The ratio of hoop stress to longitudinal stress in thin walled cylinders is 
For the analysis of thick cylinders, the theory applicable is
Lame’s theory is applicable in the analysis of thick cylinders.
According to Lame’s equation, hoop stress for a thick cylinder at any point at a radius r from centre is equal to
In a thick cylinder pressurized from inside, the hoop stress is maximum at
Hoop stress,
Hence hoop stress will be maximum at inner radius and minimum at outer radius.
The variation of the hoop stress across the thickness of a thick cylinder is
Hoop stress is tensile in nature and vary hyperbolically with a maximum at inner surface and minimum at outer surface.
If a thick cylindrical shell is subjected to internal pressure, then hoop stress, radial stress and longitudinal stress at point in the thickness will be
In a thick cylinder, hoop stress is tensile in nature while radial stress is compressive and longitudinal stress is also tensile in nature.
Principal stresses on the outside surface element of a thin cylindrical shell subjected to internal fluid pressure as shown in the figure, are represented by
A thickwalled hollow cylinder having outside and inside radii of 90 mm and 40 mm respectively is subjected to an external pressure of 800 MN/m^{2}. The maximum circumferential stress in the cylinder will occur at a radius of
The maximum hoop stress will always occurs at inner most radii irrespective of the location of pressure.
A thin cylinder contains fluid at a pressure of 500 N/m^{2}, the internal diameter of the shell is 0.6 m and the tensile stress in the material is to be limited to 9000 N/m^{2}. The shell must have a minimum wall thickness of nearly
σ_{1} = pd/2t
A thick cylindrical pressure vessel of inner diameter D_{i}. and outer diameter D_{o} is subjected to an internal fluid pressure of intensity ‘p’. The variation of the circumferential tensile stress 'p_{y}’ in the thickness of the shell will be
Variation of hoop stress (σ_{h}) and radial pressure (p_{r}) can be obtained by using Lame’s equation i.e.
σ_{h } p_{r} = 2A
at r = D_{i} we get p_{r} = p
r = D we get p_{r} = 0
Radial pressure distribution is given by figure (b).
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