Cantilever Beam Subjected to Couple:

Let us assume a cantilever beam AB of length subjected to an anticlockwise couple μ at a distance a from the fixed end as illustrated in Figure.

      Figure

As the moment is applied at C, the portion BC is not subjected to any moment.

Bending Moment (Starting from the End B)

BM at B,         M_B = 0

BM just right of C, M_C = 0     (considering right side)

BM just left of C, M_C = + μ   ('+' sign indicates right clockwise)

BM at A, M_A = + μ     ('+' sign indicates right clockwise)

As there is no load among A and C, the bending moment diagram shall be horizontal line among A and C.

Though, the beam is not subjected to any load; the SF on the beam is zero.