LECTURE 16

Change in Dimensions :

The change in length of the cylinder may be determined from the longitudinal strain.

Since whenever the cylinder will elongate in axial direction or longitudinal direction, this will also get decreased in diametre or the lateral strain will also take place. Therefore we will have to also take into consideration the lateral strain.as we know that the poisson's ratio (ν) is

 

where the -ve sign emphasized that the change is negative

Consider an element of cylinder wall which is subjected to two mutually ^r normal stresses sL and sH .

Let E = Young's modulus of elasticity

Volumetric Strain or Change in the Internal Volume:

When the thin cylinder is subjected to the internal pressure as we have already calculated that there is a change in the cylinder dimensions i.e, longitudinal strain and hoop strains come into picture. As a result of which there will be change in capacity of the cylinder or there is a change in the volume of the cylinder hence it becomes imperative to determine the change in volume or the volumetric strain.

The capacity of a cylinder is defined as

V = Area X Length

= pd2/4 x L

Let there be a change in dimensions occurs, when the thin cylinder is subjected to an internal pressure.

(i) The diameter d changes to ® d + d d

(ii) The length L changes to ® L + d L

Therefore, the change in volume = Final volume - Original volume

 

Therefore to find but the increase in capacity or volume, multiply the volumetric strain by original volume.

Hence

Change in Capacity / Volume       or

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