Question

The hoop stress for a 2 mm thick tube is 200 Pa. What will be the hoop stress if the thickness changes to 4 mm and radius remains unchanged?

100 Pa

 

400 Pa

 

200 Pa

 

50 Pa

​

Answer 1

Dhilkore dhilkoreee o lalal

Answer 2

Given:-

Hoop stress, $\sigma_{c}=200Pa$

$\text{thickness, t}=2\text{mm}$

New thickness, $t^{'}=4\text{mm}$

To Find:-

Hoop stress at new thickness

Explanation:-

Formula to calculate hoop stress is given by, $\sigma_{c}=\frac{Pr}{t}$ where,

P=pressure induced in the tube

t=thickness

r=internal radius

In the question, only thickness changes and rest parameters are same. Therefore,

$\sigma_{c}\propto\frac{1}{t}$

Let new hoop stress corresponding to t' be $\sigma_{c}^{'}$. Then,

$\frac{\sigma_{c}}{\sigma_{c}^{'}}=\frac{t^{'}}{t}$

$\frac{200}{\sigma_{c}^{'}}=\frac{4}{2}=>\sigma_{c}^{'}=100Pa$

Therefore, new hoop stress will be 100Pa