Bending Moment Formula: Understanding Its Relationship to Pure Bending

In summary: So M(x) = (E*I)/rho.In summary, the bending moment formula is derived from the Euler-Bernoulli Beam equation and specifies the relationship between beam rotation and moment as a function of x. It is related to the pure bending formula, which relates d(theta)/dx to moment and material properties. The pure bending formula can be represented as 1/rho = M/(E*I) for small theta.
  • #1
Amy54
12
0

Homework Statement


what is the bending moment formula? is it related to the pure bending formula? what's that?


Homework Equations





The Attempt at a Solution


is the formula 1/p=M/EI?
 
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  • #2
There's a particular physical setup associated with the bending moment of a small section dx of a beam under gravity. The formula would depend on how you setup and balance the forces and torque on that section. Perhaps if you describe it, the homework helpers here could help you figure it out.
 
  • #3
i am finding the bending moment of a rectangular beam of plywood. the dimensions change due to altering the variables throughout the experiment.
 
  • #4
Yes, but how do they change? You have to be more explicit here, otherwise I don't think anyone can help. Try posting the question from the textbook or notes.
 
  • #5
its not a question it is a part of a physics assignment of beam deflection.. i am trying to show for the formula (force x length^3)/(4 x young’s modulus x breadth x thickness^3) was derived. i know it was done through integration and the combining of the bending moment formula and the Torque formula (T=fr)...
 
  • #6
Amy54 said:
its not a question it is a part of a physics assignment of beam deflection.. i am trying to show for the formula (force x length^3)/(4 x young’s modulus x breadth x thickness^3) was derived. i know it was done through integration and the combining of the bending moment formula and the Torque formula (T=fr)...

Suppose we have the situation in the picture.

1.PNG


We get:

[tex] EIv_{xx} = -FL+Fx [/tex]

or after two integrations:

[tex] EIv(x) =F \frac{(x-L)^3}{6} +C_1x +C_2 [/tex]

From this point on I leave it to you...
 
Last edited:
  • #7
Amy54 said:

Homework Statement


what is the bending moment formula? is it related to the pure bending formula? what's that?


Homework Equations





The Attempt at a Solution


is the formula 1/p=M/EI?

Start with the Euler-Bernoulli Beam equation, and specifiy your boundary and loading conditions.

http://en.wikipedia.org/wiki/Euler-Bernoulli_beam_equation

CS
 
  • #9
Amy54 wrote: "What is the bending moment formula?"

d(theta)/dx = M(x)/(E*I), where theta = beam rotation, and M(x) = moment as a function of x.

Amy54 wrote: "Is it related to the pure bending formula? What's that? Is the formula 1/rho = M/(E*I)?"

Nice work, Amy54. Yes, that is the pure bending formula. For small theta, d(theta)/dx = 1/rho.
 

1. What is the bending moment formula and what does it represent?

The bending moment formula is a mathematical equation used to calculate the amount of bending stress experienced by a structural element, such as a beam or column. It represents the force or torque applied to the element that causes it to bend.

2. How is the bending moment formula derived?

The bending moment formula is derived from the fundamental principles of mechanics, specifically the equations of equilibrium. It takes into account the external forces acting on the structural element and the internal stresses caused by those forces.

3. What are the units of measurement for the bending moment formula?

The units of measurement for the bending moment formula will depend on the specific system of units being used. In the SI system, the units are newton-meters (N·m). In the US customary system, the units are pound-feet (lb·ft).

4. How is the bending moment formula used in structural engineering?

The bending moment formula is an essential tool in structural engineering for designing and analyzing structural elements. It allows engineers to determine the maximum stress that a structural element can withstand and to ensure that it is strong enough to support the applied loads.

5. Are there any limitations or assumptions associated with the bending moment formula?

Like any mathematical formula, the bending moment formula is based on certain assumptions and limitations. It assumes that the structural element is homogeneous, isotropic, and free of any defects. It also assumes that the material follows Hooke's Law and that the element is subjected to static loading conditions.

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