Problem 1: Concentrated Load, simply supported beam...A 6.6 m long beam is simply supported at the ends and carries a concentrated load of 5 kN at its center. Draw the shear and bending moment diagrams.

Solution: From the symmetry, the reactions are equal and are 2.5 kN. To determine the shear and bending moment at any point within the beam, I draw free body diagrams using a cut between A and the load and another between the load and B:
 

	V = 2.5 kN M =2.5 x   kN-m
	V = 2.5 - 5 = -2.5 kN M = 2.5x - 5(x-3.3) = 16.5 - 2.5x Note that, at x = 6.6 m, M = 0 as it should be. At 3.3 m, M has its maximum value of 8.25 kN-m.

By convention, V is positive down and M is positive counterclockwise.

The plots are: