Thick Vessel
Consider an air cylinder’s pressure gauge reads 2,100 kPa. If the cylinder is made of a 125 mm aluminum rolled plate, with an internal diameter of 600 mm, what is the tangential (hoop) stress (kPa)? Assume a thick walled cylinder.
Expand Hint
For internal pressure only, the stresses at the inside wall are:
$$$\sigma_t=P_i\frac{r_o^{2}+r_i^{2}}{r_o^{2}-r_i^{2}}$$$
where
$$P_i$$
is the internal pressure,
$$r_o$$
is the outside radius, and
$$r_i$$
is the inside radius.
Hint 2
Because this is a thick walled vessel, the stresses caused by the internal pressure on the inside wall is:
$$$\sigma_t=P_i\frac{r_o^{2}+r_i^{2}}{r_o^{2}-r_i^{2}}$$$
where
$$P_i$$
is the internal pressure,
$$r_o$$
is the outside radius, and
$$r_i$$
is the inside radius.
The radii are:
$$$r_o=\frac{600}{2}+125=425\:mm$$$
$$$r_i=\frac{600}{2}=300\:mm$$$
Solving for tangential stress:
$$$\sigma_t=2,100kPa\times \frac{425^{2}+300^{2}}{425^{2}-300^{2}}$$$
$$$=2,100kPa\times \frac{270,625}{90,625}$$$
$$$=6,271\:kPa$$$
6,271 kPa
Time Analysis
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