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.
Step-by-Step
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