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## Q. 1.27

Determine the maximum height from which a weight of 25 N shown in Fig. 1.36 can be dropped onto the flange attached to a 10 mm diameter rod of length 1 m if the maximum stress is not to exceed 150 MPa. Take E = 200 GPa.

## Verified Solution

Using Eq. 1.28,

$\sigma _{\text{max}}^2 -2\frac{W}{A}\sigma _{\text{max}}-\frac{2WhE}{AL}=0$     (1.28)

$W\left(h+\frac{\sigma_{\max } L}{E}\right)=\frac{\sigma_{\max }^2}{2 E} \times A L$

where, $\sigma_{\max }=150 MPa , \quad W=25 N$

L = 1000 mm ,  E = 200000 MPa

$A=\frac{\pi}{4} \times 10^2=78.54 mm ^2$
or, $h=\frac{150^2 \times 78.54 \times 1000}{2 \times 200000 \times 25}-\frac{150 \times 1000}{200000}$ = 175.96  mm