Why is θA L Included in the Moment Equation about B'?

[fonseh]

Homework Statement

For the moment about B ' , why there is extra θA L behind ?
2. Homework Equations

The Attempt at a Solution

is that wrong ? I think there should be no θA L behind in the equation of moment about B '

 

[CivilSigma]

The author takes moment using the conjugate beam, and at point A there is a shear force acting downward which is equal to the rotation of A in the real beam.

 

[fonseh]

The author takes moment using the conjugate beam, and at point A there is a shear force acting downward which is equal to the rotation of A in the real beam.

why theta_A multiply by L , we will get moment ? what is theta_A actually ? I'm confused

 

[CivilSigma]

why theta_A multiply by L , we will get moment ? what is theta_A actually ? I'm confused

Theta A is the angular rotation in the real beam. Conjugate beam theory tells us that the shear force in the conjugate beam is the rotation in the real beam.

In the conjugate beam, moment = shear force A * distance to B = Theta A * L

 

[fonseh]

Conjugate beam theory tells us that the shear force in the conjugate beam is the rotation in the real beam.

why? Can you explain further ? Why are they equal ?

 

[CivilSigma]

why? Can you explain further ? Why are they equal ?

review conjugate beam theory, you will find the answer there.

 

[fonseh]

review conjugate beam theory, you will find the answer there.

Can you explain further ? It's not explained in my module

 

[fonseh]

Theta A is the angular rotation in the real beam. Conjugate beam theory tells us that the shear force in the conjugate beam is the rotation in the real beam.

In the conjugate beam, moment = shear force A * distance to B = Theta A * L

http://www.ce.memphis.edu/3121/notes/notes_08b.pdf
In this link , i only notice that integral of M/EI and dx = theta(angle of rotation) ... or d(theta) /dx = M/EI

I rewrite it as M = EI(dtheta)/dx

How could that be true ? I found that (dtheta)/dx = M/EI , M/EI is the moment diagram , am i right ?

 

[fonseh]

http://www.utsv.net/conjugate_beam.pdf
Do you mean this one ?
I still can't understand why w (force per unit length ) = M / EI .?

 

[CivilSigma]

http://www.utsv.net/conjugate_beam.pdf
Do you mean this one ?
I still can't understand why w (force per unit length ) = M / EI .?

That's the 'trick' to this method. Since 'w' represents any distributed load... let it be w=M/EI , then from the equations we see that when we solve for shear in the conjugate beam, we get rotation in the real beam.