Longitudinal Stress Given Efficiency Of Circumferential Joint Calculator

Formula Used:

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

Internal Pressure in thin shell (P_i):

Inner Diameter of Cylinderical Vessel (D_i):

Thickness Of Thin Shell (t):

Efficiency of Circumferential Joint (η_c):

(0-1)

Longitudinal Stress (σ_l):

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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 vessel and is an important factor in pressure vessel design.

2. How Does the Calculator Work?

The calculator uses the formula:

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

Where:

\( \sigma_l \) — Longitudinal Stress (Pa)
\( P_i \) — Internal Pressure in thin shell (Pa)
\( D_i \) — Inner Diameter of Cylindrical Vessel (m)
\( t \) — Thickness Of Thin Shell (m)
\( \eta_c \) — Efficiency of Circumferential Joint (0-1)

Explanation: This formula calculates the longitudinal stress in thin-walled pressure vessels, accounting for joint efficiency which represents the strength reduction due to welded joints.

3. Importance of Longitudinal Stress Calculation

Details: Accurate calculation of longitudinal stress is crucial for pressure vessel design, ensuring structural integrity and safety under internal pressure conditions. It helps determine appropriate wall thickness and material selection.

4. Using the Calculator

Tips: Enter internal pressure in Pascals, inner diameter in meters, thickness in meters, and joint efficiency as a value between 0 and 1. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is the difference between longitudinal and circumferential stress?
A: Longitudinal stress acts parallel to the vessel's axis, while circumferential (hoop) stress acts circumferentially around the vessel. Circumferential stress is typically twice the longitudinal stress.

Q2: Why is joint efficiency important in this calculation?
A: Joint efficiency accounts for the reduced strength of welded joints compared to the base material, ensuring safe design calculations.

Q3: What are typical joint efficiency values?
A: Joint efficiency typically ranges from 0.6 to 1.0, depending on the type of joint, welding quality, and inspection methods used.

Q4: When is this formula applicable?
A: This formula is valid for thin-walled pressure vessels where the wall thickness is less than about 1/10 of the vessel diameter.

Q5: What units should be used for input values?
A: Use consistent SI units - Pascals for pressure, meters for dimensions, and dimensionless value for joint efficiency.