zpr(1 + cosO )
am co= (2.21)
2t[sin 00, + (r 0,)cos0 ]
Substituting Equation 2.5 into the balance of moments, Equation 2.7, yields the second
expression for om.
2M(1 + cos 0 )
"tr2 (2r 200 + sin 200 )
Combining Equations 2.21 and 2.22 by eliminating om and setting 00 = 0, yields Equation
2.23, the moment necessary to initiate wrinkling.
M = (2.23)
2
Equating the moment to initiate wrinkling, Equation 2.23, with the value of the maximum
moment in Equation 2.13 yields Equation 2.24.
L wL2 pair3
max M( )-w (2.24)
2 8 2
Solving for L and setting the load, w = F/L, gives the general expression for wrinkle
length, Equation 2.25. The wrinkle length is the length at which wrinkling first occurs in
an inflated tube subject to bending, for a given pressure and flow rate.
Lwr 4pR (2.25)
F
As expected, the wrinkle length will be reduced for high loading force, F, and
proportional to the internal pressure and the tube radius. Tube radius, r, is the largest
contributing factor to wrinkle length for these conditions.