machine element I chapter 5

1. CHAPTER 5
PRESSURE VESSEL

2. INTRODUCTION
 Pressure vessels are used to store fluids under pressure.
 The fluid stored may undergo a change of state inside.
 Material of pressure vessels may be brittle (cast iron) or ductile (mild steel)
Classification of pressure vessels, according to:
 The dimensions:
Thin shell
Thick shell
 The internal pressure (p) and the allowable stress (𝜎𝑡) of the material of the
shell.
thin shell.
Thick shell
 To the end construction
 open end
Closed end

3. Horizontal type
Vertical Type

4. CONT’D…..
Spherical
Type

5. STRESS IN A THIN CYLINDRICAL SHELL DUE TO INTERNAL
PRESSURE
The analyses of stresses in based on the following assumptions
• The effect of curvature of the cylinder wall is neglected.
• The tensile stress is uniformly distributed over the section of the walls.
• The effect of restraining action of the heads at the end of the pressure is
neglected. Likely failure of pressure vessels because of internal pressure

6. CIRCUMFERENTIAL OR HOOP STRESS
The total force acting on a longitudinal section along the diameter of the shell
is equal to:
• The intensity of internal pressure by the projected area = p(dl)
• Total resisting force acting on the cylinder wall =𝜎𝑡12tl
From both equations we have:

7. CONT’D.
It may be noted
• In design of engines cylinders a value of 6 to 12 mm is added to equation to permit re
boring after wear has taken place. Therefore:
• In constructing large pressure vessels like steam boiler, etc. riveted and welded
joints are used. In case of riveted joints the wall thickness of the cylinder of riveted
joint.
• In case of cylinders of ductile materials, circumferential stress (𝜎𝑡1 ) may be taken
0,8 times (𝜎 𝑦) and for brittle materials (𝜎𝑡1) may be taken as 0,125 times (𝜎 𝑢)
• In designing steam boilers, the wall thickness calculated, may be compared with the
minimum plate thickness provided by boiler code.

8. LONGITUDINAL STRESS
• It is the tensile stress acting in the transverse or circumferential section or on the ends of
the vessel.
• Total force acting at the transverse section, equal to the intensity of pressure by cross
sectional area by this the total force will be:
(𝜎𝑡2) longitudinal stress. Total resisting force = 𝜎𝑡2 𝜋dt
The total force: 𝑝𝜋
𝑑2
4
From equilibrium:
If (𝜂 𝑐) is the efficiency of the circumferential joint then:

9. CHANGE IN DIMENSIONS OF A THIN CYLINDRICAL SHELL DUE
TO INTERNAL PRESSURE
The increase in diameter of the shell due to internal pressure on the cylinder:
The increase in length of the shell due to internal pressure:
The increase in volume of the shell due to internal pressure is given by:

10. THIN SPHERICAL SHELL SUBJECTED TO INTERNAL PRESSURE.
• In designing thin spherical shells, we have to determine diameter of the shell
Knowing the storage capacity
• Thickness of the shell: The shell is likely to rupture along the center of the
sphere. Therefore: Force tending to rupture the shell along the center of the
sphere
• Resisting force of the shell: [Stress x Resisting area = 𝜎𝑡 𝜋𝑑𝑡 ]
• Equating equations, we have
• If (𝜂) the efficiency of the join, then

11. CHANGE IN DIMENSIONS OF A THIN SPHERICAL SHELL DUE
TO AN INTERNAL PRESSURE.
• Increase in diameter of the spherical shell due to internal pressure
• Increase in volume of the spherical shell due to internal pressure is given by
the following expression of the difference of volume:

12. EXERCISE