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 can use the formulas for hoop stress, tensile stress, and the strength of the weld.
(a) The maximum hoop stress in the tank can be calculated using the formula:
Hoop Stress = (Pressure × Internal Radius) / Wall Thickness
Since the tank has flat endplates, the internal radius is equal to half of the outer diameter minus the wall thickness. Here's the calculation:
Internal Radius = (1.20 / 2) - 0.020 = 0.580 m
Pressure = 2.00 MPa
Hoop Stress = (2.00 × 0.580) / 0.020 = 58.00 MPa
So, the maximum hoop stress in the tank is 58.00 MPa.
(b) The maximum tensile stress in the tank can be calculated using the formula:
Tensile Stress = (Hoop Stress + Internal Pressure) / 2
Here's the calculation:
Tensile Stress = (58.00 + 2.00) / 2 = 30.00 MPa
So, the maximum tensile stress in the tank is 30.00 MPa.
(c) To find the magnitude of the tensile stress that will cause the weld to burst open, we need to consider the tensile strength and shear strength of the weld. Since the shear strength is 40% of the tensile strength, we can calculate it as follows:
Shear Strength = 40% of Tensile 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:
Magnitude of Tensile Stress = Shear Strength = 140 MPa
Therefore, the magnitude of the tensile stress that will cause the weld to burst open is 140 MPa.