Bending Moment Formula: Understanding Its Relationship to Pure Bending

[Amy54]

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?

 

[Defennder]

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.

 

[Amy54]

i am finding the bending moment of a rectangular beam of plywood. the dimensions change due to altering the variables throughout the experiment.

 

[Defennder]

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.

 

[Amy54]

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)...

 

[dirk_mec1]

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.

We get:

EIv_{xx} = -FL+Fx

or after two integrations:

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

From this point on I leave it to you...

 

[stewartcs]

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

 

[dirk_mec1]

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

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

CS

Yes ...that's what I pointed out, didn't I?

 

[nvn]

Amy54 wrote:[/color] "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:[/color] "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.