Thin cylinder basics: The normal stress in the wall of a cylindrical shell measured circumferentially (due to forces acting along the hoop) is known as:

Introduction / Context:
Pressure vessels develop distinct stress components in their walls: hoop (circumferential), longitudinal (axial), and a relatively small radial stress (for thin shells). Naming and distinguishing these stresses is essential in design.

Given Data / Assumptions:

• Cylindrical shell under internal pressure.
• Thin-wall assumption so that through-thickness radial stress is small.
• Membrane theory applies (uniform stress across thickness).

Concept / Approach:
The circumferential stress acts tangentially around the cylinder and resists the tendency of the vessel to split longitudinally. It is called “hoop stress” (also termed circumferential stress). The longitudinal stress acts along the axis and is typically half the hoop stress for closed ends under the thin-wall formula.

Step-by-Step Solution:
Identify the direction: stress normal to longitudinal axis but tangent to circumference.Name this component: hoop (circumferential) stress.Recall thin-wall formulas: σ_hoop = p * D / (2 * t); σ_long = p * D / (4 * t).

Verification / Alternative check:
Cut the cylinder longitudinally; the internal pressure tends to open the cylinder along its length — resisted by hoop stress in the wall.

Why Other Options Are Wrong:
Longitudinal stress acts along the axis.Yield/Ultimate are material strength limits, not directional stress names.Radial stress acts through the thickness; small in thin shells.

Common Pitfalls:
Confusing hoop and longitudinal directions; forgetting that hoop stress is the larger of the two in closed-end thin cylinders.

Final Answer:
Hoop stress.