Okay, there must be some tension in the web and we want gravity turned on. Gravity is created using an Acceleration load. Accelerating in the +X direction causes mass to experience a downward force in the same way as if Standard Earth Gravity was set to the -X direction. The benefit of an Acceleration load over using Standard Earth Gravity is the magnitude of acceleration can be ramped up from zero using an Acceleration.

Note that a Joint Moment load was added to provide a load to turn against and create higher web tension in the top (+X side of the web) than the bottom.

The web has Membrane Stiffness only as previously mentioned.

Tension is created by an offset in the contacts, which is resolved in Step 1, with Time Integration Off.
Note that the Normal Stiffness Factor is 0.1 which helps the contact algorithm converge.

Gravity and the Moment load are ramped on in Step 2 with Time Integration Off. This concludes the setup of the model.

Step 3 is where the rotational velocity ramps up to 1 rad/sec.

Here is the Ansys 2022 R2 archive: