Structural Engineering

The condition in which all forces and moments acting on a structure or structural element sum to zero, ensuring the body remains at rest or in uniform motion. Static equilibrium is the foundational requirement for any structural analysis.

An internal moment in a structural member caused by external loads that tend to bend the member. The bending moment at any cross-section equals the algebraic sum of moments of all forces on one side of that section.

An internal force acting parallel to a cross-section of a structural member, resulting from loads that tend to slide one part of the member relative to an adjacent part.

Stress ($\sigma$) is the internal force per unit area within a material ($\sigma = \frac{F}{A}$), while strain ($\epsilon$) is the resulting deformation per unit length ($\epsilon = \frac{\Delta L}{L}$). Their relationship, governed by the material's constitutive law, is fundamental to predicting structural behavior.

The ratio of a structure's ultimate strength to the maximum expected load or working stress. It provides a margin against uncertainties in loading, material properties, and analytical assumptions.

A geometric property of a cross-section ($I$) that quantifies its resistance to bending. A larger $I$ means greater stiffness and lower bending stress ($\sigma = \frac{My}{I}$) for the same applied moment.

The route through which applied loads travel from their point of application through structural members and connections down to the foundation and into the ground.

A numerical method that subdivides a complex structure into a mesh of small, simple elements, solves the governing equations for each element, and assembles the results to approximate the behavior of the whole structure.

A sudden lateral instability failure mode in which a slender structural member under compression deflects sideways rather than shortening uniformly. The critical buckling load is given by Euler's formula: $P_{cr} = \frac{\pi^2 EI}{(KL)^2}$.

The displacement of a structural member from its original position under load. Controlling deflection is essential for serviceability, ensuring that structures do not sag, vibrate excessively, or damage attached finishes.