End Cap Vessel
Consider a vessel with end caps is filled with helium until the internal pressure reaches 900 psi. If the vessel has an outer diameter of 25 inches and a thickness of 5 inches, what is the axial stress in psi?
Expand Hint
The cylinder can be considered thin-walled if:
$$$t\leq \frac{d_i}{20}$$$
where
$$t$$
is the wall thickness, and
$$d_i$$
is the inner diameter.
Hint 2
For vessels with end caps, axial stress is:
$$$\sigma_a=P_i\frac{r_{i}^{2}}{r_{o}^{2}-r_{i}^{2}}$$$
where
$$P_i$$
is the internal pressure,
$$r_o$$
is the outside radius, and
$$r_i$$
is the inside radius.
The cylinder can be considered thin-walled if
$$t\leq \frac{d_i}{20}$$
where
$$t$$
is the wall thickness, and
$$d_i$$
is the inner diameter.
$$$t\leq \frac{(25in-5in)}{20}=\frac{(20in)}{20}=1\:inch$$$
Since
$$5\:in> 1\:in$$
, the cylinder is thick-walled.
For thick-walled vessels with end caps, the axial stress is:
$$$\sigma_a=P_i\frac{r_{i}^{2}}{r_{o}^{2}-r_{i}^{2}}$$$
where
$$P_i$$
is the internal pressure,
$$r_o$$
is the outside radius, and
$$r_i$$
is the inside radius.
$$$\sigma_a=900\frac{lb}{in^2}\times \frac{(20in/2)^{2}}{(25in/2)^{2}-(20in/2)^{2}}=900\frac{lb}{in^2}\times \frac{(10in)^{2}}{(12.5in)^{2}-(10in)^{2}}$$$
$$$=900\frac{lb}{in^2}\times \frac{100in^{2}}{156.25in^{2}-100in^{2}}=900\frac{lb}{in^2}\times \frac{100}{56.25}=1,600\:psi$$$
1,600 psi
Time Analysis
See how quickly you looked at the hint, solution, and answer. This is important for making sure you will finish the FE Exam in time.- Hint: Not clicked
- Solution: Not clicked
- Answer: Not clicked
Similar Problems from FE Sub Section: Thick-walled Cylinder
171. Thick Walled Vessel
523. Thick Vessel
528. Internal Pressure
Similar Problems from FE Section: Cylindrical Pressure Vessel
056. Tangential Stress
171. Thick Walled Vessel
266. Thin Wall Cylinder
314. Hoop Stress
376. Pressure Cylinder
523. Thick Vessel
528. Internal Pressure
532. Axial Stress