time history

A time history analysis is a computational simulation that tracks how a structure responds moment by moment as loads change over time. Rather than treating forces as static or steady-state, time history captures the dynamic behavior: vibrations, accelerations, stresses, and displacements that unfold from start to finish. The analyst feeds actual measured or predicted load patterns into a numerical model of the structure, then solves the equations of motion at small time increments, typically milliseconds or smaller, to see what happens.

The method is essential for structures facing transient or variable loading: machinery startup and shutdown, earthquakes, wind gusts, traffic impacts, explosions, drop tests, or impact events. A time history analysis of a bridge during an earthquake, for example, reveals not just peak stresses but also when they occur, how long oscillations persist, and whether resonance amplifies the motion. The results are time-series data: displacement, velocity, acceleration, and internal forces plotted against time, showing the full sequence of structural response rather than a worst-case snapshot.

Time history analysis requires three inputs: a validated finite element or lumped-mass model of the structure, damping coefficients (typically as a percentage of critical damping per mode), and the actual load time history, which might come from measured accelerograms, recorded wind speeds, or synthetic loads matching a design standard. Direct integration methods like the Newmark method or Runge-Kutta schemes step through time, solving for displacements and velocities at each increment. Nonlinear time history analysis, used when materials yield or geometry changes significantly, is computationally heavier but captures buckling, plasticity, and contact effects that linear methods miss.

Common pitfalls and interpretation

Time history results are data-rich but easily misread. Analysts must distinguish between absolute response, relative response, and peak absolute acceleration. They must also choose the time step wisely: too coarse and high-frequency content is lost; too fine and runtime explodes. The quality of results depends entirely on the accuracy of the input time history and the model itself. Many failures have occurred because the load time history used in analysis did not match the actual in-service environment.

Time history analysis sits between static analysis (which ignores dynamics) and frequency response functions (which assume linearity and steady-state behavior). It is the preferred method for seismic design of buildings, nuclear facilities, and critical infrastructure, and for testing aerospace and defense hardware under shock and vibration. Modern codes like IBC, AISC, and ASCE 41 mandate time history analysis for certain building types and seismic conditions. Software like SAP2000, ABAQUS, and OpenSees are standard tools for this work.