Cantilevers:

Cantilevers along a Point Load at the Free End

Let us assume a cantilevers beam AB of length 'l' subjected to a point load W at the free end as illustrated in Figure .

   Figure

Reaction at the support A, R_A = W ↑ (As, ∑V = 0).

Let a section XX at a distance x from the free end. SF at this section is equivalent to the unbalanced vertical force either to the right or to the left of the section.

Let right side of the section, F_x = + W (plus sign denoted right downward).

The bending moment at this section, M_x = - W_x (minus sign denoted right anticlockwise).

The SF just on the left side of the point load is + W. As there is no loading among A and B, the shear force shall remain similar over the length of the beam, that means the shear force diagram shall be horizontal for the length AB. We know that M_x = - W_x, then we obtain

 BM at B, while x is zero, M_B = 0

 BM at A, Whereas x is 'l', M_A = - Wl

As there is no other load between A and B, the bending moment diagram shall be inclined, and the bending moment equation is straight line equation.