Structural Stability & buckling stress

In summary, the conversation discusses finding the relationship between P and Beta for a structure made of axially compressible rods connected to a rigid foundation. The rods cannot buckle and in the unloaded configuration, the angle between the rods and the horizontal is (alpha). The angle becomes (1-Beta)*alpha when P does not equal 0. The conversation also mentions using the Total Potential Energy approach and the Equilibrium method, but there is confusion about how to start. The conversation also clarifies that P does not equal 0 means when P is not equal to 0, and discusses the strain energy and potential energy of the system. It is suggested to pursue the idea of work and energy to solve the problem.
  • #1
CivEngMo93
3
0
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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  • #2
What ever in the world does p =/= 0 mean?
 
  • #3
Sorry, its meant to mean when P does not equal 0.
 
  • #4
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.
 
  • #5
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?
 
  • #6
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
 

1. What is structural stability?

Structural stability refers to the ability of a structure to resist deformation or collapse under various external loads. It is an important factor in the design and construction of buildings, bridges, and other structures.

2. What is buckling stress?

Buckling stress is the critical stress at which a structure or component will buckle, or lose its ability to carry load. It occurs when a structure is subjected to compressive forces and begins to fail due to instability.

3. How is buckling stress calculated?

Buckling stress can be calculated using various methods, such as the Euler formula or the Johnson formula. These equations take into account factors such as the material properties, geometry, and boundary conditions of the structure.

4. What factors affect structural stability?

Several factors can affect the stability of a structure, including the design and materials used, the loads and forces acting on the structure, and the presence of any imperfections or defects in the structure. Changes in temperature, humidity, and other environmental conditions can also impact structural stability.

5. How can we ensure structural stability in construction?

To ensure structural stability in construction, engineers and architects must carefully consider the design, materials, and construction methods used. Thorough testing and analysis must also be conducted to ensure that the structure can withstand the expected loads and forces. Regular maintenance and inspections are also crucial in detecting and addressing any potential issues that may compromise structural stability.

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