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Chemical Engineering Basics - Engineering

Q1:

Pick out the wrong statement.

A In a thin spherical shell under internal pressure, hoop stress is equal to the half of axial stress.

B Thermoplastic material does not follow Hooke's law of elasticity.

C Components under longitudinal compression is called 'struts' and the load under which strut fails is called crippling or buckling load.

D At low temperatures (sub-zero) in pressure vessels, the ductility of metal diminishes and brittle fracture occurs while at high temperature in pressure vessels, embrittlement of material may take place.

ANS:A - In a thin spherical shell under internal pressure, hoop stress is equal to the half of axial stress.

"In a thin spherical shell under internal pressure, hoop stress is equal to the half of axial stress" is an incorrect statement. Explanation: When a thin spherical shell is subjected to internal pressure, it experiences stresses in both the circumferential (hoop) direction and the longitudinal (axial) direction. Hoop stress (σ_h) is the stress acting circumferentially around the shell, and axial stress (σ_a) is the stress acting longitudinally along the axis of the shell. In a thin spherical shell under internal pressure, the relationship between hoop stress and axial stress is not as stated in the statement. Instead, the relationship is given by the following equations:

  1. Hoop stress (σ_h): σh​=2t/pr​
  2. Axial stress (σ_a): σa​=4t/pr​
Where:
  • p is the internal pressure,
  • r is the radius of the shell,
  • t is the thickness of the shell.
As you can see from the equations, the hoop stress (σ_h) is not equal to half of the axial stress (σ_a) in a thin spherical shell under internal pressure. Instead, the hoop stress is twice the magnitude of the axial stress. Therefore, the statement "In a thin spherical shell under internal pressure, hoop stress is equal to the half of axial stress" is incorrect.