A simply supported $200$ mm deep and $75$ mm wide beam is subjected to

externally applied loading as shown in Figure Q$1$ below. The loading consists

of a concentrated point load of magnitude P $=10$ kN that is located at C$,$ a

uniformly distributed loading of magnitude w $=2$ kN$/$m$,$ and axial tensile loads

of magnitude F $=15$ kN that act through the neutral axis of the beam.

$($a$)$ Determine:

i$.$ The support reactions at A and B $(4$ marks$)$

ii$.$ The maximum bending moment in the beam and its location

$(4$ marks$)$

iii. The maximum bending stress $($in units of MPa$)$ that occurs in the

beam $(4$ marks$)$

iv$.$ The maximum axial stress $($in units of MPa$)$ that occurs in the beam