Fully Plastic Recovery Stress In Beams Calculator

Formula Used:

\[ \sigma_{rec\_plastic} = \frac{M_{rec\_plastic} \times y}{\frac{b \times d^3}{12}} \]

Fully Plastic Recovery Bending Moment (M_{rec_plastic}):

N·m

Depth Yielded Plastically (y):

Breadth of Rectangular Beam (b):

Depth of Rectangular Beam (d):

Fully Plastic Recovery Stress (σ_{rec_plastic}):

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1. What is Fully Plastic Recovery Stress?

Fully plastic recovery stress in beams can be defined as when a beam so bent is applied with a moment of same magnitude in the opposite direction, then the recovery of stress takes place.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ \sigma_{rec\_plastic} = \frac{M_{rec\_plastic} \times y}{\frac{b \times d^3}{12}} \]

Where:

\( \sigma_{rec\_plastic} \) — Fully plastic recovery stress in beams (Pa)
\( M_{rec\_plastic} \) — Fully plastic recovery bending moment (N·m)
\( y \) — Depth yielded plastically from outermost fiber (m)
\( b \) — Breadth of rectangular beam (m)
\( d \) — Depth of rectangular beam (m)

Explanation: This formula calculates the recovery stress that occurs when a bending moment of equal magnitude but opposite direction is applied to a plastically deformed beam.

3. Importance of Recovery Stress Calculation

Details: Calculating recovery stress is crucial for understanding material behavior under reverse loading conditions, assessing residual stresses, and predicting structural performance in cyclic loading scenarios.

4. Using the Calculator

Tips: Enter all values in consistent SI units. The bending moment can be positive or negative depending on direction. Beam dimensions must be positive values.

5. Frequently Asked Questions (FAQ)

Q1: What is plastic recovery in beam theory?
A: Plastic recovery refers to the stress redistribution that occurs when a plastically deformed beam is subjected to a reverse bending moment of equal magnitude.

Q2: When does fully plastic recovery occur?
A: Fully plastic recovery occurs when a beam that has yielded plastically is subjected to a moment of equal magnitude in the opposite direction, causing stress recovery.

Q3: What are the limitations of this calculation?
A: This calculation assumes ideal plastic behavior, homogeneous material properties, and perfect rectangular cross-section. Real-world materials may exhibit different behavior.

Q4: How does recovery stress affect beam performance?
A: Recovery stress can create residual stresses that affect the beam's load-carrying capacity, fatigue life, and deformation characteristics under subsequent loading.

Q5: Can this formula be used for non-rectangular beams?
A: This specific formula is derived for rectangular beams. Other cross-sectional shapes require different formulas based on their moment of inertia calculations.