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Chapter 10

Q. 10.16

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.

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Verified Solution

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.