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

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Discussion Overview

The discussion revolves around the inclusion of the term θA L in the moment equation about point B' in the context of conjugate beam theory. Participants explore the relationship between angular rotation, shear forces, and moments in beams, focusing on theoretical understanding and application in structural analysis.

Discussion Character

  • Homework-related
  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant questions the necessity of including θA L in the moment equation about B', suggesting it may be incorrect.
  • Another participant explains that in conjugate beam theory, the shear force at point A corresponds to the rotation of A in the real beam.
  • There is confusion regarding the meaning of θA and its role in calculating moments, with participants seeking clarification on why θA is multiplied by L to obtain a moment.
  • Some participants assert that θA represents the angular rotation in the real beam, and they reference the relationship between shear force and rotation in the conjugate beam.
  • Further inquiries are made about the equality of shear force in the conjugate beam and rotation in the real beam, with requests for deeper explanations.
  • One participant attempts to connect the integral of moment to angular rotation, expressing uncertainty about the derivation of the moment equation.
  • Discussion includes links to external resources, with participants expressing difficulty in understanding the relationship between distributed load, moment, and angular rotation.

Areas of Agreement / Disagreement

Participants express varying levels of understanding regarding the application of conjugate beam theory, with some agreeing on the definitions of θA and its implications, while others remain confused and seek further clarification. The discussion does not reach a consensus on the necessity of θA L in the moment equation.

Contextual Notes

Participants reference conjugate beam theory but do not provide a unified explanation of its principles. There are unresolved questions about the mathematical relationships and assumptions underlying the equations discussed.

fonseh
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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 '
 

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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.
 
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sakonpure6 said:
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
 
fonseh said:
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
 
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sakonpure6 said:
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 ?
 
fonseh said:
why? Can you explain further ? Why are they equal ?

review conjugate beam theory, you will find the answer there.
 
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sakonpure6 said:
review conjugate beam theory, you will find the answer there.
Can you explain further ? It's not explained in my module
 
sakonpure6 said:
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 ?
 
Last edited:
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fonseh said:
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.
 
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