Thin & Thick Cylinders | Civil Engineering SSC JE (Technical) - Civil Engineering (CE) PDF Download

 THIN CYLINDERS

  • If the thickness of the cylinder is less thanThin & Thick Cylinders | Civil Engineering SSC JE (Technical) - Civil Engineering (CE) of the diameter of the cylinder, it is treated as the thin cylinder.
  • It is assumed that the stresses are uniformly distributed through out the thickness of the wall.
  • ‘Hoop stress’ or ‘Circumferential stress’ is given by

 Thin & Thick Cylinders | Civil Engineering SSC JE (Technical) - Civil Engineering (CE)

  • ‘Longitudinal stress’ is given by

 Thin & Thick Cylinders | Civil Engineering SSC JE (Technical) - Civil Engineering (CE)

  • The Maximum shear stress is given by

 Thin & Thick Cylinders | Civil Engineering SSC JE (Technical) - Civil Engineering (CE)

  • Hoop strain is given by

 Thin & Thick Cylinders | Civil Engineering SSC JE (Technical) - Civil Engineering (CE)

  • Longitudinal strain is given by

 Thin & Thick Cylinders | Civil Engineering SSC JE (Technical) - Civil Engineering (CE)

  • Volumetric strain is given by

 Thin & Thick Cylinders | Civil Engineering SSC JE (Technical) - Civil Engineering (CE)

Where p = internal pressure
d = diameter of cylinder
t = thickness of the cylinder
µ = Poisson's ratio

  • If ‘σa’ be the permissible tensile stress for the shell material, then from strength point of view, the major principal stress ( σ ) should be less than or equal to σa Hence

 Thin & Thick Cylinders | Civil Engineering SSC JE (Technical) - Civil Engineering (CE)

THIN SPHERICAL SHELLS

  • In case of thin spherical shells, longitudinal stress and circumferential stress are equal and are given by

 Thin & Thick Cylinders | Civil Engineering SSC JE (Technical) - Civil Engineering (CE) (tensile in nature)

  • The maximum shear stress,

 Thin & Thick Cylinders | Civil Engineering SSC JE (Technical) - Civil Engineering (CE)

  • The strain in any direction is given by

 Thin & Thick Cylinders | Civil Engineering SSC JE (Technical) - Civil Engineering (CE)

  • The volumetric strain is given by

 Thin & Thick Cylinders | Civil Engineering SSC JE (Technical) - Civil Engineering (CE)

CYLINDERS WITH HEMISPHERICAL ENDS
Let tc = thickness of the cylinder ts = thickness of the hemisphere

 Thin & Thick Cylinders | Civil Engineering SSC JE (Technical) - Civil Engineering (CE)

  • Hoop stress in cylindrical part

 Thin & Thick Cylinders | Civil Engineering SSC JE (Technical) - Civil Engineering (CE)

  • Hoop stress in hemispherical part

 Thin & Thick Cylinders | Civil Engineering SSC JE (Technical) - Civil Engineering (CE)

  • Longitudinal stress in cylindrical part

 Thin & Thick Cylinders | Civil Engineering SSC JE (Technical) - Civil Engineering (CE)

  • Longitudinal stress in hemispherical part

 Thin & Thick Cylinders | Civil Engineering SSC JE (Technical) - Civil Engineering (CE)

  • Circumferential strain in hemispherical part

 Thin & Thick Cylinders | Civil Engineering SSC JE (Technical) - Civil Engineering (CE)

  • Circumferential strain in cylindrical part

 Thin & Thick Cylinders | Civil Engineering SSC JE (Technical) - Civil Engineering (CE)

  • For the condition of no distortion of the junction

 Thin & Thick Cylinders | Civil Engineering SSC JE (Technical) - Civil Engineering (CE)Thin & Thick Cylinders | Civil Engineering SSC JE (Technical) - Civil Engineering (CE) 

  • This means thickness of cylindrical part should be more than the hemispherical part.
  • For the condition of same maximum stress in cylindrical and hemispherical parts,

 Thin & Thick Cylinders | Civil Engineering SSC JE (Technical) - Civil Engineering (CE)

THICK CYLINDRICAL SHELL

If the thickness of shell is greater than Thin & Thick Cylinders | Civil Engineering SSC JE (Technical) - Civil Engineering (CE)of  its diameter then it is called thick shell.

In thick cylinders the circumferential stress no longer remains constant, but varies along the thickness and the radial pressure (px) is also not negligible.
The following three types of stresses are existing in thick cylinders :

(i) The radial pressure ‘px’ (compressive)
(ii) The hoop stress fx (tensile)
(iii) The longitudinal tensile stress po (tensile)

  • The longitudinal stress may be given by

 Thin & Thick Cylinders | Civil Engineering SSC JE (Technical) - Civil Engineering (CE)

  • Hoop stress, is given by

 Thin & Thick Cylinders | Civil Engineering SSC JE (Technical) - Civil Engineering (CE)

  • Radial pressure is given by

 Thin & Thick Cylinders | Civil Engineering SSC JE (Technical) - Civil Engineering (CE)

Equation (ii) and (iii) are called Lame’s equation.

ro = outer radius of shell 

ri = 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. Hyperbolically.

The document Thin & Thick Cylinders | Civil Engineering SSC JE (Technical) - Civil Engineering (CE) is a part of the Civil Engineering (CE) Course Civil Engineering SSC JE (Technical).
All you need of Civil Engineering (CE) at this link: Civil Engineering (CE)
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FAQs on Thin & Thick Cylinders - Civil Engineering SSC JE (Technical) - Civil Engineering (CE)

1. What are thin and thick cylinders in civil engineering?
Ans. Thin and thick cylinders are two types of structural elements used in civil engineering. A thin cylinder has a small ratio of its wall thickness to its radius, while a thick cylinder has a larger ratio. These cylinders are commonly used in the design of pressure vessels, pipes, and storage tanks.
2. What are the differences between thin and thick cylinders?
Ans. The main difference between thin and thick cylinders lies in their design considerations. Thin cylinders are primarily designed using membrane theory, which assumes that the stresses are uniformly distributed across the cylinder's wall thickness. In contrast, thick cylinders require the consideration of both membrane and bending stresses due to the non-uniform stress distribution in their walls.
3. How are thin cylinders designed in civil engineering?
Ans. Thin cylinders are typically designed using the principles of membrane theory. This theory assumes that the stress distribution across the cylinder's wall thickness is uniform. The design involves calculating the hoop stress, longitudinal stress, and radial stress based on the internal pressure and dimensions of the cylinder. The maximum stress values should be within allowable limits to ensure the structural integrity of the cylinder.
4. What factors should be considered in the design of thick cylinders?
Ans. The design of thick cylinders requires considering both membrane and bending stresses. Factors such as the internal pressure, cylinder dimensions, material properties, and boundary conditions influence the stress distribution and must be accounted for in the design. Additionally, the type of loading, such as static or dynamic, and the presence of any external forces or constraints should also be considered.
5. What are some applications of thin and thick cylinders in civil engineering?
Ans. Thin and thick cylinders find various applications in civil engineering. Thin cylinders are commonly used in the design of pipelines, pressure vessels, and storage tanks. Thick cylinders, on the other hand, are used in the construction of hydraulic cylinders, large-scale industrial equipment, and underground storage structures. The design considerations for each type of cylinder ensure their safe and efficient operation in their respective applications.
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