Question

In an internally pressurized thick cylinder

• A. hoop stress varies parabolically but radial stress remains constant
• B. hoop stress remains constant but radial stress varies parabolically
• C. both hoop and radial stresses vary linearly
• D. both hoop and radial stresses vary parabolically

Answer 1

Answer:

D. both hoop and radial stresses vary parabolically

In a thick cylinder, hoop stress varies parabolically from inner to outer radius, while radial stress varies parabolically with maximum value at the inner radius and zero at the outer radius. For a thick cylinder hoop stress (tangential stress) is given by,

$\sigma_{h} =\frac{P (r_{i}) ^ 2}{(r_{0}) ^ 2 - (r_{i}) ^ 2} [1 +\frac {(r_{0}) ^ 2}{x ^ 2}]$

stress is given by, For a thick cylinder Radia,

$\sigma_{h} =\frac{P (r_{i}) ^ 2}{(r_{0}) ^ 2 - (r_{i}) ^ 2} [1 -\frac {(r_{0}) ^ 2}{x ^ 2}]$