a$.$ A $10m$ span simply supported timber beam is loaded by a uniformly distributed load of $3K\frac{N}{m}.$ Its normal section is $250mmx600mm$ and $E=30$GPa.

i$.$ P CalBulate the compressive stress at the point $100mm$ from the neutral axis

$(15$ marks$)$

ii$.$ Determine change in strain at the outer most fiber of the beam if additional $20kN$ concentrated load is applied at a distance $x=3m$ from the support.

$(20$ marks$)$