Structural Dynamics / module 1
What structural dynamics is
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.
What you will understand
- Say what makes a load dynamic, in terms of the structure rather than the load
- Explain inertia as a force, and why it appears in the equation of motion
- Recognise the loadings that commonly cause dynamic problems in practice
- Explain why the same peak load can produce very different responses
- Distinguish a strength problem from a serviceability vibration problem
- Decide, for a given structure and loading, whether a dynamic analysis is needed at all
Lessons
What makes a load dynamic
Not how large it is, and not how quickly it changes on its own — but how quickly it changes compared with the structure it is applied to.
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.
Deciding whether a dynamic analysis is needed
A practical procedure: what to estimate, what to compare it against, and what to do with the answer.
Module summary
- A load is dynamic if it changes fast enough for the structure's own inertia to matter
- Whether that is true depends on the loading AND on the structure's natural period
- A suddenly applied load gives twice the static deflection, with no resonance involved
- Resonance is a ratio between the loading frequency and the structure's own frequency
- Most dynamic problems in ordinary buildings are SERVICEABILITY problems, not strength ones
- Damping decides how long a vibration lasts and barely affects how fast it vibrates
- The commonest dynamic failures are of usability and of fatigue, not of collapse
- The first question is never 'what is the dynamic load?' but 'what is the natural period?'
Teaching basis and review status
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 notesCheck your understanding
Check yourself
Two identical loads are applied to two identical structures. One is applied over 5 natural periods, the other over 0.05 natural periods. Which produces the larger response?
Practice
A mass of 25 tonnes is supported on a structure of lateral stiffness 10 MN/m. What is the natural period in seconds?
Practice
A beam deflects 5 mm under a load applied slowly. The same load is applied suddenly to a structure with 5% damping. What is the peak deflection in mm? Use DLF = 1 + exp(−ζπ/√(1−ζ²)).
Check yourself
An office floor is uncomfortably lively. Which change raises its natural frequency most effectively?
Practice
A machine runs at 900 rpm on a floor whose natural frequency is 12 Hz. What is the frequency ratio β?