Stress due to Longitudinal Bending at Bottom most Fibre of Cross Section Calculator

Stress Formula:

\[ f2 = \frac{M1}{k2 \times \pi \times R^2 \times t} \]

Bending Moment at Support:

N·m

Value of k2:

Shell Radius:

Shell Thickness:

Stress at Bottom most Fibre (N/mm²):

1. What is Stress due to Longitudinal Bending?

Definition: This calculator determines the stress at the bottommost fiber of a cross-section due to longitudinal bending moments in cylindrical vessels.

Purpose: It helps engineers evaluate structural integrity by calculating the maximum stress at critical points of pressure vessels or storage tanks.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ f2 = \frac{M1}{k2 \times \pi \times R^2 \times t} \]

Where:

\( f2 \) — Stress at bottommost fiber (N/mm²)
\( M1 \) — Bending moment at support (N·m)
\( k2 \) — Coefficient depending on saddle angle
\( R \) — Shell radius (mm)
\( t \) — Shell thickness (mm)

Explanation: The bending moment is distributed over the cross-sectional area, modified by geometric factors.

3. Importance of Stress Calculation

Details: Accurate stress calculation ensures vessel safety, prevents material failure, and helps in optimizing design parameters.

4. Using the Calculator

Tips: Enter the bending moment, k2 value (default 0.192), shell radius (mm), and thickness (mm). All values must be > 0. Results include ±5% tolerance.

5. Frequently Asked Questions (FAQ)

Q1: What is the typical k2 value range?
A: k2 typically ranges from 0.192 to 0.273 depending on the saddle angle (120°-150°).

Q2: Why is the bottommost fiber critical?
A: The bottommost fiber experiences maximum tensile stress under bending loads.

Q3: How does shell radius affect the stress?
A: Stress is inversely proportional to the square of the radius - larger vessels experience lower stresses.

Q4: What units should be used?
A: Consistent SI units are required (N·m for moment, mm for dimensions).

Q5: Does this include safety factors?
A: No, calculated stresses should be compared to allowable values with appropriate safety factors.