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Bending moment formula?

by Amy54
Tags: bending, formula, moment
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Amy54
#1
Jun18-08, 02:17 AM
P: 12
1. The problem statement, all variables and given/known data
what is the bending moment formula? is it related to the pure bending formula? what's that?


2. Relevant equations



3. The attempt at a solution
is the formula 1/p=M/EI?
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Defennder
#2
Jun18-08, 02:27 AM
HW Helper
P: 2,616
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
#3
Jun18-08, 02:37 AM
P: 12
i am finding the bending moment of a rectangular beam of plywood. the dimensions change due to altering the variables throughout the experiment.

Defennder
#4
Jun18-08, 04:03 AM
HW Helper
P: 2,616
Bending moment formula?

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
#5
Jun18-08, 04:13 AM
P: 12
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
#6
Jun18-08, 06:30 AM
P: 686
Quote Quote by Amy54 View Post
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.

Click image for larger version

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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....
stewartcs
#7
Jun18-08, 02:36 PM
Sci Advisor
stewartcs's Avatar
P: 2,284
Quote Quote by Amy54 View Post
1. The problem statement, all variables and given/known data
what is the bending moment formula? is it related to the pure bending formula? what's that?


2. Relevant equations



3. 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-B..._beam_equation

CS
dirk_mec1
#8
Jun18-08, 02:51 PM
P: 686
Quote Quote by stewartcs View Post
Start with the Euler-Bernoulli Beam equation, and specifiy your boundary and loading conditions.

http://en.wikipedia.org/wiki/Euler-B..._beam_equation

CS
Yes ...that's what I pointed out, didn't I?
nvn
#9
Jul17-08, 10:49 PM
Sci Advisor
HW Helper
P: 2,124
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.


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