Find the minimum and maximum of a ratio for equilibrium

[Aleph_null]

Homework Statement

Consider the rod as shown in the figure. The coefficient of static friction at A and B is \mu_s. I'm trying to find how big and how small the ratio l/d can be for the rod to still be in equilibrium. I have calculated how big all forces are acting upon the rod in the case just before sliding happens, but I'm not sure how to proceed.

Homework Equations

Just before sliding happens the friction force F is F = \mu_s * F_n, where F_n is the normal force.

The Attempt at a Solution

 

[Aleph_null]

They want the solution as an inequality in terms of \mu_s and theta, .i.e they want a LS and RS as LS < l/d < RS .

 

[Cutter Ketch]

I have calculated how big all forces are acting upon the rod in the case just before sliding happens, but I'm not sure how to proceed.

Have you? Could you show us that calculation? Did it involve 4 forces and 3 torques all written in terms of l, d, and θ?