THIN & THICK CYLINDERS AND SPHERES
THIN CYLINDERS
Where
p = internal pressure
d = diameter of cylinder
t = thickness of the cylinder
μ = Poisson's ratio
Hence
or
THIN SPHERICAL SHELLS
s_{1} =s_{2} = (tensile in nature)
CYLINDERS WITH HEMISPHERICAL ENDS
Let t_{c} = thickness of the cylinder
t_{s} = thickness of the hemisphere
Thus, equating the two strains in order that there shall be no distortion of the junction.
This means thickness of cylindrical part should be more than the hemispherical part.
THICK CYLINDRICAL SHELL
its diameter then it is called thick shell.
The following three types of stresses are existing in thick cylinders :
(i) The radial pressure ‘p_{x}’ (compressive)
(ii) The hoop stress f_{x} (tensile)
(iii) The longitudinal tensile stress p_{o} (tensile)
Hoop stress, is given by
Radial pressure is given by
Equation (ii) and (iii) are called Lame’s equation.
r_{o} = outer radius of shell
r_{i} = inner radius of shell
A and B are Lame’s constant
Note:
1. Longitudinal tension is uniform across the thickness.
2. Hoop tension vary form maximum at inner face to minimum at outer face hyperbolically.
3. Radial compression varies from maximum at inner face to zero at outer face (atm.) hyperbolically.
Use Code STAYHOME200 and get INR 200 additional OFF

Use Coupon Code 
6 videos89 docs55 tests
