Theoretical Question - Planar Truss Problem 2

[comhedoisl]

Hi all.

This is an interesting theoretical question from a book of Feodosiev - Advanced Stress and Stability Analysis. It reads like this:

"A plane truss consisting of n>2 equal and equally spaced rods, connected in a common node, O.
The force P acts in the plane of the truss.
Show that the displacement of the node O is always directed along the force P and that the value of this displacement does not depend on the angle /alpha."

The book does provide an answer to this problem, but not with enough detail -- at least from my point of view. I'd like to have a more detailed discussion on this problem with other folks. Could you help me providing your insights?

**the blue circle is not part of the structure



Thanks.

 

[comhedoisl]

OK, I think that makes sense. It's clearer now for me.

Thank you, Tomfh.

 

[Nick6781]

Using deformation compatibility?

 

[comhedoisl]

Using deformation compatibility?

Hi Nick. That may help answer the displacement aligned with force bit. I’m not sure how to do it with more than 3 rods, even with 3 may be difficult, I havent tried yet.

But the “displacement value independent of angle” bit would still be pending if using only displacement compatibility.

Thanks.

 

[BAretired]

We have a structure resisting a single applied load; that load can be represented by a vector in the form P = ai+bj+ck. That expression provides both magnitude and direction of the load P.

It seems to me that the resultant of all of the reactions must be equal and opposite to the applied force. Putting that another way, it seems to me that R+P = 0, where R is the vector sum of all reactions. If that is true, then the statement in the text book mentioned in the first post is correct. It would be true for the regular wheel configuration shown in the OP and it should be true for any alternative stable configuration.

 

[HTURKAK]

...a single applied load; that load can be represented by a vector in the form P = ai+bj+ck.

There is a small problem.. The OP 's question is for 2 D ( plane truss consisting of n>2 equal and equally spaced rods, making a circle ,connected in a common node, O. ).
For the 3D load, the truss shall be 3D and the rods shall be equally spaced in a sphere.



A plane truss

 

[BAretired]

That simply means that the k term is zero for both P and R. What I said before is still true.
They are 2D vectors of the form P = ai+bj and the vector sum P+R = 0.

 

[goutam_freelance]

Today, I checked with my developed FEA program for trusses with 4 symmetrical elements. The given postulates hold good in the sense that:

1. The magnitude of displacement does not vary with the direction of the applied force.
2. The displacements are along the direction of the applied force.