The relationship between the moment and curvature

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The moment in beam theory is represented as the product of bending stiffness and curvature because higher curvature indicates greater deformation of the material, leading to a larger applied moment. The relationship is derived from Euler-Bernoulli beam theory, which connects bending moments to curvature through the material's stiffness properties. Understanding this derivation involves examining how changes in curvature affect the internal forces within the beam. The curvature essentially quantifies the degree of bending, which directly influences the moment experienced by the beam. This relationship is crucial for accurately predicting the behavior of beams under various loading conditions.
Chuck88
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I want to know why the moment could be represented as the product of the bending stiffness and the curvature. I do not quite understand the function of the curvature in the formula.

http://en.wikipedia.org/wiki/Curvature
 
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Because high curvature means you deformed the material more, which means you are applying a large moment. See Euler's beam formulas
 
Curl said:
Because high curvature means you deformed the material more, which means you are applying a large moment. See Euler's beam formulas

Sorry that I did not make it clear. I want to know the steps of the derivation for the correlation between the curvature and bending stiffness.
 

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