[ME statics] Two force members

[Feodalherren]

Homework Statement

Homework Equations

The Attempt at a Solution

Was trying to solve for the horizontal reaction at B. Why is BC a two-force member but not AE?

 

[SteamKing]

Who says AE is not a two-force member?

 

[Feodalherren]

Well, nobody but the solution says: CB is a two force member so the reaction at B only in the horizontal direction. Then the sum of the moments about A bla bla bla.
How can they know that there is no reaction in the Y-direction and why isn't the same true for A?

 

[Dr.D]

For a two force member, the forces are necessarily colinear and along the axis of the link. The link ADE supports shear and bending as well as the axial load, which is why it is not a two force member.

 

[SteamKing]

I think that's why you have to work out the reactions. Remember, the two bars appear to be pin-connected at D, so what kind of forces and moments can be applied here?

 

[Dr.D]

SteamKing: I agree that the members are pinned at D (that is the way I read the figure), and, by definition, a pin only transmits forces, no moments. Without working through the details, if we think about moments wrt A, it is evident that the load at E puts bending in the member ADE.

On the other hand, since there is no applied load at C, and there are only pins at B and D, there cannot be any bending in the member BDC. No bending implies no shear, and BDC must be a two force member.

 

[Feodalherren]

I don't get that at all. It doesn't seem to make any intuitive sense to me. The force has a negative Y component so there should be a reaction force in the Y direction at D. That should create some moment on beam BC and also some reaction in it... I don't see the two force member.

 

[Dr.D]

@ Feodalherren: You have noted the negative component of the force applied at E and the fact that it must be reacted somewhere. But there is no reason it has to be reacted at D; it can be equally well reacted at A. If there were a vertical force component at D, then there would be a moment about B on the link CDB. There is nothing to react such a moment, so that moment cannot exist.