A pressure vessel has an outside diameter of 50 mm and a wall thickness of 2mm and is subject to an internal Pressure of 50 bar. It is also subject to a positive Torque of 1000 Nm. Calculate the stresses acting on an element on the outer surface of the vessel and show the resulting state of stress on a cube diagram. Calculate the principal stresses and the principal angle and show this state of transformed stress on a cube diagram. Calculate the effective stress according to both Tresca and von Mises failure criteria, and determine the minimum yield strength required to provide a factor of safety of 3 for the load case provided. Sketch a Mohr's circle of stress, showing the principal stresses calculated in (b) and the maximum shear stress.
A pressure vessel has an outside diameter of 50 mm and a wall thickness of 2mm and is subject to an internal Pressure of 50 bar. It is also subject to a positive Torque of 1000 Nm. Calculate the stresses acting on an element on the outer surface of the vessel and show the resulting state of stress on a cube diagram. Calculate the principal stresses and the principal angle and show this state of transformed stress on a cube diagram. Calculate the effective stress according to both Tresca and von Mises failure criteria, and determine the minimum yield strength required to provide a factor of safety of 3 for the load case provided. Sketch a Mohr's circle of stress, showing the principal stresses calculated in (b) and the maximum shear stress.
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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Transcribed Image Text:A pressure vessel has an outside diameter of 50 mm and a wall thickness of
2mm and is subject to an internal Pressure of 50 bar. It is also subject to a
positive Torque of 1000 Nm.
Calculate the stresses acting on an element on the outer surface of the vessel
and show the resulting state of stress on a cube diagram.
Calculate the principal stresses and the principal angle and show this state of
transformed stress on a cube diagram.
Calculate the effective stress according to both Tresca and von Mises failure
criteria, and determine the minimum yield strength required to provide a factor
of safety of 3 for the load case provided.
Sketch a Mohr's circle of stress, showing the principal stresses calculated in (b)
and the maximum shear stress.
Expert Solution
Step 1
Given data,
Outside diameter of pressure vessel, Do = 50 mm
Thickness of the pressure vessel, t = 2 mm
Internal pressure, P = 50 bar = 5 MPa
Applied torque, T = 1000 Nm
To determine:-
1) Stresses acting on the element and show on the cube diagram
2) Principal stresses and principal angle and show on the cube diagram
3) Effective stress according to both Tresca and Von Mises failure criteria
4) Draw Mohr's circle
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