Shear force diagram (SFD) and bending moment diagram (BMD) are a graph of shear force / bending moment plotted against the horizontal axis x, indicating the shear force / bending moment  withstood by the beam section along the length of the beam.

Plot an appropriate shear force diagram and bending moment diagram for each of the following situations, where necessary calculations and expressions may be needed to show the work.

Also, determine the location of the maximum bending moment and its value in each case. If the beams used in these examples have a circular cross-section, with diameter D = 55 mm, calculate the maximum stress produced by the maximum bending moment. The modulus of elasticity of the material is given E = 110 Mpa.

(1). Single point loading and uniform loading on a cantilever beam

(2). Double point loading and uniform loading on a cantilever beam 

(3). Point loading and uniform loading on a simply supported beam