Tangential Stress
Consider an air cylinder’s pressure gauge reads 1,700 kPa. If the cylinder is made of a 10 mm steel rolled plate, with an internal diameter of 500 mm, what is the tangential stress inside the tank?
Expand Hint
A cylinder is considered thin walled if
$$$\frac{t}{\frac{d_{i}}{2}}\leq 0.10$$$
where
$$t$$
is the wall thickness, and
$$d_i$$
is the inner diameter.
Hint 2
The tangential (hoop) stress formula is:
$$$\sigma _{t}=\frac{P_{i}r}{t}$$$
where
$$P_i$$
is the internal pressure,
$$t$$
and the thickness, and
$$r$$
is the average radius.
First, let’s determine if the cylinder can be considered thin-walled:
$$$\frac{t}{\frac{d_{i}}{2}}\leq 0.10\rightarrow \frac{10mm}{\frac{500mm}{2}}=0.04\leq 0.10\rightarrow cylinder\:is\:thin\:walled$$$
Thus, the tangential (hoop) stress formula is:
$$$\sigma _{t}=\frac{P_{i}r}{t}$$$
where
$$P_i$$
is the internal pressure,
$$t$$
and the thickness, and
$$r$$
is the average radius or more specifically:
$$$r=\frac{r_{i}+r_{o}}{2}=\frac{250mm+260mm}{2}=255mm$$$
Finally,
$$$\sigma _{t}=\frac{P_{i}r}{t}=\frac{1.7MPa\cdot 255mm}{10mm}=43.35\:MPa$$$
43.35 MPa
Time Analysis
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