Bending Moment In Curved Beam Given Bending Stress At Outer Fibre Calculator

Formula Used:

\[ M_b = \frac{\sigma_{bo} \times A \times e \times R_o}{h_o} \]

Bending Stress at Outer Fibre (σ_bo):

Cross Sectional Area of Curved Beam (A):

m²

Eccentricity Between Centroidal and Neutral Axis (e):

Radius of Outer Fibre (R_o):

Distance of Outer Fibre from Neutral Axis (h_o):

Bending Moment in Curved Beam (M_b):

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1. What is Bending Moment in Curved Beam?

Bending moment in curved beam is the reaction induced in a structural element when an external force or moment is applied to the element, causing the element to bend. It represents the internal moment that resists the bending deformation in curved beams.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ M_b = \frac{\sigma_{bo} \times A \times e \times R_o}{h_o} \]

Where:

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

Explanation: This formula calculates the bending moment based on the bending stress at the outer fiber and the geometric properties of the curved beam.

3. Importance of Bending Moment Calculation

Details: Accurate calculation of bending moment 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. Bending stress should be in Pascals (Pa), areas in square meters (m²), and distances in meters (m). All values must be positive.

5. Frequently Asked Questions (FAQ)

Q1: What is the significance of eccentricity in this formula?
A: Eccentricity accounts for the offset between the centroidal axis and neutral axis in curved beams, which is crucial for accurate stress and moment calculations.

Q2: How does this differ from bending moment in straight beams?
A: Curved beams have additional complexity due to the curvature, which creates non-linear stress distribution and requires consideration of eccentricity between axes.

Q3: What are typical applications of curved beam analysis?
A: Curved beams are used in hooks, crane hooks, chain links, arches, and various machine components where curvature is essential for function.

Q4: What factors affect bending stress in curved beams?
A: Bending stress depends on the bending moment, cross-sectional properties, radius of curvature, and the distance from the neutral axis.

Q5: How accurate is this calculation method?
A: This formula provides accurate results for most engineering applications, though extremely sharp curvatures or complex cross-sections may require more advanced analysis methods.