Bending Stress At Inner Fibre Of Curved Beam Given Bending Moment Calculator

Formula Used:

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

Bending Moment (M_b):

N·m

Distance of Inner Fibre (h_i):

Cross Sectional Area (A):

m²

Eccentricity (e):

Radius of Inner Fibre (R_i):

Bending Stress at Inner Fibre (σ_bi):

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is Bending Stress at Inner Fibre?

Bending stress at inner fibre is the amount of bending moment at the inner fiber of a curved structural element. It represents the maximum tensile or compressive stress experienced by the material at the inner curvature when subjected to bending loads.

2. How Does the Calculator Work?

The calculator uses the formula:

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

Where:

\( \sigma_{bi} \) — Bending stress at inner fibre (Pa)
\( M_b \) — 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)
\( e \) — Eccentricity between centroidal and neutral axis (m)
\( R_i \) — Radius of inner fibre (m)

Explanation: The formula calculates the bending stress at the inner fiber of a curved beam by considering the bending moment, geometric properties, and material distribution.

3. Importance of Bending Stress Calculation

Details: Accurate calculation of bending stress at inner fibre is crucial for structural design and analysis of curved beams, ensuring they can withstand applied loads without failure or excessive deformation.

4. Using the Calculator

Tips: Enter all values in appropriate SI units. Ensure all input values are positive and valid for accurate results.

5. Frequently Asked Questions (FAQ)

Q1: What is the difference between bending stress at inner and outer fibres?
A: The inner fibre experiences maximum tensile stress while the outer fibre experiences maximum compressive stress in curved beams under bending.

Q2: Why is eccentricity important in this calculation?
A: Eccentricity accounts for the shift between centroidal and neutral axes in curved beams, which affects stress distribution.

Q3: What are typical applications of this calculation?
A: This calculation is used in designing hooks, crane hooks, chain links, and other curved structural elements.

Q4: How does curvature affect bending stress?
A: Curvature causes non-linear stress distribution across the cross-section, with higher stresses at inner fibers compared to straight beams.

Q5: What safety factors should be considered?
A: Appropriate safety factors should be applied based on material properties, loading conditions, and application requirements.