Simply Supported Beam : Eccentric Load

Simply Supported Beam : Eccentric Load (Fig. 3.16)

Reactions : Taking moments at B,

Similarly, taking moments at A,

S.F.D. : For AC, F_x=+   …(constant from A to C)

For CB,  and is constant from C to B.

The S.F.D. is shown in Fig. 3.16(b)

B.M.D. : For AC,

When x=0, M_A=0 ; When x=a,

Similarly, for CB, M_x=-R_A.x+W(x-a)

or

At x=a,  as before

At x=L, M_B=-Wb+W(L-a)=zero.

Hence, The B.M.D. will be a triangle having maximum ordinate under the point load.