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STATIC DETERMINACY
A statically determinate structure is simply any structure that can be analyzed by using equilibrium equations and nothing more. On the other hand, when the equilibrium equations are not enough to analyze a structure, the structure is called statically indeterminate and must include constitutive equations to solve it. Constitutive equations introduce principles from strength of materials that allow us to solve for any internal or external force once one has used all of our equilibrium equations.
Equilibrium Equations
ΣFx = 0
ΣFy = 0
ΣMp = 0
Constitutive Equations
σ = ϵE
σ = (F)/(A)
δ = (PL)/(EA)
It is important to be able to distinguish between determinate and indeterminate structures. Determinacy is not entirely dependent on static equilibrium. As seen in the examples, having an object in static equilibrium does not guarantee that the object will be statically determinate. Determinacy consists of internal and external issues. If a structure is externally determinate, it means that one can solve for the reactions based on static equilibrium. If it is internally determinate, it means that one can solve for the forces in the individual components based on static equilibrium.