In statically indeterminate mechanical systems, the number of unknown internal forces exceeds the number of independent equilibrium equations, so a solution requires supplementing equilibrium with a compatibility equation describing the geometric constraints on deformation, together with a constitutive relationship (such as Hooke's law) linking stress to strain. Uniform temperature change induces thermal strain proportional to the coefficient of thermal expansion and the temperature change; if the deformation is unrestrained no stress results, but partial or total restriction of thermally induced deformation generates internal forces and thermal stresses, which for restrained members constitute an indeterminate problem solvable only through the combined use of equilibrium, compatibility, and constitutive equations. This belongs to the strength/mechanics of materials domain within structural and solid mechanics, extending the theory of axial strain analysis to indeterminate systems and temperature-driven loading.
In statically indeterminate mechanical systems, the number of unknown internal forces exceeds the number of independent equilibrium equations, so a solution requires supplementing equilibrium with a …