# Solution to Problem 133 Pressure Vessel

**Problem 133**

A cylindrical steel pressure vessel 400 mm in diameter with a wall thickness of 20 mm, is subjected to an internal pressure of 4.5 MN/m^{2}. (a) Calculate the tangential and longitudinal stresses in the steel. (b) To what value may the internal pressure be increased if the stress in the steel is limited to 120 MN/m^{2}? (c) If the internal pressure were increased until the vessel burst, sketch the type of fracture that would occur.

#### Solution 133

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*longitudinal section*):

$F = 2T$

$pDL = 2(\sigma_t tL)$

$\sigma_t = \dfrac{pD}{2t} = \dfrac{4.5(400)}{2(20)}$

$\sigma_t = 45 \, \text{MPa}$ *answer*

Longitudinal Stress (*transverse section*):

$F = P$

$\frac{1}{4} \pi D^2 p = \sigma_l (\pi Dt)$

$\sigma_l = \dfrac{pD}{4t} = \dfrac{4.5(400)}{4(20)}$

$\sigma_l = 22.5 \, \text{MPa}$ *answer*

Part (b)

$\sigma_t = \dfrac{pD}{2t}$

$120 = \dfrac{p(400)}{2(20)}$

$p = 12 \, \text{MPa}$ *answer*

The bursting force will cause a stress in the longitudinal section that is twice to that of the transverse section. Thus, fracture is expected as shown.

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