Structural Stability & buckling stress

[CivEngMo93]

Q: A structure is made from identical, axially compressible robs connected to a rigid foundation. The rods cannot buckle. In the unloaded configuration the angle between the rods and the horizontal is (alpha); then angle becomes (1-Beta)*alpha when p =/= 0. Find the relationship P(Beta). Introduce a suitable non-dimensional load P and make a plot of P vs (beta) the region of -0.5 < Beta < 2.5.

My attempt:
I thought og using the Total potential energy approach, TPE = SE - Work done... but i have no idea how to get started on it. There is another method called the equilibrium method that my tutor talked about but i can't make any sense of how to start it.. Any help will be much appreciated.

 

[Dr.D]

What ever in the world does p =/= 0 mean?

 

[CivEngMo93]

Sorry, its meant to mean when P does not equal 0.

 

[CivEngMo93]

I have got strain energy = 0 so far. Since both foundation pins are fixed and do not mov. Therefore potential energy will be a negative value but am unsure about this... In all the examples and tutorials we had. Potential energy is a positive value.

 

[Dr.D]

If strain energy is zero, the length of the bars has not changed, so the geometry has not changed. I think you are on the wrong track with that.

Your original statement about work and energy sounded promising, so why not pursue that?

What is the strain energy of an axially compressed bar?

 

[Chestermiller]

If the pin moves downward a distance δ from its initial location, what is the new length of each rod? You need this to get the strain in the rod.

Chet