Correct Answer - Option 2 : varies along the thickness
Concept:
Thin Cylinder: A cylinder is considered to be ‘thin’ if the ratio of the inner diameter to the thickness of the walls is greater than 20.
\(\frac{d}{t} > 20\)
Thick Cylinder: A cylinder is considered to be ‘thick’ if the ratio of the inner diameter to the thickness of the walls is less than 20.
\(\frac{d}{t} < 20\)
Hence statement 1 is wrong.
In case of thin cylinders, the hoop stress is determined by assuming it to be uniform across the thickness of the cylinder.
But in thick cylinders, the hoop stress (Circumferential stress) is not uniform across the thickness, it varies from a maximum value at the inner circumference to a minimum value at the outer circumference.
For thick cylinder:
\(\begin{array}{l} Radial\;stress,\;{\sigma _r} = A - \frac{B}{{{r^{2\;\;}}}}\\ Circumferential\;or\;Hoop\;stress,\;{\sigma _h} = A + \frac{B}{{{r^{2\;\;}}}} \end{array}\)
(Radial stress always compressive so its magnitude always negative)
These two equations are called Lame’s Equations. The constants A and B are obtained from the boundary conditions.
