The relationship between the moment and curvature

[Chuck88]

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

 

[Curl]

Because high curvature means you deformed the material more, which means you are applying a large moment. See Euler's beam formulas

 

[Chuck88]

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.

 

[Curl]

http://en.wikipedia.org/wiki/Euler–Bernoulli_beam_theory

 

[pmacias]

I can explain the relationship between moment and curvature in terms of the physical principles of bending and elasticity.

First, let's define what we mean by moment and curvature. Moment, also known as torque, is a measure of the force applied to an object that causes it to rotate. It is a vector quantity, meaning it has both a magnitude and a direction. Curvature, on the other hand, is a measure of how much a curve deviates from being a straight line. It is also a vector quantity, with both magnitude and direction.

Now, when we are dealing with a curved object, such as a beam or a rod, we can apply a moment to it by applying a force at a distance from its axis of rotation. This will cause the object to bend or deform. The amount of bending that occurs is related to both the moment and the curvature of the object.

In order to understand why the moment can be represented as the product of bending stiffness and curvature, we need to look at the concept of bending stiffness. Bending stiffness is a measure of how resistant an object is to bending. It is influenced by factors such as the material properties, cross-sectional area, and length of the object.

When we apply a moment to a curved object, it causes the object to bend. The curvature of the object is a measure of how much the object is bending. The greater the moment applied, the greater the curvature will be. However, the bending stiffness of the object also plays a role. A stiffer object will resist bending more, resulting in a smaller curvature for the same applied moment.

Therefore, we can say that the moment is directly proportional to the curvature of the object and inversely proportional to the bending stiffness. This relationship can be mathematically represented as the product of bending stiffness and curvature.

In summary, the curvature in the formula for moment is a crucial factor in understanding the relationship between moment and bending stiffness. It helps us to quantify the amount of bending that occurs in a curved object when a moment is applied. I hope this explanation helps to clarify the function of curvature in this formula.