Dear Josko Troselj,

If you are interested to work and publish with me I can show you how to develop a theoretical method which calculates the critical buckling loads of these designed structures from their informations (stiffness and displacemens) in the stability analysis.

Mohammed lamine Moussaoui

Dear Mohammed Lamine Moussaoui,

Thank you for your reply.

If you look at four examples that I wrote, are you sure that their instability is due to buckling but not due to bifurcation and/or internal collapse mechanism?

Dear Josko Troselj,

Under compression the deformation of a mechanism can change to another mode of deformation after a first Pcr critical load value and this is the bifurcation phenomenon. A finite element analysis can compute the possible loads values which have to be avoided and / or exceeded quickly.

Dear Mohammed Lamine Moussaoui,

If I understood your explanation correctly, you emphasize load-dependent instability. Contrary to that, I emphasize fundamental instability mechanisms, which are load-independent. In other words, some of examples 1-4 which I have drawn above will collapse even under a very small applied load, such as 0.0001 kN. A structure needs to first have satisfied all the fundamental stability rules in order to be subject for load-dependent stability analysis. The most basic example of fundamentally unstable structure is a beam with 3 parallel reactions or 3 reactions intersecting at the same point. However, some of examples 1-4 which I have drawn above are fundamentally unstable as well, although it is not obvious at the first look.

Hi

Determination of critical load, via Euler methods, is always an artificial but not a real process. That is because one should start with several assumptions, which are not necessarility representative of the actual behavior of the structure. Hence problems of this type are always a matter of theory without compliance with the test results. This is clear from, the test dependent colum curves in design codes of various nations.

When a force applied to a column, there is no clear reason to show that the column buckles, locally, laterally, distortionally, or else!

Do you mean static equilibrium for isostatic or hyperstatic structures ?

Dear Mohammed Lamine Moussaoui,

I will try to explain what do I mean by using slightly different terminology. Fundamentally stable structure (it applies both to isostatic and hyperstatic ones) is one where all support reactions can be calculated or verified by using equilibrium equations (sum Fx, Fy, M = 0). Fundamentally unstable structure is one where not all support reactions can be calculated nor verified by using equilibrium equations. Two most basic examples of fundamentally unstable structure are given in my previous post. However, I am interested to collaborate with someone who knows how to apply currently known methods to determine fundamental instability of complex structures, such as ones (examples 1-4) drawn in my attachment in the first post.

Hello,

Any system which reaches an equilibrium position after deformation can be analyzed by calculating its supports reactions even if it is hyperstatic. In this last where the number of unknowns reactions is greater than the number of equations one has to analyse the substructures in order to calculate them. The other method is the stability analysis : the structure can have another configuration without (or with) deformations of the elements.

Dear Mohammed Lamine Moussaoui,

Thank you for the answer, it is very useful.

However, your answer answers to the question "What" is used as method, but my question is more about "How" to use existing methods. I don't think that calculating system's supports reactions is the fastest way to determine stability, especially in hyperstatic systems. The method which I am planning to publish requires no longer than 20 seconds thinking time without using software, no matter how the system is complex. I am interested to compare it with currently existing methods and am seeking for experts for collaboration who know HOW to apply currently existing methods to complex structural systems, including systems 1-4 from the attachment in the first post.

I added part 2 of the paper draft (attachment file in the first post), where I explained in more detail which would be expected contributions from the collaborator who wants to write the paper with me.

I also added 4 more quiz question, making it 8 in total, so that the expert I am searching for may be able to recognize if my quiz questions are hard to solve and therefore simpler method is welcome to be introduced, or my quiz questions are already easy to solve so there is no need for introducing simpler method.

Josko Troselj

EDIT2: I have realized that I did a honest mistake in the question for which I apologize. The mistake was that I wrote that I emphasize elastic stability but in fact I emphasize geometric stability. Nevertheless, testing geometric stability should be done before testing elastic stability because it is more fundamental one, so if some of structures which I have drawn in the examples are geometrically unstable, it means they will collapse no matter whether they are elastically stable or unstable.

https://nptel.ac.in/courses/Webcourse-contents/IIT%20Kharagpur/Structural%20Analysis/pdf/m1l1.pdf

Dear Hussam Ali Mohammed,

I apologize for slow reply and than you for your link.

From your link I learned that the instability which I am focusing on is officially called "Kinematically Unstable Structure". Still, I didn't find anyone who provided explanation about how to determine Kinematic Stability on Complex Structural Frames. I guess there must be an existing method how to do so, explained in some textbook.