Get the stress tensor using virtual displacement principle

[SpaceBani]

Homework Statement
Using method of virtual displacement get the stress tensor for this problem.

http://img32.imageshack.us/img32/7272/problemba.png
The attempt at a solution

The given system is 4-times tatically indeterminate. Since it is symetrical we can split it in half vertically. We need to fix it in one point (upper end). The "new" system is 3-times statically indeterminate.

http://img853.imageshack.us/img853/2116/problem2j.png

As far as I know we need to split this into several systems; 1 main + 3 virtual. But I don't really know how and which variables do I need to have. I do not seek the answer to the whole problem (calculating when we get these variables), just some help on how to split this further.

Any help appritiated, thank you!

And I am sorry if I used some expressions that are not correct, english is not my main language. :)

 

[mark726]

To get the stress tensor for this problem using the method of virtual displacement, we first need to understand the concept of virtual displacement. A virtual displacement is a hypothetical displacement that allows us to analyze the behavior of a system under small, infinitesimal changes without actually applying any forces or displacements to the system.

In this problem, we are dealing with a symmetrical system that is statically indeterminate. We can split it in half vertically and fix it at one end, as you have correctly identified. This results in a "new" system that is 3-times statically indeterminate.

To further solve this problem using the method of virtual displacement, we need to split the "new" system into several systems, as you have mentioned. These systems will include the main system and three virtual systems.

The main system will consist of the original system, split in half vertically and fixed at one end. The three virtual systems will be created by applying a virtual displacement to each of the three remaining free ends of the "new" system.

To calculate the stress tensor for this problem, we will need to use the equations of equilibrium, compatibility, and constitutive laws. We can use the equations of equilibrium to solve for the reactions at the fixed end of the main system, and then use the equations of compatibility to determine the virtual displacements at the free ends of the three virtual systems. Finally, we can use the constitutive laws to relate the stress and strain in each of the systems.

I hope this helps you to better understand how to approach this problem using the method of virtual displacement. If you need further assistance, please do not hesitate to ask for clarification.