Influence of tire pressure and width on the rim stress

The tour Forum discussion about the effects of different tire widths

and Luftdrücke was on the load on the rim. This particular case was

about whether a MTB rim as the a 50mm tire with max. Designed 4bar, is

a 25mm tire to cope with 8 bar pressure can be bent without them too.

Since I has not left in peace, I once counted something: The bending

stress on the rim sidewalls consist primarily of two components, the

direct internal pressure acting on the flanks, and the horizontal

portion of the circumferential force of the tire. The latter one has

to think about this: The tire section is simplified seen a ring. When

this pressure is evenly under tension. Because of the "ring" but the

lower part is open and there is held together only available via the

rim, the rim must take this tension there. Interesting for the bent-up

in the case only the horizontal component of the voltage at the

junction of tire rim. This is the exit angle of the sidewall of the

rim depends. All horizontal forces are not neglected because they

hardly relevant for the question have. The calculation is based only

on one edge of the rim on the other hand, the burden of course

identical. Exposure to peripheral force: The exit angle α the sidewall

can be calculated geometrically: with b = B = inside rim width tire

width

The tangential force is calculated according to the boiler formula as

follows: p = tire pressure (1 bar corresponds to 0.1 N/mm2) D =

Outside diameter of the rim horizontal component FU_X obtained cos α

available via:

Calculation of the resulting force in the middle of the edge: the area

of the inside of the rim edge A is: h = height inner rim flank This

results in the resultant force Fp_R:

Calculation of the moment on the rim: at the foot of the Cross, the

forces lead to a bending moment to the outside: It all looks a mess

out in a formula, you get this:

h = internal height rim flank

p = tire pressure (1 bar corresponds to 0.1 N/mm2)

B = Tyre width

D = Outside diameter of the rim

b = internal width of the rim

means of this formula, you can now compare what you nicely with the appropriate

tires and air pressure of its rim so exacts. For ease, I've also

created a small Excel document to calculate.