CHAPTER 5Thin Walled Pressure

Vessels

Cylindrical Pressure Vessels

129

• Cylindrical or spherical vessels are commonly used in industry to serve as boiler or tanks.

• When under pressure, material is subjected to a loading from all direction.

• In general, thin wall refers to a vessel having an inner-radius-to-wall-thickness ratio of 10 or 1/10 of the radius of the container

• Under this condition, the stress in the wall may be considered uniform.

• Some examples of cylindrical pressure vessel:i) compressed air tanksii) rocket motorsiii) fire extinguishersiv) spray cansv) pressurized pipes

• Pressure vessels are used in a variety of applications in both industry and the private sector. They appear in these sectors as industrial compressed air receivers and domestic hot water storage tanks.

• Other examples of pressure vessels are: diving cylinder, recompression chamber, distillation towers, autoclaves and many other vessels in mining or oil refineries and petrochemical plants, nuclear reactor vessel, habitat of a space ship, habitat of a submarine, pneumatic reservoir, hydraulic reservoir under pressure, rail vehicle airbrake reservoir, road vehicle airbrake reservoir and storage vessels for liquified gases such as ammonia, chlorine, propane, butane and LPG.

A pressure tank connected to a

domestic hot water system

a Pressure Vessel used in industry

Recompression chamber

• Cylindrical vessel with principal stresses

s1 = hoop stress

s2 = longitudinal stress

t

pr

xrpxtFz

1

1 220

s

s

• Hoop stress:

21

2

22

2

2

20

ss

s

s

t

pr

rprtFx

• Longitudinal stress:

• Points A and B correspond to hoop stress, s1,

and longitudinal stress, s2

• Maximum in-plane shearing stress:

t

pr

42

12)planeinmax( s

• Maximum out-of-plane shearing stress

corresponds to a 45o rotation of the plane

stress element around a longitudinal axis

t

pr

22max s

Spherical Pressure Vessels

• a closed structure containing liquids or gases under pressure

• Example of spherical pressure vessels:

• i) roof domes

• ii) boilers

• iii) airplane wings

• iv) submarine hulls

• A pressurized sphere is subjected to uniform tensile stresses in all directions

• Spherical pressure vessel:

t

pr

221 ss

• Mohr’s circle for in-plane

transformations reduces to a point

0

constant

plane)-max(in

21

sss

• Maximum out-of-plane shearing

stress

t

pr

412

1max s

The cylindrical pressure vessel has an inner radius of 1.25 m and a wall thickness of 15 mm. It is made from steel plates that are welded along the 45 seam. Determine the normal and shear stress components along this seam if the vessel is subjected to an internal pressure of 8 MPa.

Example 1:

MPa16750067.666R

MPa5002

67.66633.333

)0,500(C

)0,67.666(B

)0,33.333(A

MPa67.6662

MPa33.333)015.0(2

)25.1(8

t2

pr

'y'x

avg

21

2

s

ss

s

Example 2:

• The cylindrical portion of the compressed air tank shown is fabricated of 6 mm thick plate welded along a helix forming an angle = 30º with the horizontal. Knowing that the allowable stress normal to the weld is 75 MPa, determine(a) the largest gage pressure that

can be used in the tank.(b) the gage pressure that will

cause a shearing stress parallel to the weld of 30 MPa.

Solution (a):

Solution (b):

Example 3:

• The pressure tank shown has a 10 mm wall thickness and butt-welded seams forming an angle = 20º with a transverse plane. For a gage pressure of 580 KPa determine:

(a) the normal stress perpendicular to the weld,

(b) the shearing stress parallel to the weld.

Solution:

Example 4:

The pressure tank shown has a 10 mm wall thickness and butt-welded seams forming an angle = 25º with a transverse plane. Determine the largest allowable gage pressure, knowing that the allowable normal stress perpendicular to the weld is 120 MPa and the allowable shearing stress parallel to the weld is 70 MPa.

Solution: