Moment Due To Eccentric Load Bending Stress On Hollow Circular Section Calculator

Formula Used:

\[ M = \sigma_b \times S \]

Moment due to eccentric load (M):

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1. What is Moment due to Eccentric Load?

Moment due to eccentric load refers to the bending moment generated at any point of a column section when a load is applied at a distance from the centroidal axis. This creates both axial and bending stresses in the structural member.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ M = \sigma_b \times S \]

Where:

\( M \) — Moment due to eccentric load (Newton Meter)
\( \sigma_b \) — Bending Stress in Column (Pascal)
\( S \) — Section Modulus (Cubic Meter)

Explanation: The formula calculates the bending moment by multiplying the bending stress by the section modulus of the cross-section.

3. Importance of Moment Calculation

Details: Accurate calculation of moment due to eccentric load is crucial for structural design and analysis, ensuring that columns and other structural members can safely withstand combined axial and bending stresses without failure.

4. Using the Calculator

Tips: Enter bending stress in Pascal and section modulus in Cubic Meter. Both values must be positive numbers greater than zero for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is eccentric loading?
A: Eccentric loading occurs when a force is applied away from the centroidal axis of a structural member, creating both axial compression/tension and bending moments.

Q2: How does section modulus affect bending moment?
A: Section modulus is a geometric property that indicates a section's resistance to bending. Higher section modulus means greater resistance to bending for the same bending stress.

Q3: What units should be used for input values?
A: Bending stress should be in Pascal (Pa) and section modulus should be in Cubic Meter (m³) for consistent results in Newton Meter (N·m).

Q4: Can this formula be used for any cross-section?
A: Yes, the formula M = σb × S is general and applies to any cross-section, though the section modulus value varies with different cross-sectional shapes.

Q5: What are typical values for section modulus?
A: Section modulus values depend on the cross-sectional geometry and dimensions. For hollow circular sections, it's calculated as S = π(D⁴ - d⁴)/(32D) where D is outer diameter and d is inner diameter.