counterclockwise couple

Problem 527
A homogeneous cylinder 3 m in diameter and weighing 30 kN is resting on two inclined planes as shown in Fig. P-527. If the angle of friction is 15° for all contact surfaces, compute the magnitude of the couple required to start the cylinder rotating counterclockwise.
 

Problem 528
Instead of a couple, determine the minimum horizontal force P applied tangentially to the left at the top of the cylinder described in Prob. 527 to start the cylinder rotating counterclockwise.
 

Problem 253
In Fig. P-253 a system of forces reduces to downward vertical force 400 lb through A plus a counterclockwise couple of 800 lb·ft. Determine the single force that will produce an equivalent effect.
 

Problem 250
The cantilever truss shown in Fig. P-250 carries a vertical load of 10.8 kN. The truss is supported by bearing at A and B which exert the forces A_v, A_h, and B_h. The four forces shown constitute two couples which must have opposite moment effects to prevent movement of the truss. Determine the magnitude of the supporting forces.