SOLID MECHANICS / ELASTICITY : what are the boundary conditions to this problem?

I am supposed to solve this by using Airy stress function. We have the general formulas for the stresses sigma_r, sigma_theta, and tau_rtheta. However, I do not quite understand what the boundary conditions are.

I understand that sigma_theta when theta = beta, which is the normal stress of the loaded side of the sheet, sigma_theta = sigma_0. And that when theta = 0, which is the unloaded side, then sigma_theta = 0

But what would sigma_r and tau_rtheta be? Since it is a thin plate, would they be zero? However, this is a generalized plane strain scenario since the sheet extends infinitely in the r-direction, so the strain epsilon_r will be 0... in that case, I suppose sigma_r would not necessarily be 0?