Length limit: There is no length limit$.$ Answer all questions below.

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 $qk\frac{N}{m}.$ 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 $1$

All dimensions in $mm.$