What is hoop stress in a thin-walled pressure vessel?

Hoop stress (circumferential stress) is σ_h = pd/(2t), where p is internal pressure, d is internal diameter, and t is wall thickness. It acts in the circumferential direction and is the dominant stress in cylinders, being twice the longitudinal stress.

What is the thin-wall assumption for pressure vessels?

A vessel is considered thin-walled when the diameter-to-thickness ratio d/t > 20 (or equivalently t/r < 0.1). Under this assumption, stress is assumed uniform through the wall thickness. For thicker walls, Lamé's equations must be used for accurate results.

How do you calculate the factor of safety for a pressure vessel?

Factor of Safety (FOS) = Yield Strength (S_y) / Maximum Stress. For a cylindrical vessel, maximum stress is the hoop stress σ_h = pd/2t. Design requires FOS ≥ 2–4 for pressure vessels. Rearranging: minimum wall thickness t = pd/(2×S_y/FOS).

Thin-Walled Pressure Vessel

Q: How do you calculate the factor of safety for a pressure vessel?

Factor of Safety (FOS) = Yield Strength (S_y) / Maximum Stress. For a cylindrical vessel, maximum stress is the hoop stress σ_h = pd/2t. Design requires FOS ≥ 2–4 for pressure vessels. Rearranging: minimum wall thickness t = pd/(2×S_y/FOS).

Hoop Stress, Longitudinal Stress & Safety Factor Simulator

Mode

Vessel Type

Pressure p 5.0 MPa

Diameter d 400 mm

Thickness t 10 mm

Yield Str. Sᵧ 250 MPa

Hoop σₕ— MPa

Long. σₗ— MPa

Factor of Safety—

d/t ratio—

Status—

Thin-Walled Pressure Vessel Theory — Hoop and Longitudinal Stress Analysis

Thin-walled pressure vessels are used in boilers, gas cylinders, pipelines, and chemical reactors. Understanding hoop stress and longitudinal stress is fundamental to safe pressure vessel design. This simulator calculates internal stresses, factor of safety, and helps students visualise how wall thickness and diameter affect structural integrity.

Hoop Stress (Circumferential Stress)

Hoop stress, also called circumferential stress, is the dominant stress in a thin-walled cylindrical vessel. It acts in the tangential (circumferential) direction and is given by σ_h = pd/(2t), where p is internal pressure (MPa), d is internal diameter (mm), and t is wall thickness (mm). Hoop stress tends to split the cylinder along its length and is always twice the longitudinal stress in a cylinder.

Longitudinal Stress

Longitudinal stress acts along the axis of the cylinder and tends to pull the end caps off. It is calculated as σ_L = pd/(4t) — exactly half the hoop stress. This is why cylindrical pressure vessels typically fail by longitudinal cracking (hoop stress failure) before axial failure. For a spherical vessel, stress is equal in all directions: σ = pd/(4t).

Thin-Wall Criterion and Design

The thin-wall assumption is valid when d/t > 20, meaning the wall thickness is small relative to the diameter. Within this regime, stress is approximately uniform through the wall. For thick-walled vessels (d/t < 20), Lamé’s equations account for stress variation through the wall. The minimum required wall thickness is t = pd/(2S_y/FOS) where FOS is the factor of safety (typically 2–4 for pressure vessels).

Who Uses This Simulator?

This pressure vessel simulator is ideal for TVET and undergraduate mechanical engineering students studying strength of materials, machine design, and manufacturing. It is also useful for boilermakers, piping engineers, and anyone preparing for professional engineering examinations that include pressure vessel design questions.

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