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.