Question $4$

The beam ABCD, shown below in figure $2$ is $12$ metres long. The beam is simply supported

at point A on the left side of the beam, and at point $C,4$ metres in from point A $.$ There are

concentrated loads of $10$ kN and $40$ kN at points B and D respectively, together with

uniformly distributed loads of $6k\frac{N}{m}$ between points A and $B,$ and $4k\frac{N}{m}$ between points

C and D$.$

Figure $2$

a$)$ Calculate the reactions of the supports A and C

$(6$ marks$)$

b$)$ Using graph paper draw the shearing force and bending $(10$ marks$)$

moment diagrams, labelling all relevant values

$(4$ marks$)$

with the position of any points of contra$-$flexure.