A third$-$point bending test was performed on a $50$x$200$mm wood

lumber according to ASTM D$198$ procedure with a span of $1\mathrm{.}5$m

and the $200$mm side is positioned vertically. A strain gauge is

glued at the centre point between the supports. The strain gauge

is zeroed at the start of the test when the force is zero. A strain of

$0\mathrm{.}00288$ is measured when the combined load is $8\mathrm{.}357$kN and

the load$-$strain curve is in the linear range. Determine the flexural

modulus of elasticity $(5$ points$).$ If the maximum combined load

on both loading bearings was $28\mathrm{.}369$kN$,$ calculate the modulus of

rupture $(5$ points$).$