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 solve this problem, we need to use the formulas for calculating stresses in a cylindrical tank under pressure. We will start by calculating the maximum hoop stress, then the maximum tensile stress, and finally, the magnitude of the tensile stress that will cause the weld to burst open.
(a) Maximum Hoop Stress:
The maximum hoop stress occurs around the circumference of the cylindrical tank and is given by the formula:
Stress_h = (P * r) / t
where:
- Stress_h is the maximum hoop stress
- P is the internal pressure
- r is the radius of the tank (half of the diameter)
- t is the wall thickness
Given:
- P = 2.00 MPa
- Diameter = 1.20 m (outer diameter)
- Wall thickness = 20.0 mm
First, we convert the pressure from MPa to Pa:
P = 2.00 MPa = 2.00 * 10^6 Pa
Next, we calculate the radius:
Radius = Diameter / 2 = 1.20 m / 2 = 0.60 m
Finally, we convert the wall thickness from mm to meters:
t = 20.0 mm = 20.0 / 1000 = 0.020 m
Now, substitute the values into the formula:
Stress_h = (2.00 * 10^6 Pa * 0.60 m) / 0.020 m
Stress_h = 60.00 * 10^6 Pa = 60.00 MPa
Therefore, the maximum hoop stress in the cylindrical tank is 60.00 MPa.
(b) Maximum Tensile Stress:
The maximum tensile stress occurs at the inner surface of the cylindrical tank and is given by the formula:
Stress_t = (P * r) / (2 * t)
where all the variables are the same as in part (a).
Using the same values for P, r, and t, we can substitute them into the formula:
Stress_t = (2.00 * 10^6 Pa * 0.60 m) / (2 * 0.020 m)
Stress_t = 60.00 * 10^6 Pa = 60.00 MPa
Therefore, the maximum tensile stress in the cylindrical tank is 60.00 MPa.
(c) Magnitude of Tensile Stress that will Cause the Weld to Burst Open:
The magnitude of tensile stress that will cause the weld to burst open depends on the tensile strength of the weld. To find this value, we need to first calculate the shear strength of the weld, which is given as 40% of the tensile strength.
Given:
- Tensile strength of the weld = 350 MPa
- Shear strength of the weld = 40% of the tensile strength
To find the shear strength, we multiply the tensile strength by the shear strength percentage:
Shear strength = 0.40 * 350 MPa = 140 MPa
The magnitude of the tensile stress that will cause the weld to burst open is equal to the shear strength of the weld. Therefore, the magnitude of the tensile stress is 140 MPa.
In conclusion,
(a) The maximum hoop stress in the tank is 60.00 MPa.
(b) The maximum tensile stress in the tank is also 60.00 MPa.
(c) The magnitude of the tensile stress that will cause the weld to burst open is 140 MPa.