Foundational principles, analytical methods, and material behaviors central to structural stress analysis. The core concepts of stress as a distributed force and strain as a measure of deformation are established through mathematical relationships, most notably Hooke's Law, which defines the elastic behavior of materials. Analysis of complex stress states is achieved through coordinate transformations, leading to the determination of principal stresses—the maximum and minimum normal stresses at a point.The behavior of materials under load is multifaceted, defined by the loading type (static, dynamic, repeated), time-dependent effects like creep, and ultimate failure. For ductile materials, failure is typically defined by the onset of plastic yielding, with the von Mises and Tresca theories being the most accepted predictive models. For brittle materials, failure is characterized by fracture, governed by theories like the Coulomb-Mohr model. Fatigue, or failure under repeated loading, is a critical consideration governed by factors such as stress range and concentration, often analyzed using Goodman diagrams.Methodologically, structural analysis is approached through three primary avenues: analytical, numerical, and experimental. Analytical methods, including the principles of superposition and energy theorems like Castigliano's, provide exact solutions for simpler problems. For complex geometries and conditions, numerical techniques are indispensable, with the Finite Element Method (FEM) being the predominant approach due to its versatility in discretizing complex domains. Experimental methods, particularly the use of electrical resistance strain gages, provide physical validation and are essential for measuring stresses in real-world components. Effective analysis requires careful attention to practical considerations, including consistent use of unit systems (SI and USCU), understanding the effects of stress concentrators, and acknowledging the inherent approximations in all analytical formulas.