Two rectangular plates, one of steel and the other of brass each $40\…

Question

Two rectangular plates, one of steel and the other of brass each $40\text{ mm}$ wide and $10\text{ mm}$ deep are placed together to form a beam $40\text{ mm} \times 20\text{ mm}$. Which is simply supported at ends and having span of $1000\text{ mm}$. The brass plate being on the top of the steel plate. Determine the maximum load which can be applied at the center of the beam, if the plates are:

(i) put one over other

(ii) firmly secured throughout their length

Maximum allowable stress in steel is $112.5\text{ N/mm}^2$ and in brass is $75\text{ N/mm}^2$. Take $E_s = 200\text{ GPa}$ and $E_b = 80\text{ GPa}$.