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## Q. 1.28

A concrete pile 6 m long has a diameter 300 mm. It is driven into the ground using a hammer of 5 kN. Calculate the height of fall of the hammer if the maximum instantaneous stress the concrete can withstand is 20 N/mm². Take the modulus of elasticity of concrete as 25000 N/mm².

## Verified Solution

Using Eq. (1.28)

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

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

$h =\frac{20^2}{2 \times 25000} \times \frac{\pi}{4} \times \frac{300^2 \times 6000}{5000}-\frac{20 \times 6000}{25000} =673.8 mm$