Task $1$

a$.$ A simply supported beam with total length of $10m$ carries concentrated load of $10kN$ and a uniformly distributed load $($UDL$)$ of $2k\frac{N}{m}$ as shown in the figure below.

i$.$ Calculate and construct the distribution of the shear force and the bending moment diagrams.

ii$.$ Determine the maximum bending moment.

iii. If the beam has a rectangular cross section with width of $15cm$ and height of $30cm,$ calculate the second moment of area and then maximum bending stress, ignoring the weight of the beam.