MIMF

Actually David, looking back through the thread I see that you have a very good FBD of a pinless bridge about 2/3 of the way down page 2.

Mario, at some point in this discussion someone inserted the concept that a pinned bridge peels off the top due to rotational forces imposed on it in exactly the same manner as an pinless bridge.
There have been attempts to prove or disprove this by both experiment and analysis.

Good to see you here, too, Mario. Yes, we’ve certainly covered a lot of ground on bridges. I think the main questions that are currently being debated are (lots of ways to phrase these):

1. What are the reactions (forces and/or pressure distribution) between a pinned bridge and the top? That is, what does the FBD look like? A particular question is as Jeff asked: “whether a pinned bridge experiences an upward lift at the rear as a result of a rotational moment?” [Edit: just saw Jeff's post. As he said, the question started earlier. Those words are how he put it recently.]:

2. How do those reactions differ between a pinned and pinless bridge?

3. What happens to those reactions when a bridge starts to peel from the top, for both pinned and pinless.

4. How sophisticated a model do we need to give good answers to the questions above: rigid vs. deformable bodies, Statics vs. more advanced methods.

There are a bunch of other interesting questions on the role of the pins themselves, and the loading and flex of the whole top related to Peter's nice experiments, but those are too much for me at the moment.

Jeff, thanks for your feedback. I think I understand the approach you're taking. It sounds like we're both trying to use mechanical insight/reasoning to make that unknown w(x) into something more specific, but we're approaching it in different ways. If I'm understanding your approach, you would like to first resolve w(x) into a single force (or two components) that can be placed to balance the string reactions on the bridge. Sum of moments shows that single force is near the front of the bridge. Then you would spread that force out into a relatively localized pressure distribution (that is, no or very minimal tension/compression stresses towards the tail of the bridge). Do I understand you correctly?

Barry, yeah, we've been at it a while, but I'd describe it as many hard questions with many different viewpoints.

Yes David I think you understand me
IF you assign values to the string height and to the distance back to the pin holes,then the reaction force which has to equal T has its location defined If h<d a single point reaction just back from the front of the saddle satisfies equilibrium.
Then you can start making decisions as to how this is distributed, but that distribution will have to produce both an equivalent force and location.

4. How sophisticated a model do we need to give good answers to the questions above: rigid vs. deformable bodies, Statics vs. more advanced methods

We would need an impossibly complex and sophisticated model... What y'all have missed is that the guitar's top is very flexible across the grain, while the bridge is, in effect, the stiffest brace of the entire structure of the top, and it runs perpendicular to the grain!

So we have a bridge pulling on the top(define "pulling" any damned way you want to at this point). The bridge is stiff. The top isn't. The top wants to bend/curve into the well-known "belly" shape behind the bridge. The bridge does not want to bend/curve. Eventually, the glue joint begins to fail, at the rear-most ends of the bridge. When this begins, the "pull" of the bridge(remember, define this "pull" any damned way you want to) is quickly spread over a much smaller area of the top, leading to a concentration of the load, which quickly leads to a complete failure of the glue line.

In 21-22 years of repairs, I've seen it happen to both pinned and pinless bridges. the only difference is that with a pinned bridge that still had good string-ball-to-bridge-plate-contact, there was usually minimal wood damage, where with the pinless bridges, there was always some major wood damage.

Back to the real world, this tell us that when the bridge began to "peel", the pinned bridge still had some mechanical "help" via the solidly anchored(to the bridge plate) strings, more or less giving the guitar's owner time to take the tension off the strings(hopefully)! and take it to a luthier, minimizing the damage. With a pinless bridge, once the peeling begins, it continues to peel-off at a exponentially rapidly increasing rate, often leading to the wood giving way before the glue line did. Thus, major damage..

Engineering is cool, computer models are cool, but in the end, the real-world is where we live in, isn't it? To truly understand a problem, we must first investigate and --understand-- existing examples. We should only resort to computer models when a new idea has never seen the light of day, thus no real-world examples for us to investigate exist.

Haven't missed anything Mario,just have not got consensus on even the basics before looking at the soundboard and bridgeplate flexibility which is the true cause of bridge detachment.

So by using the term "eventually" do you believe bridge detachment is inevitable or do you have any practical solutions to stave it off?

The "practical solutions" are what have worked for millions of steel string guitars. Good, solid joinery, well-proven glues, and offer a warranty. Some will lift, most won't.

I will add that the "looser" my top is, the thinner I'll take the bridge wings. At first it seems counter-intuitive, but back to solid engineering, what I'm doing is minimizing the stress riser that a too-stiff brace on a too-weak- top would induce. I use what is possibly the smallest bridge physically possible, even on dreadnoughts, all designed and expected to run medium gauge strings, and at least one of my clients runs heavies! I have, for sure, fewer failed bridge-to-top glue joints than any factory, and the fella who runs the heavies, multiple-time SPGBMA midwest guitar player of the year Bull Harman, hasn't had a single glue line failure yet, in over ten years. I had to replace one bridge(in a Nashville hotel room no less[LONG story there; ask me to tell it if we ever meet!]), but the bridge never lifted.... My oldest guitar has a 15/16" wide rectangular bridge held-on by LePage white glue, and it's never failed, either. I keep expecting it to, but I'm ready to bet it never will.... And yes, THAT top and bracing is -really-loose.

EDIT: as I typed this response, it became clear to me that the most likely culprit(other than poor joinery) in bridge-to-top issues is most likely a too-stiff bridge on a too-weak top, or simply a too-stiff bridge..

I'm all with you on narrow bridges Mario.
I also agree totally with the concept of analysing failures.

Trouble is when someone misreads what that failure is telling him

We tend to use loaded terms like "The bridge pulled up" which implies that the string tension pulled the bridge off.
This might lead us to "solutions" like a wide belly bridge a la Martin or putting in bolts like Gibson when the problem may be bridge to soundboard stiffness mismatch as you suggest and I agree, a weak bridgeplate, incomplete removal of finish under the bridge footprint, hot car with titebond, etc,etc

I think there was one author whose name I can't remember who advocated temporarily gluing on the (pinned)bridge only along it's front edge for testing in the white before removing it for soundboard finishing.
The Static analysis just tells us that this is a stable situation for pinned bridges, not requiring glue to "hold down" the rear of the bridge and the testing done by Peter also confirms this.

The conversation has moved on a lot since I was here last, but...

...when I were a lad...

the point about using a FBD was so you could simplify things enough such that they were statically determinate and so could be solved with your pencil, paper and (if you were lucky) your HP, reverse Polish, red led display, calculator. And the "art" in this science was in making assumptions that allowed you to solve the problem sufficiently well to guide your design work, rather than to get a "right" answer. That meant making assumptions like ignoring explicit end moments like Dave M. is employing, justified by the fact that, as Mario has pointed out, the bridge is very much stiffer than the top making the back end of the bridge/top interface more hinge-like. Sure, it's not the real world, but (to me at least) illustrates what is important. If more detail is important, FEA might help, but don't fool yourself that that is the real world, either.

Back to the Peter's initial point about the acoustics of leaving pin holes empty; I have tested this in a rather roundabout way. When building falcate braced guitars, the main braces run between the bridge pins, with little clearance, so the best way to avoid drilling into a brace is to drill the bridge pin holes first, then put the braces in (which has a few knock-on implications). You end up with a body with bridge pin holes in, and when tap tested the main air resonance is higher in frequency and of lower Q than when the holes are taped over. There's an audible tap tone difference and this would be apparent in a finished guitar as Freeman discovered. The pins don't provide a hermetic seal of course, but sufficient of a seal to avoid audible issues. There can be a similar sort of issue when you drill a guitar for an end pin jack. That 12mm (1/2 inch) hole makes a definite, audible difference, but when the jack socket is installed, the remaining 1/4" hole and the baffle formed by the contacts prodives enough of a seal that you don't hear the difference any more.

Regarding acoustic basses, the best I've heard was a ABG built by a student of Gerard's to one of Gerard's designs. It was a dense lattice (think Smallman) CF over WRC (iirc) with a cedar top on a J200 chassis. It had a pinless bridge because there was no way of getting the pins holes around the lattice. Even sounding over all strings and frets (very rare in a ABG) and seriously loud if played with a pick. Probably about 15 years old now and still going strong.

Rodger Knox wrote:I've done my best to come up with a satisfactory engineering analysis, and I've come to two conclusions:

1. String tension results in elastic compression of the top in front of the bridge and elastic tension of the top behind the bridge. The displacement of the bridge due to this is approoximately 0.003", using medium strings and average stiffnes sitka spruce 0.10" thick.

2. The rotational displacement of the bridge is beyond my capability. The assumptions necessary to simplify the system enough to allow analysis are not adequately satisfied for the results to have enough accuracy to have any real meaning.

One thing I observed in my attempt is that the deflected shape of the top is a horizontal S, with a dip in front of the bridge and a hump behind it. Since the top is likely more flexible than the bridge, the curvature would result in compression on the glue joint along the front of the bridge and tension on the glue joint along the back of the bridge. This would explain bridges beginning to lift along the back edge. On the other hand, the bridge plate should stiffen the top enough so that the curvature does not begin under the bridge, unless the bridge extends beyond the bridge plate.

All the way around the circle

The latest Stew-Mac Trade Secrets has a good example of a typical delaminated pin type bridge.

http://www.stewmac.com/tsarchive/ts0171.html

Mario, thanks for your feedback. I think your thoughts on the stiffness mismatch causing stress concentrations are on the money. That makes sense about the pinned bridges having less wood damage.

A question for Mark S and anyone else that has seen a lot of lifted bridges, to followup on Mario's thoughts on causes -- Can you tell how often the failure seems to be caused by abuse (hot car, etc), poor joinery, too much stiffness mismatch, age, some other factor(s), or just something that happens to some % of guitars but a cause isn't very clear? Also, do they usually start peeling at the rear edge or the wings?

Trevor, I think we very much agree about artfully simplifying a model to gain enough insight for guiding design work. Also that there are many valid levels of sophistication in modeling, depending on the question asked and the time and tools available to answer it. The thing that led me down the path of modeling for non-rigid parts and pressure distributions was the curious behavior of the pinned bridge FBD when I assumed rigid bodies. In my first post on page 2, if b>h, the pinned bridge doesn't lift and the rear force actually becomes compressive. So I got to wondering about how flex might change the model. I'm pretty sure the "R" force is real as I've seen it elsewhere and it explains a lot, but the rest of the distribution is more of a guess. Curious what you think.

Peter, I'm curious about a behavior in your experiment -- if you force the unglued bridge down flat against the top, does it return on its own to that same slightly rotated position?

David Malicky wrote:
In my first post on page 2, if b>h, the pinned bridge doesn't lift and the rear force actually becomes compressive. ?

David, If you work that diagram out for a reaction force and it's location, rather than assuming a distribution, you will see that it is unlikely that there is either compressive or tensile pressure at the rear of the bridge

Can you tell how often the failure seems to be caused by abuse (hot car, etc), poor joinery, too much stiffness mismatch, age, some other factor(s), or just something that happens to some % of guitars but a cause isn't very clear? Also, do they usually start peeling at the rear edge or the wings?

I see so many, but they are almost always on cheapo guitars. Once in a while I see one on a Martin or a Gibson but not nearly as often. This suggests to me that the cause is poorly done joinery. That fit is so important! I am also quite sure that when I do get the fit really good and glue the bridge on with hide glue that the guitar sounds better than it did before.
As far as what caused the failures on the cheap guitars, I have seen every possible cause, hot cars, warped plywood tops, you name it, but the thing in common the most is that fit thing.

David Malicky wrote: Peter, I'm curious about a behavior in your experiment -- if you force the unglued bridge down flat against the top, does it return on its own to that same slightly rotated position?

I clamp (with small vice grips) the rear of the bridge down while I bring the strings to tension, then release the clamp, and the rear of the bridge lifts that sub-millimeter amount. If I reclamp it and release it, it still lifts the same.

Mark, Thanks for the info! That makes sense about the poor fit -- lower glue strength and maybe cracks awaiting.

Peter, Good to hear, thanks for confirming that! Would you have a rough estimate of how much force it takes to get the bridge to lie down flat?

Jeff, thanks for the suggestion. Yes, that approach does resolve the odd rigid FBD behavior. On the one hand, I don't want to try to convince you, but I'd like to explain why I don't adopt it... To make make a FBD of a glued bridge, I 'cut' through the glue line. For a rigid free-body, that cut face needs 3 reactions: N, S, and M. I can't assume M=0, particularly since it's a long glue line. M is also equivalent to a couple of 2 normal forces, placed anywhere (though the front and rear are most likely).

N, S, and M can also be transformed into the single reaction force (and subsequent distribution) that you described. That is an elegant transformation, but I can't assume it's how the bridge behaves. When I draw that diagram, it looks like it treats the bridge as a particle with all forces pointing through the particle center. For finding bridge reactions, I think it's best to model the bridge as a body, but for modeling effects far away from the bridge, a particle model would be good.

On the experimental side, Peter's model shows the unglued bridge rotates slightly. In order to get it to lay as flat as a glued bridge, the bridge needs to be clamped at the rear. If we wanted to remove the clamp but keep the bridge just as flat, the bridge would need tensile reactions at its bottom rear.

Nothing to do with particles at all David, just finding the centre of the reaction through basic principles of equilibrium of the vectors and of moments about any point of the body. Done it on retaining walls plenty of times in the past
I think one of the issues you are having with trying to analyse this is that you are not putting any dimensions on this. If you give h and b dimensions as I suggested then you can actually solve this for a single reaction located back from the front of the bridge.
If you can give a dimension to the width of the bridge w then you can solve for a two point support.

On the experimental side, I think what you are seeing is mostly due to the deformation of the test soundboard creating a hump under the bridge. The downforce at the front of the bridge is maintaining contact there while the back separates

David Malicky wrote: Peter, Good to hear, thanks for confirming that! Would you have a rough estimate of how much force it takes to get the bridge to lie down flat?

I'm out of town. When I get back I'll see what I can do.

Jeff Highland wrote:On the experimental side, I think what you are seeing is mostly due to the deformation of the test soundboard creating a hump under the bridge. The downforce at the front of the bridge is maintaining contact there while the back separates

No, it's not due to deformation of the soundboard - it was present in the first experimental model on the essentially solid plank.

Then from the drag of the strings friction on the top of the hole and the saddle as tensioning?

Peter, do you have the correct "neck angle" built-in to this test rig?

In the physical model, the bridge's rotation is being limited by the bridge pins. When the clamp is removed, the moment is transfered to the pins.
If that is correct, tighter pins should reduce the rotation.
By the way, has anyone measured the horizontal displacement of the bridge due to string tension? I'd like to know if the estimate I came up with is in the ballpark.