Bending Moment at Centre of Vessel Span Calculator

Bending Moment Formula:

\[ M2 = \frac{Q \times L}{4} \times \left(\frac{1+2\left(\frac{R_{vessel}^2 - DepthHead^2}{L^2}\right)}{1+\frac{4}{3}\left(\frac{DepthHead}{L}\right)} - \frac{4A}{L}\right) \]

Total Load per Saddle:

Tangent to Tangent Length:

Vessel Radius:

Depth of Head:

Distance from Tangent Line to Saddle Centre:

Bending Moment at Centre: N·mm

1. What is Bending Moment at Centre of Vessel Span?

Definition: This calculator determines the maximum bending moment that occurs at the midpoint of a vessel's span between supports.

Purpose: It helps engineers design proper support systems for pressure vessels by calculating critical stress points.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ M2 = \frac{Q \times L}{4} \times \left(\frac{1+2\left(\frac{R_{vessel}^2 - DepthHead^2}{L^2}\right)}{1+\frac{4}{3}\left(\frac{DepthHead}{L}\right)} - \frac{4A}{L}\right) \]

Where:

\( M2 \) — Bending moment at center (N·mm)
\( Q \) — Total load per saddle (N)
\( L \) — Tangent to tangent length (mm)
\( R_{vessel} \) — Vessel radius (mm)
\( DepthHead \) — Depth of head (mm)
\( A \) — Distance from tangent line to saddle center (mm)

3. Importance of Bending Moment Calculation

Details: Accurate bending moment calculation ensures vessel structural integrity, prevents deformation, and maintains safety standards.

4. Using the Calculator

Tips: Enter all required dimensions in millimeters. The ±5% indicates typical tolerance ranges for these measurements.

5. Frequently Asked Questions (FAQ)

Q1: What affects bending moment most significantly?
A: The vessel length (L) and load (Q) have the greatest impact, followed by the head depth and saddle position.

Q2: Why is the ±5% tolerance important?
A: Manufacturing tolerances and measurement uncertainties mean actual values may vary slightly from design specifications.

Q3: How do I determine the total load per saddle?
A: Include the weight of the vessel, contents, insulation, and any other permanent loads distributed between saddles.

Q4: What's the typical range for DepthHead?
A: For standard ASME heads, depth is typically 0.25-0.5 times the vessel diameter.

Q5: How does saddle position affect results?
A: Moving saddles closer to the ends reduces bending moment but increases local stresses at the saddles.