This document discusses analysis and design of structures with displacement-dependent damping systems. It begins with basic definitions and classifications of damping systems. Possible configurations of damping systems integrated with the primary structure are shown. Common types of damper devices include metallic, friction, and fluid viscous dampers. Benefits of damping systems include enhanced seismic performance through increased energy dissipation. Challenges include nonlinear response and potential degradation over time. Parameters influencing response and design criteria for efficiency are reviewed. Case studies evaluate performance of different damper types in steel and reinforced concrete frames through numerical analysis and shake table testing.

1. 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
STRUCTURAL
PROTECTIVE
SYSTEMS
SEISMIC PASSIVE ENERGY SEMI-ACTIVE
(BASE) DISSIPATION AND ACTIVE
ISOLATION SYSTEMS CONTROL
Source: Soong, T.T. and G.F. Dargush. Passive Energy Dissipation Systems
in Structural Engineering. J. Wiley & Sons, 1997.
2

3. 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

4. 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

5. Possible configurations
5

6. Possible configurations (cont.)
6

7. 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

8. 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

9. Performance in terms of energy dissipation
Global energy balance: Ei = Ek + Es + Eξ + Eh
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

10. 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

11. 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

12. Parameters influencing the response of a
simple friction-damped frame
Illustration of the damper action
12

13. Definition of the equivalent
bilinear-hysteresis SDOF-model
F K t = K f + K bd Yield strength Fs = U s K t = (M f ha ) (K t K bd )
Kp = Kf Normalized damper strength η M = M f M u
SR = K bd K f
Kp
Fs 1
1
Kt
Kbd
Kf
1 1
O Us U
13

14. Criteria for efficiency of supplemental damping
(1)
Fu & Cherry (1999)
Rd + R 2 → min
2
f
14

15. Criteria for efficiency of supplemental damping
(2)
Belev (2000)
15

16. Numerical evaluation of DS efficiency for a
simple friction-damped frame (PGA=0.35g)
Seismic performance index, SPI = f(Rd, Rf, Re)
3
2.5
2
El Centro
SPI
1.5 Taft EW
Cekmece
1
0.5
0
0 0.2 0.4 0.6 0.8 1
Normalized damper strength
16

17. 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

18. TADAS steel damper
18

19. Arrangement of UFP or FDD devices within
the primary RC portal frame
19

20. Layout of original steel frame
Originally designed as CBF for design GA=0.27g and q=2.0
20

21. Performance comparison of TADAS and
FDD installed in the steel frame
Record PGA scaled Roof displacement (cm) Base Shear (kN) Energy Ratio (%) Energy T-ADAS Energy FDD
2
m/s 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
Roof Displacement Base Shear Energy Ratio
35 2000 100
Hysteretic / Input Energy, %
1750 90
30
Roof Displacement, cm
80
25 1500
Base Shear, kN
70
1250 60
20 TADAS
BRACED 1000 BRACED 50
15 40
750
10 30
TADAS 500 TADAS
20 FDD
5 250 10
0 FDD 0 FDD 0
El Centro
Cekmece
Vrancea
El Centro
Cekmece
El Centro
Cekmece
Vrancea
Vrancea
Taft EW
Taft EW
Taft EW
NS
NS
NS
NS
NS
NS
NS
NS
NS
Note: All acceleration histories scaled to PGA=0.27g except Vrancea NC,
which was left with its original PGA=0.20g
21

22. Performance comparison of UFP and FDD
installed in the RC frame
El Centro NS, PGA = 1.5x0.35g=0.52g
40
30
Displacement (mm)
20
10
0
0 2 4 6 8 10 12 14 16 18 20
-10
-20
-30
-40
Time (s)
FDD (1.5) UFP (1.5) Bare frame (1.5)
22

23. Estimated plastic rotations
in the primary RC frame members
Мax. plastic rotation in the columns Мax. plastic rotation in the girder
Ground (mRad) (mRad)
PGA
acceleration
(g) Bare RC Frame Frame Bare RC Frame Frame
history
frame with UFPs with FDDs frame with UFPs with FDDs
El Centro NS 0,35 6,3 2,7 1,7 4,9 1,9 0,7
El Centro NS 0,52 18,5 7,9 7,8 10,2 4,9 5,3
23

24. Pushover analysis:
Deformed shape and plastic hinges
at roof displacement = 30cm
24

25. Basic steps of improved analysis procedure
1. 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

26. Comparison of results for El Centro NS
with PGA=0.27g
RESPONSE PARAMETER
ANALYSIS PROCEDURE
Lateral roof Energy ratio Ed/Ei
Base shear (kN)
displacement (cm) (%)
Direct partially NL
dynamic TH Analysis 8.12 644 45
of the MDOF-system
NL Static Pushover + NL
dynamic TH Analysis of the 8.78 613.5 50
equivalent SDOF-system
Difference (%) 8 5 10
26

27. Shake table testing of friction-damped frame
in NCREE, Taiwan (2001)
27

28. Numerical predictions of the seismic
performance
50
Experiment
40 Numerical
Displacement, (mm)
30
20
10
0
0 5 10 15 20 25 30
-10
-20
-30
Time, (s)
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

29. Conclusions
from 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

30. 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

31. Typical FDD arrangement in X-direction
31

32. Energy dissipation by the damping system
32

33. Under construction…
33

34. 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

35. Thank you for your attention!