Cycling Mob Cycling Forums - View Single Post - Potential good news for Mt. Washington access.

01-18-2005, 08:44 AM

Joe Riel writes:

>> Here is an approximation. Assume that we can model this by
>> computing the transverse bending of a circular plate of radius a
>> with a load F uniformly distributed around a concentric circle of
>> radius b. The diameter of the plate is set to the width of the
>> rim, the diameter of the loading circle to that of the spoke hole.
>> From [1,article 314 (vi)] the displacement, w, is

>> w = F/8/Pi/D*((a^4-b^4)/2/a^2 - (a^2+b^2)*ln(a/b))

>> where

>> D = 2/3*E*(T/2)^3/(1-sigma^2)
>> T = material thickness = 1mm
>> sigma = Poisson ratio = 1/3
>> E = elasticity of aluminum = 75kN/mm^2

>> a = half rim width = 25mm/2
>> b = radius of spoke hole = 3.2mm

>> This gives

>> w/F = 8.3um/kgf

>> So a change in the spoke tension causes a deflection in the nipple
>> hole of approximately (75kgF)(8.3um/kgF) = 0.6mm. That represents
>> 0.2% of the spoke length. For a 100degC rise the diameter of the
>> rim increased by 0.25%. So it appears as though much of the
>> compliance is in the bottom of the rim. The proper technique is to
>> combine this compliance with the previous computation---but its
>> late and I'm tired.

>> Reference
>> ---------
>> [1] A. E. H. Love "A Treatise on the Mathematical Theory of Elasticity"

> I assumed the entire load was supported by one wall (the inner
> surface) of the rim. With sockets distributing the load to both
> walls, the compliance should be about half that computed.

The rims I used in deflection analysis were socketed and support spoke
load on both walls and distribute the load in such a way that there is
no tent pole effect around spokes. If there were, it would be
permanent, considering the concentration of the deformation. It would
take the rim to yield and remain as a permanent shape. Besides, if
this were the case, rims would crack there fairly soon... as some do,
but for other reasons.

Rims can readily be modeled as straight beams between spokes, rigidly
connected at their ends with no effect on the deflection results. The
arch in rim segments is not a buckling element in that axis.

Jobst Brandt
jobst.brandt@stanfordalumni.org

01-18-2005, 08:44 AM	#255 (permalink)
jobst.brandt@stanfordalumni.org Posts: n/a	Re: Rim brake heat and spoke tension Joe Riel writes: >> Here is an approximation. Assume that we can model this by >> computing the transverse bending of a circular plate of radius a >> with a load F uniformly distributed around a concentric circle of >> radius b. The diameter of the plate is set to the width of the >> rim, the diameter of the loading circle to that of the spoke hole. >> From [1,article 314 (vi)] the displacement, w, is >> w = F/8/Pi/D((a^4-b^4)/2/a^2 - (a^2+b^2)ln(a/b)) >> where >> D = 2/3E(T/2)^3/(1-sigma^2) >> T = material thickness = 1mm >> sigma = Poisson ratio = 1/3 >> E = elasticity of aluminum = 75kN/mm^2 >> a = half rim width = 25mm/2 >> b = radius of spoke hole = 3.2mm >> This gives >> w/F = 8.3um/kgf >> So a change in the spoke tension causes a deflection in the nipple >> hole of approximately (75kgF)(8.3um/kgF) = 0.6mm. That represents >> 0.2% of the spoke length. For a 100degC rise the diameter of the >> rim increased by 0.25%. So it appears as though much of the >> compliance is in the bottom of the rim. The proper technique is to >> combine this compliance with the previous computation---but its >> late and I'm tired. >> Reference >> --------- >> [1] A. E. H. Love "A Treatise on the Mathematical Theory of Elasticity" > I assumed the entire load was supported by one wall (the inner > surface) of the rim. With sockets distributing the load to both > walls, the compliance should be about half that computed. The rims I used in deflection analysis were socketed and support spoke load on both walls and distribute the load in such a way that there is no tent pole effect around spokes. If there were, it would be permanent, considering the concentration of the deformation. It would take the rim to yield and remain as a permanent shape. Besides, if this were the case, rims would crack there fairly soon... as some do, but for other reasons. Rims can readily be modeled as straight beams between spokes, rigidly connected at their ends with no effect on the deflection results. The arch in rim segments is not a buckling element in that axis. Jobst Brandt jobst.brandt@stanfordalumni.org