A cylindrical tank with flat endplates is constructed from two sections that are welded together circumferentially.The outer diameter of the tank is 1.20, and the wall of the tank is 20.0 mm thick and the mamimum internal pressure is 2.00 MPa.
(a) Calculate the maximum hoop stress in the tank
(b) Calculate the maximum tensile stress in the tank
(c) The tensile strength of the weld is 350 MPa and the shear strength of the weld is 40% of the tensile strength. what is the magnitude of the tensile stress that will cause the weld to burst open
To find the maximum hoop stress and maximum tensile stress in the tank, we can use the equations related to the pressure vessel.
(a) Maximum hoop stress:
The maximum hoop stress (σ_h) is given by the formula:
σ_h = (p * r) / t
where p is the internal pressure, r is the radius of the tank, and t is the thickness of the wall.
First, we need to find the radius of the tank. Since the outer diameter is given as 1.20, the radius can be calculated as half of the diameter:
radius = 1.20 / 2 = 0.60 m
Next, we can plug in the values:
σ_h = (2.00 MPa * 0.60 m) / (20.0 mm)
Note: We need to convert the thickness from millimeters to meters because the pressure is in megapascals.
Let's convert the thickness:
t = 20.0 mm = 20.0 / 1000 = 0.020 m
Now let's calculate the maximum hoop stress:
σ_h = (2.00 MPa * 0.60 m) / (0.020 m) = 60 MPa
Therefore, the maximum hoop stress in the tank is 60 MPa.
(b) Maximum tensile stress:
The maximum tensile stress (σ_t) occurs at the inner surface of the tank and is given by the formula:
σ_t = (p * r_in) / t
where r_in is the radius of the inner surface of the tank.
To find r_in, we need to subtract the wall thickness from the radius:
r_in = radius - t
Substituting the values:
r_in = 0.60 m - 0.020 m = 0.580 m
Now we can calculate the maximum tensile stress:
σ_t = (2.00 MPa * 0.580 m) / (0.020 m) = 58 MPa
Therefore, the maximum tensile stress in the tank is 58 MPa.
(c) Magnitude of tensile stress that will cause the weld to burst open:
To calculate the magnitude of the tensile stress that will cause the weld to burst open, we need to consider the tensile strength of the weld and the shear strength of the weld.
Given that the tensile strength of the weld is 350 MPa and the shear strength of the weld is 40% of the tensile strength:
Shear strength of the weld = 40% of 350 MPa = 0.40 * 350 MPa = 140 MPa
Since the weld will burst open due to tensile stress, we can consider the tensile strength of the weld.
Therefore, the magnitude of the tensile stress that will cause the weld to burst open is 350 MPa.