Reaction using Castiglano's method.

[mohamadh95]

I'm a bit lost. I began by the cuts but then got lost: should I introduce the reactions like Ra when writing the equations? And about the force P I should introduce, should it be equal to Rc or Vc? If anyone could give me the proper plan on how to solve this problem I will be thankful. Thank you.

 

[mohamadh95]

Anyone??

 

[pongo38]

Good start, but it would be better to have a plan at the beginning. Yes, you do include RA if it is in the free body diagram (fbd) you have isolated in your cut, because you are making equilibrium statements for all the actions on the fbd you have. The overall plan is that, having cut the beam's moment at C, you will have to restore it with another equation so that the continuity at C is maintained. However, it is clear that this is one of your first exercises. It would be easier to understand if you were to 'cut' (that is, remove) the reaction at C, calculate the deflection there, and 'restore' the reaction with a force P with the property that its upward deflection equals the downwards deflection you have calculated with reaction C removed. The same principle can be applied to the moment cut you have introduced, but it's not so easy to explain or achieve.

 

[mohamadh95]

thank you.

 

[rezeew]

Hello,

I understand that it can be overwhelming and confusing when first learning a new method. Castiglano's method is a powerful tool for analyzing structures and determining reactions, but it can take some time to fully grasp.

To begin, it is important to first identify all the cuts and determine the unknown reactions (Ra, Rc, and Vc). Once you have identified the unknown reactions, you can start writing the equilibrium equations for each cut. In these equations, the unknown reactions should be included as variables.

When introducing the external force P, it is important to consider its direction and location in relation to the cuts. If P is acting on a point that is on a cut, then it should be included in the equilibrium equation for that specific cut. If P is acting on a point that is not on a cut, then it should be included in the equilibrium equation for the closest cut.

In terms of the force P being equal to Rc or Vc, it depends on the specific problem and how it is set up. Without more information, it is difficult to provide a definite answer. However, I suggest carefully reviewing the problem and determining where P is acting and in what direction to determine its relationship to Rc or Vc.

Overall, the key to solving problems using Castiglano's method is to carefully identify all the cuts and unknown reactions, and then systematically write and solve the equilibrium equations for each cut. If you are still feeling lost, I recommend seeking help from a professor, tutor, or colleague who is familiar with Castiglano's method. Practice and patience are also key in mastering this method.

I hope this helps and good luck with your problem-solving!