HJD INSTITUTE OF TECHNICAL EDUCATION & RESEARCH

Krutarthsinh gohilKrupa shahAshish vyasBhavik dhapaPradeepsinh vaghela

Introduction

Cylindrical and spherical vessels are used in the engineering field to store and transport fluids. Such vessels are tanks ,boilers , compressed air receivers , pipe lines etc. these vessels, when empty, are subjected to atmospheric pressure internally as well as externally and the resultant pressure on the walls of the shell is nil.

but whenever a vessel is subjected to an intenal pressure(due to air , water , steam etc.) its walls are subjected to tensile stresses.

Thin cylindrical shell.

When t/d <= d/10 to d/15, it is called thin cylindrical shell. t = thickness of the shell d =internal diameter of shell.

in thin cylindrical shells hoops stress and longitudinal stresses are constant over the Thickness and radial stresses are negligible.

When t/d > d/10 to d/15, it is called THICK cylindrical shell.

Stresses in thin cylindrical sheels : whenever, a thin cylindrical shell is subjected to an internal pressure (p). Its Walls are subjected to two types of tensile stresses. (a) Hoop stress (circumferential stress) (b) Longitudinal stress.

Consider a thin cylindrical shell subjected to an internalPressure as shown in fig. = circumferential stress in the shell material. p =internal pressure d =internal diameter of shell t =thickness of the shell. Total pressure, p = Pressure * Area =p.d.l Resisting area = A = 2.t.l = P/A = p.d.l/2.t.l

= p.d/2t.

Hoop stress (circumferential stress) :

(b) Longitudinal stress ):

Total pressure p = Pressure * Areap = p

Resisting area,A =

= P/A = p

= pd/4t

Change in dimensions of a thin cylindrical shell due to internal pressure:

𝜺𝟏=𝒑𝒅 /𝟐𝒕𝑬 (𝟏−𝟏𝟐𝒎

)

=

Circumferential strain,

Longitudinal strain,

=

Let, =change in dia. Of shell =change in length of shell

Change in volume of a thin cylindrical shell due to internal pressure:Volume of shell,V = Final volume,V+Change in volume,

= [

=

=

= =/ = = (= , = ) =V(

Thin spherical shells

Consider a thin spherical shell subjected to internal pressure p as shown in fig.

p =internal pressure d =internal diameter of shell t =thickness of the shell stress in the shell material

Total force

P = Resisting section =

Stress in the shell force/resisting section = /

Chenge in diameter and volume of a thin spherical shell due to internal pressure

Consider a thin spherical shell subjected to internal pressure.

p =internal pressure d =internal diameter of shell t =thickness of the shell stress in the shell material

We know that for thin spherical shell Strain in any direction=

We know that, strain,

= ……(1)

Original volume of sphere,

V=Final volume,V+Volumetric strain, =-/

= …………(2)

Substiute,value of

V =

=

Thank you….!!!