Breakthroughs in Structural Engineering ======================================= .. include:: /_generated/nav/structural_engineering.rst These landmarks trace a conceptual development from a physical law to a useful engineering model. The order is a learning path, not a dated chronology or a claim that any idea had a single inventor. SI units apply unless documented otherwise. Hooke: material response becomes measurable ------------------------------------------- The proportional relation between stress and strain connects a material test to a structural displacement. It supplies the constitutive law that equilibrium alone cannot provide. .. math:: \sigma=E\varepsilon,\qquad \delta=FL/(EA) Use :py:obj:`engineeringkit.structural_engineering.axial_deformation` to explore the model. Uniform sections, small strains and linear elasticity are assumed. Yielding requires a different constitutive model. Euler: stability differs from strength -------------------------------------- A slender column can lose stability before its material reaches a strength limit. Effective length captures the ideal support conditions and reveals the strong length dependence. .. math:: P_{cr}=\pi^2 EI/(KL)^2 Use :py:obj:`engineeringkit.structural_engineering.euler_buckling_load` to explore the model. The formula describes ideal elastic buckling; imperfections and inelastic behavior require additional analysis. Energy methods: loads and displacements connect ----------------------------------------------- Castigliano and reciprocal-work ideas organize displacement calculations around stored energy. They also motivate stiffness methods, where compatibility and equilibrium are assembled across members. .. math:: U=F^2 L/(2EA),\qquad \delta=\partial U/\partial F Use :py:obj:`engineeringkit.structural_engineering.strain_energy_axial` to explore the model. Linear elastic reciprocal behavior is assumed. The derivative must actually be evaluated before using castigliano_deflection. Explore and verify ------------------ :doc:`/guides/structural_engineering` records units, conventions and independent checks. Compare the gallery output against the equations before extending a model. .. minigallery:: ../../examples/structural_engineering/plot_structural_engineering_models.py ../../examples/structural_engineering/plot_structural_engineering_benchmark.py Further reading --------------- `University or agency teaching reference `_ provides background beyond the implemented subset. The equations and examples here are concise original explanations, not reproductions of that reference.