Pressure Vessels

Example: (continued)

Identify “face A” and “face B” on the element oriented along and perpendicular to the axis of

the cylinder. Then show the circumferential and longitudinal stresses on each face.

Plot Mohr’s Circle. Rotate the element so it aligns with the weld line as shown below.

Note “face A” becomes “face A’ “ along the weld line with a rotation of 30^o on the element

or 60^o on Mohr’s Circle.

The radius of the circle is r = (62.5 – 31.25)/2 = 15.625 MPa

The center of the circle is at (31.25 + 15.625), 0) = (46.875,0)

The shearing stress on face A’ along the weld line is then 15.625 sin(60) = 13.53 MPa

The normal stress on face A’ perpendicular to the weld line

is then 46.875 – 15.625 cos(60) = 39.1 MPa

Suppose the allowable shearing stress in the cylindrical pressure vessel without failure is 15 MPa

and instead of 60^o the weld line is at 45^o to the longitudinal axis of the vessel. For the same

internal pressure and wall thickness will the tank rupture? Yes, since the shearing stress on a

face along this new weld line is 15.625 MPa which exceeds the allowable shearing stress.

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