How can we relate the internal moment to the radius of curvature?

Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
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How can we relate the internal moment to the radius of curvature?

Expert Solution
Step 1

In order to proceed the question, we must take some assumptions.

  1. Pure bending of beam.
  2. The internal moment at the cross section is the bending moment at that cross section.

 

Step 2

Write the Euler Bernoulli’s equation for bending of beams.

Mechanical Engineering homework question answer, step 2, image 1

Where,

M is the bending moment at the particular cross section

IN.A is the second moment of the area of the cross section about the neutral Axis.

σb is the bending stress at a fiber of distance y from the neutral axis of the beam at s particular cross section.

E is the modulus of elasticity of the material.

R A is the radius of the neutral axis of the beam.

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