Question $2$:

A $75$ mm by $200$ mm deep sawn timber beam in a domestic dwelling supports an applied characteristic uniformly distributed permanent action of $1\mathrm{.}3k\frac{N}{m},$ an applied characteristic uniformly distributed medium term variable action of $1\mathrm{.}5k\frac{N}{m}$ and an applied characteristic point load permanent action of $1$ kN at mid span. The beam is simply supported and rests directly on a bearing plate having a bearing length of $100$ mm at each end of the beam. Each bearing plate in turn rests on a masonry wall of thickness $250$ mm and the beam has a clear span of $2\mathrm{.}75$ m $.$ The timber is of strength class C$24$ to BS EN $338$:$2003$ and functions in service class $2$ conditions. The beam is laterally restrained against lateral buckling along its length. Determine whether the beam is adequate in bending, shear, bearing and deflection according to the requirements of Eurocode $5.$