Draw the shear and bending moment diagrams for the beams shown in the following figures an...

Draw the shear and bending moment diagrams for the beams shown in the following figures and find the values of the maximum bending stress.

Moments M1 and M2 are applied to the ends of the simply supported beam shown in Fig. 1. Light pointers of lengths 2l/3 and l/3 are attached to the ends as shown and are directed along the axis of the beam before applying the moments. If the distance a is measured, and if E, I, and l are known, show that moment M1 is equal to 6EIa/l2.

The idea of this problem can be used for finding the value of the unknown end moments acting on a beam. The pointers are clamped in position, and distance a is measured. Length l must be free from transverse loads.

Figure 1