Module 17 · Lesson 17.1
The period shift
Why putting a soft layer under a building reduces the force it attracts, and exactly what that reduction costs.
Why 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)
The idea in one sentence
An earthquake delivers most of its energy in a band of periods roughly between 0.1 s and 1 s. Ordinary buildings have periods in that band. Move the building's period well outside it, and the earthquake has much less to grip.
Why the superstructure stops mattering
Put isolators of total horizontal stiffness Kiso under a building of total mass M. The isolators are typically fifty to a hundred times softer than the building above them. Two stiffnesses in series are dominated by the softer one, so the combined stiffness is essentially Kiso, and
Tiso ≈ 2π√(M/Kiso)
The building's own stiffness barely appears. That is not an approximation being tolerated — it is the design objective. A designer who can set Kiso can set the period of the whole structure, without touching the frame.
This is why an isolated building's first mode is nearly a rigid-body translation. The structure above the isolators moves as a block, and the deformation is concentrated in the bearings where it can be inspected and, if necessary, replaced.
The trade, and it is not optional
On a design spectrum, a longer period means:
Lower spectral acceleration. Beyond the corner period, Sa falls roughly as 1/T. This is the benefit, and it is large.
Higher spectral displacement. Sd = Sa T²/4π², so as Sa falls like 1/T, Sd GROWS like T. This is the cost, and it is equally large.
There is no way to take one without the other. Isolation converts force demand into displacement demand, and the displacement has to go somewhere: into a moat around the building, into flexible service connections, into stairs and lifts that can accommodate the movement.
Damping in the isolation layer
Isolators are usually given substantial damping — 10% to 30%, from lead cores, from high-damping rubber compounds, or from separate dampers across the layer.
This mainly reduces the DISPLACEMENT, which is the demand that is hard to accommodate. It slightly increases the force, because a damped bearing transmits a damping force in addition to the spring force. The trade is nearly always worth taking, but the two effects should be reported separately rather than netted off.
Too much damping starts to defeat the purpose: it couples the isolation layer back to the superstructure, raises the higher-mode response, and the floor accelerations that isolation exists to reduce start climbing again.
What a healthy isolated model looks like
Three numbers say whether the isolation is doing its job, and all three come straight from the modal analysis:
First-mode effective mass near 100%. The isolated first mode should carry essentially all the mass, because it IS the whole building translating. Anything much below 95% means the superstructure is deforming more than intended.
Large period separation. T₁/T₂ should be a factor of five or more. A well-isolated building on the course's five-storey teaching model gives a separation above eleven. Small separation means the isolation period is too close to the structure's own, and the two will interact.
First mode shape nearly uniform above the isolators. Plot it: all the floors should move together, with a step at the isolation plane. Curvature in the superstructure means it is taking deformation it was not meant to take.
If the first mode does not carry nearly all the mass, the isolation system is not isolating. That is a modelling result available before any time-history analysis is run, and it should be checked first.
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
An isolated building's modal analysis reports a first-mode effective mass of 71%. What does that indicate?
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
- Force falls in proportion to the period shift; displacement grows by the same proportion
- Force ratio × displacement ratio ≈ 1 along the velocity branch — the demand is converted, not removed
- Isolator damping buys displacement back at a small cost in force
- First-mode effective mass near 100% and period separation above 5 are the health checks
This is educational material. It uses simplified examples to teach principles, and must not be relied on for real design or safety-critical decisions. Module overview and checkpoint