Structural Dynamics / Dynamic modelling and software-result checking

Building a model that answers the question

Mass, stiffness, damping and constraints — the four modelling decisions that decide whether the analysis is about your building.

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.
Independent validation of the associated interactive implementation, input domain and project applicability remains required; this review checks lesson context and selected calculations, not design certification.
Independent model audit should compare with a physical mass take-off and justified stiffness/period estimates. Generic V/W,period,weight and modal-mass bands are not acceptance criteria.

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 notes

Why this matters

A dynamic model is not a drawing of the building. It is a statement of what you believe matters, and every element of it is a decision.

The decisions are usually made quickly, often by accepting a default, and they are almost never revisited. A model with the right geometry and the wrong mass gives beautifully plotted, entirely wrong answers, and nothing in the output says so.

This lesson is about making those decisions deliberately, and knowing which ones the answer is sensitive to.

By the end of this lesson you should be able to

State what the seismic mass includes and what it does not
Choose a stiffness that reflects the state the structure will be in
Apply damping consistently with the analysis method
Recognise which constraints the model needs and which it must not have

What you should already know

Degrees of freedom and lumped mass (Module 2)
Rigid diaphragms and mass matrices (Module 10)
Rayleigh and modal damping (Module 12)

Mass

Define the mass source from the governing seismic procedure and the material that participates in the modelled motion. Include structural self-weight, permanent finishes, cladding and equipment, plus the specified portions of variable actions. Do not use a factored gravity ULS load combination as a substitute. Variable-load factors depend on the occupancy and applicable requirements; the0.3factor used later is an explicit teaching assumption.

Check special systems such as isolated plant and liquid tanks, where some mass moves relative to the structure. Reconcile total physical mass with an independent take-off and check its distribution.

Stiffness

Use stiffness appropriate to the material state and response being assessed. Connection and panel-zone flexibility may matter in steel frames. Concrete cracking, axial force, reinforcement and load history affect effective stiffness. Generic fractions of gross stiffness are preliminary modelling choices, not universal values for every seismic or vibration check.

A stiffness change shifts periods and response distribution. Its effect on spectral force and drift depends on the input spectrum; a shorter period does not always mean a larger force. Assess infill contributions and possible loss of stiffness where relevant.

Damping

State whether damping represents inherent behaviour or explicit devices and avoid double counting. Independent modal damping requires a justified classical approximation. Direct integration needs a damping model whose response is checked over the relevant frequency range. Rayleigh calibration at two frequencies does not guarantee appropriate damping elsewhere.

Constraints and supports

Use a rigid in-plane diaphragm only when its deformation is negligible for the response being studied. Openings, geometry and connections warrant investigation, but do not automatically prohibit the idealisation. A semi-rigid model may be needed to resolve diaphragm and collector actions.

Review foundation flexibility, the effective support level, rigid links, releases and connectivity. Plot suspect modes. Unintended restraints can increase stiffness; unintended freedoms can produce mechanisms. The mode and physical load path, not a single period or participation percentage, establish the diagnosis.

Try it

Audit the output

Six analyses that ran to completion without a single warning. Each one has something wrong with it.

Cases

A four-storey steel frame, braced in both directions, modelled in a general-purpose package. The modal analysis runs without error and reports the following.

Analysis output

Model: 4-storey braced steel frame, 3D
Total mass: 1 640 tonne
Mode 1 period: 47.2 s
Mode 1 effective mass, X: 0.1%
Mode 2 period: 0.61 s
Mode 2 effective mass, X: 71%
Analysis status: Completed. No warnings.

M_eff,X = 0.1%

M_eff,X = 71%

What is wrong with this analysis?

What this shows: Analysis software reports a mechanism, a missing mass, a wrong unit and an unresolved time step in exactly the same confident format it uses for a correct answer. The checks that catch them are performed by the engineer, not the program.

Worked example

Setting up the model before running anything

Given

An eight-storey reinforced concrete frame, 3.4 m storey height, plan 24 m × 18 m
Slab 250 mm; superimposed dead 1.5 kN/m²; imposed 3.0 kN/m², quasi-permanent factor 0.3
Cladding 1.2 kN/m² on elevation; concrete density 25 kN/m³
The analysis must produce inter-storey drifts and base shear

Find

The seismic mass per floor, the expected first period, and the modelling decisions to record.

Assumptions

Regular plan and elevation; rigid diaphragms justified by a solid slab with no large openings
Beams and columns cracked; gross properties would be wrong for a concrete frame at this demand

Predict first

An eight-storey concrete frame is modelled with gross section properties instead of cracked. What happens to the reported drift?

Practice

A floor is 24 m × 18 m with an imposed load of 3.0 kN/m² and a quasi-permanent factor of 0.3. What imposed load contributes to the seismic mass, in kN?

Practice

An eight-storey building is 27.2 m tall. What first period does the empirical rule T ≈ 0.075H^0.75 predict, in seconds?

Practice

A building has a total seismic weight of 35 900 kN over eight floors of 432 m². What is the seismic weight per unit floor area, in kN/m²?

Check yourself

A floor around a large atrium has significant in-plane deformation affecting load distribution. Which idealisation would conceal that deformation?

Worked example

The same building, three different models

Given

A ten-storey frame
Three questions: the fundamental period, the floor vibration response, and the seismic base shear

Find

Whether one model serves all three

Summary

Use the governing seismic mass definition and document the included permanent and variable actions
Use effective concrete stiffness appropriate to cracking, loading and the response being assessed
Damping must match the method: modal ratios for modal, a matrix for direct integration
Rigid diaphragms only where the floor really is rigid in plane
Accidental restraints stiffen; accidental mechanisms give near-zero-frequency modes
Estimate the period and the mass by hand BEFORE running the analysis