A cylindrical shell 3 m long, which is closed at the ends, has an internal diameter of 1m and a wall thickness of 15 mm. Calculate the circumferential and longitudinal stresses induced and also change in dimensions of the shell if it is subjected to an internal pressure of 1.5 mn/m2. Take e=200 gn/m2 and 1/m = 0.3.
Answers
Given A cylindrical shell 3 m long, which is closed at the ends, has an internal diameter of 1 m and a wall thickness of 15 mm. Calculate the circumferential and longitudinal stresses induced and also change in dimensions of the shell if it is subjected to an internal pressure of 1.5 N/mm^2. Take e=200 N/mm^2 and µ = 0.3.
Length l = 3 m = 3000 mm
Diameter = 1 m = 1000 mm
Thickness t = 15 mm
Pressure p = 1.5 N / mm^2
e = 2 x 10^5 N/mm^2
µ = 0.3
We need to find circumferential stresses and longitudinal stresses
So Circumferential stress
σ c = pd / 2t
= 1.5 x 1000 / 2 x 15
= 1500 / 30
= 50 N / mm^2
Longitudinal stress
σ l = σ c / 2
= 50 / 2
= 25 N / mm^2
Now to calculate change in diameter and length
Δ d = pd^2 / 2te(1 - µ/2)
= 1.5 x (1000)^2 / 2 x 15 x 2 x 10^5 (1 – 0.3/2)
= 1.5/6(1.7/2)
= 2.55 / 12
Δ d = 0.2125 mm
Now we have change in length
Δ l = pdl / 2te (1/2 - µ)
= 1.5 x 1000 x 3000 / 2 x 15 x 2 x 10^5(1/2 – 0.3)
= 1.5 x 5 / 10 (0.4 / 2)
= 3/20
Δ l = 0.15 mm