Stresses in thick-walled cylinders

Question 1

when is a cylinder considered to be thick

Answer 1

t:r 1:10

Question 2

hoop stress (σΘ) in thin-walled cylinders

Answer 2

σΘ = pa / t

*internal pressure (p)
*internal radius (a)
*thickness (t)

Question 3

show stress distribution for hoop and radial stress in thick-walled cylinders when both internally and externally pressurised

Answer 3

σΘ = C1 + C2 / r^2
σr = C1 - C2 / r^2

*radial stress (σr)
*hoop stress (σΘ)
*internal radius (r)

Question 4

C1 and C2

Answer 4

C1 = pi a^2 - po b^2 / b^2 - a^2
C2 = (pi - po) a^2 b^2 / b^2 - a^2

*internal radius (a)
*external radius (b)
*internal pressure (pi)
*external pressure (po)

Question 5

hoop and radial stress in thick-walled cylinders when internally pressurised

Answer 5

σr = - pi a^2/b^2-a^2 * (1 - b^2/r^2)
σΘ = pi a^2/b^2-a^2 * (1 + b^2/r^2)

σr is compressive and σΘ is tensile throughout the thickness of the cylinder

*internal radius (a)
*external radius (b)
*internal pressure (pi)
*radius to point (r)
*radial stress (σr)
*hoop stress (σΘ)

Question 6

hoop and radial stress in thick-walled cylinders when externally pressurised

Answer 6

σr = - po b^2/b^2-a^2 * (1 - a^2/r^2)
σΘ = - po b^2/b^2-a^2 * (1 + a^2/r^2)

both are compressive throughout the thickness of the cylinder

*internal radius (a)
*external radius (b)
*internal pressure (po)
*radius to point (r)
*radial stress (σr)
*hoop stress (σΘ)

Question 7

Radial Shrinkage allowance

Answer 7

= (σΘ_outer - σΘ_inner) r/E

*radius (r)
*youngs modulus (E)
*hoop stress (σΘ)