Stress due to Longitudinal Bending at Mid-Span Calculator

Stress due to Longitudinal Bending at Mid-Span Formula:

\[ f_3 = \frac{M_2}{\pi \times R^2 \times t} \]

Bending Moment at Centre of Vessel Span:

N·m

Shell Radius:

Shell Thickness:

Tolerance:

Stress due to Longitudinal Bending at Mid-Span: Pa

Acceptable Range (±5%): Pa

1. What is Stress due to Longitudinal Bending at Mid-Span?

Definition: This refers to the amount of stress that develops at the extreme fibre located at the bottom of a cross section when a vessel is subjected to bending moments.

Purpose: It helps engineers determine if the vessel's shell can withstand the bending stresses it experiences during operation.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ f_3 = \frac{M_2}{\pi \times R^2 \times t} \]

Where:

\( f_3 \) — Stress due to Longitudinal Bending at Mid-Span (Pa)
\( M_2 \) — Bending Moment at Centre of Vessel Span (N·m)
\( R \) — Shell Radius (m)
\( t \) — Shell Thickness (m)

Explanation: The bending moment is divided by the product of π, the square of the shell radius, and the shell thickness to determine the stress.

3. Importance of Stress Calculation

Details: Proper stress calculation ensures vessel integrity, prevents structural failure, and helps in designing safe pressure vessels.

4. Using the Calculator

Tips: Enter the bending moment in N·m, shell radius in meters, shell thickness in meters, and tolerance percentage. All values except tolerance must be > 0.

5. Frequently Asked Questions (FAQ)

Q1: What is a typical tolerance percentage?
A: ±5% is common, but this depends on material specifications and safety factors.

Q2: How do I determine the bending moment?
A: The bending moment can be calculated from the vessel's loading conditions and support configuration.

Q3: What units should I use?
A: Use consistent SI units: N·m for moment, meters for dimensions, and Pascals for stress.

Q4: Does this include safety factors?
A: No, you should apply appropriate safety factors to the calculated stress values.

Q5: What if my stress exceeds the material's yield strength?
A: You should increase the shell thickness or reduce the bending moment through design changes.