(Solved): A glue-laminated timber beam is reinforced by carbon fiber reinforced plastic (CFRP) material bonde ...

A glue-laminated timber beam is reinforced by carbon fiber reinforced plastic (CFRP) material bonded to its bottom surface. The cross section of the composite beam is shown. The elastic modulus of the wood is $9.9\mathrm{GPa}$ and the elastic modulus of the CFRP is $114\mathrm{GPa}$. The simply supported beam spans $4\mathrm{m}$ and carries a concentrated load $P$ at midspan. Assume $b_w=68\mathrm{mm},b=55\mathrm{mm},d_w=220\mathrm{mm}$ and $\mathrm{t}=5\mathrm{mm}$. (a) Determine the maximum bending stresses ${\sigma }_t,{\sigma }_p$ produced in the timber and the CFRP if $P=3.4\mathrm{kN}$. (b) Assume that the allowable bending stresses of the timber and the CFRP are $8.6\mathrm{MPa}$ and $1680\mathrm{MPa}$, respectively. Determine the largest acceptable magnitude for concentrated load $P$. (You may neglect the weight of the beam in your calculations.)