Stress and Strain Fundamentals

Stress and strain are fundamental concepts in structural engineering that describe the internal forces and deformations within materials subjected to external loads. Stress ($\sigma$) is defined as the force applied per unit cross-sectional area ($\displaystyle \sigma = \frac{F}{A}$), measured in Pascals (Pa). Strain ($\varepsilon$) is the dimensionless ratio of the change in length to the original length of the material (). Normal stress acts perpendicular to a surface, while shear stress acts parallel. Within the elastic limit of a material, Hooke's Law applies, establishing a linear relationship between stress and strain as , where is Young's modulus, representing material stiffness. Elastic deformation is reversible, whereas beyond the yield point, plastic deformation causes permanent changes. Poisson's ratio () relates lateral strain to axial strain and typically ranges from 0 to 0.5 for metals. Understanding these properties is critical to predicting material behavior, ensuring structural safety, optimizing material use, and avoiding failure modes such as yielding or fracture.