Find hoop and longitudinal stress in thin-walled cylinders or stress in spheres. Calculate required thickness from a given allowable stress.
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Worked examples
These are the solver's own reference problems — the answers come from published sources or independent hand computation, never from the solver itself. The solution below is the live solver output for each.
Example 1
SI cylinder: p = 1.2 MPa, D = 1 m, t = 10 mm
Given
internal pressure
1.2 MPa
diameter
1 m
wall thickness
10 mm
Assumptions
Thin-wall membrane theory: uniform stress through the wall, valid for r/t of about ten or more; p is gage pressure.
Solution steps
Hoop and longitudinal stresses
The hoop direction carries twice the longitudinal stress — cylinders split along their length, not around it.
σh = p·r/t; σl = p·r/(2t)
r/t = 50; σh = 60 MPa; σl = 30 MPa
= 60 MPa
Results
Hoop (circumferential) stress σh
60MPa
Longitudinal (axial) stress σl
30MPa
r/t ratio
50
Where this answer was checked
source
σh = p·r/t, σl = p·r/2t (NCEES FE Reference Handbook) — hoop and longitudinal stresses
verified by
hand-recomputed
derivation
r = 0.5 m. σh = 1.2e6·0.5/0.010 = 60 MPa; σl = 30 MPa; r/t = 50.
Example 2
US cylinder: p = 200 psi, r = 18 in, t = 0.5 in
Given
internal pressure
200 psi
radius
18 in
wall thickness
0.5 in
Assumptions
Thin-wall membrane theory: uniform stress through the wall, valid for r/t of about ten or more; p is gage pressure.
Solution steps
Hoop and longitudinal stresses
The hoop direction carries twice the longitudinal stress — cylinders split along their length, not around it.