Determine principal stresses in point A of the cylindrical pressure vessel given in the Figure. The thickness of the wall is 3 mm, the radius is 300 mm, working pressure is 2 bars (1 bar = 105 Pa ≈ 1 atm).
Illustrate the stresses with the Mohr circle.
Determine the stresses in a coordinate system rotated 40 degrees
from the horizontal axis.
Solve Problem
Stress, [MPa]= Stress, [MPa]= Stress, [MPa]= Step 1. Determine hoop and axial stresses in the wall of the pressure vessel. Use pressure vessel formula. Step 2. Find principal directions and illustrate the stresses with the Mohr circle. In the coordinate system attached to the hoop and axial directions only tensile forces (and no shear) arise in the wall of the pressure vessel. Thus this directions are the principal directions. Step 3. Transform stresses into the rotated coordinate system. Step 4. Draw transformed stresses on the Mohr cicle. Hoop and axial stresses in the wall of the pressure vessel can be determined by the pressure vessel formula. The hoop stress is The axial stress is In the coordinate system attached to the hoop and axial directions only tensile forces (and no shear) arise in the wall of the pressure vessel. Thus this directions are the principal directions as it is illustrated by the Mohr circle. Stress transformation into rotated coordinate system results in Transformed stresses are shown also on the Mohr circle. Solve
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Steps
Step by step
Check hoop stress
Check axial stress
Check Mohr circle
Check transformed stresses
Check figure
Results
Worked out solution