Bending Moment at Support Calculator

Bending Moment at Support Formula:

\[ M1 = Q \times A \times \left(1 - \frac{1 - \frac{A}{L} + \frac{R_{vessel}^2 - DepthHead^2}{2 \times A \times L}}{1 + \frac{4}{3} \times \frac{DepthHead}{L}}\right) \]

Total Load per Saddle (Q):

Distance from Tangent Line to Saddle Centre (A):

Tangent to Tangent Length of Vessel (L):

Vessel Radius (R_vessel):

Depth of Head:

Tolerance:

Bending Moment at Support (M1):

1. What is Bending Moment at Support?

Definition: Bending Moment at Support refers to the maximum moment or torque experienced by a structural member (like a beam or vessel) at its support point.

Purpose: This calculation is crucial for designing pressure vessels and ensuring they can withstand operational loads without failure.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ M1 = Q \times A \times \left(1 - \frac{1 - \frac{A}{L} + \frac{R_{vessel}^2 - DepthHead^2}{2 \times A \times L}}{1 + \frac{4}{3} \times \frac{DepthHead}{L}}\right) \]

Where:

\( M1 \) — Bending Moment at Support (N·m)
\( Q \) — Total Load per Saddle (N)
\( A \) — Distance from Tangent Line to Saddle Centre (m)
\( L \) — Tangent to Tangent Length of Vessel (m)
\( R_{vessel} \) — Vessel Radius (m)
\( DepthHead \) — Depth of Head (m)

3. Importance of Bending Moment Calculation

Details: Accurate bending moment calculation ensures structural integrity, prevents overstressing of vessel supports, and helps in proper material selection.

4. Using the Calculator

Tips: Enter all required dimensions and loads. The tolerance field (default ±5%) allows you to see the acceptable range of values.

5. Frequently Asked Questions (FAQ)

Q1: What is the typical tolerance for bending moment calculations?
A: A ±5% tolerance is common, but this may vary based on engineering standards and specific project requirements.

Q2: How do I determine the total load per saddle?
A: The total load includes the weight of the vessel, contents, and any additional operational loads divided by the number of saddles.

Q3: What if my vessel has different head depths?
A: Use the average depth or calculate separately for each end if significantly different.

Q4: Can this calculator be used for horizontal vessels?
A: Yes, this formula is specifically designed for horizontal vessels supported by saddles.

Q5: How does vessel radius affect the bending moment?
A: Larger radius vessels typically experience higher bending moments due to increased leverage effects.