Stiffness of X bracing

[Philstix]

Perhaps I misunderstand the question. The stiffness of a point is not in question in your picture, the stiffness of a line is. But the stiffness of the top at any point is not carried by a line across the top due to the fact that the top is not made up of independent lines on a horizontal axis but of a solid membrane physically attached all along the length of the braces and to the whole perimeter. Since the perimeter is curved (i.e. it has an induced arch) and the braces are also curved the points where any two of these intersect will be the stiffest areas of the top. The farthest points away from these intersections will be the weakest, or least stiff, or if you will the easiest to deflect or distort. Thus the area at the waist will be relatively stiffer than the lower bout. Where exactly between these two points (the intersection of the x and the sides) the least resistance to deflection will occur will be determined by the relative stiffness of the braces and the sides. That is, if the sides are relatively stiffer the point will be closer to the intersection of the x, if the braces are stiffer it will be closer to the sides.

[Dominic]

Finger braces play one part in spreading the load thereby reducing the stress at the X junction.

Must agree Nick,

I see the finger braces (1 or 2 a side) as a kind of pipehead on a dam...(Yeah OK, its the best I could come up with @ such short notice ) The fingers angle from the X to spread rotational load emitting from the outter edges of the bridge plate into the waist and 'sides'. Sort of a reverse flying buttress if you will. The more substantial the fingers, (The more open the pipehead) the less load will be transferred into the X brace and as a result, the less tension will be 'pulled' into the top behind the bridge (the dam wall).

The trick is to carve away the fingers to close up the pipehead 'just' enough so the top behind the bridge will be loaded or stretched into responsiveness. The X of course is the framework for that exchange so it must be strong enough to withstand that constant tension, but also flexible enough to allow that tension to be put to good use and allow large oscillation of the top otherwise there will be a lack of bass response. I have no data on this, it just not how I work 'but' I am yet to find a nasally trebley sounding guitar that did not improve with shaved fingers.

You can build without any finger braces at all of course but you would then need to beef up the X to handle the roll of the bridge plate and I am not certain that would work well structurally in the long term even if you did get it to sound OK. Much better to have the finger there to balance things out and allow adjustment of where the load goes.

Cheers

Kim

Kim, my point was that finger braces may add to the stiffness at point A, but they also add stiffness to many other points on either side of A. So all you are doing is making a proportional increase in stiffness in those areas, hence for the exercise of determining the weakest point on the X can be eliminated. Of course we do lots of carving and this may even up the stiffness profile of the finished X but as a structure that is less the point.
From a structural view point, that dip in the stiffness profile at the junction will always be there so adding braces to the side makes the junction stiff enough to do the job. But that implies there is additional mass in the X legs on either side of the junction, that they are over-built. And i suppose that is the point of falcate bracing. It does not have this massive knob of brace wood at the X that serves no useful function. Perhaps it also means we could be a lot more agressive at carving the excess wood from around the X junction and not compromise stiffness.

Agreed Jeff, that the actual difference in stiffness depends. i think I only ever said that there is twice the area of brace. If i did then say this means it is twice as stiff I apologise, I did not mean to say that. But it has to be significantly stiffer.
Cheers
Dom

[Dominic]

Perhaps I misunderstand the question. The stiffness of a point is not in question in your picture, the stiffness of a line is. But the stiffness of the top at any point is not carried by a line across the top due to the fact that the top is not made up of independent lines on a horizontal axis but of a solid membrane physically attached all along the length of the braces and to the whole perimeter. Since the perimeter is curved (i.e. it has an induced arch) and the braces are also curved the points where any two of these intersect will be the stiffest areas of the top. The farthest points away from these intersections will be the weakest, or least stiff, or if you will the easiest to deflect or distort. Thus the area at the waist will be relatively stiffer than the lower bout. Where exactly between these two points (the intersection of the x and the sides) the least resistance to deflection will occur will be determined by the relative stiffness of the braces and the sides. That is, if the sides are relatively stiffer the point will be closer to the intersection of the x, if the braces are stiffer it will be closer to the sides.

We are discussing the stiffness at points along the x and 90 degrees to the string pull. We don't even need to complicate it with the top but that is why I drew rectangle tops to take it out of the equation. Now, take you rectangle top with an uncarved X brace on it and rest the top and bottom edges on two paralell supports. If a weight is applied to the top, which part of the structure is the weakest? It has to the junction of the X.
Dom

[jeffhigh]

Just a quick word with the mods hat on.

Can we please avoid making any generalisations based upon geographical location...It's great we are able to discuss things here in a mature way but we don't want to find ourselves bathing in the dirty water pour out by one boorish participant on another forum. Keep in mind that we have some very respected and 'forward thinking' members of this forum who are kind enough to share their thoughts with us from their home in the USA and I am certain that every single one of them are just patriotic as the rest of us.

So please, let's not wave any red rags with the potential to commit the very same offence we complain of. I know that would never be done intentionally by anyone at this forum, but we need to be aware that when ever we get nationalistic in a topic, things can go south 'very' quickly...its emotive and right up there with religion for causing good people to fall out so it has no place in a good discussion.

Hat off

Cheers

Kim

Hey Kim no nationalistic slurs on my part, Wouldn't be wise on my part being a dual national, just pointing out the flaws in logic of one individual who stated that Smallmans sound like Banjos, therefore all australian guitars are Banjos.

[Philstix]

The point of greatest flex will be the centerpoint of any span. If that also happens to be the point at which the two braces cross then that will be the point of greatest flex. The fact that the x braces in a guitar are not equally long above and below the intersection, are not freestanding from the sides, and are not unattached to the top render that point rather meaningless as it relates to building guitars. But I do concede that point. I just don't see why it is relevant.

[Allen]

To follow that analogy Phil, the flex of a single brace will be in it's centre point. No argument there.

But Dom's premise is that we have 2 braces crossing at some point. Therefore if a weight is placed on those braces we have twice the bracing material on either side of the intersection, so twice the stiffness until we get to that point of intersection. Then it drops down to 1/2 the stiffness of the 2 braces combined. If that point of intersection is exactly 1/2 the span, then it's going to deflect in the middle, but if it's moved towards one end, then as it's far less stiff at this point, we can expect to see the point of greatest deflection move along from the centre to that point.

I know that we have all kinds of other variables involved, such as the spread of the X, the narrowing of the waist, where the load is placed, how well the joint is made, caped or not, etc etc. etc. And those numbers of twice and 1/2 are just rough approximations when you consider the variables, But taken in isolation that is the way I understand how a X brace system works when it comes to the load we place on it.

[jeffhigh]

In this scenario with a point load on the centre of the X, you would analyse it as a two way mechanism rather than one way.
The material at the x centre would be taking stresses in perpendicular directions rather than just one.

[graham mcdonald]

I think Allan has suggested the answer to all the questions be posed. Deflection testing measures stiffness. If you set up a jig which put a set weight on various points of the soundboard, perhaps both as a free plate and glued to a rib structure, surely the deflections caused by that weight would indicate stiffness. At the same time I can't see why knowing how stiff the soundboard is at any particular point is all that important. What is important is really the overall stiffness and where the resonances sit. That, I would suggest, is all about a combination of all the bracing, top thickness etc etc.

cheers

graham

[jeffhigh]

I think Allan has suggested the answer to all the questions be posed. Deflection testing measures stiffness. If you set up a jig which put a set weight on various points of the soundboard, perhaps both as a free plate and glued to a rib structure, surely the deflections caused by that weight would indicate stiffness. At the same time I can't see why knowing how stiff the soundboard is at any particular point is all that important. What is important is really the overall stiffness and where the resonances sit. That, I would suggest, is all about a combination of all the bracing, top thickness etc etc.

cheers

graham

Graham , Unfortunately a simple point deflection test at different locations will not tell you the stiffness of the material at that point It only tells you what the overall soundboard does when loaded at that point. Deflection is just telling you the net effect of the support that point has from the whole soundboard and the bracing
Doing a deflection test at the bridge location as trevor does is relevant because that is where the soundboard is driven from.
I agree, the stiffness of the soundboard at any point is not that important, except that in looking at the X you can make the decision whether or not to cap it.

[Philstix]

Since we assumed a perfect joint and the deflection is of the entire brace the stiffness of the bracing at the intersection of the braces is exactly the same as at any other point crossing the braces. That is exactly the total of the strength of each individual brace added together. Since it is at the midpoint it is at the point of greatest flex. It is not halved because each brace is considered full at each point along the brace and the center point can be considered to belong equally to each brace. As others have said, I don't really see a use for this in luthiery but that doesn't change the fact that the strenght is no diminished. Remembeer, this is a perfect joint.

[Alastair]

Just 2c worth from someone who is neither steeped in the lore, nor equiped with the tools of theoretical analysis....


I would venture the following:

Dom's analysis is logical, particularly if you consider the braces in isolation. If you suspended a cross brace system at the ends, and loaded it, I would expect it to fail at the intersection. Both since this would be the point where the stresses would focus, as well as Dom's analysis of a point of minimum cross sectional area, and hence stiffness. I'm not sure what the effect of the included angle would be though.

However, I would venture that in the case of a soundboard, you would be dealing with a composite system, where the whole would be greater than the sum of the parts. The soundboard would transform the load from a point load to a distributed load??

I would venture further, that if you were to set up your "X", and measure deflection under load at the middle, and do this for an unbraced soundboard, suspended between headblock and tailblock ends, then glue them together, the combined stiffness would be way higher than total of the individual systems?

To take this further, I would be interested in the views on the following:

Take said X-brace, and glue on a bit of soundboard, (say 1" x 2") at the intersection. What about a bigger bit?

I would expect that the increase in strength would be significant, due to the transfer of forces between the braces, through the soundboard??

Braced for flaming

Alastair

[jeffhigh]

It's a 2 way structure and has to be analysed that way
The material at the joint can actually take stresses in two perpendicular directions at the same time (joint detailing and capping allowing)
That is why a simple crossectional comparison may be misleading.

[Dominic]

Yes, a simple deflection at points along the brace will indicate most deflection in the middle but that has to be converted to stiffness with some maths first so you are comparing like for like. Simple high school physics. Check out your old physics book if you are not sure.

If you put the X right near the end of the braces it would still be the weakest point.

And I agree with everyone that we are talking about a system. But that does not negate the fact that the main component of the system, the X, is weakest at the junction and that will always be the case. It can't magically be made any different because there are other components in the system.

This information is useful because it

suggests designs such as falcate bracing are superior because the braces are more matched the their load needs

And to me, it means that I could carve a lot more brace material from around the X and get a smoother stifness profile.
But that I mean I could get a smoother transition between the scalloped section and X section which tends to be full hieght, the junction and so on. Trevor has pics of the stiffness profiles of braced tops and so does Somogyi.

Anyway, I think there is plenty of info about this now and if people are still unsure have a read through the previous posts first. Its all there.
Cheers
Dom

[jeffhigh]

For those who want to know what all these opposing theories mean in practice, I did a quick test this morning of an Xbrace on my deflection testing setup
Brace crossection 8.5 wide 9.9 deep silky oak
Initial seating load 73.8g
Added test load 295g
-First I tested a single brace diagonally across the jig
Deflection on adding the test load was 1.21mm

- I then added a crossbrace just butted and glued to the sides and capped on the underside with a 0.75mm thick strip using superglue gel.
Deflection 0.62mm

-I then chiseled off the cap so the crossbrace was only glued to the sides of the original through brace
Deflection 0.74 mm

Multiple readings were taken to get consistent results in each case

Make of these what you will

[jeffhigh]

Pictures of the setup

[Philstix]

Let me try this another way. A brace does not support an area simply with the mass directly under that area but spreads the load. If the point of crossing simply halved the strength at that point due to its having half the mass all you would need to do to make the brace full strength all of the way is double the depth of the brace directly under the point of the crossing. Try it. It won't add any significant stiffness to the brace. If you add depth to the brace for a significant distance along it or conversely shave it down you will change its stiffness. The resistance to the top distorting from string pressure will be greater at point b or c because the pressure will be applied to the top nearer to the bracing. That is, the outside strings and the pressure they apply will be applied to a point on the top closer to a brace and therefore have less tendency to distort.

[ozwood]

Thanks Jeff,

Awsome Practical display and test of the theory, makes all the diffence .

Again thanks for the Demo.

Cheers,

[jeffhigh]

Yes Phil I agree it's is the effect of stiffness all along the length of the brace that affects the deflection behaviour.
I would however expect a fairly large change in centrespan deflection with centre loading if there was a large local weakness there
If there is no weakness at the X intersection, I would expect to see deflection of half that of a single brace.

[Dominic]

Jeff, thanks for doing the test. If you still have your set up I think to test this theory you need to do it like I have in the pic. The horizontal lines are your rests. To test the deflection of the junction set the rests as in the first panel. Then move then to the position in the second panel and exactly the same distance apart and compare the two.

Another way to do it would be to test your single brace, then test two single braces side by side sharing the load, then test the constructed X brace. If the X introduces no weakness it will deflect the same as two braces.

As we agreed, the stiffness at A is not necessarily half that of B or C. But the way you have tested is based on the assumption that the junction is only as stiff as one brace. However, I think turning two braces at an angle and having the junction supported by the two braces backing it up slightly does add structural integrity and means this assumption may not hold. But if you do it using either of the techniques I suggested you don't need to make that assumption and you should get less ambiguous results. And use a larger weight so you push the braces harder and any measurement or set up errors become a smaller per cent of the total.

Cheers
Dom

X Pic4.png (5.58 KiB) Viewed 21417 times

[jeffhigh]

What I assumed Dom was that if a single diagonal brace deflected X amount then two would deflect X/2 under the same load, which is a valid assumption within the elastic range.
So the single brace deflected 1.21mm you would expect two braces to deflect only 0.605mm
The capped X went to 0.62
With the cap removed it went to 0.74

I havent got adjustable rests and I did cut it apart afterwards to retest the single brace setup, but my X brace test was equivalent to your first diagram and the single brace equivalent to the left half of your second drawing disregarding material outside the span.

Yeah I could have used slightly heavier weights but the weights off my beam balance were all I had at hand
Also I was concerned that in the single brace test, if I loaded it too heavily it would twist giving a higher result
It's not obvious from the pictures but there is a smaller initial weight under the larger one shown, The procedure was to put on the small weight, take that as a zero reading and then add the larger weight on top.

Cheers
Jeff

[Philstix]

If you move the weight to a different point along the x it will be more stiff. Not because there is more bracing, the same two braces are still each carrying half the load, and not because of the angle between the braces because each of the two braces is at the exact same angle to the load as at the center, but because you have moved away from the centerpoint of the span. By the way great demonstration Jeff. If it were possible to achieve a perfect joint the deflection would be exactly half.

[Dominic]

Philstix, I think you are still confusing the amount a brace deflects with its stiffness. A good brace will be the same stiffness anywhere along its length but will deflect differently depending where you apply the load in relation to the fulcrums.
For example, a brace that deflects 10mm over a 500mm span may only deflect 3mm over a 200mm span. Same brace, same stiffness.

I'll do some tests on various braces this weekend and put up the data.
Cheers
Dom

[Philstix]

I think the whole difference we have here is semantic. What you wrote to me as an explanation is exactly what I said. The deflection is dependent upon the length of the brace and the distance from the ends. The original question was whether the crossing point of an x brace was the weakest or the strongest point. I maintain that, given a perfect joint, it is exactly twice the strength of a single brace. It is the point of greatest deflection simply because in the example it is at the midpoint. If stiffness does not mean resistance to deflection under load what does it mean? If the question we want to ask is where on the top is the greatest resistance to the torqueing action of the bridge it becomes a much more complicated question.
I hope this doesn't come across as argueing just for the sake of arguement. I like this forum because the people on it are friendly, helpful and knowledgeable. I aspire to ther level of craftsmanship I see so often displayed.

[jeffhigh]

The trouble is Phil that there are a number of different terms and ways of looking at "Stiffness"
There is the modulus of elasticity E which is a measure of material properties
Then if you apply it to a beam crossection it is EI or flexural rigidity
You can also consider stiffness of a beam in total and the length then becomes relevant as well as crossectional properties but deflection will also be related to load distribution and other factors such as support conditions.

So the semantics does become confusing

[kiwigeo]

One reason I became a Geologist rather than an Engineer.