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

In summary, the conversation discusses the use of conjugate beam theory in finding the moment about point B' and the confusion over the inclusion of θA L in the equation. The author explains that θA is the angular rotation in the real beam and according to conjugate beam theory, the shear force in the conjugate beam is equal to the rotation in the real beam. This leads to the equation for moment being M = θA * L. The author also provides links to further resources for understanding this concept.
  • #1
fonseh
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2

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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  • #2
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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  • #3
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
 
  • #4
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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  • #5
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 ?
 
  • #6
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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  • #7
sakonpure6 said:
review conjugate beam theory, you will find the answer there.
Can you explain further ? It's not explained in my module
 
  • #8
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 ?
 
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  • #10
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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FAQ: Why is θA L Included in the Moment Equation about B'?

1. What is a moment about a point on a beam?

The moment about a point on a beam, also known as the bending moment, is a measure of the force created by a load acting on a beam, causing it to bend at a specific point. It is a crucial concept in structural engineering and mechanics.

2. How is the moment about a point on a beam calculated?

The moment about a point on a beam is calculated by multiplying the force acting perpendicular to the beam by the distance from the point to where the force is applied. The resulting unit is usually pound-force times inches (lb-in) or Newton-meters (Nm).

3. How is the direction of the moment about a point on a beam determined?

The direction of the moment about a point on a beam is determined by the direction of the force acting on the beam. If the force is acting upwards, the moment will be in a clockwise direction, and if the force is acting downwards, the moment will be in a counterclockwise direction.

4. What is the significance of the moment about a point on a beam?

The moment about a point on a beam is significant because it indicates the amount of stress and deformation that the beam will experience at a specific point. It is essential to consider when designing and analyzing structures to ensure they can support the expected loads.

5. How does the distribution of loads affect the moment about a point on a beam?

The distribution of loads along a beam affects the moment about a point on the beam. A concentrated load at a specific point will result in a higher moment, while a distributed load along the entire beam will result in a more evenly distributed moment. This distribution of moment affects the overall strength and stability of the beam.

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