Repeat Prob. 3-104 with the tank being pressurized to 50 psig.
The maximum state of stress in the tank.
The principle normal stress.
The principle shear stress.
Answer to Problem 105P
The tangential stress on the cylinder is
The principle normal stresses are
The principle shear stresses are
Explanation of Solution
Write the expression for tangential stress in pressurized cylinders due to water present in the tank.
Here, the tangential stress is
Write the expression for tangential stress in pressurized cylinders due to internal pressure.
Here, the tangential stress is
Write the expression for total tangential stress.
Here, the total tangential stress is
Write the expression for inner radius of cylinder.
Here, the thickness of cylinder is
Write the expression for radial stress in pressurized cylinders due to weight of water.
Here, the radial stress is
Write the expression for radial stress in pressurized cylinders due to internal pressure.
Here, the radial stress is
Write the expression for the total radial stress.
Here, the total radial stress is
Write the expression for the area of the wall.
Here, the area of the wall is
Write the expression for the volume of the wall of the cylinder.
Here, the volume of the cylinder wall is
Substitute
Write the expression for the volume of dome.
Here, the volume of dome is
Write the expression for the weight of the complete structure.
Here, the weight of the structure is
Write the expression for the stress at the wall.
Here, the stress at the wall is
Write the expression for the internal pressure on cylinder due to water.
Here, the weight density of water is
Write the expression for principle shear stress.
Here, the principle shear stress is
Write the expression for principle shear stress.
Here, the principle shear stress is
Write the expression for principle shear stress.
Here, the principle shear stress is
Write the expression for longitudinal stress on the cylindrical vessel.
Here, the longitudinal stress is
Write the expression for the total longitudinal stress.
Here, the total longitudinal stress is
Conclusion:
Convert the outer diameter from feet to inch.
The outer radius of the cylinder is
Substitute
The inner diameter of the cylinder is
Substitute
Substitute
Substitute
Refer to Table A-5 “Physical Constants of Materials” to obtain the properties of unit weight of carbon steel as,
Substitute
Substitute
Substitute
Since the external pressure is zero, the maximum tangential stress will occur at inside radius.
Substitute
Substitute
Substitute
Thus, the tangential stress on the cylinder is
Substitute
Substitute
Substitute
Thus, the radial stress on the cylinder is
Substitute
Substitute
Thus, the longitudinal stress is
Since the maximum principle normal stresses are assumed as
Thus, the principle normal stresses are
Substitute
Substitute
Substitute
Write the decreasing arrangement of principle shear stress.
Thus, The principle shear stresses are
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Chapter 3 Solutions
Shigley's Mechanical Engineering Design (McGraw-Hill Series in Mechanical Engineering)
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