Question $5$

Two wood beams, each of rectangular cross$-$section $(100mm90mm,$ actual dimensions$),$ are glued together to form a solid beam with dimensions $200mm90mm$ as shown in the figure. The beam is simply supported with a span of $2\mathrm{.}5$ m and loaded as shown in the figure. What is the maximum moment $M_{\text{m}\text{a}\text{x}}$ that may be applied at the left support if the allowable shear stress in the glued joint is $1\mathrm{.}4$ MPa and the allowable bending stress in wood is $17\mathrm{.}25$ MPa $?($Include the effects of the beam's own weight, assuming that the wood weighs $5\mathrm{.}4k\frac{N}{m^3}.)$

$[$Ans$.M_{\text{m}\text{a}\text{x}}=3\mathrm{.}24kN-m]$