A cylindrical shell 1m in diameter and 3m long is having a 1.5mm metal thickness. And pressure of 1.5N/mm² find hoop stress and longitudinal stress *
Answers
Answer:
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
Explanation:
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