# the neutral axis

The concept has been mentioned in a few threads, so I figured I’d give it a permanent home. A good summary of the neutral axis can be found here (http://www.answers.com/topic/bending-3?hl=neutral&hl=axis).

“The internal forces and the cross-sectional stress distribution in a beam in bending.”

I’m not an engineer, so please correct me if I’m wrong, but that diagram and the line “These last two forces [the compression of the upper and tension along the lower] form a couple or moment as they are equal in magnitude and opposite in direction” implies to me that the general location of the naxis is relatively simple to control. Make the top skin stronger (or weaken the bottom) and you’ll move the naxis downward. Conversely, strengthen the bottom skin (or weaken the deck) and you’ll move the naxis upward.

With perimiter stringers limiting the amount of torsional flex, how much can the naxis move from side to side?

Is it better to have the naxis near to the deck (as close to the rider’s feet as possible), or closer to the bottom? The first would seem preferable to me, but the current trend towards making the bottom skin as flexible as possible would seem to do the opposite (if my theory in the paragraph above is in fact correct).

I was thinking about this some more today… what would happen if you were to actually slice your blank in half (hotwire a cut parallel to the rocker at whatever proportional distance between the skins is desired – kind of like the buns on a burger)? Seems like you’d still have all the advantages that a lightweight foam core offers while also effectively achieving a core capable of unlimited shear (? there would still be friction between the two surfaces, but would it be enough to cause anything?).

Losos,

Here’s a thought - a core material that allows shear movement but quickly returns to it’s resting state would promote the flex return of the skins. I’m not sure to what degree EPS resists shear - it might be that slicing along the neutral axis actually diminishes flex return if the effect described above is ocurring with compsand.

Is it really the core that is promoting the flex return, or is it the skins? One lb EPS is flimsy as hell until you get some kind of skin on it, so I can’t imagine it produces much flex return force.

Uhmm- this is kind of a complex problem. You may not really want to think about the board as a homogeneous beam as much as a box girder, where it’ll flex and such but beyond a certain point you’ll get buckling and failure.

For instance, lets look at a surfboard under compression from the deck, or the equivalent bottom tension caused by a hard turn;

Now, the length of curved deck down to the rails is all in compression. But it’s not gonna deform unless it kinda fails, buckles, and then it won’t return, it’s permanently deformed. So, what can deform and return in this structure?

Well, the bottom is a curved plate, or we can treat it as such. It can bend and even deform in more than one direction. While it’s restrained near the rails, you have a material ( glass cloth plus resin) that is pretty strong in tension, so it’s gonna want to retain the same length overall. How will it do that? Perhaps by compressing the foam under it, as shown above. Kinda like cinching your belt up real tight, you compress what’s underneath it.

Especially as the line from end of nose to end of tail is both longer and under greater tension. It should deform more, as shown. That’d take some slight wracking of the lamination itself, but probably not beyond what the laminate can survive. As it rebounds as tension is released, it’d return to its original shape.

Now, how to optomise the structure for rebound? That gets kinda interesting, as is this topic…

doc

Interesting points doc. So say you flip the board over and jump on it as bert has been known to do. In that case the bottom is now in compression and the deck is in tension – the board flexes a good couple inches – those inches are all attributable to the core being compressed rather than the skins actually being shortened or elongated? Is the change in thickness readily measureable or is it a case where a little goes a long way?

Going with that theory you can see where the vertical center stringer is a hindrance as it pretty much prevents the compression of the core.

Looking at the middle figure… is it safe to say that the rail line defines the location of the neutral axis? The neutral axis is no more than the location where the force on the core transitions from compression to tension (or vice versa), and that seems to be what the diagram is showing along the rail line.

Or are there multiple neutral axes? One for the skin (at the rail line) and a separate one for the core?

(Sorry if this is elementary mechanics – I’ve never studied it before so I’m none the wiser. I’m trying to borrow my ME buddy’s materials and dynamics books but I haven’t got my hands on them yet)

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Interesting points doc. So say you flip the board over and jump on it as bert has been known to do. In that case the bottom is now in compression and the deck is in tension – the board flexes a good couple inches – those inches are all attributable to the core being compressed rather than the skins actually being shortened or elongated? Is the change in thickness readily measureable or is it a case where a little goes a long way?

Ahmm… let me start off with something of a cop-out. I don’t know as much about Bert’s construction methods as perhaps I should, so any answer/analysis is likely to be wrong and his analysis will be far better. Besides which, his boards, as I understand them , are a special case, with multiple foams and laminations acting in a way that’s very different indeed from standard single-foam boards.

Having said that, let me hazard a guess: the denser foam layer he has on there along with the glass/resin, that too acts like a panel or plate, so that it’ll flex side-side not terribly unlike the sketch I threw in, and add to that a much less dense foam than is commonly used which will accept compression even easier. Also, considering that the board is upside down, if the deck won’t deform end-end, perhaps it will bulge up in the middle before rebounding?

Unfortunately, this is something that’d require high-speed photography or something to figure out correctly. I would suspect that if you think about these as circumferences, maybe of segments of a very large circles, well, a little does go quite a way.

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Going with that theory you can see where the vertical center stringer is a hindrance as it pretty much prevents the compression of the core.

Yep, and it’s going to act independantly of foam, such that it can trigger glass failure.

[=1]

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[ 3]Looking at the middle figure… is it safe to say that the rail line defines the location of the neutral axis? The neutral axis is no more than the location where the force on the core transitions from compression to tension (or vice versa), and that seems to be what the diagram is showing along the rail line.

Or are there multiple neutral axes? One for the skin (at the rail line) and a separate one for the core?

[/]

Good question. My call would initially be that the widest point of the board is gonna define where it’d stop compressing and start being in tension. But at the centerline? Dunno…

Now, something to think about is this: the neutral axis might be more of a ‘neutral surface’, a kind of curvilinear surface inside the board about which the forces balance. Again, this isn’t a homogeneous beam, it’s a composite of two very different materials such that finding where the actual movements about a neutral point balance out is a complex problem.

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(Sorry if this is elementary mechanics – I’ve never studied it before so I’m none the wiser. I’m trying to borrow my ME buddy’s materials and dynamics books but I haven’t got my hands on them yet)

Reverting to the vernacular of my youth… oh, wow, man, this is a long way from simple mechanics.

This is more like vector analysis of a curvilinear composite structure under stress… for instance modelling this on a computer in a meaningful way would be a bear: something on the same order as modelling waterflow around a boat, say an America’s Cup hull under sail, and they used Crays for that. To the best of my knowledge the way they analyse this sort of thing is to test it and measure what happens, frequently testing to destruction and seeing how it breaks.

I will say this, though - if you’re not an engineer, maybe you should be. Contrary to popular opinion, engineering at the highest level is an art, where intuition and craft combine to make the numbers dance. I have a feeling you’d enjoy it.

doc…[/]

Some comments from an engineer (bambam808 will hoot, if he’s still here)…

For any stressed cross section (we’re two dimensional for the moment) there’s only one neutral axis. It won’t move unless there are significant deformations in the cross section. In the case of surfboards, this isn’t gonna happen.

The neutral plane (3-d now) of a stessed surfboard won’t be parallel to the bottom, because of the somewhat complex nature of the cross section. Assuming a flat(tish) bottom and domed deck, the neutral plane will be something between them, more resembling the domed deck but flatter. It will be farther from the bottom at the stringer line, and closer to the bottom near the rails. The neutral axis is the locus of points above and below which the stress is equal.

A simple case, and usually presented to engineering students, is to bend a deck of cards. Nice rectangular cross section, you can see the effect shear between adjacent cards. This is the shear that the innards of a surfboard (and the skin) will resist when you flex it.

Another simple and useful mental action is the “principle of linear superposition”. That is, the net result is the linear sum of the parts. For example, the bending strength of a hollow beam (surfboard?) is the sum of the total strength of an identical but non-hollow beam, minus the strength of the hollow part if the hollow part were actually a solid of the same material. Other practical considerations will intrude, but until buckling (significan deformation of the structure, which changes the geometry), the principal is useful.

Yer doc, this is an interesting thread for sure.

I’m feeling stoked, because i’m studying engineering at the moment, and i’ve been chained to the desk reading all about materials science for the last few weeks for upcoming exams. It’s exciting to have a link between surfing and engineering to talk about, well more exciting than other engineering babble.

I’ve got some points, facts and figures to add from my books that can help out. What i say may not be right, but hopefully the examiners dont know that

Losos -

the board flexes a good couple inches – those inches are all attributable to the core being compressed rather than the skins actually being shortened or elongated?

Flex is very complex is composites.

Percentage elongation (%EL) is probably a good thing to start with when talking about flex. Basically its about how much the material stretches before it fractures. The elongation (and also the force sustained) is greater along the longitidinal direction (length wise) compared to the transverse (width wise) direction.

The %EL for a composite of E-GLASS AND EPOXY is around 2 - 3 % (longitudinal) . and the %EL for the same composite is 0.4% (transverse)

So lets say we had a 6ft epoxy and e-glass board, this is about 1800 mm board lengthwise and 20" wide so 508mm wide. The one thing that is very difficult is assume how the load is applied. There is the loading from the board on the wave face (millions of combinations) and the point impact loading of the riders feet etc. Stretch or elongation of the board would be a combination of transverse and longitudinal depending on the forces.

Anyways, we can just imagine some constant uniform force along the entire board, but the board will stretch in both directions.

So with 2-3% elongation longitudinally, this relates to the length changing from 1800 to 1845. Thats 45mm increase lengthwise.

And with 0.4% elongation transversly, this gives a change from 508mm to 510mm. Only a change of 2mm

So from this you can see that the flex will come from extending the board lengthwise, but this will create a compressive force on the core inside. Using the belt as an example again, if you fold the belt in half, and start pulling at either end (extending the belt lengthwise) then the two halves pull together and meet in the middle, place someones arm in there and pull, and they will feel a compressive force. Its interesting to note, that this compressive force they feel will be significantly less than the force you are pulling the belt with.

The fatter the arm, the more compressive force they will feel, but if you change it to just having a few fingers in there, the height of arm(fingers) is really small, and so most of the tensile forces stretching the belt, or surfboard, stay in tension, as they are acting in a pretty straight line.

I guess its easier explained in a diagram.

The green arrows will be providing more force as compared to the yellow arrows with the red arrows being the tension forces.

So the thicker the board, the more the core will be compressed, but the core compression occurs due to stretch of the skin, so they are related in the fact that the stiffer or stronger the core, the less compression, and consequently the less stretch or elongation of the board.

So if the core could collapse (compress 100%) then all the flex would be taken by the skins… so i would say that the thickness, and compressive ability (or hardness) of the core is a big factor.

Its hard in topics like these because the real scenarios are so so much more complex, but hopefully the babble i put out there can be made sense of and some usefull ideas made.

Happy brain strainining

L

Ah - I love it when we do engineering…miss my pocket full of mechanical pencils with different colored leads and now I have to fake it with Windows Paint, alas…

Charlie, I think we’re describing the same thing, I called it a surface rather than a plane 'cos a plate deformed in 3D kinda messes with how I think of planes. Though it should be a smooth surface, give or take anomalies like odd bits in the foam or stringers. Something like the upper part of the truly awful sketch below.

I miss my blackboard…

Lavz. I agree, and I didn’t think the previous example through completely. Thinking that maybe there’s some elongation without permanent damage, but what may be more involved would be that glass squashing the foam and the whole structure changing shape temporarily.

Given a material that’s pretty good in tension and an easily compressible substrate, I start to think of what degrees of freedom the structure has: how the beastie can distort. In boats we think of the same things, especially ply, steel or aluminum which likes to bend in one direction only, like any plate or the deck of cards Charlie mentioned. The curved upper surface can’t distort without buckling, considered longitudinally, but it can bend to increase the curve, and a little bit of upward pressure could push that a bit further ( pardon the pun) . More so if it’s constrained, at least partly, along the edges.

Now, if the curved plate that is the bottom distorts upwards there’s a little pressure, plus it’ll ( good tensile strength ) suck in the sides a bit - the above exaggerated sketch- and tend to increase the deck curve/camber. If anything, that’d tend to increase stiffness along the centerline of the deck distortion, but the overall structure would bend. And even a little, easy-rebound compression of the foam would bring the structure back, fast.

Okay, thinking about the multi-foam structures in Bert’s boards and how those would work with this… shear action between foam layers?

Damn…I missed this ‘engineering babble’. And lavz, I think there’s a thesis in this if you want it…

doc…

hey gents,

while im not at all interested in NA discussion as it pertains to board mechanics, i will touch on mat’l mechs in general…

Lavz, i really dig your post there’s some dandy nuggets in there wrt making stiff construction flex, but there is one fatal flaw…everything above the NA is in compression…your analysis would work to explain whats happening below the NA but not the entire structure…but like a said, good insight regardless…

just to clarify…i think it has been said, but the NA is usually midway between the top and bottom assuming the shear stress distribution is symmetrical…to understand the NA you need to know that 1) it is simply a neutral plane where there is NO shear stress and 2) it is also a transition point between tensile and compressive stresses…it is purely a shear stress analysis…there are NA in torqued/twisted cylindrical shafts as well…many more examples

it will move up and down accordingly based on the shear stress distribution…in a non symm sitch, the NA will move further away from the plane with the most strain or shear movement, say the bottom elongates more than the top compresses, the NA will move further away from the bottom…there are some shear stress complexities wrt to this last statement…shear movement and shear force are different things…a rubber band can have large shear movement but requires less force to make the movement…so again it can get complicated

Lavz, you hit some nice highlights…thats why i dont use balsa on my bottoms…good luck with your studies

Doc, nice drawings

Losos, if you really want to learn something useful, redirect your focus further away from the NA…

post edit: had to change my over use of “force” with the proper use of “stress”

Hey meecrafty,

Your right, i totally forgot the one half in compression, but thanks for the encouragement.

Those are nice drawings doc, but i think mine are far better… haha the magic one can create with windows paint… i even had multicoloured arrows!

I looked through a few textbooks to procrastinate even more from studies, but meecrafty has pretty much covered the rest of the points i can find

usefull in the textbook.

A little web googling and i found a really good site in relation to composites, stresses, cores etc… This guy is a kayak builder but the principles are the same.

Check this website out:

http://www.oneoceankayaks.com/Sandcore.htm

Loving the engineering babble, we should do it again some time

Cheers!

L

Be good, or be good at it.

now get back to your studies lavz .

and the rest of you , for your sakes , go SURFING !!!

…[my interpretation of doc’s comment ]:-

" Losos, if you really want to learn something useful, redirect your focus further away from the NA… "

get your hand off it , and go and catch some waves…

Lavz

I’ve found all the imput above very interesting. Correct my if I’m wrong, but most composite engineering theory I’ve been able to find on the net, seems to deal with single sandwich panals. With sandwich construction in surfboards (and sailboards) you’ve got a sandwich where two of the skins are sandwichs in themselves. So you’ve got three cores. Add peritmeter stringers into the mix and you’ve got a complex set of problems - I’m interested to see what insights the engineers here on Sways might have on this type of construction.

I think i get what your saying. I made another paint masterpiece!! To try and help out … basic cross section…

“…the two skins are sandwichs in themselves. So you’ve got three cores…”

There is obviously the foam core, and its the main core. It has definate body and is enclosed by thinner layers of different materials. I don’t think you can consider the skins as sandwiches, if your meaning that fibreglass is the core for the resin skins. The reasons being

a.) the fibreglass has no relative body, meaning that its thickness is much much less than the “skins” of resin around it, so it wouldn’t really have properties like compression amounts etc, well it does… but they are so small its hardly worth it.

b.) Secondly the purpose of the fibreglass is to provide reinforcement and increase tensile properties of the resin. Cores act to provide I-beam cross sections for strength.

I’ve found a definition in my books for sandwhich panels…

“…Sandwich panels, considered to be a class of structural composites, consist of two stronger outer sheets, or faces, seperated by a layer of less-dense material, or core, which has lower stiffness and lower strength.”

So by that definition, the fibreglass doesn’t fit in as a “core” material. Core is basically a filler, which fibreglass is not…

Forget adding stringers… the problem is complex enough!

One thing that hasn’t been addressed… are the CONTACT SURFACES between each layer. At each contact surface, say resin/core surface, the stresses in the two materials are different because their elastic moduli (how much they stretch) is different, something to think about…

so not only does the stress vary with position in relation to a GENERAL N.Axis there will be variations between contact surfaces, and each layer of material will have different stresses…

Very complex… and you have to remember that its this complex and we’ve hardly talked about torsion, non-uniform loadings etc etc etc, so dont get drawn into the simplification of nice lines of stress and its all nice and even over the board…

Thanks for helping me to procrastinate, i’m loving it

L

dam …

and i cant not at least acknowledge it and say i will be back …

the neutral axis will move depending on where the load is applied …

some loads we want to feel and enhance , other loads we want to ignore and minimise , both of which come from the wave …

then we have the load from the rider , we have the most control when the riders load always keeps the neutral axis directly under the center of gravity , so regardless of our exact foot posistion , a neutral axis that has a large range of movement , has a better chance of being in the right spot when we arent …

it means bending and flexing always extend out around us , keeping us feeling like we have more control …

a stringer creates multiple neutral axis’s within a board , that are not as free to move with us …

i really have to go …

leave you with those thoughts …

regards

BERT

Lavz,

If it were only that simple. I’m not talking about a traditional glassed blank. I’m talking about a similar construction method to sailboards. Diagram below shows a sectional view.

Hey lavz,

I never have forgotten about the shear/interface layer. That layer can effectively magnify the amouont of force a structure can handle.

When dealing with tension, in non-composite structures, the overwhelming majority of load failure is at or near the surface (non-surfboard tech again here, sorry). Finding a way to move a percentage of that tension load below the surface means that the surface can still handle the same amount of force as before. But the sub-surface layer can also handle that additional load. And that also serves to spread the tension between the two layers further reducing the load on the tensioned surface. Of course, this only holds up so far. But the potential benefit is huge (and the practical benefit has been proven in non surfboard tech).

What about compression? Well, I am not sure No, not a cop-out. Just honesty. I think the rules are a little different there. My understanding is that there’s two effects in place. First, how much load the compression structure can handle (pretty substantial with timber, compared to it’s tension strength). The second is how thick the compression structure is (and with timber twice as thick is eight times as resistant). I think spreading the compression through interface/shear layers is possible. But I am unsure of the benefits and somewhat unsure of this area. Any thoughts?

On a side-note. Springers/top-hats can also be used to help bring tension more towards the centre, moving the neutral plane more (and I think it is a plane in relation to the outer surfaces - which are complex curves).

Thoughts? Abuse?

-doug

Wow Bert. You never cease to amaze me…I was thinking in the same direction as meecrafty( I think…) that is, not too intersted in the NA. This is Mainly because with a concaved deck, and concaves at different spots in the bottom, different materials, and different sandwiche composite layers the NA is incredible hard to pin point( do you actaully use a formula for this Bert?!!) I can see the importance of what your saying now, having the center of gravity and neutral axis aligned. I venture what you (Bert) are trying to do is get the spot where it’s suppoused to be the neutral axis to stress. You do this by replacing the foam from the NA up with a free floating horizotal stringer, I’m guessing you epoxy wood to both side of the EPS to create an addition I-beam that lays in that spot. This way you can create stress where the neutral axis WAS by having the bottom of the beam (a beam may be the wrong terminology here) in tension. However, in actuality you’re just creating different NA’s. I really don’t understand how you can create an accurate “beam” where the pre-existing NA was prior to the replacing of that foam with springer. I’m guessing you’re not actually finding the real NA but something close…and having it machined out and then putting in the springer.