Recovery Bending Moment For Non Linear Relation Calculator

Formula Used:

\[ M_{rec} = -\sigma_y \cdot d \cdot \left( \frac{d^2}{4} - \frac{n \cdot \eta^2}{n+2} \right) \]

Yield Stress (Non-linear):

Depth of Rectangular Beam:

Material Constant:

Depth of Outermost Shell Yields:

Non Linear Recovery Bending Moment:

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1. What is Recovery Bending Moment For Non Linear Relation?

The Recovery Bending Moment for Non Linear Relation can be defined as when a beam so bent is applied with a moment of same magnitude in the opposite direction and the opposite moment is called Recovery bending moment. This calculation is particularly important in materials that exhibit non-linear stress-strain relationships.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ M_{rec} = -\sigma_y \cdot d \cdot \left( \frac{d^2}{4} - \frac{n \cdot \eta^2}{n+2} \right) \]

Where:

\( M_{rec} \) — Non Linear Recovery Bending Moment (N·m)
\( \sigma_y \) — Yield stress (non-linear) (Pa)
\( d \) — Depth of rectangular beam (m)
\( n \) — Material constant
\( \eta \) — Depth of outermost shell yields (m)

Explanation: The formula accounts for the non-linear material behavior and calculates the recovery moment needed to return the beam to its original state after plastic deformation.

3. Importance of Recovery Bending Moment Calculation

Details: Accurate calculation of recovery bending moment is crucial for understanding material behavior under cyclic loading, designing structures that undergo plastic deformation, and predicting the residual stresses and deformations after unloading.

4. Using the Calculator

Tips: Enter yield stress in Pascals, depth of beam in meters, material constant (dimensionless), and depth of outermost shell yields in meters. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is the significance of the negative sign in the formula?
A: The negative sign indicates that the recovery bending moment acts in the opposite direction to the original bending moment that caused the plastic deformation.

Q2: When is this non-linear relation applicable?
A: This non-linear relation is applicable for materials that exhibit non-linear stress-strain behavior beyond the elastic limit, particularly in plastic deformation analysis.

Q3: What does the material constant represent?
A: The material constant represents the non-linear characteristics of the material's stress-strain relationship beyond the yield point.

Q4: How does depth of outermost shell yields affect the result?
A: The depth of outermost shell yields indicates how far the yielding has progressed through the beam cross-section and significantly influences the magnitude of the recovery moment.

Q5: Can this formula be used for all materials?
A: This formula is specifically designed for materials that follow the particular non-linear stress-strain relationship described by the equation parameters.