Why is it first necessary to relate the internal moment to the radius of the curvature of the elastic curve?

Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
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Why is it first necessary to relate the internal moment to the radius of the curvature of the elastic curve?

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It is necessary to relate the internal moment to the radius of curvature because the radius of curvature can show the behavior of any beam easily on the application of load. Moreover, if the beam has a high moment of resistance then we can say that on the application of load the following beam will have the less tendency of bending & this is even desirable as far as the design of any beam is concerned.

From the bending moment equation we know:

           Mechanical Engineering homework question answer, step 1, image 1

From the differential equation of elastic curvature:

           Mechanical Engineering homework question answer, step 1, image 2

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