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NRI INSTITUTE OF TECHNOLOGY STRENGTH OF MATERIALS-2 FOR CIVIL-2-2

M.VENKANNABABU

UNIT-5

THIN CYLINDERS AND SPHERES

1. Derive the Expression for Hoop stress and longitudinal stress in a thin cylinder shells subjected to

internal fluid pressure? (OR) Show that in thin cylinder shells subjected to internal fluid pressure,

the Hoop stress is twice the longitudinal stress?

Ans:

THIN CYLINDRICAL VESSEL SUBJECTED TO INTERNAL PRESSURE:

The figure shows a thin cylindrical vessel in which a fluid under pressure is stored.

Let d = internal diameter of the thin cylinder

t = thickness of the wall of the cylinder

p = Internal pressure of the fluid

L = Length of the cylinder

EXPRESSION FOR CIRCUMFERENTIAL STRESS (HOOP STRESS):

Let p = Internal pressure of fluid

d = Internal diameter of the cylinder

t = Thickness of the wall of the cylinder

σ 1 = Circumferential or hoop stress in the material


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EXPRESSION FOR LONGITUDINAL STRESS:

Let p = Internal pressure of fluid, d = Internal diameter of the cylinder

t = Thickness of the wall of the cylinder, σ 2 = Longitudinal stress in the material


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2. A cylinder of internal diameter 2.5m and of thickness 5cm contains a gas. If the tensile stress in the

material is to exceed 80 N/mm2, determine the internal pressure of the gas?

Ans:

3. Derive the Expression for effect of internal pressure on the dimensions of a thin cylindrical shell?

Ans:

EXPRESSION FOR EFFECT OF INTERNAL PRESSURE ON THE DIMENSIONS OF A THIN

CYLINDRICAL SHELL:

&


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4. A cylindrical vessel is 1.5m diameter and 4m long is closed at ends by rigid plates. It is subjected to

an internal pressure of 3N/mm2. If the maximum principal stress is not to exceed 150 N/ mm2, find

the thickness of the shell. Assume E = 2 X 105 N /mm

2 and poisson’s ratio = 0.25. Find the changes

in diameter, length and volume of the shell?

Ans:


M.VENKANNABABU

&

5. Derive the Expression for Thin spherical shells subjected to internal fluid pressure?

Ans:

&


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The ratio of change in volume to the original volume is known as volumetric strain.

,

6. A vessel in the shape of a spherical shell of 1.20m internal diameter and 12mm shell thickness is

subjected to pressure of 1.6 N / mm2. Determine the stress induced in the material of the vessel?

Ans:


M.VENKANNABABU

UNIT-8

THICK CYLINDERS AND SPHERES

1. Derive the expressions for the stresses in a thick cylindrical shell subjected to an internal fluid

pressure? (OR) Derive the Lame’s equations?

Ans:


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These equations are called Lame’s Equations.


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Boundary conditions are :

2. Find the thickness of a metal necessary for a cylindrical shell of internal diameter 160 mm to

withstand an internal pressure of 8 N / mm2. The maximum hoop stress in the section is to exceed

35 N /mm2 ?

Ans:


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3. Determine the hoop stresses in a thick compound cylinder?

Ans:

4. A compound cylinder is made by shrinking a cylinder of external diameter 300mm and internal

diameter of 250mm over another cylinder of external diameter 250mm and internal diameter

200mm. the radial pressure at the junction after shrinking is 8 N/ mm2. Find the final stresses set up


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across the section, when the compound cylinder is subjected to an internal fluid pressure of 84.5 N/

mm2?

Ans:


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M.VENKANNABABU

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M.VENKANNABABU

5. Derive the expression for the radial pressure and hoop stress for a thick spherical shell?

Ans:


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6. A thick spherical shell of 200mm internal diameter is subjected to an internal fluid pressure of 7 N /

mm2. If the permissible tensile stress in the shell material is 8 N / mm

2 , find the thickness of the

shell?

Ans:


M.VENKANNABABU

nri institute of technology strength of materials...

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