In a statically indeterminate structure, the internal forces and deformations cannot be determined solely by applying the equations of static equilibrium. This means that the structure will undergo a redistribution of internal forces and deformations when subjected to external loads.
When a statically indeterminate structure is loaded beyond its elastic limit, plastic hinges start to form in the structure. A plastic hinge is a location in the structure where plastic deformation occurs due to excessive loading. As the load increases, the plastic hinge deforms plastically, and the internal forces in the structure are redistributed to other parts of the structure.
For a statically indeterminate structure to fail, it is necessary for at least two plastic hinges to form. This is because if only one plastic hinge forms, the structure will still be able to redistribute the internal forces and deformations to other parts of the structure. However, if two plastic hinges form, the structure loses its ability to redistribute internal forces and deformations, and it will collapse.
Therefore, the number of plastic hinges required for the failure of a statically indeterminate structure is never less than two.
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