Question 10.16: A weight 200 N falls through a height h = 300 mm onto the mi...
A weight 200 N falls through a height h = 300 mm onto the middle of a simply supported beam of length 3 m. Calculate the required cross-sectional area A and the maximum bending is not to exceed 7 MPa and E = 10 GPa for the beam material.
We note the static deflection, \delta_{ st } of the simply supported beam due to 200 N load at midpoint is \delta_{\text {st }}=W L^3 / 48 E I and this assumed to be much less than 300 mm. Therefore, from the results of the previous problem
\sigma_{\max }=\sqrt{\frac{18 E h W}{A L}}
Therefore, the cross-sectional area is
A=\frac{18 W E h}{\sigma_{\max }^2 L}=18 \frac{W}{\sigma_{\max }} \frac{E}{\sigma_{\max }} \frac{h}{L}
=\frac{(18)(200)}{(7)\left(10^6\right)} \frac{10\left(10^3\right)}{7} \frac{300}{3000} m ^2
or A = 0.07347 m² ⇒ A = 734.7 cm²
The required cross-sectional area of the beam is 734.7 cm².