PPT: Pressure Vessels (Thin Cylinder) | Strength of Materials (SOM) - Mechanical Engineering PDF Download

 Page 1


TOPICS
? INTRODUCTION
? STRESSES IN THIN CYLINDRICAL SHEELS
?HOOP STRESS(CIRCUMFERENTIAL STRESS)
?LONGITUDINAL STRESS
? C (IN) D (OF) (A) TCS (DUE) (TO) IP
? C (IN) V (OF) (A) TCS (DUE) (TO) IP
? THIN SPHERICAL SHEELS
Page 2


TOPICS
? INTRODUCTION
? STRESSES IN THIN CYLINDRICAL SHEELS
?HOOP STRESS(CIRCUMFERENTIAL STRESS)
?LONGITUDINAL STRESS
? C (IN) D (OF) (A) TCS (DUE) (TO) IP
? C (IN) V (OF) (A) TCS (DUE) (TO) IP
? THIN SPHERICAL SHEELS
THIN CYLINDER
If the wall thickness is less than about 7% of the inner 
diameter then the cylinder may be treated as a thin one. 
Thin walled cylinders are used as boiler shells,pressure
tanks, pipes and in other low pressure pocessing
equipments. 
Ingeneral three types of stresses are developed in pressure 
cylinders viz.
Circumferential or Hoop stress, Longitudinal stress in 
closed end cylinders and Radial stresses. 
Page 3


TOPICS
? INTRODUCTION
? STRESSES IN THIN CYLINDRICAL SHEELS
?HOOP STRESS(CIRCUMFERENTIAL STRESS)
?LONGITUDINAL STRESS
? C (IN) D (OF) (A) TCS (DUE) (TO) IP
? C (IN) V (OF) (A) TCS (DUE) (TO) IP
? THIN SPHERICAL SHEELS
THIN CYLINDER
If the wall thickness is less than about 7% of the inner 
diameter then the cylinder may be treated as a thin one. 
Thin walled cylinders are used as boiler shells,pressure
tanks, pipes and in other low pressure pocessing
equipments. 
Ingeneral three types of stresses are developed in pressure 
cylinders viz.
Circumferential or Hoop stress, Longitudinal stress in 
closed end cylinders and Radial stresses. 
In a thin walled cylinder the circumferential 
stresses may be assumed to be constant over the 
wall thickness and stress in the radial direction 
may be neglected for the analysis. Considering 
the equilibrium of a cut out section the 
circumferential stress and longitudinal stress can 
be found. 
Page 4


TOPICS
? INTRODUCTION
? STRESSES IN THIN CYLINDRICAL SHEELS
?HOOP STRESS(CIRCUMFERENTIAL STRESS)
?LONGITUDINAL STRESS
? C (IN) D (OF) (A) TCS (DUE) (TO) IP
? C (IN) V (OF) (A) TCS (DUE) (TO) IP
? THIN SPHERICAL SHEELS
THIN CYLINDER
If the wall thickness is less than about 7% of the inner 
diameter then the cylinder may be treated as a thin one. 
Thin walled cylinders are used as boiler shells,pressure
tanks, pipes and in other low pressure pocessing
equipments. 
Ingeneral three types of stresses are developed in pressure 
cylinders viz.
Circumferential or Hoop stress, Longitudinal stress in 
closed end cylinders and Radial stresses. 
In a thin walled cylinder the circumferential 
stresses may be assumed to be constant over the 
wall thickness and stress in the radial direction 
may be neglected for the analysis. Considering 
the equilibrium of a cut out section the 
circumferential stress and longitudinal stress can 
be found. 
Page 5


TOPICS
? INTRODUCTION
? STRESSES IN THIN CYLINDRICAL SHEELS
?HOOP STRESS(CIRCUMFERENTIAL STRESS)
?LONGITUDINAL STRESS
? C (IN) D (OF) (A) TCS (DUE) (TO) IP
? C (IN) V (OF) (A) TCS (DUE) (TO) IP
? THIN SPHERICAL SHEELS
THIN CYLINDER
If the wall thickness is less than about 7% of the inner 
diameter then the cylinder may be treated as a thin one. 
Thin walled cylinders are used as boiler shells,pressure
tanks, pipes and in other low pressure pocessing
equipments. 
Ingeneral three types of stresses are developed in pressure 
cylinders viz.
Circumferential or Hoop stress, Longitudinal stress in 
closed end cylinders and Radial stresses. 
In a thin walled cylinder the circumferential 
stresses may be assumed to be constant over the 
wall thickness and stress in the radial direction 
may be neglected for the analysis. Considering 
the equilibrium of a cut out section the 
circumferential stress and longitudinal stress can 
be found. 
2. Longitudinal Stress (s
L
) – This stress is directed along the
length of the cylinder. This is also tensile in nature and tends
to increase the length.
3. Radial pressure ( p
r
) – It is compressive in nature.
Its magnitude is equal to fluid pressure on the inside wall and
zero on the outer wall if it is open to atmosphere.
1. Hoop or Circumferential Stress (s
C
) – This is directed along the 
tangent to the circumference and tensile in nature.  Thus, there 
will be increase in diameter.