Analysis and Design of Structures with Displacement-Dependent Damping Systems

Borislav Belev, Atanas Nikolov and Zdravko Bonev

Faculty of Civil Engineering, UACEG

Sofia, Bulgaria

2

Introduction and essential definitions

Source: Soong, T.T. and G.F. Dargush. Passive Energy Dissipation Systems

in Structural Engineering. J. Wiley & Sons, 1997.

STRUCTURAL

PROTECTIVE

SYSTEMS

PASSIVE ENERGY

DISSIPATION

SYSTEMS

SEMI-ACTIVE

AND ACTIVE

CONTROL

SEISMIC

(BASE)

ISOLATION

Basic Components of a Damping System

1 = Primary frame; 2 = Damper device; 3 = Supporting member

Damping system = damping devices + supporting members (braces, walls, etc.)

3

Classification of FEMA 450(Chapter 15: Structures with damping systems)

The chapter defines the damping system as:

The collection of structural elements that includes: (1) all

individual damping devices, (2) all structural elements or

bracing required to transfer forces from damping devices to

the base of the structure, and (3) all structural elements

required to transfer forces from damping devices to the

seismic-force-resisting system (SFRS).……………………………

The damping system (DS) may be external or internal to

the structure and may have no shared elements, some

shared elements, or all elements in common with the

seismic-force-resisting system.

4

Possible configurations

5

Possible configurations (cont.)

6

Types of damper devices (FEMA 273)

� Displacement-dependent devices

(metallic dampers, friction dampers)

� Velocity-dependent devices

(fluid viscous dampers,

solid visco-elastic dampers, etc.)

� Other types (shape-memory alloys, self-centering devices,

etc.)

7

Expected benefits of application of DS

� Added damping (viscous dampers)

� Added stiffness and damping (visco-elastic, metallic, friction)

� As a result, enhanced control of the interstorey drifts

------------------------------------------

� In new structures:

� Enhanced performance (reduced damage)

� Less stringent detailing for ductility (economy)

� In existing structures:

� Alternative to shear walls (speed-up retrofit)

� Correction of irregularities

� Supression of torsional response

8

Performance in terms of energy dissipation

� The structures differ in the way they “manage” and ”distribute” the total input seismic energy Ei

� Conventional structures:

energy dissipation through cyclic plastic deformation

ductile response means damage and losses

code-based design does not explicitly evaluate Eh/Ei

dissipation capacity is exhausted after a major quake

� Structures with damping systems:

energy dissipation performed by “specialized parts”

primary structure/frame has mainly gravity load supporting function and re-centering function

9

Global energy balance: Ei = Ek + Es + Eξ + Eh

Advantages of displacement-dependent damper devices

� Relatively cheap

� Easy maintenance

� Durability

� Well-defined and predictable response, so that the

supporting members can be safely designed according

to the capacity design rules

10

Drawbacks of displacement-dependent damper devices

� Nonlinear response which complicates the analysis/design

� Relatively stiff and thus not very efficient in weak quakes

� Relatively small number of working cycles and potential

low-cycle fatigue problems (metallic dampers only)

� Possible variation of the coefficient of friction with time

and degradation of contact surfaces (friction dampers only)

� React to static displacements due to temperature effects and

long-term deformations (shrinkage, creep)

11

Parameters influencing the response of a simple friction-damped frame

Illustration of the damper action

12

Definition of the equivalent bilinear-hysteresis SDOF-model

13

Us U

Fs

F

O

Kt

1

1

Kt

Kp

1Kf

1

Kbd

( ) ( )bdtaftss KKhMKUFstrengthYield ==bdft KKK +=

fp KK =

fbd KKSR =

ufM MMstrengthdamperNormalized =η

Criteria for efficiency of supplemental damping (1)

14

Fu & Cherry (1999)

min22→+ fd RR

Criteria for efficiency of supplemental damping (2)

15

Belev (2000)

Numerical evaluation of DS efficiency for a simple friction-damped frame (PGA=0.35g)

16

Seismic performance index, SPI = f(Rd, Rf, Re)

0

0.5

1

1.5

2

2.5

3

0 0.2 0.4 0.6 0.8 1

Normalized damper strength

SP

I

El Centro

Taft EW

Cekmece

Comparison of performance of several displacement-dependent devices

List of the damper devices under consideration:

� TADAS (steel triangular plate damper, analog of ADAS)

� FDD (friction damper device, already discussed)

� UFP (steel U-shaped Flexure Plate)

Frames used as “Primary structure”:

� Steel six-storey frame, originally designed as CBF

� RC single-storey portal frame (L=7.6 m, H=5.3 m)

Software tools: SAP2000 Nonlinear (for the steel frame)

DRAIN-2DX (for the RC frame)

EXTRACT (for the RC cross-section analysis)

17

TADAS steel damper

18

Arrangement of UFP or FDD devices within the primary RC portal frame

19

Layout of original steel frame

Originally designed as CBF for design GA=0.27g and q=2.0

20

Performance comparison of TADAS and FDD installed in the steel frame

Record PGA scaled

m/s2

to BRACED T-ADAS FDD BRACED T-ADAS FDD T-ADAS FDD Ei Ed Ei Ed

El Centro NS 3.417 0.27g 8.21 8.12 5.35 1351 644 281 45 70 155.1 69.98 146.7 102.3

Taft EW 1.505 0.27g 6.12 8.78 7.27 1153 583 301 38 68 144.6 54.8 156 105.8

Cekmece NS 2.296 0.27g 11.20 8.00 7.47 1974 610 310 37 69 123.6 45.58 159.8 110.8

Vrancea NS 1.949 0.20g 4.71 24.3 29.2 900 1173 530 69 53 540.7 375.5 314.4 167.2

Energy T-ADAS Energy FDDRoof displacement (cm) Base Shear (kN) Energy Ratio (%)

Roof Displacement

0

5

10

15

20

25

30

35

El C

entr

o

NS

Taft

EW

Cekm

ece

NS

Vra

ncea

NS

Ro

of

Dis

pla

cem

en

t, c

m

BRACED

TADAS

FDD

Base Shear

0

250

500

750

1000

1250

1500

1750

2000

El C

entr

o

NS

Taft

EW

Cekm

ece

NS

Vra

ncea

NS

Base S

hear,

kN

BRACED

TADAS

FDD

Energy Ratio

0

10

20

30

40

50

60

70

80

90

100

El C

entr

o

NS

Taft

EW

Cekm

ece

NS

Vra

ncea

NS

Hyste

reti

c /

In

pu

t E

nerg

y,

%

TADAS

FDD

Note: All acceleration histories scaled to PGA=0.27g except Vrancea NC,

which was left with its original PGA=0.20g

21

Performance comparison of UFP and FDD installed in the RC frame

El Centro NS, PGA = 1.5x0.35g=0.52g

-40

-30

-20

-10

0

10

20

30

40

0 2 4 6 8 10 12 14 16 18 20

Time (s)

Dis

pla

cem

en

t (m

m)

FDD (1.5) UFP (1.5) Bare frame (1.5)

22

Estimated plastic rotations in the primary RC frame members

5,34,910,27,87,918,50,52El Centro NS

0,71,94,91,72,76,30,35El Centro NS

Frame

with FDDs

Frame

with UFPs

Bare RC

frame

Frame

with FDDs

Frame

with UFPs

Bare RC

frame

Мax. plastic rotation in the girder

(mRad)

Мax. plastic rotation in the columns

(mRad)PGA

(g)

Ground

acceleration

history

5,34,910,27,87,918,50,52El Centro NS

0,71,94,91,72,76,30,35El Centro NS

Frame

with FDDs

Frame

with UFPs

Bare RC

frame

Frame

with FDDs

Frame

with UFPs

Bare RC

frame

Мax. plastic rotation in the girder

(mRad)

Мax. plastic rotation in the columns

(mRad)PGA

(g)

Ground

acceleration

history

23

Pushover analysis:Deformed shape and plastic hinges

at roof displacement = 30cm

24

Basic steps of improved analysis procedure1. Conventional modal analysis – estimate T1 and {Φ1}

2. Nonlinear static pushover analysis – trace the “roof

displacement vs. base shear” relationship

3. Calculate the properties of the Equivalent SDOF-system

4. Nonlinear time-history analysis of the ESDOF-system –

find the max. base shear, max. displacement and Ed / Ei

5. Determine the performance point of the real MDOF-

structure (in terms of base shear and roof displacement)

6. Check the location of the performance point on the

pushover curve from Step 2

7. Estimate deformations and forces in the members and

dampers corresponding to the performance point

25

Comparison of results for El Centro NS with PGA=0.27g

1058Difference (%)

50613.58.78

NL Static Pushover + NL

dynamic TH Analysis of the

equivalent SDOF-system

456448.12

Direct partially NL

dynamic TH Analysis

of the MDOF-system

Energy ratio Ed/E

i

(%)Base shear (kN)

Lateral roof

displacement (cm)

RESPONSE PARAMETER

ANALYSIS PROCEDURE

26

Shake table testing of friction-damped frame in NCREE, Taiwan (2001)

27

Numerical predictions of the seismic performance

-30

-20

-10

0

10

20

30

40

50

0 5 10 15 20 25 30

Time, (s)

Dis

pla

cem

ent,

(m

m)

Experiment

Numerical

Note 1: Seismic input – El Centro NS with PGA=0.2g

Note 2: Modal damping ratios for the first and second modes of vibration assumed 1.5% and

0.5%, respectively, to reflect the findings of previous system identification analyses

28

Conclusionsfrom the shake-table testing

� The full-scale testing at the NCREE proved the excellent

capacity of the proposed damping system to significantly

reduce earthquake-induced building vibrations

� The seismic performance of such friction-damped frames

could be predicted reasonably well by conventional

software for non-linear time history analysis such as

DRAIN-2DX and SAP2000

� Dampers supported by tension-only braces seem sensitive

to imperfections - deviations from the design brace slope

influenced the brace stiffness, periods of vibration and

seismic response.

29

An example of successful application

� Seismic protection of industrial facility

� Design PGA=0.24g, I=1.00, Soil type=B (stiff soil)

� Seismic weight W=7800 kN

� Design objective: To reduce the base shear to levels below

1120 kN, for which the existing supporting RCsub-structure

was originally designed

� Conventional design as CBF system with chevron braces is

inappropriate due to higher base shear level

(2.5x0.24x7800/1.5=3120 kN)

� Design solution: use friction dampers with slip capacity of 50-

60 kN per device (total slip capacity per direction ≤ 600 kN)

30

Typical FDD arrangement in X-direction

31

Energy dissipation by the damping system

32

Under construction…

33

Concluding remarks

� The passive energy dissipation systems are now a mature

and reliable technology for seismic protection

� The metallic and friction dampers offer certain advantages

that can be put to work if a proper system of supporting

members is employed

� The analysis and design of such displacement-dependent

damping systems require increased efforts and time but

could be really rewarding

� The option of supplemental damping should be considered

at the very early stages of conceptual design and planning

34

Thank you for your attention!