Answer to Question #293705 in Mechanical Engineering for Niaz

Question

A cylinder contains pressurized gas at 500 MPa and has the outer and inner diameters of 600 mm and 450 mm respectively. Determine the maximum permissible radial crack dimension on the outer surface of the cylinder in order to avoid further propagation of crack based on safety factor of 2.0. The cylinder material is BS 816 M40 of yield strength 1515 MPa.

Answer 1

Solution;

For thin cylinders under internal pressure only;

$\sigma_t=\sigma_r=\frac{r_i^2p_i}{r_o^2-r_i^2}(1+\frac{r_o^2}{r^2})$

Where subscript i is for internal and o for outer

$r_i=225mm=0.225m$

$r_o=300mm=0.3m$

$r=\frac{r_i+r_o}{2}=0.2625m$

By substitution;

$\sigma=\frac{0.225^2×500}{0.3^2-0.225^2}×(1+\frac{0.3^2}{0.2625^2})$

$\sigma=1482.5MPa$

The factor of safety is 2;

$\sigma_{allowable}=\frac{1482.5}{2}=741.25MPa$

But we know;

$E=\frac{\sigma}{\epsilon}$

$\epsilon=\frac{\sigma}{E}=\frac{741.25}{1515}=0.4893$

But;

$\epsilon=\frac{\Delta C}{C_o}$

C is the circumference;

$\Delta C=π×0.6×0.4893=0.922m$