Problem $2$

The $150300$ wood beam has been strengthened by bolting the steel reinforcement shown to it$.$ The modulus of elasticity for wood is $12\mathrm{.}4$ GPa $,$ and for steel is $200$ GPa $.$ Knowing that the beam is bent about a horizontal axis by a bending moment $M=50kN.$m$.$ Determine the maximum compressive and tensile stresses in the wood and steel.

M

$A=2175m{m}^2$

$d=203\mathrm{.}2mm$

$t_w=5\mathrm{.}6mm$

$b_f=57\mathrm{.}4mm$

$t_f=9\mathrm{.}9mm$

$I_x=13\mathrm{.}5{10}^{6}m{m}^4$

$I_y=0\mathrm{.}55{10}^{6}m{m}^4$

$\stackrel{}{x}=15mm$