Simply Supported Beam : Point Load at the Centre

Simply Supported Beam : Point Load at the Centre (Fig. 3.15)

S.F.D. : From symmetry ,

For AC, F_x=+R_A=+ , and is constant from A to C.

For CB, F_x=R_A-W= -W=-  and is constant from C to B.

The S.F.D. is shown in Fig. 3.15(a).

B.M.D. : For AC, M_x=-R_A.x=- x (linear)

When x=0, M_A=0 ; When x= , MC=- .

By symmetry, M_B=0.

The B.M.D. will be a triangle, having maximum ordinate the centre, as shown in Fig. 3.15(c).