Stresses in Thin-Walled Pressure Vessels

A thin-walled pressure vessel is a closed container designed to hold fluids or gases at a pressure substantially different from the ambient pressure. Examples include tanks, pipes, and boilers. When such a vessel is subjected to internal pressure, stresses are developed within the walls of the vessel. For thin-walled vessels (where the wall thickness is small compared to the diameter), we primarily consider two main types of stresses that act perpendicular to each other in the plane of the wall:

• Hoop Stress ($\sigma_h$): This stress acts tangentially along the circumference of the vessel. It is also known as circumferential stress. This stress arises from the internal pressure trying to expand the vessel radially. It is the stress that tends to burst the vessel along a longitudinal seam.
• Longitudinal Stress ($\sigma_l$): This stress acts axially along the length of the vessel. It is also known as axial stress. This stress arises from the internal pressure acting on the ends of the vessel, trying to pull it apart along a transverse section.

These two stresses, hoop stress and longitudinal stress, are the primary stresses present in the wall of a thin-walled pressure vessel due to internal pressure. They are both tensile stresses under internal pressure.

Let's look at the given options:

• Option 1: Longitudinal stress and Hoop stress

  This option correctly identifies the two main stresses present in a thin-walled pressure vessel. Hoop stress acts circumferentially, and longitudinal stress acts axially.

• Option 2: No two stresses

  This is incorrect. As explained, internal pressure creates significant stresses within the vessel walls.

• Option 3: Compressive and hoop Stress

  Under internal pressure, the stresses in the vessel walls (hoop and longitudinal) are tensile, not compressive. While localized compressive stresses can occur (e.g., at supports), the primary stresses mentioned for the vessel wall under internal pressure are tensile hoop and longitudinal stresses. Therefore, this option is incorrect.

• Option 4: None of the given options

  This is incorrect because Option 1 correctly lists the two main stresses.

Based on the analysis of the stresses developed in a thin-walled pressure vessel under internal pressure, the two principal stresses are the longitudinal stress and the hoop stress.