Question
Download Solution PDFWhich 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)
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFExplanation:
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
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Neutral Axis: The axis within the beam where the stress is zero during bending.
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Linear Stress Distribution: Bending stress varies linearly from the neutral axis.
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Pure Bending Assumption: Assumes no shear forces; bending moment is constant along the length.
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Valid for Elastic Range: The formula holds until the material behaves elastically (no plastic deformation).
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Derivation: Based on the geometry of deformation and Hooke’s Law.
Last updated on Jun 7, 2025
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