In strength of materials, a structural system's unknown reactive or internal forces can be found from the equations of static equilibrium alone only when the number of unknowns does not exceed the number of independent equilibrium equations; when unknowns exceed available equilibrium equations, the system is statically indeterminate and requires supplementary compatibility equations, derived from the geometric constraints imposed on the system's deformation, combined with Hooke's law to relate deformations to forces. This extends the generalized (three-dimensional) form of Hooke's law — relating normal strain in each direction to the normal stresses in all three directions via the modulus of elasticity and Poisson's ratio — to solve for internal forces in axially loaded indeterminate members. This belongs to strength of materials / mechanics of solids, connecting stress-strain analysis (Hooke's law, Poisson's ratio, shear modulus) to the broader analysis of structural systems.
In strength of materials, a structural system's unknown reactive or internal forces can be found from the equations of static equilibrium alone only when the number of unknowns does not exceed the nu…