Theoretical Question - Planar Truss Problem 5

[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.

 

[BAretired]

Congratulations comhedoisl, you were correct.

Duh!! Thinking about it last night, I realized that Node "O" had to deflect upwards since member 3 is in compression and is pinned at the top. Now we have the proof thanks to Retrograde and goutam-freela. Thanks guys!

 

[rb1957]

yeah, but ... you've modelled the spokes as beams, and the lateral one is picking up a lot of load. If axial rods then the result would be "different" (for the load given it would all be reacted by the aligned spoke; for different loads each spoke would react the component load).