$(3)$ A timber beam $($simply supported span $=8$ feet, cross$-$section $($width $x$ depth$)=$

$10$ inch $12$ inch$)$ is loaded with two concentrated load $($magnitude of each concentrated load $=100lb.,$ two point loading$).$ Deflectometer connected at midspan shows a reading of $20($each small division of deflectometer $=0\mathrm{.}001$ inch$).$ What will be the modulus of elasticity & bending stiffness $($flexural rigidity$)$ of the beam material?

$(4)$ A steel I$-$beam $($simply supported span $=8$ feet, flange $=20$ inch width $x1$ inch thickness, web $=24$ inch depth $1$ inch thickness, modulus of elasticity $=29{10}^3$ksi $)$ is loaded with two$-$point loading. What will be the maximum value of concentrated load if

$($i$)$ deflection will not exceed $0\mathrm{.}0025$ inch.

$($ii$)$ allowable bending stress in tension is $40$ksi& allowable bending stress in compression $30$ksi.

$($iii$)$ deflection will not exceed $0\mathrm{.}001$ inch and bending stress is not allowed to exceed $40$ksi $($both in tension and compression$).$