Eccentricity Between Centroidal And Neutral Axis Of Curved Beam Given Bending Stress At Inner Fibre Calculator

Formula Used:

\[ e = \frac{M_b \cdot h_i}{A \cdot \sigma_{bi} \cdot R_i} \]

Bending Moment in Curved Beam (M_b):

N·m

Distance of Inner Fibre from Neutral Axis (h_i):

Cross Sectional Area of Curved Beam (A):

m²

Bending Stress at Inner Fibre (σ_bi):

Radius of Inner Fibre (R_i):

Eccentricity Between Centroidal and Neutral Axis (e):

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1. What is Eccentricity Between Centroidal and Neutral Axis?

The eccentricity between centroidal and neutral axis is the distance between these two axes in a curved structural element. This parameter is crucial in analyzing bending stresses and deformations in curved beams.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ e = \frac{M_b \cdot h_i}{A \cdot \sigma_{bi} \cdot R_i} \]

Where:

\( e \) — Eccentricity between centroidal and neutral axis (m)
\( M_b \) — Bending moment in curved beam (N·m)
\( h_i \) — Distance of inner fibre from neutral axis (m)
\( A \) — Cross sectional area of curved beam (m²)
\( \sigma_{bi} \) — Bending stress at inner fibre (Pa)
\( R_i \) — Radius of inner fibre (m)

Explanation: This formula calculates the offset between the centroidal axis (geometric center) and neutral axis (zero stress plane) in curved beams under bending.

3. Importance of Eccentricity Calculation

Details: Accurate calculation of eccentricity is essential for determining bending stresses, designing curved structural elements, and ensuring structural integrity in applications like arches, hooks, and curved machine components.

4. Using the Calculator

Tips: Enter all values in appropriate SI units. Ensure bending moment, distances, area, stress, and radius are positive values greater than zero for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: Why is eccentricity important in curved beams?
A: Eccentricity affects stress distribution and must be considered for accurate structural analysis and design of curved elements.

Q2: How does this differ from straight beams?
A: In straight beams, centroidal and neutral axes coincide, while in curved beams they are separated due to curvature effects.

Q3: What are typical values for eccentricity?
A: Eccentricity values depend on beam geometry and loading, typically ranging from millimeters to centimeters in practical applications.

Q4: When is this calculation most critical?
A: This calculation is particularly important in highly curved beams and components where bending stresses are significant.

Q5: Can this formula be used for composite materials?
A: The formula applies to homogeneous materials. For composites, additional considerations for material properties are needed.