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In a beam subjected to bending, what is the relationship between the bending mom

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Question: In a beam subjected to bending, what is the relationship between the bending moment and the curvature?

Options:

  1. M = EI * ρ
  2. M = ρ / EI
  3. M = E * I * ρ
  4. M = ρ / E

Correct Answer: M = EI * ρ

Solution: 

The relationship between the bending moment (M) and the curvature (ρ) in a beam is given by M = EI * ρ, where E is the modulus of elasticity and I is the moment of inertia.

In a beam subjected to bending, what is the relationship between the bending mom

Practice Questions

Q1
In a beam subjected to bending, what is the relationship between the bending moment and the curvature?
  1. M = EI * ρ
  2. M = ρ / EI
  3. M = E * I * ρ
  4. M = ρ / E

Questions & Step-by-Step Solutions

In a beam subjected to bending, what is the relationship between the bending moment and the curvature?
  • Step 1: Understand that a beam can bend when a force is applied to it.
  • Step 2: Know that the bending moment (M) is a measure of the internal forces that cause the beam to bend.
  • Step 3: Recognize that curvature (ρ) is a measure of how much the beam bends.
  • Step 4: Learn that the relationship between bending moment and curvature is expressed in the formula M = EI * ρ.
  • Step 5: Identify that E is the modulus of elasticity, which measures the stiffness of the material of the beam.
  • Step 6: Understand that I is the moment of inertia, which depends on the shape of the beam's cross-section.
  • Step 7: Conclude that as the bending moment increases, the curvature of the beam also increases, assuming E and I are constant.
  • Bending Moment and Curvature Relationship – The bending moment in a beam is directly proportional to the curvature, with the proportionality constant being the product of the modulus of elasticity (E) and the moment of inertia (I).
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