Structural Stability & buckling stress

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Discussion Overview

The discussion revolves around the structural stability and buckling stress of a system made from axially compressible rods connected to a rigid foundation. Participants explore the relationship between the load and the angle of the rods under compression, focusing on the mathematical modeling of this relationship and the application of potential energy methods.

Discussion Character

  • Exploratory
  • Technical explanation
  • Mathematical reasoning

Main Points Raised

  • One participant seeks assistance in finding the relationship P(Beta) using the Total Potential Energy approach, expressing uncertainty about how to begin.
  • Another participant questions the notation "p =/= 0," which is clarified to mean "when P does not equal 0."
  • A participant mentions having calculated strain energy as zero, suggesting that since the foundation pins are fixed, the potential energy must be negative, but expresses confusion over this point.
  • Another participant challenges the claim of zero strain energy, arguing that if strain energy is zero, the geometry of the system has not changed, indicating a potential misunderstanding of the system's behavior.
  • A later reply prompts the original poster to consider the strain energy of an axially compressed bar, suggesting a more promising direction for their inquiry.
  • One participant asks about the implications of a downward movement of the pin and its effect on the length of the rods, indicating the need to understand strain in the rods for further analysis.

Areas of Agreement / Disagreement

Participants express differing views on the calculation of strain energy and its implications for the system's geometry. There is no consensus on the correct approach to modeling the problem or the interpretation of potential energy in this context.

Contextual Notes

Participants have not resolved the assumptions regarding the behavior of the rods under compression and the definitions of potential and strain energy in this specific setup.

CivEngMo93
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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.
 

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What ever in the world does p =/= 0 mean?
 
Sorry, its meant to mean when P does not equal 0.
 
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.
 
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?
 
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
 

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