Q$1$: A simply supported beam with overhang $($beam ABC in Figure $1)$ has span and overhang lengths of $Sm$ and $4m,$ respectively. The beam is subjected to a uniformly distributed load $($UDL$)$ of $k\frac{N}{m}.$ The beam has an I$-$shaped cross section with unequal top and bottom flanges as shown in Figure $1.$ The beam has also unequal allowable strengths in compression and tension, i$.$e$.$: compression: ${}_c=100$MPa; and tension: ${}_t=150$MPa. Calculate the maximum value of UDL $q$ in $k\frac{N}{m}$ that can be carried by the beam.

$(20$ marks$)$

Figure $1$

Not to scale. All dimensions in $mm.$

Figure $1$ Beam problem