Suppose I have stretched a rubber band around a cylinder of radius $R$ such that the rubber band is under tension $T$. My understanding is that in the ideal situation, with no friction, the band applies a force per unit length of $T/R$ radially to the cylinder. If the band has width $W$ and everything is uniform then it exerts a pressure of $T/RW$ to the cylinder. This is based on my own reasoning (though I haven't done any physics problems like this in over a decade), and some online sources:
This one says $4T/2\pi$ (so it does not depend on $R$) but I think that is incorrect (please correct me if I am wrong): Elastic band around a cylinder
My question is how does this change (if at all) if the friction between the rubber band and the cylinder is taken into account?