Longitudinal Stress In Cylindrical Vessel Material Calculator

Formula Used:

\[ \text{Longitudinal Stress} = \frac{\text{Internal Pressure} \times \text{Inner Diameter of Cylinder}}{4 \times \text{Thickness Of Thin Shell}} \] \[ \sigma_l = \frac{P_i \times D_i}{4 \times t} \]

Internal Pressure (Pi):

Pascal

Inner Diameter of Cylinder (Di):

Meter

Thickness Of Thin Shell (t):

Meter

Longitudinal Stress (σl):

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1. What is Longitudinal Stress in Cylindrical Vessels?

Longitudinal stress is the stress developed along the length of a cylindrical vessel when it is subjected to internal pressure. It is an important parameter in pressure vessel design and analysis, helping engineers ensure structural integrity and safety.

2. How Does the Calculator Work?

The calculator uses the formula for longitudinal stress in thin-walled cylindrical vessels:

\[ \sigma_l = \frac{P_i \times D_i}{4 \times t} \]

Where:

\( \sigma_l \) — Longitudinal Stress (Pascal)
\( P_i \) — Internal Pressure (Pascal)
\( D_i \) — Inner Diameter of Cylinder (Meter)
\( t \) — Thickness Of Thin Shell (Meter)

Explanation: This formula calculates the stress acting along the longitudinal axis of a cylindrical pressure vessel, which is half the value of the hoop (circumferential) stress for the same internal pressure.

3. Importance of Longitudinal Stress Calculation

Details: Accurate calculation of longitudinal stress is crucial for pressure vessel design, material selection, and safety assessment. It helps determine if the vessel can withstand internal pressures without failure.

4. Using the Calculator

Tips: Enter internal pressure in Pascal, inner diameter in meters, and thickness in meters. All values must be positive numbers greater than zero.

5. Frequently Asked Questions (FAQ)

Q1: What is the difference between longitudinal stress and hoop stress?
A: Longitudinal stress acts along the length of the cylinder, while hoop stress acts circumferentially. Hoop stress is typically twice the longitudinal stress in thin-walled cylinders.

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: Pressure is typically measured in Pascal (Pa), diameter and thickness in meters (m), though other consistent unit systems can be used.

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: What are safety considerations for pressure vessels?
A: Pressure vessels must be designed with appropriate safety factors, considering material properties, operating conditions, and potential failure modes.