Structural Dynamics / Base isolation
The period shift
Why putting a soft layer under a building reduces the force it attracts, and exactly what that reduction costs.
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.
- Isolation specialist review needed for bearing qualification, upper/lower property bounds, bidirectional histories, torsion, stability/uplift, recentering, moat and services. Example factors and record statistics are not code verification.
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.
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Read the lesson register and outstanding review notesWhy this matters
Every method so far has taken the structure as given and asked what it will do. Base isolation inverts that. It says: the response is decided by the period, the period is decided by the stiffness, so let us CHOOSE the stiffness — and choose it at a single horizontal plane rather than throughout the building.
Put a layer of deliberately flexible bearings under a building and the whole thing becomes a single-degree-of-freedom system whose period you specify. The complicated flexible structure above becomes, dynamically, a block.
That is an unusually direct piece of engineering, and its consequences are just as direct. This lesson is about both halves: what the shift buys, and what it costs.
By the end of this lesson you should be able to
- Derive the isolated period and see why the superstructure barely enters it
- Read the force and displacement consequences off a spectrum
- Recognise a healthy isolated mode from effective mass and period separation
- State what the displacement demand means for the building's edges
What you should already know
- Response spectra and their acceleration and displacement branches (Module 14)
- Effective modal mass and period separation (Module 11)
- Base excitation (Module 13)
Period shift
A flexible isolation layer can shift a stiff building to a period with lower spectral demand. Whether that helps depends on the site-specific input, damping and the coupled building response. Ground motions do not all have the same dominant period band.
When the superstructure is much stiffer than the isolation layer, an approximate isolated period is Tiso=2π√(M/Kiso). The first translational mode then has relatively little deformation above the bearings. Check this approximation against the full model.
Force and displacement
On an ideal constant-pseudo-velocity branch at equal damping, PSa varies as1/T and Sd asT. This explains why a longer isolation period can reduce elastic force while increasing movement. The ratios are consequences of that spectral assumption, not a conservation law or a universal trade for every record.
Isolation-layer damping
Damping changes displacement, transmitted force and floor acceleration together. The damping force is an additional component of bearing force, but the resulting peak total force can increase or decrease depending on input and system properties. Assess the combined response rather than automatically adding independent peak forces. Excessive coupling can reduce the high-frequency isolation benefit.
Model checks
Inspect mode shapes, directional effective masses and the separation between isolation-dominated and superstructure modes. In a simple one-direction shear-building model, nearly uniform floor motion and a large first-mode mass support the rigid-superstructure approximation.
A95%first-mode mass or period ratio of5 is a teaching diagnostic, not a universal acceptance limit. In three dimensions, translation and torsion can split participation across several modes. Evaluate the actual deformation and response before judging whether the isolation system meets its objectives.
Try it
Fixed base against base isolated
The same building, the same earthquake, with and without an isolation layer.
Record
- Fixed base, ζ = 5%
- Isolated, ζ = 15%
- Fixed base, ζ = 5%
- Isolated, ζ = 15%
| Fixed base | Isolated | Ratio | |
|---|---|---|---|
| First period | 0.494 s | 2.635 s | 5.34× |
| Spectral acceleration | 3.03 m/s² | 0.739 m/s² | 0.24× |
| Base shear | 7270 kN | 1770 kN | 0.24× |
| Base shear coefficient | 0.309 | 0.075 | — |
| Displacement | 18.7 mm | 130 mm | 6.94× |
- Isolator stiffness required
- 14 MN/m
- Isolated first-mode effective mass
- 100.0%
- Period separation T₁/T₂
- 9.8×
- Fixed-base first-mode effective mass
- 88.0%
- Isolator displacement to accommodate
- 130 mm
- Second isolated period
- 0.269 s
The moat, the services and the isolators themselves must all take this.
The superstructure's own mode, now largely uncoupled from the ground.
The isolated first mode carries 100.0% of the mass and is 10× longer than the second. That is what a working isolation system looks like: the building above moves essentially as a rigid block on the isolators, and the superstructure's own modes are barely excited.
What isolation does not do
- It does not help a structure whose fixed-base period is already long. There is no acceleration branch left to move down, and the displacement penalty applies anyway.
- It does not remove the need for the superstructure to be designed. It reduces the demand; it does not eliminate it.
- On soft soil the spectrum can still be rising at 2–3 s, so an isolation system tuned for a rock site may buy far less there. Change the record and watch what happens.
- The isolator displacement is a hard constraint on the building: a moat that is too narrow turns a working isolation system into an impact problem.
What this shows: Isolation lengthens the period. That moves the structure DOWN the acceleration branch of the spectrum and UP the displacement branch — so it buys force reduction with displacement, and the displacement must be accommodated somewhere.
From first principles
The isolation period shift, and what it costs
We want to show: Find the period of an isolated building from the bearings alone, and show exactly what the force reduction costs in displacement.
Two springs in series share the same force and add their movements, so the soft one does nearly all the moving. Stack a very soft bearing under a stiff building and you have exactly that: the building barely deforms, the bearing takes it all, and the pair behaves like one soft spring carrying the whole mass. Once you accept that, the period follows from the bearing alone, and the consequences follow from the shape of the spectrum — down the acceleration branch and up the displacement branch, by the same factor, at the same time. The derivation is short because the physics is: this is one degree of freedom, chosen on purpose.
Worked example
Isolating a five-storey building, and paying for it
Given
- Five storeys of 400 tonnes each, plus a 400 tonne base slab above the isolators
- Fixed-base first period 0.494 s (from the modal analysis of the shear building)
- Target isolated period 3.0 s
- A synthetic firm-ground record; fixed-base spectrum at 5% damping, isolated at 20%
Find
The isolator stiffness, the actual isolated period, and the force and displacement consequences.
Assumptions
- Linear isolators at their design displacement; superstructure remains elastic
- The record is synthetic and generated for teaching — it is not a real strong-motion record
Predict first
In the one-direction teaching model, isolation is intended to leave the superstructure almost rigid. Its first-mode effective mass is71%. What should be investigated?
Practice
A building of total mass 2 400 tonnes sits on isolators of total horizontal stiffness 10.53 MN/m. What is the isolated period, in seconds?
Practice
What total isolator stiffness is needed to give a 2 400 tonne building a period of 2.5 s? Answer in MN/m.
Practice
A fixed-base building has a period of 0.494 s and its isolated version 3.030 s. What is the period shift ratio?
Practice
The isolated base shear is 1.09 MN and the fixed-base value is 7.27 MN. What is the force ratio?
Check yourself
Base isolation reduces the force on a building primarily by:
Worked example
What isolation actually achieves
Given
- A building with a fixed-base period of 0.6 s
- Isolators that lengthen the period to 2.5 s
- Isolator damping of 15 %
Find
The transmissibility, and what it means for the superstructure
Worked example
Isolation that makes things worse
Given
- A stiff plant item on soft mounts
- The mounts lengthen the period from 0.05 s to 0.06 s
- The forcing is at 20 Hz
Find
Whether the mounts help
Summary
- Isolation is period shift, deliberately chosen at one plane
- Tiso = 2π√(M/Kiso); the superstructure's stiffness changes it by a per cent or two
- On the assumed velocity-sensitive branch at equal damping, force scales as1/T and displacement asT
- The force/displacement ratio product is approximately1 only for the stated velocity-branch, equal-damping idealisation
- Check the effect of isolator damping on displacement, total force and floor acceleration
- Use mode shapes, directional participation and period separation to assess the intended isolation behaviour