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Why are high arched orthoses stiffer than low arched orthoses?

Discussion in 'Biomechanics, Sports and Foot orthoses' started by Simon Spooner, Mar 19, 2011.


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    All, a high arched orthosis will deform less under load than a low arched orthosis, all other factors being equal. Thus the high arched orthosis is stiffer. What is the mechanics that makes this so? What is the relationship between curvature and deformation under load?
     
  2. Simon this maybe something - DYNAMIC FAILURE AND ENERGY ABSORPTION OF
    COMPOSITES WITH TOPOLOGICAL CONTROL
     
  3. Thanks Mike. I suspect it is down to the second moment of area. Which is linked to bending moment.

    Does this principle apply to both shank independent and so called shank dependent devices? Or is it purely the cross sectional thickness that is important in shank dependent devices?
     
  4. My guess would be a combination, but the cross secional thinkness having a greater effect. The topographic make up of the shank dependent device must also change the stiffness of the device as well.

    I made a comment re heating up of shank dependent device the other day, Craig P and Davinci were making posts about the result of heating not having any positive effect, I stated that the changed shape would also increase stiffness of the device so it would have some mechancial effect - they never got back to me.
     
  5. Yeah Craig said something similar at his boot camp. I let it go, but if you change the shape, you change the stiffness.
     
  6. Craig Payne

    Craig Payne Moderator

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    Sorry Mike, I missed that previous comment. However, you can't change the shape of a shank dependent EVA/polyurthane prefab by heating it. The only way you can change the shape of them is by changing the thickness of the material and heating does not do that.
     
  7. Griff

    Griff Moderator

    I read in a bridge engineering book once that arch stiiffness is dependent on the stiffness of it's abutments. I know you know this already, as it was you that taught most of us that an extrinsic post increases orthosis stiffness (off the back of your FEA).

    Taking this into a scenario where we are comparing a high arched orthosis with a low arched orthosis, and all other factors are equal (material thickness, length of arch etc) is this difference in arch stiffness not just explained by the vector of the forces at the arches abutments? (i.e. a more vertical loading pattern in a higher arch?). Perhaps I'm thinking too simply...?
     
  8. That's span length not sure about vector of forces at abutments. What about in a filled arch device?
     
  9. Griff

    Griff Moderator

    Are we talking distribution models instead then?
     
  10. What's a distribution model?
     
  11. Griff

    Griff Moderator

    Its something I recall reading in a book about bridges/arches. And something I have to admit I don't have a good enough understanding of to write about from memory. Give me a couple of hours to get back from the gym and I'll dig it out while the rugby is on.
     
  12. From what I have read on the subject, it seems that the stiffness of a beam depends on its length, its cross-sectional shape, the material, where the deflecting force is applied, and how the beam is supported.

    http://www.clag.org.uk/beam.html

    In the case of a higher arched orthosis, there is a thicker cross-sectional shape (second moment of inertia) than in a flatter arched orthosis. In addition, it is possible that the front edge of a higher arched orthosis will "dig into the shoe insole" more than a flatter arched orthosis, better preventing elongation of the orthosis under vertical loads.
     
  13. Griff

    Griff Moderator

    Can't find the book. Not much online either other than this: http://www.bne.uwe.ac.uk/short/masonryarchbridges/presentations/13_billharvey.pdf

    On reflection, I think it's probably not as relevant as Kevin's observations in any case.
     
  14. Is a shank dependent device a beam? So, if we had two devices with identical superior surface geometry, identical arch height, and identical stiffness. Yet one was shank dependent but one shank independent should they work the same? My answer is yes. So, shank dependent / independent is irrelevant. It is the stiffness and interface geometry which is significant.
     
  15. Next question how much can an orthosis deform under loading?
     
  16. Simon:

    Stiffness in orthoses is not a constant so there will not be one stiffness in any one orthosis since the load vs deformation curve will not be linear, but will rather be a curve. In other words, the orthosis stiffness will increase as the arch deformation and/or deforming force increases in most orthosis constructions.

    For example, in a shank independent orthosis, let's say a 4 mm polypropylene orthosis with an average arch height and made for a size 10 foot, it may deform 3 mm at the apex of the medial longitudinal arch (MLA) when a 30 Newton force is applied. Therefore, the initial stiffness of this device is 10 N/mm. Now, the loading force on the MLA is increased to 60 N and the orthosis only deforms 1.5 mm to 4.5 mm total deformation. The slope of the load vs deformation curve (i.e. stiffness) of the MLA is now measured to be 20 N/mm.

    However, in a shank dependent orthosis, let's say a Plastazote #3 orthosis of the same dimensions as the shank independent device, the device deforms 4 mm initially with a 30 N force application and then deform only 1 mm when the MLA deforming force is increased to 60 N. For this shank dependent orthosis, the stiffness from 0 to 30 N is 7.5 N/mm and the stiffness from 30 to 60 N is now 30 N/mm.

    Using these two examples, to say then that whether the orthosis is shank dependent or shank independent is irrelevant does not take into account the mechanical fact that these two types of orthoses will behave quite differently under varying magnitudes of loading forces and may have widely varying stiffnesses depending on how they are constructed and on how the shoe sole and upper mechanically interacts with the orthosis. For example, converting a shank independent orthosis into a shank dependent orthosis by adding a packing material such as EVA or korex into the plantar arch of the orthosis will signficantly change its load vs deformation curve and increase its stiffness. Therefore, the mechanical change of the orthosis from a shank indepenent device to a shank dependent device did significantly change its load vs deformation curve and did significantly change its stiffness and would therefore be quite mechanically relevant to how that foot orthosis behaved under the loading forces that were being applied to it by the weigthbearing foot.

    However, if you were to say that if the load vs deformation curves of two different types of orthosis have previously been measured to be identical and that, because they are identical, the construction characteristics of each orthosis are now irrelevant to how these orthoses would deform under load, then I would agree with you.

    I hope this helps clarify my thoughts on this very important subject which, I feel, is critical to every practicing podiatrist.

    Great discussion!:drinks
     
  17. Griff

    Griff Moderator

    Is it possible to have a shank dependent and a shank independent device which have identical stiffness? Is this not one of the factors which dictates their dependency/independency in the first place?
     
  18. So what you saying is PU and EVA can not change shape after being heated ?

    I beleive EVA retains a new shape after being heated a pressed, an altered shape will have different stiffness, if this has any kinetic effect thats another story.
     
  19. Craig Payne

    Craig Payne Moderator

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    You can heat them up and twist them into any shape you like, but as soon as you stand on it, the device rests on the shank of the shoe and its then is totally dependant on the material thickness and not the shape you heated it into.

    Try this - get a EVA/PR prefab - use calipers to measure the thickness of the material at a numer of points. Heat it up and mold it to the foot. Then use the calipers to measure the thickness again at the same points.....its does not change in thickness.

    Having said that, yes, heat and a few 100 tonnes of pressure can change the shape.
     
  20. Load vs deformation is that not defined by a materials stiffness?

    So if shank dependent vs shank independent have the exact same stiffness the load vs deformation curves should be the exact same ?

    Ironing out a few thoughts so my thinkings not way off
     
  21. RobinP

    RobinP Well-Known Member

    I agree with this as I have tried doing exactly that before with no discernable difference in the arch thickness.

    However, creating a sweet spot/relief in a device (particularly on an edge), I can heat and push the EVA into a new shape. I am relying on the fact that the shoe is not rigid enough at the interphase between the shoe and the orthosis to allow this shape change to be "allowed"

    Now, I'm not sure of the definition of the shank in shank dependant(does it literally refer to the shank of the shoe as in the rear 2/3 of the base of the shoe or does it refer to the shoe as a whole) but that would mean that it is possible to change the shape of a shank dependant EVA device by heating. That is for custom made as opposed to a prefab(although I can't see what difference that would make)

    I suppose that is allowing for the fact the "shank" is not a rigid constant, which presumably a shoe is not?

    Great topic
     
  22. Good. So we agree that if we took two devices and measured the load/ deformation at a point on their surface and found that they both deformed by 3 mm at this point when a 30 Newton force was applied and under 60 N loading at this point both the orthosis deformed by a further 1.5 mm to 4.5 mm total, then ostensibly they show identical stiffness characteristics at this point and should behave the same within these loading limits regardless of whether the arch is filled or hollow. i.e. the classification of shank-dependent or shank-independent is irrelevant in this situation.

    Your example regarding converting a shank independent to a shank dependent device just illustrates that the change in stiffness is the important factor not the shank dependency.

    It is obvious that stiffness is not constant across the entire structure of the foot orthosis and will show point to point variability. Of interest, I put a Vasyli Dananberg Prefab in a materials testing machine on Friday and loaded the centre of the heel cup- it was almost perfectly linear until it bottomed out. I'll do some studies of other devices at medial longitudinal arch and centre heel-cup this coming week.

    What limits the amount of deformation that can be produced in an orthosis under loading? My guess is that the deformation must always be less than the distance between the superior surface and the supporting surface along the line of action of the loading force. So if we take our two devices, one "shank dependent" and one "shank independent" and measure the vertical distance between the highest point on the medial longitudinal arch and the supporting surface as 30mm and we apply an infinite vertical load to this point on both devices, assuming that neither device fails under loading and that the supporting surface does not deform, the maximum deformation in both orthosis will be just less than 30mm, regardless of whether it is "shank dependent" or not.
     
  23. RobinP

    RobinP Well-Known Member

    That is the important distinction to make isn't it? If the load deformation characteristics are the same, the construction is irrelevant, as is the stiffness

    If the stiffness is the same at given load, this does not remain a constant depending on the load and construction, therefore the load deformation charcteristics may differ.

    Am I right there?
     
  24. Has anyone got the equation which relates material stiffness to material thickness?
     
  25. So, surface geometry is not important in modifying the magnitude, position nor timing of the reaction forces at the foot orthosis interface in shank dependent devices?

    If the heating and molding process changed the thickness, you'd agree that the stiffness would be changed? Lets say we changed the the distance between the supporting surface and the highest point on the medial longitudinal arch via heat molding, would this change the second moment of area?
     
  26. can an orthotic be model as a single leaf spring, if so

    Leaf Spring Formula:

    k=8Enbt3/3l3

    where,

    E = Youngs modulus [Nm-2]
    n = Number of leaves
    b = Width of leaves [m]
    t = Thickness of leaves [m]
    L = Span [m]
     
  27. Not sure you can say stiffness is irrelevent if stiffness defines the load deformation characteristics and then stiffness is defined by surface geometry and thickness of material among other things.

    Thats my point about bending a prefab EVA device you may not see a discernable difference in function but you have changed the geometry of the device therefore the stiffness therefore the load deformation characteristics - if this changes the fuction of the device of your patient is not the point- you have changed the stiffness of the device.
     
  28. Mike, not really what I meant, but useful none-the less. But is it useful in a "shank dependent device"? Kevin, in his first book (p.73), says that bending stiffness increases in relation to the square of the thickness of the material- just wondered where this comes from?

    Interesting, the equation you cite above is not dependent upon the geometry of the curvature of the leaves.
     
  29. Craig Payne

    Craig Payne Moderator

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    I'd agree totally that IF the heating and molding process changed the tickness that the stiffness would be changed. The problem is that the heating and molding process does not change the thickness of the device - do the exercise with calipers I suggested above.
     
  30. Stiffness is the slope of the load-deformation curve. So, at any value of loading there is an amount of deformation which defines the stiffness value. So you cannot say the stiffness is irrelevant. The load-deformation curve may have linear and non-linear portions within it.
     
  31. RobinP

    RobinP Well-Known Member

    OK I see - just reread this properly and get it now - Thanks
     
  32. OK so we have in the diagram a "shank dependent" piece of eva insole which happens to be flat (top line of the diagram), we heat it up and bend it so that it resembles the curved bottom line in the diagram- the thickness hasn't changed. Have its stiffness characteristics changed?
     

    Attached Files:

  33. Griff

    Griff Moderator

    Going back to beam and arch physics, I'd say yes. The stiffness characteristics must have changed.
     
  34. Yes that's right. But why?

    So, next up we have a "shank independent" device in the first picture and a "shank dependent" device in second, both devices have the same load/ deformation curve for a point at the highest aspect of their curvatures. Does it make any difference to the reaction forces at the foot's interface with this point that one is filled-in beneath the surface?

    Which device will deform more under loading?

    Now, lets say the curve in picture one has load-deformation characteristics that make it more or less stiff (take your pick) than the curve in picture two, what is the maximum deformation that can be exerted in each device? i.e. does it make any difference to the maximum achievable deformation when the area beneath the arch is filed in or not?
     

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  35. Simon:

    I believe I got that from an physics textbook many, many years ago, but I'm not sure what the reference was. It made sense to me at the time.

    Here is a reference that explains that stiffness goes up by the power of 4 of the thickness of a material.

    http://www.captainastounding.co.uk/x_to_the_4.html

    Also, the formula for second moment of inertia states that the second moment of inertia is proportional to the cube of the thickness of the beam.

    http://en.wikipedia.org/wiki/Second_moment_of_area

    Looks like stiffness will increase by at least the square of the increase in thickness of the orthosis material. It would be nice to have an engineer help us out with this one.
     
  36. Would the addition of the arch packing material to the shank indepedent orthosis make it a stiffer orthosis? Yes.

    Would the removal of arch packing material from a shank dependent orthosis make it a less stiff orthosis? Yes.

    Is it, therefore, mechanically irrelevant whether an orthosis is shank independent or shank dependent? No.

    ;):cool:
     
  37. Kevin, all you are stating is that the stiffness changes when you add packing under the arch or remove it, all other factors being equal. Thus, what is ultimately important is the stiffness, not whether it is packed under the arch or not. Unless you can tell us how two devices with identical load-deformation characteristics, one packed under the arch, the other one not, should result in different reaction forces at the foot-orthosis interface? As we have established two devices: one packed under the arch, the other one not, with the same load-deformation characteristics would function the same. Therefore, packing under the arch (or not) is irrelevant. The load-deformation and stiffness characteristics are what is relevant, not the geometry of the device below the foot-orthosis interface.

    Would the addition of the arch packing material to the shank indepedent orthosis make it a stiffer orthosis? Yes.
    Would thickening the shell material to the shank independent orthosis make it a stiffer orthosis? Yes
    Would making the shank dependent device out of a denser material make it a stiffer orthosis? Yes
    Would the removal of arch packing material from a shank dependent orthosis make it a less stiff orthosis? Yes.
    Would thinning the shell material of the shank independent orthosis make it a less stiff orthosis? Yes
    Would making the shank dependent device out of a less dense material make it a less stiff orthosis? Yes

    Is it, therefore, mechanically irrelevant whether an orthosis is shank independent or shank dependent? Yes.
    Is it, therefore, the stiffness of an orthosis that is mechanically relevant in determining the location, magnitude and timing of the reaction forces at the foot-orthosis interface? Yes.
     
  38. Indeed, is it now more or less stiff as loading is increased from zero to 100N?

    What would the load-deformation curves for the two conditions look like?
     

    Attached Files:

  39. Simon:

    You first make these observations which I all agree with:

    Then you make the following statement which, to my way of thinking, directly contradicts the observations you have made above:

    I don't understand how you can first say that changing a shank dependent orthosis to a shank independent orthosis will make the orthosis less stiff, and then say it is mechanically irrelevant whether an orthosis is shank independent or shank dependent. Please explain.:confused:

    In other words, do you believe that it is mechanically relevant to the kinematics and kinetics of a foot when a shank dependent orthosis is made less stiff by removing packing material from its arch therefore making it a more compliant shank independent orthosis?
     
  40. I believe that foot orthosis work by altering the stiffness characteristics at the foot-orthosis interface; by altering the topography at the foot-orthosis interface and by altering the frictional characteristics at the foot-orthosis interface. Thus, I believe that the stiffness of the device is mechanically relevant, I believe that packing a device beneath the arch is one way to make it stiffer in this area. Yet, I believe that ultimately it is the stiffness that is significant, along with the interface geometry and frictional characteristics, not whether or not it is packed under the arch or not to achieve a certain stiffness characteristic. I believe that there are many ways to achieve variation in orthosis stiffness. I believe that the terms "shank dependent" and "shank independent" are weak since they tell us nothing about the stiffness of the device, nor the foot-orthosis interface topography, nor the frictional characteristics at the foot-orthosis interface.

    Is a "shank dependent device" stiffer or more compliant than a "shank independent device"?

    The foot and the body above it don't care whether an orthosis is "shank dependent" or "shank independent", the body is only interested in the surface stiffness, surface shape and the frictional characteristics of the surface. The terms "shank dependent" and "shank independent" tell us nothing about any of these. So, what is the usefulness of these terms?

    Unless, of course "shank dependent devices" exert a different mechanical effect on the foot than "shank independent devices" irrespective of their stiffness characteristics at the foot-orthosis interface, their topography at the foot-orthosis interface or their frictional characteristics at the foot-orthosis interface- do they? If so, what is this difference?

    Perhaps, Mike Burns could tell us why he felt the need to differentiate devices into "shank dependent" and "shank independent" and why he thought this was a useful dichotomy?
     
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