so thin relative to overall thickness of the laminate that they can be assumed as "thin" sheets separated by the thickness of the core.

You get good results for a particular layup if you calculate the bending moment in the section being carried by opposing forces separated by the core thickness. These forces can be used to determine the stress in the fabric. Remember that standard twill weave cloth has 50% of strands in either direction so only half of the strands are load bearing if you are dealing with only one axis. So the calculation is really very simple if you work from first principles. Neglect any contribution from the resin/epoxy and the foam. These essentially hold the fabric in place. (This is an important role of course and you need good cores that can take the shear stress on the laminate.)

If you do this exercise for different fabrics you will see why carbon fibre is such a desirable material where you need stiffness. If you compare glass and carbon panels of the same weight they are literally cheese to chalk in terms of stiffness.

For a complete boat you have to consider the laminate from a number of perspectives. There is the gross strength to consider. Worst case load case may be the bow and stern each perched on a rock. The boat has to be able to carry these loads. With a beamy boat a quartering sea will set up a twist you need to be able to handle the resulting stress.

You then have to consider the slamming loads. The localised water pressure as the boat slams into a wave at speed or just drops off a wave.

Then there is the local point load of the boat rubbing against a fender or sitting on the rock. A problem with a cored laminate is the risk of delaminating if the fabric is prised from the foam at some point. It can just peel the fabric off the core from the exposed point. So the skins have to have enough strength to handle expected abuse.

There are standards that apply to the required strength and others more knowledgeable than I, can direct you. However working through standards is a painstaking task and better to get advice from someone doing it regularly than wasting a lot of effort working out what should be specified for any particular application.

Rick W

[marshmat]

Hi Haus,

It sounds like you're more interested in what's going on with the material and why, more than you're interested in figuring out how much of it is needed for a boat.

In boat design, it's fairly common to work with scantling rules or approximations to the actual forces, rather than deriving every last detail from scratch for each new shape. Scantling rules tend to give semi-empirical formulae, often with hefty safety factors built in, that have to apply over a broad range of cases.

To actually understand composites requires a different approach. As a suitably rigorous, but not excessively complex, introduction to composite sandwich panel design, see the attached publication from Hexcel (pub.# AGU075b). Although written with honeycomb cores in mind, the formulae work for foam cores as well if you adapt the core properties accordingly, and provide good insight into what is actually happening to the forces within the panel.