Fully Plastic Recovery Bending Moment Calculator

Fully Plastic Recovery Bending Moment Equation:

\[ M_{rec\_plastic} = -\frac{b \times d^2 \times \sigma_0}{4} \]

Fully Plastic Recovery Bending Moment (M_rec_plastic):

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1. What is Fully Plastic Recovery Bending Moment?

Fully Plastic Recovery Bending Moment can be defined as when a beam so bent is applied with a moment of same magnitude in the opposite direction and moment is recovery bending moment. It represents the moment required to recover a beam from its fully plastic state.

2. How Does the Calculator Work?

The calculator uses the Fully Plastic Recovery Bending Moment equation:

\[ M_{rec\_plastic} = -\frac{b \times d^2 \times \sigma_0}{4} \]

Where:

\( M_{rec\_plastic} \) — Fully Plastic Recovery Bending Moment (N·m)
\( b \) — Breadth of rectangular beam (m)
\( d \) — Depth of rectangular beam (m)
\( \sigma_0 \) — Yield Stress (Pa)

Explanation: The negative sign indicates that the recovery moment acts in the opposite direction to the original bending moment that caused the plastic deformation.

3. Importance of Fully Plastic Recovery Bending Moment

Details: Understanding the recovery bending moment is crucial in structural engineering for analyzing the behavior of beams under cyclic loading, designing structures that can recover from plastic deformation, and assessing the residual strength of structural elements.

4. Using the Calculator

Tips: Enter the breadth and depth of the rectangular beam in meters, and the yield stress in Pascals. All values must be positive and non-zero for accurate calculation.

5. Frequently Asked Questions (FAQ)

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

Q2: When is this calculation typically used?
A: This calculation is used in structural analysis when dealing with beams that have undergone plastic deformation and need to be returned to their original state.

Q3: What are the limitations of this formula?
A: This formula applies specifically to rectangular beams and assumes homogeneous material properties and perfect plastic behavior.

Q4: How does beam geometry affect the recovery moment?
A: The recovery moment is directly proportional to the beam's breadth and the square of its depth, making depth the most significant geometric factor.

Q5: Can this formula be used for other beam cross-sections?
A: No, this specific formula is derived for rectangular cross-sections. Other cross-sections have different formulas for plastic recovery bending moment.