How to treat moment release in FBD

[jmarcian]

Homework Statement

from book
"The compound beam ABC shown in the figure has a guided support at A and a fixed support at C. The beam consists of two members joined by a pin connection (i.e moment release) at B. find deflection 'del' under the load P"

http://photos-a.ak.fbcdn.net/photos-ak-snc1/v688/183/78/25803658/n25803658_38292392_5314.jpg

Homework Equations

i guess just knowing your FBD!

The Attempt at a Solution

http://photos-b.ak.fbcdn.net/photos-ak-snc1/v688/183/78/25803658/n25803658_38292393_5680.jpg

sorry but the images are reversed, i figure we are all smart people and can see the mirror images in our minds. so in my drawing i broke the beam at the couple, and drew two equal and opposite moments, is this correct? because the moment at the couple should be zero, right? and having two opposing moments would cause that. please let me know if this is right! thanks!

 

[anathema]

Thank you for your post. Yes, you are correct in breaking the beam at the pin connection and adding two equal and opposite moments at B. This is because, as you mentioned, the moment at the pin connection should be zero since it is a moment release.

To find the deflection, you can use the moment-area method or the conjugate-beam method. Both methods involve finding the moment and deflection equations for the individual members and then combining them to find the overall deflection.

I hope this helps. Let me know if you have any further questions.

 

[thomate1]

I would like to clarify that moment release in FBD (Free Body Diagram) refers to the condition when a beam or structure has a pin connection, allowing it to rotate freely at that point. In this case, the pin connection at B allows the two members of the compound beam to rotate separately, creating a moment release condition.

To properly treat moment release in FBD, we need to consider the reaction forces and moments at each support point. At support A, there will be a vertical reaction force and a horizontal reaction force to balance the external load P. At support C, there will be a vertical reaction force and a moment reaction to resist the rotation caused by the external load.

In order to find the deflection 'del' under the load P, we need to solve the equations of equilibrium for the entire beam, taking into account the moment release at B. This can be done by considering the two separate members of the compound beam and their individual moments and reactions at the pin connection.

Finally, it is important to note that the moment at the pin connection should be zero, as you correctly stated. This is because the pin allows for free rotation, and therefore, the moment at that point will be zero. It is also important to consider the direction of the moments, as they will be equal and opposite due to the moment release condition.

Overall, treating moment release in FBD requires careful consideration of the reactions and moments at each support point, as well as the individual moments and reactions at the pin connection. By properly solving the equations of equilibrium, we can determine the deflection 'del' under the given load P.