Structural Dynamics

Why a structure that passes every static check can still be unusable, and what changes the moment a load arrives quickly enough for the structure's own mass to matter.

Turning a physical structure into something that can be analysed — and keeping an honest record of what each simplification discarded.

The equation of motion, derived three ways, and the four forces that balance at every instant of a structure's movement.

Displace a structure, let go, and watch what happens — the source of the natural frequency, the three damping regimes, and the measurement that gets damping out of a real building.

What happens when a load keeps arriving in step with the structure's own motion — the one mechanism by which a small force produces a large response.

Response to a load history of any shape, built from the response to a single blow — and the discovery that for a short enough pulse the shape stops mattering altogether.

The same problem seen through a different window — and the one check that will tell you whether a time-history analysis is right, when nothing in the displacement plot will.

How the equation of motion is actually solved — what Newmark's method assumes, why stability and accuracy are different questions, and how to demonstrate that a time step is small enough.

The smallest system that has mode shapes — small enough that the eigenvalue problem can be solved by hand, and large enough that everything important about many degrees of freedom is already present.

Assembling the matrices of a real model — lumped against consistent mass, rotational inertia, rigid diaphragms — and the entries that get left at zero without anyone noticing.

The eigenproblem in general — and why a mode-shape ordinate printed by software means nothing on its own, while the ratio between two of them means everything.

Turning one coupled problem into many independent ones — what participation and effective mass actually measure, what truncation costs, and the point at which the whole method stops being valid.

No force is applied to the structure at all — the ground moves and the structure's own inertia does the rest. Which is why mass is a liability in an earthquake and an asset under wind.

One curve that summarises what an earthquake does to every possible structure — what it contains, what it deliberately throws away, and why that discarded information has to be replaced by a combination rule.

The full answer, instant by instant — and the four choices an analyst makes that decide whether it is worth having.

What changes when the restoring force depends on history: hysteresis, tangent stiffness, iterative equilibrium, ductility demand, residual displacement, and why superposition and response spectra stop applying.

Period shift as a design strategy: what it buys in force, what it costs in displacement, how the isolated first mode should look, and the practical constraints — moat, services, wind restraint, re-centring.

Manufactured viscous dampers: velocity-dependent force, the velocity exponent and what it is for, brace geometry and the cos²θ penalty, damper placement, sizing and the analysis they require.

Passive, semi-active and active control at an accessible level, with tuned mass dampers given the strongest practical treatment; sensors, actuators, feedback, robustness and fail-safe behaviour.

The faults that analysis software reports without a warning — missing mass, wrong units, accidental mechanisms, absent diaphragm constraints, too few modes, an unresolved time step — and the checks that catch each one.