Answered: What is required to relate the stress…

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Question

What is required to relate the stress distribution to the resultant bending moment?

Expert Solution

Step 1

The restoring force per unit area which is equal in magnitude of the applied force but in opposite direction is known as stress.

The distribution of stress in a curved flexural member is expressed as $σ = ε E = \frac{E (r - ρ) d x}{ρ x}$

now the sum of the normal force acting is equal to zero that is

$\int_{}^{} σ d A = E \frac{d x}{x} \int_{}^{} \frac{(r - ρ) d A}{ρ} = 0 E \frac{d x}{x} [\int_{}^{} \frac{(r) d A}{ρ} - \int_{}^{} d A] = 0 \int_{}^{} \frac{(r) d A}{ρ} - A = 0 r = \frac{A}{\int_{}^{} \frac{d A}{ρ}}$

this equation indicates that the neutral axis and centroidal axis doesn't coincide

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