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explain every step including why f=2T Problem 133 A cylindrical steel pressure v

ID: 1713356 • Letter: E

Question

explain every step including why f=2T

Problem 133 A cylindrical steel pressure vessel 400 mm in diameter with a wall thickness of 20 mm s subjected to an internal pressure of 4.5 MN/m2. (a) Calculate the tangential and longitudinal stresses in the steel. (b) To what value may the internal pressure be increased if the stress in the steel is limited to 120 MN/ma? (c) If the internal pressure were increased until the vessel burst, sketch the type of fracture that would occur Solution 133 ·49400. 21 220 .-45MPa 4(20) G-25MPa this shones that tangential stress is the critical. 120- P400) 2020 P-12 MP c) The bursting fonce will cause a stress on the longitadinal section that is twice to that of the transverse section Thus, fracture is expected as

Explanation / Answer


f = 2T

into the function f(x) = x^2 + x

f(2T) = (2T)^2 + 2T

f(2T) = 4T^2 + 2T   

Now we have two quantities that equal f(2T)

f(2T) = 4T^2 + 2T

f(2T) = 30

Set them equal to each other

4T^2 + 2T = 30

4T^2 + 2T 30 = 0

2(2T^2 + T 15) = 0

Divide both sides by 2.

2T^2 + T 15 = 0

(2T 5)(T + 3) = 0

(2T 5) = 0 and (T+ 3) = 0

T = 5/2 and T = 3