Longitudinal Stress In Material Given Resisting Force On Thin Cylindrical Vessel Calculator

Longitudinal Stress Formula:

\[ \sigma_l = \frac{F}{\pi \cdot D_i \cdot t} \]

Force On Cylindrical Shell (F):

Inner Diameter Of Cylinder (D_i):

Thickness Of Thin Shell (t):

Longitudinal Stress (σ_l):

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is Longitudinal Stress?

Longitudinal stress is defined as the stress produced when a pipe or cylindrical vessel is subjected to internal pressure. It acts parallel to the longitudinal axis of the cylinder and is an important parameter in pressure vessel design.

2. How Does the Calculator Work?

The calculator uses the longitudinal stress formula:

\[ \sigma_l = \frac{F}{\pi \cdot D_i \cdot t} \]

Where:

\( \sigma_l \) — Longitudinal stress (Pa)
\( F \) — Force on cylindrical shell (N)
\( D_i \) — Inner diameter of cylinder (m)
\( t \) — Thickness of thin shell (m)
\( \pi \) — Archimedes' constant (approximately 3.14159)

Explanation: The formula calculates the stress distribution along the longitudinal direction of a thin-walled cylindrical pressure vessel under internal pressure.

3. Importance of Longitudinal Stress Calculation

Details: Accurate calculation of longitudinal stress is crucial for designing pressure vessels, piping systems, and cylindrical containers to ensure they can withstand internal pressures without failure.

4. Using the Calculator

Tips: Enter force in newtons (N), inner diameter in meters (m), and thickness in meters (m). All values must be positive and non-zero.

5. Frequently Asked Questions (FAQ)

Q1: What is the difference between longitudinal and hoop stress?
A: Longitudinal stress acts parallel to the cylinder's axis, while hoop stress acts circumferentially around the cylinder. Hoop stress is typically twice the longitudinal stress in thin-walled pressure vessels.

Q2: When is this formula applicable?
A: This formula is valid for thin-walled cylindrical pressure vessels where the wall thickness is less than about 1/10 of the radius.

Q3: What are typical units for these measurements?
A: Force is measured in newtons (N), diameter and thickness in meters (m), and stress in pascals (Pa).

Q4: How does material properties affect longitudinal stress?
A: The calculated stress must be compared to the material's yield strength and ultimate tensile strength with appropriate safety factors.

Q5: Can this formula be used for thick-walled cylinders?
A: No, this formula is specifically for thin-walled cylinders. Thick-walled cylinders require more complex calculations involving Lame's equations.