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Question answers on thin shells increase

clarity and deep understanding. It is useful

in the design and construction of thin

shells. Thin shells are used almost in every

industry. LPG cylinder, pressure cooker,

boiler are common.

What is a thin sell?

where D/t > 20 and where stress are uniform from the inner surface to the outer surface of the shell.

What are the various types of thin shells?

Two types: (i) Cylindrical like a pipe (ii) Spherical like a ball

 What is the effect of joint efficiencies on the stress induced in the thin cylinder?

Joint efficiencies  increase the stresses in the cylinder.
Efficiency of longitudinal joint increase the hoop stress.
Efficiency of circumferential joint increase the longitudinal stress.

How is the stress variation in a thin shell?

(a) Linear variation

(b) Parabolic

(c) Linear and parabolic

(d) None

ANS: (d)

Discuss similarity and differences between thin and thick cylinder.

Both have hoop stress, longitudinal stress and radial stress
Thin cylinder:
(i) Stresses are uniform in the thin cylinder wall.
(ii) D/t >20
(iii) Radial stress is very small and neglected.
Thick Cylinder:
(I) Stresses are non uniform in the wall of the cylinder.
(ii) When (D / t) <20
(iii) Longitudinal stress is small and is neglected.


Which has the higher maximum stress?

(i) Cylindrical shell
(ii) Spherical shell
(iii) Both cylindrical and spherical shells
(iv) None
ANS: ( i)

Why is the radial stress neglected in a thin cylinder?

Hoop stress               σh = pi Di / 2t
Longitudinal stress   σL = pi Di / 4t
Radial stress               σr = pi
Minimum value of Di / t is 20.
Hoop stress                σh = 10 pi
Longitudinal stress    σL =5 pi
Radial stress               σr = pi
Radial stress is equal to fluid pressure and is very small as compared to hoop stress as well as longitudinal stress.

A boiler shell 200 cm diameter and 1.5 cm thickness is subjected to an internal fluid pressure of 1.5 M Pa. What is the hoop, longitudinal and radial stresses induced in the vessel? Also calculate the hoop and longitudinal strains.

Boiler is always a cylindrical vessel.
Hoop stress = σh = pi Di/2t = 1.5 x 200/ (2 x1.5) = 100 MPa
Longitudinal stress=pi Di/4t = 1.5 x 200/ (4 x1.5) = 50 MPa
Radial stress=pi Di/2t = 1.5  = 1.5 MPa
Hoop strain=(1/2E)[σh-μσl) =(1/2×200 x 1000)[100- 0.25 x 50)
=87.5/400000 = 0.000021875
Longitudinal strain=(1/2E)[σl-μσh) =(1/2×200 x 1000)[50- 0.25 x 100)                                                =25/400000 = 00000625