Bending: force and moment diagrams

A cantilever beam is fully constrained on one end, attached to a wall for example, and has a load acting at the other end.

Static equilibrium conditions

Static equilibrium conditions are applied to determine the external support reactions, and the external moment acting on the beam in the embedded end:

Sum of forces including internal transverse (shear) force Q in Y-direction is equal to zero.

Sum of the moments relative to the chosen point, including internal bending moment M_x, is equal to zero.

The resulting internal bending moment in the beam is proportional to the distance from the free end z. The situation is similar if load is distributed q.

The figures show different loading schemes and corresponding diagrams of shear force Q and bending moment M. For the same external load, the support structure can affect the maximum values of the bending moment M.