Problem: The cylindrical portion of the compressed air tank shown is fabricated of 3/8 inch - thick plate welded along a helix forming an angle of 28 degrees with the horizontal. Determine the largest allowable gage pressure, given that the allowable normal stress perpendicular to the weld is 24 ksi.
Solution: From the discussion on page 463, the longitudinal stress and the hoop stress are:
Since the allowable stress perpendicular to the weld is 24 ksi, this picture may help explain what must be done...
To summarize the data given, the wall thickness is 3/8 in, so the inside radius r = 24 - 3/8 = 23.6". Also,
For an element oriented as shown (upper case), there are no shearing stresses and Mohr's Circle is drawn as shown with the two normal stresses as the principal (max & min) stresses:
I have used L and H in place of x and y in referring to the axes. From Mohr's Circle,
Using the formula for the longitudinal stress,
1 This is problem 6.106
from Beer & Johnston's 2nd Edition of Mechanics of Materials.