Fully Plastic Bending Moment Calculator

Formula Used:

\[ M_f = \frac{b \times d^2 \times \sigma_0}{4} \]

Fully Plastic Bending Moment (Mf):

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1. What is Fully Plastic Bending Moment?

Fully Plastic Bending Moment occurs in a beam which has yielded fully. It represents the maximum moment a beam can sustain when the entire cross-section has reached the yield stress, indicating complete plastic deformation.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ M_f = \frac{b \times d^2 \times \sigma_0}{4} \]

Where:

\( M_f \) — Fully Plastic Bending Moment (N·m)
\( b \) — Breadth of rectangular beam (m)
\( d \) — Depth of rectangular beam (m)
\( \sigma_0 \) — Yield Stress (Pa)

Explanation: This formula calculates the moment capacity when the entire cross-section of a rectangular beam has yielded plastically.

3. Importance of Fully Plastic Bending Moment Calculation

Details: Calculating the fully plastic bending moment is crucial for structural design and analysis, particularly in plastic design methods where the ultimate load-carrying capacity of structures is determined based on plastic collapse mechanisms.

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 numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is the difference between elastic and plastic bending moment?
A: Elastic bending moment is the maximum moment before yielding begins, while plastic bending moment is the maximum moment when the entire section has yielded.

Q2: Does this formula apply to non-rectangular sections?
A: No, this specific formula is for rectangular sections. Other cross-sectional shapes have different formulas for plastic moment calculation.

Q3: What is the shape factor for rectangular sections?
A: The shape factor (ratio of plastic moment to yield moment) for rectangular sections is 1.5.

Q4: How does temperature affect the plastic moment capacity?
A: Elevated temperatures typically reduce the yield stress of materials, thereby reducing the plastic moment capacity of the section.

Q5: Is strain hardening considered in this calculation?
A: No, this formula assumes ideal plastic behavior without strain hardening effects.