There may be other ways to achieve what you want. Here is how I would achieve your goal.

Analysis Settings

   Auto Time Stepping, On

      Initial Substeps 10

      Minimum Substeps 10

   Large Deflection, On

In the Solution Branch, insert a directional deformation plot using the horizontal coordinate direction and scope it to the top of the cylinder.

After you solve, you will have tabular data for Time, Applied Force and Horizontal Deformation.  Pick the value of force when the horizontal deformation reaches the threshold.

This assumes that the applied force is large enough.  If the horizontal deformation didn't reach the threshold, make it larger. If you want more resolution in the tabular output, use more substeps.