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Chapter 1

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.

Screenshot 2022-10-09 164444

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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