Cantilever along a Uniformly Distributed Load:

Let a cantilever beam AB of length l carrying uniformly distributed load of w per unit run, over the total length of the beam as illustrated in Figure

Figure

Let a section XX at a distance x from the right end B,

SF at this section, F_x = + w x (plus sign denoted right downward)

 SF at B, FB = 0          (at x = 0)

SF at A, FA = + w l    (at x = l )

Reaction at the support A, RA = wl.

As the loading is uniformly distributed load, the SF diagram shall be inclined and also, the shear force equation is straight line equation.

BM at section xx, M_x = - w × l × (l/2) (minus sign indicates right anticlockwise).

SF at B, M_B = 0          (at x = 0)

SF at A, MA = - wl ² / 2 (at x = l )

The bending moment diagram shall be in the form of parabolic curve.