Distance Of Inner Fiber From Neutral Axis Of Curved Beam Given Bending Stress At Fibre Calculator

Formula Used:

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

Bending Stress At Inner Fibre (σ_bi):

Pascal

Cross Sectional Area (A):

m²

Eccentricity (e):

Radius of Inner Fibre (R_i):

Bending Moment (M_b):

N·m

Distance Of Inner Fibre From Neutral Axis (h_i):

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1. What is Distance Of Inner Fiber From Neutral Axis?

Distance of Inner Fibre from Neutral Axis is the point where the fibers of a material undergoing bending are stretched maximum. It represents the maximum distance from the neutral axis where bending stress occurs in a curved beam.

2. How Does the Calculator Work?

The calculator uses the formula:

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

Where:

\( h_i \) — Distance of Inner Fibre from Neutral Axis (m)
\( \sigma_{bi} \) — Bending Stress at Inner Fibre (Pa)
\( A \) — Cross sectional area of curved beam (m²)
\( e \) — Eccentricity Between Centroidal and Neutral Axis (m)
\( R_i \) — Radius of Inner Fibre (m)
\( M_b \) — Bending moment in curved beam (N·m)

Explanation: This formula calculates the distance from the neutral axis to the inner fiber based on bending stress, cross-sectional properties, and applied bending moment.

3. Importance of This Calculation

Details: Calculating the distance of inner fiber from neutral axis is crucial for determining stress distribution in curved beams, designing curved structural elements, and ensuring structural integrity under bending loads.

4. Using the Calculator

Tips: Enter all values in appropriate SI units. Bending stress, cross-sectional area, eccentricity, radius, and bending moment must all be positive values greater than zero for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is the neutral axis in a curved beam?
A: The neutral axis is the line through a beam where there is no longitudinal stress or strain when the beam is subjected to bending.

Q2: Why is this calculation important for curved beams?
A: Curved beams have different stress distributions compared to straight beams, and accurate calculation of fiber distances is essential for proper design and analysis.

Q3: What units should be used for input values?
A: All inputs should be in SI units: Pascals for stress, square meters for area, and meters for distance measurements.

Q4: Can this formula be used for any curved beam?
A: This formula is specifically derived for curved beams and provides accurate results for such structural elements.

Q5: What if the calculated distance is negative?
A: The distance should always be positive. If negative values occur, check input values for errors as all parameters should be positive.