Civil Engineering - Matrix Flexibility Method

[Civil Engg]

I have strayed from the template because I am querying a methodology, not an explicit case.

This is Civil Engineering - Matrix Flexibility Method.

Given "m" members and "n" nodes I can use this matrix to solve the basic member forces:

(sorry about the size I don't know how to scale)

As far as I understand this can be easily done when the system is one degree indeterminate. My problem lies in calculating the above when the degree of indeterminacy rises above 1.

Say, for example, I have a structure that is two degree indeterminate. Can I do the following?

i.e. Can I continue expanding that displacement matrix vertically or must I include both redundant support reactions in one equilibrium equation (the first picture)?

I understand that this is a very specific portion of matrix methods and it may not be too clear. If anyone has any ideas or thoughts it would be greatly appreciated.

Thanks in advance.

 

[KataKoniK]

Hello,

Thank you for bringing up this interesting topic. As a scientist in the field of civil engineering, I can certainly understand your query regarding the matrix flexibility method.

Firstly, let me clarify that the matrix flexibility method is used to analyze structures that are statically indeterminate. In simpler terms, this means that the structure cannot be solved using traditional equilibrium equations alone, and additional equations are required to solve for the unknown forces.

Now, coming to your question, when the degree of indeterminacy rises above 1, it is not possible to continue expanding the displacement matrix vertically. This is because the displacement matrix is based on the degree of indeterminacy, and it cannot be expanded indefinitely.

Instead, when dealing with a structure that is two degree indeterminate, it is necessary to include both redundant support reactions in one equilibrium equation, as shown in the first picture. This is because the equilibrium equations are based on the principle of statics, and they must be satisfied for a stable and safe structure.

I hope this clarifies your doubts regarding the matrix flexibility method. If you have any further questions or concerns, please do not hesitate to reach out. As scientists, it is our duty to continuously question and improve existing methodologies, so your query is much appreciated.