Determinancy and Geometric Stability

In a statically determinate system, all reactions and internal member forces can be calculated solely from equations of equilibrium. However, if equations of equilibrium alone do not provide enough information to calculate these forces, the system is statically indeterminate.
In this case, adequate information for analyzing the system will only be gained by also considering the resulting structural deformations. Static determinacy is never a function of loading. In a statically determinate system, the distribution of internal forces is not a function of member cross section or material properties.
In general, the degree of static determinacy n for a truss may be determined by

If n is greater than zero, the system is geometrically stable and statically indeterminate;
if n is equal to zero, it is statically determinate and may or may not be stable; if n is less than zero, it is always geometrically unstable. Geometric instability of a statically determinate truss (n  0) may be determined by observing that multiple solutions to the internal forces exist when applying equations of equilibrium.
Figure 3.65 provides several examples of statically determinate and indeterminate systems.
In some cases, such as the planar frame shown in Fig. 3.65e, the frame is statically indeterminate for computation of internal forces, but the reactions can be determined from equilibrium equations.

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