Supply Supported Beam Subjected to an Eccentric Couple:

Let a simply supported beam AB of span l, subjected to an anticlockwise couple μ at a distance from the left end A as illustrated in Figure.

 Figure

Taking moments about A and equating to zero,

R_B  × l + μ = 0

R_B  =- μ/ l

 (Negative sign denote the reaction at B is downward)

R_A  = Total downward load - R_B   = 0 - (μ/ l)  = +( μ/l)

Shear Force (Staring from the Left End A)

SF at A,            F_A =+ l/ μ

SF just left of B,            F _B   =+ μ/ l  =  Reaction at the support B.

Since, there is no load among A and B, the shear force diagram is horizontal.        

Bending Moment (Beginning from the Left End A)

BM at A,         M_A = 0

BM just left of C,

M _C =   ( μ/l) × a = + μa /l

 MB just right of C,       M _C   = + μa/ l - μ = μ (a - l )/ l = - μ (l - a)/ l

= - μb/ l                     (Q l - a = b)

BM just right of C, M _C = - l × b       (considering right side)