Structural Dynamics

Base shear is the total horizontal force that a structure's foundation must resist during an earthquake, representing the sum of all inertial forces developed throughout the building. It is the primary design force in equivalent lateral force procedures and the starting point for seismic design of most buildings.

The damping ratio (ζ) is a dimensionless measure of how much a structure dissipates vibrational energy, expressed as a fraction of critical damping. It determines how quickly free vibrations decay and how strongly the structure amplifies response at resonance, with typical values ranging from 2% for steel structures to 10% for structures with significant energy dissipation devices.

Ductility is the ability of a structure or structural element to undergo large inelastic deformations without significant loss of strength. It is the fundamental property that allows structures to dissipate seismic energy and is the basis for the response modification factors used in modern seismic design codes.

Modal analysis is the process of determining a structure's natural frequencies, mode shapes, and damping ratios — collectively called its modal properties. It is the foundation of dynamic analysis in earthquake engineering and is performed analytically, numerically, or experimentally.

A mode shape is the characteristic deformation pattern of a structure when vibrating at one of its natural frequencies. Each mode shape describes the relative displacement of all points in the structure and is fundamental to modal analysis and response spectrum analysis.

The natural frequency is the rate at which a structure oscillates in free vibration, measured in cycles per second (Hz). It is the inverse of the natural period and determines how the structure interacts with the frequency content of earthquake ground motion.

The natural period is the time required for a structure or structural element to complete one full cycle of free vibration. It is the single most important dynamic property of a structure, governing how it responds to earthquake ground motion and determining whether resonance effects will amplify the response.

Resonance is the phenomenon in which a structure experiences amplified response when the frequency of the applied dynamic load matches one of its natural frequencies. In earthquake engineering, resonance is a primary cause of disproportionate damage and a critical consideration in structural design.

A single-degree-of-freedom (SDOF) system is an idealized dynamic system with one independent coordinate of motion, characterized by a single mass, spring, and damper. It is the fundamental building block of structural dynamics and the basis for the response spectrum concept.

Story drift is the lateral displacement of one floor of a building relative to the floor below it, caused by seismic or wind forces. It is a critical design parameter because excessive drift damages non-structural elements, causes instability, and is often the governing limit state in seismic design codes.