Statically indeterminate systems

[reterty]

I am interested in the following question: whether we can use the principle of virtual work to solve approximately (in the limit of small deformations) the statically indeterminate systems or this principle is ultimately equivalent to the the system of the independent equilibrium equations?

 

[PhanthomJay]

Yes this method is often used in the analysis of indeterminate beams and trusses. Often called the ‘unit load’ method, and considering a beam say supported on multiple pinned supports, the extra supports are removed and the beam analyzed as a determinate system with the equilibrium equations. Then the supports are one by one replaced with a unit load multiplied by the unknown reaction load, and solved again as a determinate beam . Summing the deflections of each result equal to zero at the supports, the beam can then be solved for the unknown reactions and moments, etc.