Which of the following is the correct expression for the bending equation in pure bending?

(Where M = Bending moment, I = Moment of inertia of the cross-section about the neutral axis, f = Bending stress at a distance y from the neutral axis, y = Distance from the neutral axis, E = Modulus of elasticity, and R = Radius of curvature of the beam)

Explanation:

The correct expression for the bending equation in pure bending is:

\(\rm \frac{M}{I}=\frac{f}{y}=\frac{E}{R}\)

(Where M = Bending moment, I = Moment of inertia of the cross-section about the neutral axis, f = Bending stress at a distance y from the neutral axis, y = Distance from the neutral axis, E = Modulus of elasticity, and R = Radius of curvature of the beam)

Additional Information

1. Neutral Axis: The axis within the beam where the stress is zero during bending.

2. Linear Stress Distribution: Bending stress varies linearly from the neutral axis.

3. Pure Bending Assumption: Assumes no shear forces; bending moment is constant along the length.

4. Valid for Elastic Range: The formula holds until the material behaves elastically (no plastic deformation).

5. Derivation: Based on the geometry of deformation and Hooke’s Law.