Q$4.$ A solid softwood timber beam is $130mm$ wide and $720mm$ in depth and is simply supported over a span of $5m.$ It is exposed to fire on $3$ sides. The beam system is at $600mm$ spacing and carries a permanent action on the beam of $5k\frac{N}{m}$ and a total variable load of $8k\frac{N}{m}.$ The characteristic flexural strength of the timber is $f_b=25\mathrm{.}0$MPa

a$.$ After $30$ minutes, what are the remaining dimensions of the beam?

b$.$ Check the design for normal conditions and for $30$min fire resistance rating, exposed to fire on three sides.

c$.$ Calculate the deflection under fire condition