Plastic Moment for Circular Section Calculator

Plastic Moment Formula:

\[ M_{pc} = \frac{D^3}{6} \times f_y \]

Plastic Moment Capacity: N·mm

Tolerance Range (±5%):

1. What is Plastic Moment for Circular Section?

Definition: The plastic moment capacity is the maximum moment a circular cross-section can resist when the entire section has yielded.

Purpose: This calculation is essential for structural engineers designing beams and columns to ensure they can withstand plastic deformation.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ M_{pc} = \frac{D^3}{6} \times f_y \]

Where:

\( M_{pc} \) — Plastic moment capacity (N·mm)
\( D \) — Diameter of the circular section (mm)
\( f_y \) — Yield stress of the material (MPa)

Explanation: The formula calculates the moment when the entire circular cross-section reaches yield stress, considering the geometric properties of the circle.

3. Importance of Plastic Moment Calculation

Details: Accurate plastic moment calculation ensures structural safety, prevents collapse, and helps in economical design by avoiding over-engineering.

4. Using the Calculator

Tips: Enter the diameter in mm, yield stress in MPa, and tolerance percentage (default ±5%). All values must be positive.

5. Frequently Asked Questions (FAQ)

Q1: What is the significance of the tolerance percentage?
A: The tolerance accounts for material variations and manufacturing imperfections, providing a safe range of values.

Q2: What's a typical yield stress for structural steel?
A: Common structural steel has yield stress around 250 MPa, but this varies by grade and material.

Q3: Does this formula account for buckling?
A: No, this is purely for plastic moment capacity. Buckling analysis requires additional calculations.

Q4: Can I use this for hollow circular sections?
A: No, this formula is for solid circular sections only. Hollow sections require a different formula.

Q5: Why is the diameter cubed in the formula?
A: The moment capacity depends on the section modulus, which for a circle is proportional to the diameter cubed.