Dimensional Analysis & Scaling Laws

This lecture covers the fundamental concepts of dimensional analysis and scaling laws, including base dimensions and units, the Buckingham-Pi Theorem, physical similarity, and scalings. The instructor explains the recipe to solve problems using dimensional analysis and discusses the importance of physical similarity in structural mechanics. The lecture delves into the equations related to strain-displacement, equilibrium, stress tensor, strain tensor, and constitutive relation (elasticity). The slides provide detailed information on buckling, instability of elastic structures, compression causing bending, and the expansion of beam theory. The lecture concludes with examples of how dimensional analysis can be applied to solve otherwise analytically intractable problems.