The relationship between the moment and curvature

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Discussion Overview

The discussion centers on the relationship between moment and curvature in the context of bending stiffness, particularly within the framework of beam theory. Participants explore the underlying principles and derivations related to this relationship.

Discussion Character

  • Technical explanation, Conceptual clarification, Debate/contested

Main Points Raised

  • One participant expresses confusion about how curvature functions in the formula relating moment to bending stiffness and curvature.
  • Another participant suggests that high curvature indicates greater deformation of the material, which correlates with a larger moment, referencing Euler's beam formulas.
  • A subsequent post reiterates the previous point about high curvature leading to increased moment and requests clarification on the derivation connecting curvature and bending stiffness.

Areas of Agreement / Disagreement

Participants do not appear to reach a consensus, as there is a request for clarification on the derivation, indicating ongoing uncertainty and exploration of the topic.

Contextual Notes

Limitations include a lack of detailed derivation steps and potential assumptions underlying the relationship between moment, curvature, and bending stiffness that are not explicitly stated.

Who May Find This Useful

This discussion may be of interest to students and professionals in engineering and physics, particularly those focused on structural analysis and beam theory.

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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