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

Stress Bending Moment Formula:

\[ f1 = \frac{M1}{k1 \times \pi \times R^{2} \times t} \]

Bending Moment at Support (M1):

N·m

Value of k1 depending on Saddle Angle:

Shell Radius (R):

Shell Thickness (t):

Stress Bending Moment at Topmost (f1):

1. What is Stress due to Longitudinal Bending at Top most Fibre?

Definition: This calculator determines the stress at the topmost fiber of a vessel's cross-section due to longitudinal bending moments.

Purpose: It helps engineers assess the structural integrity of pressure vessels and storage tanks under bending loads.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ f1 = \frac{M1}{k1 \times \pi \times R^{2} \times t} \]

Where:

\( f1 \) — Stress at topmost fiber (Pascals)
\( M1 \) — Bending moment at support (N·m)
\( k1 \) — Coefficient depending on saddle angle
\( R \) — Shell radius (meters)
\( t \) — Shell thickness (meters)

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

3. Importance of Stress Calculation

Details: Accurate stress calculation ensures vessel safety, prevents structural failure, and helps optimize material usage.

4. Using the Calculator

Tips: Enter all required values with appropriate units. The ±5% indicates typical manufacturing tolerances. All values must be > 0.

5. Frequently Asked Questions (FAQ)

Q1: What is the typical value of k1?
A: k1 is typically 0.107 for 120° saddle angles, but varies with different support configurations.

Q2: How is the bending moment M1 determined?
A: M1 is calculated from vessel weight, contents, and external loads using structural analysis.

Q3: Why is the topmost fiber critical?
A: The topmost fiber experiences maximum tensile stress during bending, often being the failure initiation point.

Q4: What units should I use?
A: Use consistent SI units: Newtons, meters, and Pascals for accurate results.

Q5: How does shell thickness affect the stress?
A: Thicker shells reduce stress as the bending moment is distributed over more material.