Solve using Macaulay's method for beam theory.

A beam ABCDEF is uniformly supported at A and E.

It carries point loads of 100kN, 150kN and 80kN at B, D and F respectively and a uniformly distributed load of 40kN between C and E.

If AB = BC = 1m and, CD = DE = EF =2m and the flextural-stiffness of the beam is 1200 x 10³kNm²:

a. Calculate the deflection of the beam midway between the supports and at the overhanging end F.

b. Calculate the slope at the points A, E and F. (Comment).

Finally, sketch and annotate the slope and deflection diagrams for this beam.

**Subject Engineering Mechanical Engineering**