Structural Dynamics / What structural dynamics is
Where dynamics actually matters in practice
The loadings that cause real problems, what each one does, and why most of them threaten usability rather than collapse.
Lesson review: expert verification remains open
This lesson has received a full-context editorial review and a check of its technical explanations. Selected arithmetic has been checked separately. This is not independent engineering sign-off.
Checks needed for project use
- A dynamics reviewer must confirm excitation models, damping, modal assumptions and any comfort or serviceability interpretation. Small displacement alone is not an acceptance criterion.
These are educational models and exercises. Check their assumptions before using the results. The full technical content and every diagram have not yet been independently verified.
Concrete and steel calculations retain their stated first-generation Eurocode teaching basis. Use the standards and amendments specified for your project; do not mix generations without an appropriate design basis.
Read the lesson register and outstanding review notesWhy this matters
It is easy to leave a first dynamics lesson thinking the subject is about earthquakes. Earthquakes are the most demanding application and they are not the most common. Most engineers who need dynamics need it for a floor that bounces, a bridge that people can feel, a chimney that hums in the wind, or a machine whose foundation is transmitting vibration into the building next door.
Almost none of those are strength problems. They are problems of usability, of comfort, of the equipment that has to work in the building, and — over years — of fatigue. Recognising which kind of problem you have decides which analysis you need, and the two are often confused.
By the end of this lesson you should be able to
- Name the common sources of structural dynamic loading and their frequency ranges
- Distinguish periodic, transient and random loading
- Explain why most dynamic problems in buildings are serviceability problems
- Recognise fatigue as a consequence of vibration rather than a separate subject
- Say what structural monitoring can and cannot tell you
Periodic, transient and random loading
Periodic loading repeats. A rotating imbalance or reciprocating machine may produce sustained harmonic forces and resonant amplification near a natural frequency.
A transient event has a finite duration. A dropped load, impact or blast can produce motion during the event and free vibration afterwards. The peak response and its timing depend on the force history and structural properties.
Random loading has no fixed repeating history. Wind turbulence and earthquake motion contain energy across a frequency range. They can produce a resonant contribution when that energy excites structural modes; resonance is not restricted to perfectly periodic input.
Sources of excitation
Pedestrian loading includes a pacing frequency and harmonics. The illustrative walking range used here is 1.6 to 2.4 Hz, with a second harmonic from 3.2 to 4.8 Hz. Lateral and vertical effects differ. Select a loading model and assessment criteria appropriate to the bridge or floor and its occupancy.
A rotating imbalance at 1,500 rpm produces a fundamental force at 25 Hz. For a fixed imbalance, force amplitude varies with speed squared. Check normal operation and passage through structural frequencies during start-up and shutdown, including relevant harmonics.
Vehicle and rail response depends on moving loads, suspension, surface or track irregularities and interaction with the structure. A moving-load calculation and a vibration calculation answer different aspects of that behaviour.
Wind turbulence produces broad-band buffeting. Vortex shedding can produce narrow-band excitation and, under suitable conditions, interaction with structural motion over a range of wind speeds. The applicable model depends on the shape and flexibility of the structure.
Piling, compaction, demolition and blasting can transmit ground-borne vibration to nearby structures. Assess occupants, equipment and potential structural effects against relevant criteria.
Impact and blast require suitable force-time or contact models and, where relevant, nonlinear and strain-rate-dependent behaviour. They are specialist subjects introduced here only for context. Earthquake excitation is developed through the ground-motion and response-analysis lessons in Stage C.
Vibration and fatigue
Repeated vibration can create stress cycles. Continuous vibration at 3 Hz would produce about 94.6 million cycles in a 365-day year. For a footbridge, estimate the actual duration and stress-range distribution rather than assuming continuous excitation.
Passing a static strength check does not establish fatigue adequacy. Fatigue assessment needs an appropriate detail category or resistance model and the relevant stress ranges and cycle counts. These may come from dynamic analysis, a suitable sequence of load cases and a loading history, or measurements.
Interpreting measurements
Acceleration measurements can support estimates of natural frequencies, mode shapes and damping when the sensor arrangement, excitation and identification method are adequate. Check uncertainty and repeatability, especially for damping estimates.
Acceleration records do not directly give every member stress or identify the applied loading. Those inferences require additional measurements or a justified model.
Damping may vary with amplitude, fit-out, connections and other conditions. A value estimated from a low-amplitude ambient test may not represent the response under a larger event. Record the measurement conditions and examine sensitivity before adopting a damping value for analysis.
Predict first
A long-span office floor is found to bounce noticeably when people walk across it. Its natural frequency is 4.6 Hz. Which change is most likely to fix it?
Worked example
Is this floor going to be a problem?
Given
- An open-plan office floor, 12 m span composite beams at 3 m centres
- Calculated fundamental vertical frequency: 4.3 Hz
- Damping estimated at 3% (bare floor with light partitions)
- Occupancy: normal office use, some walking traffic across the bay
Find
Whether a vibration problem is likely, and what would change the answer.
Assumptions
- The calculated frequency is for the bare structure plus a realistic allowance for permanent fit-out mass
- Human comfort thresholds are taken as design guidance, not as absolute limits
Practice
A machine runs at 1 200 rpm. What is its forcing frequency in Hz?
Practice
A floor has a natural frequency of 5.0 Hz and 2% damping. If a harmonic force is applied at exactly that frequency, by what factor is the response amplified compared with the same force applied slowly?
Check yourself
Which loading most directly gives a sustained harmonic forcing at one frequency?
Summary
- Periodic and random loading can both produce resonant amplification; their response measures and analysis methods differ
- Pedestrians excite at 1.6–2.4 Hz and their second harmonic catches many floors near 4 Hz
- Comfort is an important vibration criterion; strength, fatigue and connection performance still require their own checks
- Depth raises frequency; strength does not; mass lowers it
- Fatigue is what vibration does over time, through stress range and cycle count
- Measured damping depends on amplitude, which is why design damping is uncertain