A cylindrical shell that is 36 -in. ID by 2.5-in. thick contains a perpendicular nozzle that is 4 -in. ID by 0.75-in. thick. The design pressure is 1900 psi at a design temperature of 450°F. The vessel is subjected to cyclic operation and a fatigue analysis is required. Peak stresses and stress

Question

A cylindrical shell that is 36 -in. ID by 2.5-in. thick contains a perpendicular nozzle that is 4 -in. ID by 0.75-in. thick. The design pressure is 1900 psi at a design temperature of 450°F. The vessel is subjected to cyclic operation and a fatigue analysis is required. Peak stresses and stress concentration factors are not known for the specific geometry to be used. What method can be used to evaluate the peak stresses for a fatigue analysis?

Accepted Answer

At the intersection of the nozzle to the shell, peak stresses are obtained according to Eq. 11.48. The nominal stress is determined as

[latex]\sigma=I \frac{P D_{m}}{4 T_{s}}[/latex] (11.48)

[latex]\sigma=\frac{P D_{m}}{2 T_{s}}=\frac{1900(36+2.5)}{2(2.5)}=14,630 \ psi[/latex]

The peak stresses are determined as follows using the factors for stress index I from Table 11.5:

Table 11.5 Stress Index I
Stress	Spherical Shells and Formed Heads		Cylindrical Shells
	Spherical Shells and Formed Heads		Longitudinal Plane		Transversc Planc
	Inside	Outside	Inside	Outside	Inside	Outside
[latex]\sigma_{n}[/latex]	2.0 - (r/R)	2.0 - (r/R)	3.1	1.2	1.0	2.1
[latex]\sigma_{t}[/latex]	-0.2	2.0 - (r/R)	-0.2	1.0	-0.2	2.6
[latex]\sigma_{r}[/latex]	[latex]-4 T_{s} / D_{m}[/latex]	0	[latex]-2 T_{s} / D_{m}[/latex]	0	[latex]-2 T_{s} / D_{m}[/latex]	0

Stress (psi)	Longitudinal Plane		Transversc Planc
Stress (psi)	Inside	Outside	Inside	Outside
Hoop stress	+45,350	+17,560	+14,630	+30,720
Longitudinal stress	-2,930	+14,630	-2,930	+38,040
Radial stress	-1,900	0	-1,900	0

These values are the peak stresses due to internal pressure only and must be combined with other peak stresses occurring at the same location on the shell for a fatigue evaluation.

Question 11.14: A cylindrical shell that is 36 -in. ID by 2.5-in. thick cont...

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