miranda damping ratios v5 for seaonc

1

Damping Ra*os in Buildings Obtained from Instrumented Buildings in California

SEAONC, Structural Engineers Associa5ons of Northern California January 29th, 2014

Eduardo Miranda Dept. of Civil and Environmental Engineering

Stanford University

January Mini -‐Seminar

Damping Ratios in Buildings 2

ACKNOWLEDGEMENTS

SEAONC’S con8nuing educa8on commi;ee

Lukki Lam, ARUP

Tim Hart, LBL

Tony Shakal and Moh Huang, CSMIP, CGS

Masume Dana, Forell-‐Elsesser


Mo5va5on

Unlike the sta8c response on structures, the response to dynamic loads (earthquake, wind, blast, etc) depends on the damping in the structure.

Our knowledge of damping mechanisms in structures is rather limited and design provisions do not provide a lot of guidance in this respect.

Therefore, knowledge of the level of damping in a structure is essen8al for the ra8onal analysis and design of structures subjected to dynamic loads.


Mo5va5on I encourage you to do a search on the word damping on, for example, ASCE 7-‐10. I found it men8oned on 81 pages. Yet, I do not think there is a lot of guidance

Chapter 16 SEISMIC RESPONSE HISTORY PROCEDURES includes the following: 16.1.2 Modeling Mathema8cal models shall conform to the requirements of Sec8on 12.7 But as men8oned above sec8on 12.7 provides no guidance on damping.

But none of these sec8ons say anything about damping and in par8cular what damping value to use.

Sec*on 12.7 MODELING CRITERIA has sec8ons on 12.7.1 Founda8on modeling 12.7.2 Effec8ve seismic weight 12.7.3 Structural modeling

Sec*on 12.9 MODAL RESPONSE SPECTRUM ANALYSIS interes8ngly it doesn’t say anything about damping and just says to use the 5% damped spectrum as input, essen8ally recommending to use 5% damping ra8o for all modes for all structures.

2


Mo5va5on

Chapter 17 SEISMIC DESIGN REQUIREMENTS FOR SEISMICALLY ISOLATED STRUCTURES doesn’t help a lot either. For example:

17.6.3.3 Response-‐Spectrum Procedure Response-‐spectrum analysis shall be performed using a modal damping value for the fundamental mode in the direc8on of interest not greater than the effec8ve damping of the isola8on system or 30 percent of cri8cal, whichever is less. Modal damping values for higher modes shall be selected consistent with those that would be appropriate for response-‐ spectrum analysis of the structure above the isola8on system assuming a fixed base.

But what is an “appropriate” damping ra5o for a fixed-‐base structure?


18.6.2.1 Inherent Damping Inherent damping, β

I, shall be based on the material type, configura8on,

and behavior of the structure and nonstructural components responding dynamically at or just below yield of the seismic force-‐resis8ng system. Unless analysis or test data supports other values, inherent damping shall be taken as not greater than 5 percent of cri8cal for all modes of vibra8on.

Perhaps the chapter where you find a li;le bit more informa8on is

Chapter 18 SEISMIC DESIGN REQUIREMENTS FOR STRUCTURES WITH DAMPING SYSTEMS Where there is a sec8on that says

Mo5va5on

But again that is not a lot of guidance !

(Interes8ngly enough wind design provisions (4 chapters and 117 pages) don’t provide any guidance either.)


Mo5va5on

Bo\om line… Design provisions do not provide much guidance as to what damping we should use when analyzing/designing buildings

Fortunately there are some excep5ons …


Mo5va5on

3


(Ager Newmark and Hall, 1973)

Mo5va5on


Mo5va5on

“Whereas five percent of critical damping has been traditionally assumed for conventional buildings designed by code procedures, there is indisputable evidence that this is higher than the actual damping of modern tall buildings.” “A damping ratio of between 1% and 2% appears reasonable for buildings more than 50 m and less than 250 m in height.”


Mo5va5on

L o s A n g e l e s T a l l B u i l d i n g s S t r u c t u r a l D e s i g n C o u n c i l

AN ALTERNATIVE PROCEDURE FOR SEISMIC ANALYSIS AND DESIGN OF TALL BUILDINGS LOCATED IN THE LOS ANGELES REGION

A CONSENSUS DOCUMENT

2011 Edition including 2013 Supplement

C.3.5.2.2 Damping effects of structural members that are not incorporated in the analysis model (e.g., gravity framing), founda8on-‐soil interac8on, and nonstructural components that are not otherwise modeled in the analysis can be incorporated through equivalent viscous damping. The amount of viscous damping should be adjusted based on specific features of the building design and may be represented by either modal damping, explicit viscous damping elements, or a combina8on of s8ffness and mass propor8onal damping (e.g., Rayleigh damping).

3.5.2.2. Damping Significant hystere8c energy dissipa8on shall be captured directly by inelas8c elements of the model. A small amount of equivalent viscous or combined mass and s8ffness propor8onal damping may also be included. The effec*ve addi*onal modal or viscous damping should not exceed 2.5% of cri5cal for the primary modes of response.


Mo5va5on

“A number of studies have a;empted to characterize the effec8ve damping in real buildings. These studies range from evalua8on of the recorded response to low-‐ amplitude forced vibra8ons to review and analysis of strong mo8on recordings. Using data obtained from eight strong mo8on California earthquakes, Goel and Chopra (1997) found that effec8ve damping for buildings in excess of 35 stories ranged from about 2% to 4% of cri8cal damping. Using data obtained from Japanese earthquakes, Satake et al. (2003) found effec8ve damping in such structures to be in the range of 1% to 2%. Given this informa8on and the impossibility of precisely defining damping for a building that has not yet been constructed, these Guidelines recommend a default value of 2.5% damping for all modes for use in Service Level evalua5ons. “

TBI Guidelines for

Performance-

Based Seismic

Design of

Tall Buildings !"#$%&'()*+(

,&-"./"#(0+)+(

PEER

4


Mo5va5on

Modeling and acceptance criteria

for seismic design and analysis of

tall buildings

Pacific Earthquake Engineering Research Center

Applied Technology Council

PEER/ATC 72-1

foundation

main backstay diaphragm

tower core wall

M

V

foundation

main backstay diaphragm

tower core walltower core wall

M

V

PEER/ATC-72-1 2: General Nonlinear Modeling 2-55

damping should be adjusted based on specific features of the building design,

and may be represented by either modal damping, explicit viscous damping

elements, or a combination of stiffness- and mass-proportional damping (e.g.,

Rayleigh damping). Among the various alternatives, it is generally

recommended to model viscous damping using modal damping, Rayleigh

damping, or a combination of the two. Care should be taken when specifying

stiffness-proportional damping components of Rayleigh damping to avoid

overdamping in higher modes, or force imbalances in gap-type elements and

rigid-plastic materials and components.

Generally, the amount of damping is quantified in terms of a percentage of

critical damping in one or more elastic vibration modes, although it is also

recognized that distinct vibration modes and frequencies do not exist for

nonlinear response as they do with elastic analysis. Existing guidelines

suggest the use of viscous damping values ranging from 2% to 5% of critical

for nonlinear response history analyses of typical buildings subjected to

strong ground motions. Laboratory tests suggest that damping values of

about 1% for steel frame structures and 2% to 3% for reinforced concrete

structures be used to model energy dissipation that occurs in bare structural

systems, under small deformations, that is not accounted for in typical

hysteretic models. Measured data from earthquake induced motions of actual

buildings suggest damping values in the range of 1% to 5% for quasi-elastic

response of buildings over 30 stories tall. Measurements in actual buildings

indicate that the damping in tall buildings is lower than damping in low- to

mid-rise buildings.

The following values of equivalent viscous damping are suggested as

appropriate for use in nonlinear response history analysis of typical

buildings, in which most of the hysteretic energy dissipation is accounted for

in the nonlinear component models of the structural members of the seismic-

force-resisting system:

D = ;/30 (for N < 30) (2-9)

D = ;/N (for N > 30) (2-10)

where D is the maximum percent critical damping, N is the number of

stories, and ;)is a coefficient with a recommended range of ; = 60 to 120. In

general, structural steel systems would tend toward the lower range of

damping (; = 60), and reinforced concrete systems of would tend toward the

upper range (;)= 120). Figure 2-28 shows damping ranges between 2% to

4% for 30-story buildings and 1% to 2% for 70-story buildings. Damping

PEER/ATC-72-1 2: General Nonlinear Modeling 2-47

models. For fiber-type models, the best agreement was obtained using zero

damping. For plastic hinge models, the best agreement was obtained using

5% stiffness-proportional viscous damping, where the damping was based on

the tangent stiffness matrix (i.e., the damping terms were reduced in

proportion to the changes in the tangent stiffness during the analysis). Thus,

when compared to models with constant damping, effective damping in the

plastic hinge models was probably much less than 5%.

Recommendations from Gulkan and Sozen (1971) equate dissipated energy

to equivalent viscous damping. While originally envisioned for elastic

analyses, their recommendations help relate damping effects to displacement

amplitudes. They recommended a threshold value for damping in an

undamaged reinforced concrete structure at 2% of critical damping, and

demonstrated how equivalent damping quickly increased to 5% at an

imposed displacement ductility of 1.4, and 10% at an imposed ductility of

2.8. In the context of nonlinear analysis, these findings suggest a minimum

value of 2% critical damping, where any increase in viscous damping beyond

this value would depend on how well the nonlinear analysis captured

hysteretic energy dissipation in the structural components.

2.4.4 Modeling Techniques for Damping

The quantification and definition of damping are integrally linked with how

damping is modeled. For elastic analyses, damping is defined in terms of

equivalent viscous damping through the velocity dependent term, [C], in the

equation of motion, as follows:

< => ? < => ? < => ? < => ? < =PxMxKxCxM g @23@@ !!!!! (2-3)

This is done for mathematical convenience, since the velocity is out of phase

with displacement and acceleration, and thus provides an easy way to

incorporate a counteracting force to damp out motions in a linear analysis.

To facilitate modal analyses, the damping matrix is often defined using either

the classical Rayleigh damping assumption, where [C] is calculated as a

linear combination of the mass [M] and stiffness [K] matrices, or modal

damping, where [C] is a combination of specified damping amounts for

specific vibration modes (usually elastic vibration modes). These damping

formulations are explained below.

Rayleigh Damping. The damping matrix and resulting critical damping

ratios are calculated as follows:

[ ] [ ] [ ]M KC a M a K3 @ (2-4)


Mo5va5on

But how good or how bad are these guidelines ?


There is not adequate guidance either as to what change in level of response one may expect from changes in the level of damping. e.g., How much larger my response will be if my structure has 1% damping instead of 5%? How much smaller my response will be if my structure has 10% damping instead of 5%?

Mo5va5on


CHAPTER 18 SEISMIC DESIGN REQUIREMENTS FOR STRUCTURES WITH DAMPING SYSTEMS

190

! = "RD

RD

RT2# (18.5-25)

where

!1D = design story velocity due to the fundamental mode of vibration of the structure in the direction of interest

!RD = design story velocity due to the residual mode of vibration of the structure in the direction of interest

18.5.3.5 Maximum Considered Earthquake ResponseTotal and modal maximum fl oor defl ections at

Level i, design story drifts, and design story velocities shall be based on the equations in Sections 18.5.3.1, 18.5.3.3, and 18.5.3.4, respectively, except that design roof displacements shall be replaced by maximum roof displacements. Maximum roof displacements shall be calculated in accordance with Eqs. 18.5-26 and 18.5-27:

D

g S TB

g S TB

T TMMS M

M

MS

EM S1 2 1

12

12 1

12

11

4 4= $

%&'()

* $%&

'()

<# #

+ + ,

(18.5-26a)

D

g S TB

g S TB

T TMM M

M

M

EM S1 2 1

1 1

12 1

1 1

11

4 4= $

%&'()

* $%&

'()

*# #

+ + ,

(18.5-26b)

Dg S T

Bg S T

BRM R

M R

RR

MS R

R

= $%&

'()

, $%&

'()4 42

12

2

# #+ + (18.5-27)

where

SM1 = the MCER, 5 percent damped, spectral response acceleration parameter at a period of 1 s adjusted for site class effects as defi ned in Section 11.4.3

SMS = the MCER, 5 percent damped, spectral response acceleration parameter at short periods adjusted for site class effects as defi ned in Section 11.4.3

B1M = numerical coeffi cient as set forth in Table 18.6-1 for effective damping equal to -mM (m = 1) and period of structure equal to T1M

18.6 DAMPED RESPONSE MODIFICATION

As required in Sections 18.4 and 18.5, response of the structure shall be modifi ed for the effects of the damping system.

18.6.1 Damping Coeffi cientWhere the period of the structure is greater than

or equal to T0, the damping coeffi cient shall be as prescribed in Table 18.6-1. Where the period of the structure is less than T0, the damping coeffi cient shall be linearly interpolated between a value of 1.0 at a 0-second period for all values of effective damping and the value at period T0 as indicated in Table 18.6-1.

18.6.2 Effective DampingThe effective damping at the design displace-

ment, -mD, and at the maximum displacement, -mM, of the mth mode of vibration of the structure in the direction under consideration shall be calculated using Eqs. 18.6-1 and 18.6-2:

- - - µ -mD I Vm D HD= + + (18.6-1)

- - - µ -mM I Vm M HM= + + (18.6-2)

where

-HD = component of effective damping of the structure in the direction of interest due to post-yield hysteretic behavior of the seismic force-resisting system and elements of the damping system at effective ductility demand, µD

-HM = component of effective damping of the struc-ture in the direction of interest due to post-yield hysteretic behavior of the seismic force-resist-ing system and elements of the damping system at effective ductility demand, µM

-I = component of effective damping of the struc-ture due to the inherent dissipation of energy

Table 18.6-1 Damping Coeffi cient, BV+I, B1D, BR, B1M, BmD, BmM (Where Period of the Structure ! T0)

Effective Damping, -(percentage of critical)

Bv+I, B1D, BR, B1M, BmD, BmM

(where period of the structure * T0)

,2 0.85 1.0

10 1.220 1.530 1.840 2.150 2.460 2.770 3.080 3.390 3.6

*100 4.0

c18.indd 190c18.indd 190 4/14/2010 11:03:35 AM4/14/2010 11:03:35 AM

Damping modifica8on factors used in U.S. prac8ce

For structures with damping systems For seismically isolated structures

Mo5va5on

CHAPTER 17 SEISMIC DESIGN REQUIREMENTS FOR SEISMICALLY ISOLATED STRUCTURES

170

1. The structure is located on a Site Class A, B, C, or D.

2. The isolation system meets the criteria of Item 7 of Section 17.4.1.

17.4.2.2 Response-History ProcedureThe response-history procedure is permitted for

design of any seismically isolated structure and shall be used for design of all seismically isolated struc-tures not meeting the criteria of Section 17.4.2.1.

17.5 EQUIVALENT LATERAL FORCE PROCEDURE

17.5.1 GeneralWhere the equivalent lateral force procedure is

used to design seismically isolated structures, the requirements of this section shall apply.

17.5.2 Deformation Characteristics of the Isolation System

Minimum lateral earthquake design displacements and forces on seismically isolated structures shall be based on the deformation characteristics of the isolation system. The deformation characteristics of the isolation system shall explicitly include the effects of the wind-restraint system if such a system is used to meet the design requirements of this standard. The deformation characteristics of the isolation system shall be based on properly substantiated tests per-formed in accordance with Section 17.8.

17.5.3 Minimum Lateral Displacements

17.5.3.1 Design DisplacementThe isolation system shall be designed and

constructed to withstand minimum lateral earthquake displacements, DD, that act in the direction of each of the main horizontal axes of the structure using Eq. 17.5-1:

DgS T

BD

D D

D

= 124!

(17.5-1)

where

g = acceleration due to gravity. The units for g are in./s2 (mm/s2) if the units of the design displace-ment, DD, are in. (mm)

SD1 = design 5 percent damped spectral acceleration parameter at 1-s period in units of g-s, as determined in Section 11.4.4

TD = effective period of the seismically isolated structure in seconds, at the design displacement in the direction under consideration, as pre-scribed by Eq. 17.5-2

BD = numerical coeffi cient related to the effective damping of the isolation system at the design displacement, "D, as set forth in Table 17.5-1

17.5.3.2 Effective Period at Design DisplacementThe effective period of the isolated structure at

design displacement, TD, shall be determined using the deformational characteristics of the isolation system and Eq. 17.5-2:

TW

k gD

D

= 2!min

(17.5-2)

where

W = effective seismic weight of the structure above the isolation interface as defi ned in Section 12.7.2

kDmin = minimum effective stiffness in kips/in. (kN/mm) of the isolation system at the design displacement in the horizontal direction under consideration, as prescribed by Eq. 17.8-4

g = acceleration due to gravity

17.5.3.3 Maximum DisplacementThe maximum displacement of the isolation

system, DM, in the most critical direction of horizontal response shall be calculated using Eq. 17.5-3:

DgS T

BM

M M

M

= 124!

(17.5-3)

Table 17.5-1 Damping Coeffi cient, BD or BM

Effective Damping, "D or "M (percentage of critical)a,b BD or BM Factor

#2 0.85 1.0

10 1.220 1.530 1.740 1.9

$50 2.0

a The damping coeffi cient shall be based on the effective damping of the isolation system determined in accordance with the requirements of Section 17.8.5.2.b The damping coeffi cient shall be based on linear interpolation for effective damping values other than those given.

c17.indd 170c17.indd 170 4/14/2010 11:02:59 AM4/14/2010 11:02:59 AM

5


0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

0 20 40 60 80 100 120

Damping Ratio, %

Damping Modification Factor B

Chapter 18

Chapter 17


Mo5va5on



Mo5va5on

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

0 20 40 60 80 100 120

Damping Ratio, %

1 / B

Chapter 17

Chapter 18


There are various deficiencies with these factors:

Mo5va5on

1.  Even if based on sta8s8cal studies one must take into account that:

E 1B!

"#$

%&≠

1E B[ ]

With the difference increasing with the level of dispersion/variability


0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

0% 20% 40% 60% 80% 100%

Damping Ratio, %

1 / B

T = 0.2 s

T = 1 s

T = 5 s

Mo5va5on

2.  They either neglect or do not correctly account for the effect of period/frequency dependency on these factors.

(Ager Lin, Miranda and Chang 2005)

6


0.5

0.6

0.7

0.8

0.9

1.0

1.1

1.2

1.3

1.4

1.5

0% 5% 10% 15% 20%

Damping Ratio, %

1 / B

T = 0.2 s T = 1 s T = 5 s Chapter 17 Chapter 18

Mo5va5on

Despite these two problems if one compares the damping modifica8on factors with expected values obtained from sta8s8cal results, things don’t look too bad…

(Ager Lin, Miranda and Chang 2005) Damping Ratios in Buildings 22

0.5

0.6

0.7

0.8

0.9

1.0

1.1

1.2

1.3

1.4

1.5

0% 5% 10% 15% 20%

Damping Ratio, %

1 / B


Mo5va5on

How much larger my response will be if my structure has 1% damping instead of 5%?

25% larger


0.5

0.6

0.7

0.8

0.9

1.0

1.1

1.2

1.3

1.4

1.5

0% 5% 10% 15% 20%

Damping Ratio, %

1 / B


Mo5va5on

How much smaller my response will be if my structure has 10% damping instead of 5%?

20% smaller


Mo5va5on

3.  They neglect the large effect of period from record-‐to-‐record OK, but …

0"

200"

400"

600"

800"

1000"

1200"

0" 1" 2" 3" 4" 5"

Sa#[cm/s2]#

Period#[s]#

ξ = 0.01"

ξ = 0.02"

ξ = 0.05"

ξ = 0.1"

ξ = 0.15"

ξ = 0.2"

ξ = 0.25"

ξ = 0.3"

1999 Chi-‐Chi TCU136N

7


0"

10"

20"

30"

40"

50"

60"

70"

80"

0" 1" 2" 3" 4" 5"

Sd#[cm]#

Period#[s]#

ξ = 0.01"

ξ = 0.02"

ξ = 0.05"

ξ = 0.1"

ξ = 0.15"

ξ = 0.2"

ξ = 0.25"

ξ = 0.3"

Mo5va5on OK, but …



0.4$

0.6$

0.8$

1.0$

1.2$

1.4$

1.6$

1.8$

2.0$

2.2$

2.4$

0$ 1$ 2$ 3$ 4$ 5$

Sd#[ξ]/Sd[5%]#

Period#[s]#

ξ = 0.01" ξ = 0.02" ξ = 0.05" ξ = 0.1" ξ = 0.15" ξ = 0.2" ξ = 0.25" ξ = 0.3"




0"

500"

1000"

1500"

2000"

2500"

0" 1" 2" 3" 4" 5"

Sa#[cm/s2]#

Period#[s]#

ξ = 0.01"

ξ = 0.02"

ξ = 0.05"

ξ = 0.1"

ξ = 0.15"

ξ = 0.2"

ξ = 0.25"

ξ = 0.3"


1999 Chi-‐Chi CHY034N


0.4$

0.6$

0.8$

1.0$

1.2$

1.4$

1.6$

1.8$

2.0$

2.2$

2.4$

0$ 1$ 2$ 3$ 4$ 5$

Sd#[ξ]/Sd[5%]#

Period#[s]#

ξ = 0.01" ξ = 0.02" ξ = 0.05" ξ = 0.1" ξ = 0.15" ξ = 0.2" ξ = 0.25" ξ = 0.3"



Response of 1% damped is 75% larger than 5% damped (3 8mes larger than assumed by the code)

8


0.4$

0.6$

0.8$

1.0$

1.2$

1.4$

1.6$

1.8$

2.0$

2.2$

2.4$

0$ 1$ 2$ 3$ 4$ 5$

Sd#[ξ]/Sd[5%]#

Period#[s]#

ξ = 0.01" ξ = 0.02" ξ = 0.05" ξ = 0.1" ξ = 0.15" ξ = 0.2" ξ = 0.25" ξ = 0.3"



Response of 1% damped is SMALLER than 5% damped ! (code assumes 25% larger)


Mo5va5on

Bo\om line… The effects of damping can be much larger than we typically assume

But when can we expect larger effects and when smaller effects of damping?


0"

200"

400"

600"

800"

1000"

1200"

1400"

1600"

1800"

0" 1" 2" 3" 4" 5"

Sa#[cm/s2]#

Period#[s]#

ξ = 0.01"

ξ = 0.02"

ξ = 0.05"

ξ = 0.1"

ξ = 0.15"

ξ = 0.2"

ξ = 0.25"

ξ = 0.3"

0"

200"

400"

600"

800"

1000"

1200"

0" 1" 2" 3" 4" 5"

Sa#[cm/s2]#

Period#[s]#

ξ = 0.01"

ξ = 0.02"

ξ = 0.05"

ξ = 0.1"

ξ = 0.15"

ξ = 0.2"

ξ = 0.25"

ξ = 0.3"


0"

500"

1000"

1500"

2000"

2500"

0" 1" 2" 3" 4" 5"

Sa#[cm/s2]#

Period#[s]#

ξ = 0.01"

ξ = 0.02"

ξ = 0.05"

ξ = 0.1"

ξ = 0.15"

ξ = 0.2"

ξ = 0.25"

ξ = 0.3"


1999 Chi-‐Chi TCU055E

0"

200"

400"

600"

800"

1000"

1200"

1400"

0" 1" 2" 3" 4" 5"

Sa#[cm/s2]#

Period#[s]#

ξ = 0.01"

ξ = 0.02"

ξ = 0.05"

ξ = 0.1"

ξ = 0.15"

ξ = 0.2"

ξ = 0.25"

ξ = 0.3"

1999 Chi-‐Chi CHY073E

Mo5va5on Suppose T1 = 1.0s RECORDS WHERE Ti IS IN A PEAK RECORDS WHERE Ti IS IN A VALLEY


Mo5va5on

Bo\om line… The effects of damping will be larger for periods of vibra5on located on spectral peaks while they will be much smaller when they are located in spectral valleys

9


0

50

100

150

200

250

300

0.0 1.0 2.0 3.0 4.0 5.0

Sa [cm/s2]

PERIOD [s]

April 26th, 1989 Station 09

Station 01

Station 53

Mo5va5on

Damping effects will be par5cularly large for example for sof soil sites (that produce quasi-‐harmonic mo5ons) and for periods near the predominant period of the site.


Mo5va5on

0

50

100

150

200

250

300

0.0 1.0 2.0 3.0 4.0 5.0

Sa [cm/s2]

PERIOD [s]


Station 01

Station 53

Mean

However, you’ll miss not only the shape of the spectra but also damping effects if you work with mean spectra from different sof soil sites


Mo5va5on

0

50

100

150

200

250

300

0.0 0.5 1.0 1.5 2.0

Sa [cm/s2]

T / Tg


Station 01

Station 53

Mean

But if you normalized the spectra by the predominant period of the site not only you will the an excellent characteriza5on of the spectral shape but also of spectral regions where damping effects will be much larger


Nobel prize in physics 1904

John William Stru;, Baron of Rayleigh (Lord Rayleigh)

Early work on viscous damping

First published in 1877

(I strongly recommend at least browsing through these extraordinary books now freely available on Google books)

10



From volume 1


284 EFFECTS OF FRICTION. [346.

as .c iucrcascs. Assuming tliat M varies M e' we find as ia§14.8.

lu tho application to air at ordinary pressures ma.y bc con-Hidcred to bo a vury smaM qu:mtity and its square may Le

ue~lected. Thus

It appca-rs th~t to tilis ordcr of a.pproxima.tion tlie vclocity ofsound is unnH'cctcd Ly Huid friction. If we rcptuce M by 27ra\thc expression fur the cocfHcicnt of d(jc:t.y bccomcs

s)icwM)g that tue inimcncc of viscosity is greatest on the wavcs of

short wavc-)L'j)gth. Tlie :unplitudc is ditnhus!tud iu thu ratioC 1, wlicu x =fï" In c. O.S. mca.surc wu may take

Thus the amplitude of wavcs of one centimètre wavc-Icngth isdiminishod in the ratio e 1 after travc)IIng a, distance of 88jnctres. A wave-lcngth of 10 centimètres would

correspond ncarlyto for this case a; = 8800 mètres. It a.ppe:u's therefore thu.t atatmospheric pressures t))e influence of fricLion is not Hkdy to busensible to ordiuary observation, cxcept nc:).r tite upper II)nit of themusical sca)e. 'Die mellowing of soonds by distance, as obscrved Itimountainous countrics, is pcrhaps to bc attribnted to friction, bythé opération of which the higher and Iuu's))cr componcnts arc

gradually climinated. It must oftcn have bccn noticecl that thesuund s is scareciy, if at al], rctnrncd by echos, and I hâve fuund~that at a, distance of 200 nictrcs a powcrfui hiss loses its charactcr,even whcn Uicrc is no refiection. Proba.b!y Uns enect aiso is ducto viscosity.

AcofitictU Observations, P/t~. ~/<t.'7., Junc, 1877.





ue~lected. Thus








From volume 2




ue~lected. Thus









Early work on viscous damping Rayleigh’s damping Also from volume 1



Also from volume 1 Rayleigh’s quo5ent

11


Damping mechanisms in buildings

Our knowledge of damping mechanisms in buildings is rather limited. Some of the main mechanisms are:

•  Intrinsic material damping (thermoelas8c damping)

•  Soil-‐structure interac8on, mainly radia8on damping but also intrinsic damping in the soil

•  Fric8onal damping in structural elements (e.g., fric8on in bolted connec8ons, fric8on in nailed connec8ons, fric8on in micro and macro cracking of concrete, etc.)

•  Fric8onal damping in nonstructural components and their connec8ons to the structure

•  Aerodynamic damping

LARGEST SOURCE OF DAMPING

SECOND LARGEST SOURCE OF DAMPING


Although it is possible (and has been done in a few buildings) to obtain damping ra8o in buildings from pull back tests and using logarithmic decrement technique, in most cases this method is not used.

(Ager Chopra, 1994)

Methods to obtain damping ra5os Logarithmic decrement


This is a frequency-‐domain method in which a power density spectrum is computed from a measured response. The damping ra8o is obtained as half the width of the resonance peak measured at 2^0.5 of the peak amplitude normalized by the resonance frequency.

Methods to obtain damping ra5os Half-‐Power Band Width Method

(Ager Chopra, 1994)


This is a 8me-‐domain method which has recently become popular for obtaining damping ra8os in wind-‐excited buildings. It is based on the decomposi8on of band-‐filtered signals into the superposi8on of the forced vibra8on response with the homogeneous component or free vibra8on decay from given ini8al condi8ons obtaining a Random Decrement Signature which is propor8onal to the autocorrela8on func8on of the system.

Methods to obtain damping ra5os Random Decrement Technique

for this lightly damped system. As long as the white noise assumption remains valid (implicationsof this are discussed in [1,7]), the analogs between Eqs. (5) and (6) may be exploited for systemidentification, via least squares minimization to obtain best-fit estimates of damping ! and naturalfrequency fn, letting C=xo/Rx(0). Though this approach was used in this study, logarithmicdecrement or other identification techniques may also be used to determine the damping of thesystem. Though this simplified approach is designated only for SDOF systems, the RDT can beused to analyze multi-degree of freedom (MDOF) systems by the approach described herein withthe incorporation of bandpass filtering [8,9] or by introducing the recently developed vector ran-dom decrement technique [10]. However, as this study is concerned with establishing the relia-bility of RDT estimates of system parameters, it is su!cient for demonstrative purposes toconsider only the SDOF formulation.The resulting RDS will be unbiased with variance that can be expressed by [5]:

var Dxo "! "! "

# E D2xo

"! "h i

$ E Dxo "! "! "2# Rx 0! "=Nr 1$ R2

x "! "=R2x 0! "

! "

!7"

where Nr=the number of segments averaged in the estimate. The presence of noise was ignored inthis idealized derivation, as was the potential correlation between the captured segments. To

Fig. 2. Conceptualization of the random decrement technique.

T. Kijewski, A. Kareem / Structural Safety 24 (2002) 261–280 265

(Ager Kijweski-‐Correa, 2002)

12


Methods to obtain damping ra5os Commonly used methods such as the Half Power Band Width method or the Random Decrement Technique which are commonly used techniques for extrac8ng damping informa8on from buildings subjected to wind loading, they may lead to unreliable results for earthquake loading given their much shorter dura5on or because it required the excita5on frequency to be assumed to be a white noise at least in the vicinity of the spectral peak (HPBW method) which may not be valid for earthquake excita8ons.

Furthermore, Stagner and Hart (1971) found that damping ra8os obtained using the Half Power Band Width method were affected by the record dura5on, insufficient frequency resolu5on, spectral smoothing and zero padding can lead or the Random Decrement Technique which are commonly used techniques for extrac8ng damping informa8on from buildings subjected to wind loading, they may lead to unreliable results for earthquake loading given their much shorter dura8on.


Methods to obtain damping ra5os System Iden5fica5on Technique

Although recently there have been some developments on output-‐only system iden8fica8on techniques, most methods infer dynamic proper8es from the rela8onship between input and output of the system.

STRUCTURE EXCITATION RESPONSE


Previous studies

Despite its importance, very limited informa8on exists on damping ra8os in building as we cannot obtain this type of informa8on in the lab or from sta8c tes8ng. We primarily need to obtain them by measuring them in actual buildings subjected to dynamic loading.

However, there are some limita8ons on previous studies:

1.  There are typically based on very small number on buildings (e.g., Chopra and Goel (1997) only studied 22 buildings and only in one earthquake, the 1994 Northridge earthquake).

2.  Most of the data is based on ambient vibra8on, small forced vibra8on or wind loading (e.g., the study by Satake (2003) gathered informa8on on 205 Japanese buildings but only 18 building measurements were based on earthquake loading).

3.  Most studies have gathered data from different sources using different methods ogen leading to inconsistent results (mixing “apples with oranges”)


Previous studies

(Ager Goel and Chopra, 1997)

13


Previous studies

Full-Scale Data on Dynamic Properties of Buildingsin Japan

Collection of Full-Scale DataRecent full-scale data on the dynamic properties of buildingswere provided by over 40 institutes !universities, general contrac-tors, and offices of structural designers". Other full-scale datawere collected through a survey of journals and proceedings onbuilding engineering issued in Japan since 1970.Damping ratios and natural periods were picked up for trans-

lational vibration modes in two orthogonal directions and tor-sional vibration modes, together with amplitudes obtained fromvibration tests and observations. The database includes informa-tion on vibration-testing methods and damping evaluation meth-ods. Data were also compiled on building features that may in-fluence dynamic properties, including building height, number ofstories, building plan, building use, structural type, foundationtype, depth of foundations, and length of piles.

Selection of Reliable Damping Data

Only reliable data were selected from the collected full-scaledamping data. It was intended to confirm or supplement the col-lected full-scale data twice through questionnaires to the institutesthat had performed the vibration tests or observations. However,some full-scale data with unknown data items remained. Somethat contained no information on vibration amplitude for vibrationtests and observations or damping evaluation method were ne-glected. In a few cases, it was determined that damping ratioswere not accurately evaluated when the damping evaluationmethod was applied with an improper measurement condition!Davenport and Hill-Carroll 1986; AIJ 2000". In these cases, datawere also omitted. Data on buildings with odd or complicatedshapes were also discarded.Lastly, data on 137 steel-framed buildings, 25 reinforced con-

crete !RC" buildings, 43 steel-framed reinforced concrete !SRC"buildings, and 79 towerlike structures were compiled in the Japa-nese damping database. Data were categorized by structural type.

Table 1. Number of Buildings in DatabaseStructure Type Steel-Framed Buildings RC/SRC Buildings

Building heightH(m)

250–300

200–250

150–200

100–150

50–100 0–50 Total

150–200

100–150

50–100 0–50 Total

Total 1 5 14 39 60 18 137 1 5 37 25 68

Building use

Office 1 5 11 26 45 11 99 14 6 20Hotel 3 9 12 1 25 2 2

Apartment 1 3 4 1 5 20 9 35School 1 1 2 1 3 4Shops 1 1Hospital 1 1 1 1Laboratory 1 1Unknown 2 1 1 4 6 6

Foundation typePile 1 7 16 22 15 61 1 4 27 18 50Spread 1 4 7 21 38 2 73 1 10 5 16Unknown 2 1 3 2 2

Table 2. Number of Buildings Tested by Each Vibration MethodStructure Type Steel-Framed Buildings RC/SRC Buildings

Building heightH(m)

250–300

200–250

150–200

100–150

50–100 0–50 Total

150–200

100–150

50–100 0–50 Total

Forced vibration testby mechanical shaker

11 27 8 46 1 14 12 27

Forced vibration testby vibration control devices

2 1 3

Free vibration testby mechanical shaker

1 1 2 4 2 10 1 1

Free vibration testby vibration control devices

1 2 1 4

Free vibration testby man power

1 4 9 19 4 37 2 10 5 17

Free vibration testby pull and release

2 2 4

Free vibration test by swing 1 3 5 9Microtremor observation 1 2 8 21 17 5 54 1 3 16 8 28Wind response observation 1 2 2 2 2 9Earthquake observation 1 2 3 3 2 11 1 2 3 1 7

JOURNAL OF STRUCTURAL ENGINEERING © ASCE / APRIL 2003 / 471

J. Struct. Eng. 2003.129:470-477.

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(Ager Satake, 2003) PRIMARY INTEREST IN CALIFORNIA


Previous studies

Profile of Full-Scale DataStatistics of building features are exemplified in Table 1 as tobuilding height, building use, and foundation type. Most of thesteel-framed buildings in the database are 50–150 m high and areused as offices or hotels. As the building height increases, spreadfoundations become preferable. However, most RC/SRC build-ings in the database are 50–100 m high and are used as apart-ments. Pile foundations are preferred for RC/SRC buildings.As shown in Table 2, various vibration-testing methods were

used. These methods can be divided into two types according tothe excitation method. One uses artificial excitation by mechani-cal shakers, vibration control devices, man power, etc. The otheruses natural excitation, such as microtremors, earthquakes, orwind forces. The former can also be classified as forced vibrationtests and free vibration tests. As shown in Table 2, microtremorobservations, forced vibration tests by mechanical shakers, andman-power free vibration tests were applied to many buildings.Therefore, most of the data in the database were evaluated in thesmall amplitude region.Damping evaluation methods are closely related to the

vibration-testing methods !Davenport and Hill-Carroll 1986; Ka-reem and Gurley 1996; Tamura and Suganuma 1996". For eachvibration-testing method using artificial excitation, the dampingratios were evaluated restrictively by corresponding dampingevaluation methods. A half-power method and curve fitting for aresponse curve were applied most frequently to the forced vibra-tion tests. For most of the free vibration tests, a logarithmic decayfactor method was used. However, various damping evaluationmethods were employed for vibration tests using natural excita-tion. The statistics for applied damping evaluation methods areexemplified in Table 3 as to microtremor observation. A randomdecrement technique, curve fitting for power spectra, half-powerbandwidth method, and autocorrelation decay method are oftenused for microtremor observation.

Damping Properties of Buildings

This section categorizes data for 137 steel-framed buildings and68 RC/SRC buildings, and characteristics of damping ratios foreach structural type are analyzed.

Natural PeriodsBefore presenting damping properties, natural period propertiesare discussed. Fig. 1 shows the relation between natural periods intranslational first-mode T1 and building height H. The tallestbuilding in Japan at present is 282 m high and is included in thedatabase. In Japan, there are not many supertall buildings as in the

United States and some Asian countries !Davenport et al. 1970;Maebayashi et al. 1989". Not only low-rise buildings but alsomost supertall building are compiled in the database. Fig. 2 showsthe relation between T1 and natural periods in torsional first-modeTt1 . Fig. 3 shows the relation between T1 and natural periods intranslational second and third modes, T2 and T3 . Figs. 1–3 alsoindicate a regression line and its correlation factor r. It is clarifiedthat r values for both steel-framed buildings and RC/SRC build-ings in Figs. 1–3 are very high. These results indicate that thenatural periods of buildings in Japan can be predicted from build-ing height.

First-Mode Damping RatiosFirst, translational first-mode damping ratios were analyzed. Fig.4 shows the relation between first-mode damping ratios h1 andbuilding heights H. In Fig. 5, the natural periods T1 are adoptedinstead of H. Figs. 4 and 5 show that the larger the H or the T1 ,the smaller the h1 except at one point at 250 m height. Thisparticular piece of data was for a building built on soft groundwhose plan has a large dimension ratio. In order to show thistendency, a curve fit for the plot has been attempted in Figs. 4 and5. It seems that the main reason for the dependency betweendamping ratio and building height may be the effects of soil–structure interaction and radiational damping.The h1 values in many steel-framed buildings are under 2%,

which is frequently assumed in designing high-rise steel-framed

Fig. 1. Building height H versus translational first-mode naturalperiod T1

Fig. 2. First-mode natural period in translational mode T1 versus thatin torsional mode Tt1

Fig. 3. Natural period of first-mode T1 versus that of higher modesT2 , T3 in translational mode

Table 3. Number of Buildings Classified by Each DampingEvaluation Method in Microtremor Observation Data

Structure typeSteel-framedbuildings

RC/SRCbuildings

Logarithmic damping factor method 1 0Autocorrelation decay method 14 4Random decrement technique 26 10Half-power bandwidth method 15 4Curve fitting !power spectra" 8 14Curve fitting !transfer function" 1 5System identification 0 1

472 / JOURNAL OF STRUCTURAL ENGINEERING © ASCE / APRIL 2003

J. Struct. Eng. 2003.129:470-477.

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(Ager Satake, 2003) MOST RELIABLE METHOD


Previous studies

Several studies (e.g., Stagner and Hart, 1971; Davenport and Carroll, 1986; Lagosmarino 1993; Kijewski and Kareem, 2002) have shown that different methods to extract damping ra8os in buildings from measured response can lead to different values and introduce bias in the es8mated damping ra8os.

Band Width (HPBW) Technique, while the time domain analysisemploys Analytic Signal Theory using Hilbert Transformsapplied to locally averaged Random Decrement Signatures (RDS)(Kijewski and Kareem, 2003). This implementation of the RandomDecrement Technique (RDT) begins with pre-processing byButterworth bandpass filters to isolate each mode of interestand a positive point trigger value is enforced to select thesegments of the response averaged to generate the RDS (Bashoret al., 2005). As RDT is inherently sensitive to the trigger condi-tions, which directly influence the number of segments capturedand thereby the quality of the RDS, repeated triggering isimplemented, as proposed by Kijewski-Correa (2003) and pre-viously implemented in the context of the CFSMP by Bashor et al.(2005) and Kijewski-Correa and Pirnia (2007). This is accom-plished by generating a suite of RDSs associated with a range ofpositive point triggers that are within a few percent of the desiredtrigger Xp. The resulting RDSs are then processed using the HilbertTransform and the natural frequency and the critical dampingratio are determined from the phase and amplitude of the analyticsignal, respectively. The resulting vector of frequency and damp-ing estimates are then averaged to yield mean estimate andcorresponding coefficient of variation (CoV). The reliability ofthese frequency and time domain approaches for system identi-fication from wind-induced vibration data has been previouslyevaluated by Kijewski and Kareem (2002).

Both of the aforementioned approaches assume stationarity ofthe data, to varying extents. Although in practice wind is oftenviewed as a stationary random process, transient or nonstationaryfeatures are generally present in most field data. Therefore, beforedata is processed by any of the aforementioned techniques, itsstationarity is established using the Run and Reverse Arrange-ments Tests (Bendat and Piersol, 2000). In addition to these twotests, additional verifications are made using a method proposedby Montpellier (1996).

5. In-depth study of two wind events

Before exploring the trends in dynamic properties over multi-ple wind events, two wind events are selected for in-depthdiscussion to evaluate the performance of the system identifica-tion techniques being employed. It should be noted that con-firmation of stationarity by at least two of the three testsdiscussed in the previous section was executed to qualify thetwo wind events featured here as stationary; the same criteriawill be used for all data presented in later sections of the paper.The identified natural frequencies and critical damping ratios arerespectively presented in Tables 2 and 3 for Wind Events 1 and2 with respective mean hourly gradient winds and average winddirections of 20 m/s and 2251 (SW) and 24 m/s and 2881 (WNW).The dynamic properties estimated by the RDT with local trigger-ing are accompanied by their CoV to provide an indicator ofrelative reliability of the estimate.

5.1. Performance of system identification techniques

For both wind events the natural frequency estimates arecompletely consistent between the time and frequency domaintechniques, with RDT CoVs less than 1%. When comparing valuesbetween the wind events, the natural frequencies diminishslightly in the y-sway response of Building 2 in the second event.Note that for this event, the y-axis experiences acrosswind actionand comparatively larger responses; therefore, the reduction infrequency is consistent with the amplitude dependence noted inprevious studies (Kijewski-Correa and Pirnia 2007). On the otherhand, critical damping ratios estimated by RDT have CoVs that areone to two orders of magnitude higher than those associated withnatural frequency estimates. In fact, the CoVs are larger for thesteel buildings, particularly Building 3, which is the building withthe strongest degree of coupling between modes. Interestingly,the time and frequency domain system identification approachesare most consistent in their damping estimate for the concretestructure (within 14%) and show the most significant deviationfor the steel structures whose power spectra are more narrow-band and generated with fewer spectral averages for a fixedduration wind event. Furthermore, given the low bias require-ment placed on the estimation of the power spectra, it is notsurprising that the damping estimates in the frequency domainare not consistently larger than the unbiased time domainestimates, affirming that the residual error source is indeedrandom. When comparing damping values between the twoevents, Building 2 yields the most consistent damping values,regardless of the method employed, with HPBW results beingwithin 22% and RDT results being within 18%. For Building 1,while RDT results are quite consistent (within 12% betweenevents), HPBW results deviate by as much as 50%.The case is similar for Building 3, where RDT damping resultsare within 19% of one another, while HPBW results deviate by asmuch as 48%. This again can be credited to the fact that the twosteel buildings are characterized by considerably more narrow-band spectra and are thereby more susceptible to variance errorsin the presence of limited amounts of data. Interestingly, whileRDT proves to be the more consistent damping estimator, parti-cularly for the two steel buildings, when comparing resultsbetween the two events, the consistency is generally an order ofmagnitude better in the x-axis than the y-axis, which againexperiences higher amplitude acrosswind response in Event 2.As a result the lack of ‘‘consistency’’ may not be the result oferrors inherent to the method but potentially due to the ampli-tude-dependence previously observed in damping values in thesebuildings (Kijewski-Correa and Pirnia, 2007). In particular, in non-symmetric systems, the axes of the buildings typified by greaterframe action tend to manifest more amplitude dependence intheir dynamic properties: Building 1’s x-axis as a result ofpotential shear lag along the elongated floor plate and Building2’s y-axis where primary lateral resistance is derived fromslab and frame elements. The potential effects of amplitude

Table 2Estimated dynamic properties for wind event 1.

Direction Test Building 1 Building 2 Building 3

fn (Hz) z (%) fn (Hz) z (%) fn (Hz) z (%)

x-Sway HPBW 0.204 0.65 0.178 1.62 0.116 1.46RDT 0.204 0.87 0.178 1.42 0.116 1.04(CoV, %) (0.10) (23.88) (0.22) (7.43) (0.25) (20.63)

y-Sway HPBW 0.141 1.14 0.177 2.07 0.116 1.06RDT 0.141 0.88 0.177 2.41 0.116 1.21(CoV, %) (0.19) (8.89) (0.68) (8.01) (0.14) (22.96)

Table 3Estimated dynamic properties for wind event 2.

Direction Test Building 1 Building 2 Building 3

fn (Hz) z (%) fn (Hz) z (%) fn (Hz) z (%)

x-Sway HPBW 0.204 1.37 0.178 1.66 0.117 1.59RDT 0.204 0.89 0.178 1.52 0.117 1.01(CoV, %) (0.13) (12.61) (0.31) (11.33) (0.15) (10.18)

y-Sway HPBW 0.141 0.88 0.176 2.53 0.117 2.01RDT 0.141 1.00 0.176 2.95 0.116 1.44(CoV, %) (0.13) (6.43) (0.96) (5.54) (0.34) (24.20)

R. Bashor et al. / J. Wind Eng. Ind. Aerodyn. 104–106 (2012) 88–9790

(Ager Bashor et al, 2012) HPBW: Half Power Band Width method RDT: Random Decrement Technique


Previous studies

(Ager Reinoso and Miranda, 2005) The building is instrumented by the United States Geological Survey (USGS). There are a total of

21 uniaxial accelerometers installed in the first, 13th, 21st and 30th floor levels (Anderson et al., 1991;Çelebi and Safak, 1992). It was shaken by the 1989 Loma Prieta earthquake, whose epicenter was 96km away, yielding peak ground accelerations of 173 and 208cm/s2 for the NS and the EW compo-nents, respectively.

3.1.2 42-story building in San Francisco (SF42)This is a moment-resisting steel-frame building, 183m high (Figure 4), designed in 1972, slender andrectangular in plan, and founded over 10m long piles (Çelebi, 1998; Anderson and Bertero, 1998).

ESTIMATION OF FLOOR ACCELERATION DEMANDS 115

Copyright © 2005 John Wiley & Sons, Ltd. Struct. Design Tall Spec. Build. 14, 107–130 (2005)

EM30 SF42 SF47

SF48 LA52 LA54

Figure 4. Tall buildings with accelerometric recorded data used in this study. They are located in Emeryville(EM), San Francisco (SF) and Los Angeles (LA)

14


Objec5ves of this study

•  To obtain informa8on about damping ra8os in buildings to be used when conduc8ng seismic analysis in combina8on with modal analysis (either response spectrum analysis or response history modal analysis).

•  To use a significantly larger number of buildings with different characteris8cs (number of stories, materials, lateral resis8ng systems).

•  To use exclusively data from earthquake loading and with a wide range of levels of intensity.

•  To use a single and reliable method for inferring the damping ra8os.


Main Source of Informa5on


Summary of data used in this study

•  74 Buildings located in California (more than three 8mes of those analyzed by Chopra and Goel, 2003) (more than four 8mes of those analyzed by Satake with EQ loading)

•  12 Earthquakes ²  6 in the San Francisco Bay Area and 6 from LA Metropolitan area ²  Magnitudes ranging from 4.1 to 7.1

•  Heights ranging from 1 to 54 stories

•  Wide range of materials and lateral resis8ng systems



29 Buildings in the San Francisco Bay Area

15



45 Buildings in the Los Angeles Metropolitan Area


Basics of System Iden5fica5on Time-‐invariant Parametric System Iden5fica5on

Obtain computed accelera*on *me histories by conduc*ng a modal

response history analysis

Store inferred damping ra*os

Select structural parameters

Obtain ground and structural response accelera*on records

Computed response

≈ Recorded response ?

NO

YES


-200

-100

0

100

200

0 5 10 15 20 25 30

Acc [in/s2]

TIME [s]

Ground Acceleration Time History (Accelerogram)

EXCITATION RESPONSE

Basics of System Iden5fica5on

STRUCTURE

T = ?, ξ = ?

!200$

!100$

0$

100$

200$

0$ 5$ 10$ 15$ 20$ 25$ 30$

Accel%%[in/s2]%

Time%[s]%

$MEASURED$


-200

-100

0

100

200

0 5 10 15 20 25 30

Acc [in/s2]

TIME [s]


EXCITATION RESPONSE


STRUCTURE

T = 0.8, ξ = 0.05

!200$

!100$

0$

100$

200$

0$ 5$ 10$ 15$ 20$ 25$ 30$

Accel%%[in/s2]%

Time%[s]%

$MEASURED$$COMPUTED$

16


-200

-100

0

100

200

0 5 10 15 20 25 30

Acc [in/s2]

TIME [s]


EXCITATION RESPONSE


STRUCTURE

T = 1.0, ξ = 0.05

!200$

!100$

0$

100$

200$

0$ 5$ 10$ 15$ 20$ 25$ 30$

Accel%%[in/s2]%

Time%[s]%



-200

-100

0

100

200

0 5 10 15 20 25 30

Acc [in/s2]

TIME [s]


EXCITATION RESPONSE


STRUCTURE

T = 1.2, ξ = 0.05

!200$

!100$

0$

100$

200$

0$ 5$ 10$ 15$ 20$ 25$ 30$

Accel%%[in/s2]%

Time%[s]%



-200

-100

0

100

200

0 5 10 15 20 25 30

Acc [in/s2]

TIME [s]


EXCITATION RESPONSE


STRUCTURE

T = 1.37, ξ = 0.05

!200$

!100$

0$

100$

200$

0$ 5$ 10$ 15$ 20$ 25$ 30$

Accel%%[in/s2]%

Time%[s]%



-200

-100

0

100

200

0 5 10 15 20 25 30

Acc [in/s2]

TIME [s]


EXCITATION RESPONSE


STRUCTURE

T = 1.37, ξ = 0.03

!200$

!100$

0$

100$

200$

0$ 5$ 10$ 15$ 20$ 25$ 30$

Accel%%[in/s2]%

Time%[s]%


17


When comparing how close the recorded (measured) response is to the computed response we use an objec5ve func5on defined as :

where

mj,i is the measured response in the jth sensor during the ith time step

cj,i is the measured response in the jth sensor during the ith time step

J =mj,i − cj,i"# $%

2

mj,i2

i=1

n

∑j=1

N

∑


System iden5fica5on is essen5ally an op5miza5on problem in which we want to find the parameters of the model which minimize the objec5ve func5on (that minimize the difference between computed and measured response in all sensors)


0"

0.02"

0.04"

0.06"

0.08"

0.1"

")"""""1,000"""2,000"""3,000"""4,000"""5,000"""6,000"""7,000"""8,000"""9,000""

"10,000""

0.05"

0.30"

0.55"

0.80"

1.05"

1.30"

1.55"

1.80"

"9,000")"10,000"""8,000")"9,000"""7,000")"8,000"""6,000")"7,000"""5,000")"6,000"""4,000")"5,000"""3,000")"4,000"""2,000")"3,000"""1,000")"2,000""")""")"1,000""

DAMPING

RATIO

PERIOD

OBJECTIVE FUNCTION J (ERROR)



1.20%

1.22%

1.24%

1.26%

1.28%

1.30%

1.32%

1.34%

1.36%

1.38%

1.40%

0%600%1200%1800%2400%3000%3600%4200%4800%5400%6000%

0.010%

0.013%

0.016%

0.019%

0.022%

0.025%

0.028%

5400,6000%

4800,5400%

4200,4800%

3600,4200%

3000,3600%

2400,3000%

1800,2400%

1200,1800%

600,1200%

0,600%

DAMP

ING RA

TIO

PERIOD


OBJECTIVE FUNCTION J (ERROR)


1.30%

1.31%

1.32%

1.33%

1.34%

1.35%

1.36%

1.37%

1.38%

1.39%

1.40%

0%50%100%150%200%250%300%350%400%450%500%

0.010%

0.013%

0.016%

0.019%

0.022%

0.025%

0.028%

450-500%

400-450%

350-400%

300-350%

250-300%

200-250%

150-200%

100-150%

50-100%

0-50%

DAMPING

RAT

IO

PERIOD

Basics of System Iden5fica5on OBJECTIVE FUNCTION J (ERROR)

T = 1.37, ξ = 0.021

18


0"

5000"

10000"

15000"

20000"

25000"

0" 0.5" 1" 1.5" 2"

Obje%ve'Func%on,'J,'(error)'

Period'[s]'


T = 1.37s

ξ = 0.021

∂J∂T


0"

100"

200"

300"

400"

0.000" 0.005" 0.010" 0.015" 0.020" 0.025" 0.030"

Objec&ve(Func&on(J((error)(

Damping(Ra&o(


T = 1.37s

ξ = 0.021

∂J∂ξ

∂J∂ξ


0"

100"

200"

300"

400"

0.000" 0.005" 0.010" 0.015" 0.020" 0.025" 0.030"

Objec&ve(Func&on(J((error)(

Damping(Ra&o(


T = 1.37s

ξ = 0.021

0"

5000"

10000"

15000"

20000"

25000"

0" 0.5" 1" 1.5" 2"

Obje%ve'Func%on,'J,'(error)'

Period'[s]'

T = 1.37s

ξ = 0.021

These slope (formally par5al deriva5ves of an N-‐dimensional objec5ve func5on) will control how fast you converge to the minimum (inferred parameters) but more importantly the accuracy on your parameters.


0.030.04

0.050.06

0.070.08

0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5

0

1

2

3

4

5

6

7

8

9

10

ξ [%]

T [s]

Objec*ve func*on:

α = 50 ξi > 1 = 5% 15-‐Mass

T [s]

ξ [%

]

Objective Function J

0.85 0.9 0.95 1 1.05 1.13

3.5

4

4.5

5

5.5

6

6.5

7

7.5

8

(Ager C. Cruz and E. Miranda, 2014)

19


-200

-100

0

100

200

0 5 10 15 20 25 30

Acc [in/s2]

TIME [s]


EXCITATION RESPONSE


STRUCTURE

T = 1.37, ξ = 0.021

!200$

!100$

0$

100$

200$

0$ 5$ 10$ 15$ 20$ 25$ 30$

Accel%%[in/s2]%

Time%[s]%



CSMIP Station: 58354 Earthquake: Loma Prieta Building parameters:Location: Hayward Component: EWref T1 = 1.34 [ = 0.025 D0 = 15Number of stories: 13 Lateral Resisting System: Steel & RConcrete MRF

Use/Type: CSUH Admin Building

ROOF

-5-4-3-2-1012345

0 5 10 15 20 25 30 35 40Time [s]

Displ. [cm]

CHAN4 - CHAN14Computed

5TH FLOOR

-5-4-3-2-1012345

0 5 10 15 20 25 30 35 40Time [s]

Disp. [cm]


2ND FLOOR

-5-4-3-2-1012345

0 5 10 15 20 25 30 35 40Time [s]

Disp. [cm]


1ST FLOOR

-5-4-3-2-1012345

0 5 10 15 20 25 30 35 40Time [s]

Disp. [cm]

CHAN12 - CHAN14

Computed

BASE

-5-4-3-2-1012345

0 5 10 15 20 25 30 35 40Time [s]

Disp. [cm]

CHAN14 - CHAN14

Computed

Examples of System Iden5fica5on


CSMIP Station: 58354 Earthquake: Loma Prieta Building parameters: 1.9

Location: Hayward Component: NSref T1 = 1.25 [ = 0.03 D0 = 29.5 Manual

Number of stories: 13 Lateral Resisting System: Steel & RConcrete MRF


ROOF

0

250

500

750

1000

0.0 1.0 2.0 3.0 4.0 5.0 6.0PERIOD [s]

Accel. [cm/s2]

From recorded resp. From computed resp.

ROOF

-250-200-150-100

-500

50100150200250

0 5 10 15 20 25 30Time [s]

Accel. [cm/s2]

CHAN3Computed

5TH FLOOR

-250-200-150-100

-500

50100150200250

0 5 10 15 20 25 30Time [s]

Accel. [cm/s2]

CHAN5Computed

2ND FLOOR

-250-200-150-100

-500

50100150200250

0 5 10 15 20 25 30Time [s]

Accel. [cm/s2]

CHAN8Computed

5TH FLOOR

0

250

500

750

1000

0.0 1.0 2.0 3.0 4.0 5.0 6.0PERIOD [s]

Accel. [cm/s2]


2ND FLOOR

0

250

500

750

1000

0.0 1.0 2.0 3.0 4.0 5.0 6.0PERIOD [s]

Accel. [cm/s2]


0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

0 1 2 3 4PFA / PGA

x=z/H

Recorded Computed

1ST FLOOR

-250-200-150-100

-500

50100150200250

0 5 10 15 20 25 30Time [s]

Accel. [cm/s2]CHAN11Computed

1ST FLOOR

0

250

500

750

1000

0.0 1.0 2.0 3.0 4.0 5.0 6.0PERIOD [s]

Accel. [cm/s2]


BASE

-250-200-150-100

-500

50100150200250

0 5 10 15 20 25 30Time [s]

Accel. [cm/s2]

CHAN16Computed

BASE

0

250

500

750

1000

0.0 1.0 2.0 3.0 4.0 5.0 6.0PERIOD [s]

Accel. [cm/s2]





Location: Hayward Component: NSref T1 = 1.25 [ = 0.03 D0 = 29.5 Manual

Number of stories: 13 Lateral Resisting System: Steel & RConcrete MRF


ROOF

0

250

500

750

1000

0.0 1.0 2.0 3.0 4.0 5.0 6.0PERIOD [s]

Accel. [cm/s2]


ROOF

-250-200-150-100

-500

50100150200250

0 5 10 15 20 25 30Time [s]

Accel. [cm/s2]

CHAN3Computed

5TH FLOOR

-250-200-150-100

-500

50100150200250

0 5 10 15 20 25 30Time [s]

Accel. [cm/s2]

CHAN5Computed

2ND FLOOR

-250-200-150-100

-500

50100150200250

0 5 10 15 20 25 30Time [s]

Accel. [cm/s2]

CHAN8Computed

5TH FLOOR

0

250

500

750

1000

0.0 1.0 2.0 3.0 4.0 5.0 6.0PERIOD [s]

Accel. [cm/s2]


2ND FLOOR

0

250

500

750

1000

0.0 1.0 2.0 3.0 4.0 5.0 6.0PERIOD [s]

Accel. [cm/s2]


0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

0 1 2 3 4PFA / PGA

x=z/H

Recorded Computed

1ST FLOOR

-250-200-150-100

-500

50100150200250

0 5 10 15 20 25 30Time [s]


1ST FLOOR

0

250

500

750

1000

0.0 1.0 2.0 3.0 4.0 5.0 6.0PERIOD [s]

Accel. [cm/s2]


BASE

-250-200-150-100

-500

50100150200250

0 5 10 15 20 25 30Time [s]

Accel. [cm/s2]

CHAN16Computed

BASE

0

250

500

750

1000

0.0 1.0 2.0 3.0 4.0 5.0 6.0PERIOD [s]

Accel. [cm/s2]



Main ques*on I was interested in answering: (and its what dis*guishes this research from other apart from using a much larger number of buildings excited by earthquake loading) What is the modal damping ra5o I should use if I am interested in reproducing the measured response when: a)  I am compu5ng the response with a modal response history analysis; b)  I am using a linear elas5c model fixed at the base;

20


CSMIP Station: 58354 Earthquake: Loma Prieta Building parameters:Location: Hayward Component: EWref T1 = 1.34 [ = 0.025 D0 = 15Number of stories: 13 Lateral Resisting System: Steel & RConcrete MRF


ROOF

-5-4-3-2-1012345

0 5 10 15 20 25 30 35 40Time [s]

Displ. [cm]


5TH FLOOR

-5-4-3-2-1012345

0 5 10 15 20 25 30 35 40Time [s]

Disp. [cm]


2ND FLOOR

-5-4-3-2-1012345

0 5 10 15 20 25 30 35 40Time [s]

Disp. [cm]


1ST FLOOR

-5-4-3-2-1012345

0 5 10 15 20 25 30 35 40Time [s]

Disp. [cm]

CHAN12 - CHAN14

Computed

BASE

-5-4-3-2-1012345

0 5 10 15 20 25 30 35 40Time [s]

Disp. [cm]

CHAN14 - CHAN14

Computed


ξ = 0.025



Location: San Francisco Component: NSref T1 = 0.66 [ = 0.035 D0 = 5.9 Manual

Number of stories: 4 Lateral Resisting System: Steel MRF

Use/Type: Office Building

ROOF

0

800

1600

2400

3200

0.0 1.0 2.0 3.0 4.0 5.0 6.0PERIOD [s]

Accel. [cm/s2]


ROOF

-600-450-300-150

0150300450600

0 5 10 15 20 25 30 35 40Time [s]

Accel. [cm/s2]

CHAN10Computed

2ND FLOOR

-600

-450

-300

-150

0

150

300

450

600

0 5 10 15 20 25 30 35 40Time [s]

Accel. [cm/s2]

CHAN7Computed

BASE

-600

-450

-300

-150

0

150

300

450

600

0 5 10 15 20 25 30 35 40Time [s]

Accel. [cm/s2]

CHAN3Computed

2ND FLOOR

0

800

1600

2400

3200

0.0 1.0 2.0 3.0 4.0 5.0 6.0PERIOD [s]

Accel. [cm/s2]


BASE

0

800

1600

2400

3200

0.0 1.0 2.0 3.0 4.0 5.0 6.0PERIOD [s]

Accel. [cm/s2]


0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

0 1 2 3 4 5PFA / PGA

x=z/H

Recorded Computed





Location: San Francisco Component: NSref T1 = 0.66 [ = 0.035 D0 = 5.9 Manual



ROOF

0

800

1600

2400

3200

0.0 1.0 2.0 3.0 4.0 5.0 6.0PERIOD [s]

Accel. [cm/s2]


ROOF

-600-450-300-150

0150300450600

0 5 10 15 20 25 30 35 40Time [s]

Accel. [cm/s2]

CHAN10Computed

2ND FLOOR

-600

-450

-300

-150

0

150

300

450

600

0 5 10 15 20 25 30 35 40Time [s]

Accel. [cm/s2]

CHAN7Computed

BASE

-600

-450

-300

-150

0

150

300

450

600

0 5 10 15 20 25 30 35 40Time [s]

Accel. [cm/s2]

CHAN3Computed

2ND FLOOR

0

800

1600

2400

3200

0.0 1.0 2.0 3.0 4.0 5.0 6.0PERIOD [s]

Accel. [cm/s2]


BASE

0

800

1600

2400

3200

0.0 1.0 2.0 3.0 4.0 5.0 6.0PERIOD [s]

Accel. [cm/s2]


0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

0 1 2 3 4 5PFA / PGA

x=z/H

Recorded Computedξ = 0.03


Examples of System Iden5fica5on ξ = 0.03

CSMIP Station: 58261 Earthquake: Loma Prieta Building parameters:Location: San Francisco Component: NSref T1 = 0.66 [ = 0.035 D0 = 5.9Number of stories: 4 Lateral Resisting System: Steel MRF


ROOF

-8

-6

-4

-2

0

2

4

6

8

0 5 10 15 20 25 30 35 40Time [s]

Displ. [cm]


2ND FLOOR

-8

-6

-4

-2

0

2

4

6

8

0 5 10 15 20 25 30 35 40Time [s]

Disp. [cm]


BASE

-8

-6

-4

-2

0

2

4

6

8

0 5 10 15 20 25 30 35 40Time [s]

Disp. [cm]


21




Location: Palo Alto Component: NSref T1 = 0.28 [ = 0.2 D0 = 10 Manual

Number of stories: 2 Lateral Resisting System: Masonry SW


ROOF

0

200

400

600

800

1000

0.0 1.0 2.0 3.0 4.0 5.0 6.0PERIOD [s]

Accel. [cm/s2]


ROOF

-400-300-200-100

0100200300400

0 5 10 15 20 25 30 35 40Time [s]

Accel. [cm/s2]

CHAN7Computed

BASE

-400

-300

-200

-100

0

100

200

300

400

0 5 10 15 20 25 30 35 40Time [s]

Accel. [cm/s2]

CHAN1Computed

BASE

0

200

400

600

800

1000

0.0 1.0 2.0 3.0 4.0 5.0 6.0PERIOD [s]

Accel. [cm/s2]


0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

0 1 2 3 4PFA / PGA

x=z/H

Recorded Computed




Location: Palo Alto Component: NSref T1 = 0.28 [ = 0.2 D0 = 10 Manual

Number of stories: 2 Lateral Resisting System: Masonry SW


ROOF

0

200

400

600

800

1000

0.0 1.0 2.0 3.0 4.0 5.0 6.0PERIOD [s]

Accel. [cm/s2]


ROOF

-400-300-200-100

0100200300400

0 5 10 15 20 25 30 35 40Time [s]

Accel. [cm/s2]

CHAN7Computed

BASE

-400

-300

-200

-100

0

100

200

300

400

0 5 10 15 20 25 30 35 40Time [s]

Accel. [cm/s2]

CHAN1Computed

BASE

0

200

400

600

800

1000

0.0 1.0 2.0 3.0 4.0 5.0 6.0PERIOD [s]

Accel. [cm/s2]


0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

0 1 2 3 4PFA / PGA

x=z/H





Location: Walnut Creek Component: EWref T1 = 0.78 [ = 0.032 D0 = 7.5 Manual

Number of stories: 10 Lateral Resisting System: Shear Walls

Use/Type: Commercial Building

ROOF

0

300

600

900

1200

0.0 1.0 2.0 3.0 4.0 5.0 6.0PERIOD [s]

Accel. [cm/s2]


ROOF

-300

-200

-100

0

100

200

300

0 5 10 15 20 25 30 35 40Time [s]

Accel. [cm/s2]

CHAN3Computed

8TH FLOOR

-300

-200

-100

0

100

200

300

0 5 10 15 20 25 30 35 40Time [s]

Accel. [cm/s2]

CHAN7Computed

3RD FLOOR

-300

-200

-100

0

100

200

300

0 5 10 15 20 25 30 35 40Time [s]

Accel. [cm/s2]

CHAN10Computed

8TH FLOOR

0

300

600

900

1200

0.0 1.0 2.0 3.0 4.0 5.0 6.0PERIOD [s]

Accel. [cm/s2]


3RD FLOOR

0

300

600

900

1200

0.0 1.0 2.0 3.0 4.0 5.0 6.0PERIOD [s]

Accel. [cm/s2]


0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

0 1 2 3 4 5PFA / PGA

x=z/H

Recorded Computed

BASE

-300

-200

-100

0

100

200

300

0 5 10 15 20 25 30 35 40Time [s]


BASE

0

300

600

900

1200

0.0 1.0 2.0 3.0 4.0 5.0 6.0PERIOD [s]

Accel. [cm/s2]





Location: Walnut Creek Component: EWref T1 = 0.78 [ = 0.032 D0 = 7.5 Manual



ROOF

0

300

600

900

1200

0.0 1.0 2.0 3.0 4.0 5.0 6.0PERIOD [s]

Accel. [cm/s2]


ROOF

-300

-200

-100

0

100

200

300

0 5 10 15 20 25 30 35 40Time [s]

Accel. [cm/s2]

CHAN3Computed

8TH FLOOR

-300

-200

-100

0

100

200

300

0 5 10 15 20 25 30 35 40Time [s]

Accel. [cm/s2]

CHAN7Computed

3RD FLOOR

-300

-200

-100

0

100

200

300

0 5 10 15 20 25 30 35 40Time [s]

Accel. [cm/s2]

CHAN10Computed

8TH FLOOR

0

300

600

900

1200

0.0 1.0 2.0 3.0 4.0 5.0 6.0PERIOD [s]

Accel. [cm/s2]


3RD FLOOR

0

300

600

900

1200

0.0 1.0 2.0 3.0 4.0 5.0 6.0PERIOD [s]

Accel. [cm/s2]


0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

0 1 2 3 4 5PFA / PGA

x=z/H

Recorded Computed

BASE

-300

-200

-100

0

100

200

300

0 5 10 15 20 25 30 35 40Time [s]


BASE

0

300

600

900

1200

0.0 1.0 2.0 3.0 4.0 5.0 6.0PERIOD [s]

Accel. [cm/s2]


ξ = 0.032

22



CSMIP Station: 58364 Earthquake: Loma Prieta Building parameters:

Location: Walnut Creek Component: EWref T1 = 0.78 [ = 0.032 D0 = 7.5Number of stories: 10 Lateral Resisting System: Shear Walls


ROOF

-4

-3

-2

-1

0

1

2

3

4

0 5 10 15 20 25 30 35 40Time [s]

Displ. [cm]

CHAN3 - CHAN16

Computed

8TH FLOOR

-4

-3

-2

-1

0

1

2

3

4

0 5 10 15 20 25 30 35 40Time [s]

Disp. [cm]

CHAN7 - CHAN16

Computed

3RD FLOOR

-4

-3

-2

-1

0

1

2

3

4

0 5 10 15 20 25 30 35 40Time [s]

Disp. [cm]

CHAN10 - CHAN16

Computed

BASE

-4

-3

-2

-1

0

1

2

3

4

0 5 10 15 20 25 30 35 40Time [s]

Disp. [cm]

CHAN16 - CHAN16

Computed

ξ = 0.032



Location: San Francisco Component: EWref T1 = 6.70 [ = 0.011 D0 = 30 Manual



ROOF

0

300

600

900

1200

0.0 1.0 2.0 3.0 4.0 5.0 6.0PERIOD [s]

Accel. [cm/s2]


ROOF

-400-300-200-100

0100200300400

0 5 10 15 20 25 30 35 40 45 50 55 60Time [s]

Accel. [cm/s2]

CHAN16Computed

16th FLOOR

-400

-300

-200

-100

0

100

200

300

400

0 5 10 15 20 25 30 35 40 45 50 55 60Time [s]

Accel. [cm/s2]

CHAN11Computed

BASE

-400

-300

-200

-100

0

100

200

300

400

0 5 10 15 20 25 30 35 40 45 50 55 60Time [s]

Accel. [cm/s2]

CHAN7Computed

16th FLOOR

0

300

600

900

1200

0.0 1.0 2.0 3.0 4.0 5.0 6.0PERIOD [s]

Accel. [cm/s2]


BASE

0

300

600

900

1200

0.0 1.0 2.0 3.0 4.0 5.0 6.0PERIOD [s]

Accel. [cm/s2]


0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

0 1 2 3 4PFA / PGA

x=z/H

Recorded Computed





Location: San Francisco Component: EWref T1 = 6.70 [ = 0.011 D0 = 30 Manual



ROOF

0

300

600

900

1200

0.0 1.0 2.0 3.0 4.0 5.0 6.0PERIOD [s]

Accel. [cm/s2]


ROOF

-400-300-200-100

0100200300400

0 5 10 15 20 25 30 35 40 45 50 55 60Time [s]

Accel. [cm/s2]

CHAN16Computed

16th FLOOR

-400

-300

-200

-100

0

100

200

300

400

0 5 10 15 20 25 30 35 40 45 50 55 60Time [s]

Accel. [cm/s2]

CHAN11Computed

BASE

-400

-300

-200

-100

0

100

200

300

400

0 5 10 15 20 25 30 35 40 45 50 55 60Time [s]

Accel. [cm/s2]

CHAN7Computed

16th FLOOR

0

300

600

900

1200

0.0 1.0 2.0 3.0 4.0 5.0 6.0PERIOD [s]

Accel. [cm/s2]


BASE

0

300

600

900

1200

0.0 1.0 2.0 3.0 4.0 5.0 6.0PERIOD [s]

Accel. [cm/s2]


0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

0 1 2 3 4PFA / PGA

x=z/H



Examples of System Iden5fica5on ξ = 0.011

CSMIP Station: 58532 Earthquake: Loma Prieta Building parameters:Location: San Francisco Component: EWref T1 = 6.26 [ = 0.012 D0 = 30Number of stories: 47 Lateral Resisting System: Steel MRF


ROOF

-60

-45

-30

-15

0

15

30

45

60

0 5 10 15 20 25 30 35 40 45 50 55 60Time [s]

Displ. [cm]


16th FLOOR

-60

-45

-30

-15

0

15

30

45

60

0 5 10 15 20 25 30 35 40 45 50 55 60Time [s]

Disp. [cm]


BASE

-60

-45

-30

-15

0

15

30

45

60

0 5 10 15 20 25 30 35 40 45 50 55 60Time [s]

Disp. [cm]


23


CSMIP Station: 24602 Earthquake: Landers Building parameters:Location: Los Angeles Component: EWref T1 = 6.04 [ = 0.009 D0 = 6.6Number of stories: 52 Lateral Resisting System: Steel MRF


ROOF

-80-60-40-20

020406080

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80Time [s]

Displ. [cm]


49th FLOOR

-80-60

-40-20

0

2040

6080

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80Time [s]

Disp. [cm]


35th FLOOR

-80-60-40-20

020406080

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80Time [s]

Disp. [cm]


22nd FLOOR

-80

-60-40

-200

20

4060

80

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80Time [s]

Disp. [cm]

CHAN10 - CHAN05

Computed

14th FLOOR

-80-60

-40-20

020

4060

80

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80Time [s]

Disp. [cm]

CHAN08 - CHAN05

Computed

BASE

-80

-60-40

-200

20

4060

80

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80Time [s]

Disp. [cm]

CHAN05 - CHAN05

Computed




CSMIP Station: 24602 Earthquake: Landers Building parameters:Location: Los Angeles Component: EWref T1 = 6.04 [ = 0.009 D0 = 6.6Number of stories: 52 Lateral Resisting System: Steel MRF


ROOF

-80-60-40-20

020406080

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80Time [s]

Displ. [cm]


49th FLOOR

-80-60

-40-20

0

2040

6080

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80Time [s]

Disp. [cm]


35th FLOOR

-80-60-40-20

020406080

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80Time [s]

Disp. [cm]


22nd FLOOR

-80

-60-40

-200

20

4060

80

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80Time [s]

Disp. [cm]

CHAN10 - CHAN05

Computed

14th FLOOR

-80-60

-40-20

020

4060

80

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80Time [s]

Disp. [cm]

CHAN08 - CHAN05

Computed

BASE

-80

-60-40

-200

20

4060

80

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80Time [s]

Disp. [cm]

CHAN05 - CHAN05

Computed

ξ = 0.009


0.00#0.05#0.10#0.15#0.20#0.25#0.30#0.35#0.40#

0# 50# 100# 150# 200# 250#

ξ"

Data#Number#

Results from all buildings/earthquakes

244 Damping ra8os

Characterized by very large variability and values ranging from much lower (e.g., <1%) to much larger (e.g., >20%) than the 5% commonly used


0.0#

0.2#

0.4#

0.6#

0.8#

1.0#

0.00# 0.05# 0.10# 0.15# 0.20# 0.25# 0.30#

P(ξ<x)#

Damping#Ra8o,#ξ"

#Data#

#Lognormal#


Mean ξ = 6.7% σξ = 6.1% COV = 0.92

GeoMean ξ = 5.0% σLn ξ = 0.73

This level of variability is much larger than for example the one in a GMPE (spectral ordinate for a given magnitude and distance) which is typically between 0.45 and 0.60.

Variability and probability distribu8on

Median ξ = 5.0%

24


0.00#0.05#0.10#0.15#0.20#0.25#0.30#0.35#0.40#

0# 50# 100# 150# 200# 250#

ξ"

Data#Number#


0.00#0.05#0.10#0.15#0.20#0.25#0.30#0.35#0.40#

0# 50# 100# 150# 200# 250#

ξ"

Data#Number#

Results from N>3 (elimina8ng data from 1 and 2 story buildings)

Then the average damping ra5o from all buildings drops from 6.7% to 5.4% which is a reduc5on of 20% (afer elimina5ng about one fifh of the data from one and two-‐story buildings)



Many ques8ons “under this head”. For example:

How different are the damping ra5os in steel buildings compared to RC buildings?

0.00#

0.05#

0.10#

0.15#

0.20#

0# 50# 100# 150# 200# 250#

ξ"

Data#Number#

#RC#Bldgs.#

#Steel#Bldgs.#


0.00#

0.05#

0.10#

0.15#

0.20#

0# 50# 100# 150# 200# 250#

ξ"

Data#Number#

#RC#Bldgs.#

#Steel#Bldgs.#


Are the differences sta5s5cally significant ?

ξ = 0.066 ξ = 0.041

Average Values

YES, THEY ARE

This suggest that a more ra5onal approach would be to use a lower level of damping for steel structures than for reinforced concrete buildings. Some of this is already acknowledged by ASCE 41 but not by ASCE 7, so is different whether you are designing a new building or evalua5ng an exis5ng one when in reality an earthquake will not ask you which document you are using.


0.00#0.05#0.10#0.15#0.20#0.25#0.30#0.35#0.40#

0# 100# 200# 300# 400# 500# 600# 700# 800#

ξ"

Height#[3]#

#All#Bldgs.#

Changes in damping ra5o with building height

ρ = -‐0.36

There is indisputable evidence both from wind and seismic loading that damping ra5o tends to decrease as building height increases. Therefore it doesn’t make sense to use a damping ra5o of 5% for all buildings regardless of their height.

25


0.00#

0.05#

0.10#

0.15#

0.20#

0# 50# 100# 150# 200# 250#

ξ"

Height#[.]#

!RC!Bldgs.!

#RC#Bldgs.#




y"="0.0862e*0.005x"R²"="0.15679"

0.00"

0.05"

0.10"

0.15"

0.20"

0" 50" 100" 150" 200" 250"

ξ"

Height"[8]"

!!"RC"Bldgs."

y"="0.2506x*0.341"R²"="0.14925"

0.00"

0.05"

0.10"

0.15"

0.20"

0" 50" 100" 150" 200" 250"

ξ"

Height"[8]"

!RC!Bldgs.!"RC"Bldgs."

Two possible models:

Cau8on should be exercised when using this type of models as their associated coefficient of determina8on is rather low due to the large variability in the data. A beFer approach is to bracket your analysis and use two values



0.00#

0.05#

0.10#

0.15#

0.20#

0# 100# 200# 300# 400# 500# 600# 700# 800#

ξ"

Height#[3]#

!Steel!Bldgs.!

#Steel#Bldgs.#



0.00#

0.05#

0.10#

0.15#

0.20#

0# 100# 200# 300# 400# 500# 600# 700# 800#

ξ"

Height#[3]#

#RC#Bldgs.#

#Steel#Bldgs.#

No8ce that we do not have data on very tall reinforced concrete buildings. One excep8on in Northern California is the PPP, but fortunately this has been iden8fied and both CSMIP and USGS have recently instrumented several tall RC buildings (we now just need EQs to learn more about their damping ra8os J )

26



y"="0.0534e*0.003x"R²"="0.60853"

0.00"

0.05"

0.10"

0.15"

0.20"

0" 100" 200" 300" 400" 500" 600" 700" 800"

ξ"

Height"[9]"

!!

"Steel"Bldgs."

y"="0.5066x)0.576"R²"="0.58953"

0.00"

0.05"

0.10"

0.15"

0.20"

0" 100" 200" 300" 400" 500" 600" 700" 800"

ξ"

Height"[:]"

"Steel"Bldgs."

Two possible models:

Even though the number of data points is smaller, the coefficients of determina8on are are much larger than for RC buildings, so one can use these models with more confidence. No8ce that for H>500 N the damping ra8os are 1% or less which agrees with the level of damping measured in strong wind storms.


Damping mechanisms and varia5on of damping ra5os with height

Which of these mechanisms would explain a decrease in damping ra8o with increasing height ?

•  Intrinsic material damping (thermoelas8c damping)

•  Soil-‐structure interac8on, mainly radia8on damping but also intrinsic damping in the soil

•  Fric8onal damping in structural elements (e.g., fric8on in bolted connec8ons, fric8on in nailed connec8ons, fric8on in micro and macro cracking of concrete, etc.)

•  Fric8onal damping in nonstructural components and their connec8ons to the structure

•  Aerodynamic damping


CSMIP Station: 24322 Earthquake: Landers Building parameters:Location: Sherman Oaks Component: EWref T1 = 2.54 [ = 0.045 D0 = 29.5Number of stories: 13 Lateral Resisting System: RConcrete MRF


ROOF

-15

-10

-5

0

5

10

15

0 5 10 15 20 25 30 35 40Time [s]

Displ. [cm]


8TH FLOOR

-15

-10

-5

0

5

10

15

0 5 10 15 20 25 30 35 40Time [s]

Disp. [cm]


2ND FLOOR

-15

-10

-5

0

5

10

15

0 5 10 15 20 25 30 35 40Time [s]

Disp. [cm]


BASE

-15

-10

-5

0

5

10

15

0 5 10 15 20 25 30 35 40Time [s]

Disp. [cm]

CHAN10 - CHAN10

Computed

Evalua5on Changes with Amplitude


CSMIP Station: 24322 Earthquake: Whittier Building parameters:Location: Sherman Oaks Component: EWref T1 = 2.57 [ = 0.04 D0 = 29.5Number of stories: 13 Lateral Resisting System: RConcrete MRF


ROOF

-15

-10

-5

0

5

10

15

0 5 10 15 20 25 30 35 40Time [s]

Displ. [cm]


8th FLOOR

-15

-10

-5

0

5

10

15

0 5 10 15 20 25 30 35 40Time [s]

Disp. [cm]


2nd FLOOR

-15

-10

-5

0

5

10

15

0 5 10 15 20 25 30 35 40Time [s]

Disp. [cm]


BASE

-15

-10

-5

0

5

10

15

0 5 10 15 20 25 30 35 40Time [s]

Disp. [cm]

CHAN10 - CHAN10

Computed

ξ = 0.04 CSMIP Station: 24322 Earthquake: Whittier Building parameters:Location: Sherman Oaks Component: EWref T1 = 2.57 [ = 0.04 D0 = 29.5Number of stories: 13 Lateral Resisting System: RConcrete MRF


ROOF

-15

-10

-5

0

5

10

15

0 5 10 15 20 25 30 35 40Time [s]

Displ. [cm]


8th FLOOR

-15

-10

-5

0

5

10

15

0 5 10 15 20 25 30 35 40Time [s]

Disp. [cm]


2nd FLOOR

-15

-10

-5

0

5

10

15

0 5 10 15 20 25 30 35 40Time [s]

Disp. [cm]


BASE

-15

-10

-5

0

5

10

15

0 5 10 15 20 25 30 35 40Time [s]

Disp. [cm]

CHAN10 - CHAN10

Computed


27


CSMIP Station: 24322 Earthquake: Northridge Building parameters:Location: Sherman Oaks Component: EWref T1 = 2.92 [ = 0.05 D0 = 29.5Number of stories: 13 Lateral Resisting System: RConcrete MRF


ROOF

-60

-40

-20

0

20

40

60

0 5 10 15 20 25 30 35 40Time [s]

Displ. [cm]


8th FLOOR

-60

-40

-20

0

20

40

60

0 5 10 15 20 25 30 35 40Time [s]

Disp. [cm]


2nd FLOOR

-60

-40

-20

0

20

40

60

0 5 10 15 20 25 30 35 40Time [s]

Disp. [cm]


BASE

-60

-40

-20

0

20

40

60

0 5 10 15 20 25 30 35 40Time [s]

Disp. [cm]

CHAN10 - CHAN10

Computed

CSMIP Station: 24322 Earthquake: Northridge Building parameters:Location: Sherman Oaks Component: EWref T1 = 2.92 [ = 0.05 D0 = 29.5Number of stories: 13 Lateral Resisting System: RConcrete MRF


ROOF

-60

-40

-20

0

20

40

60

0 5 10 15 20 25 30 35 40Time [s]

Displ. [cm]


8th FLOOR

-60

-40

-20

0

20

40

60

0 5 10 15 20 25 30 35 40Time [s]

Disp. [cm]


2nd FLOOR

-60

-40

-20

0

20

40

60

0 5 10 15 20 25 30 35 40Time [s]

Disp. [cm]


BASE

-60

-40

-20

0

20

40

60

0 5 10 15 20 25 30 35 40Time [s]

Disp. [cm]

CHAN10 - CHAN10

Computed

ξ = 0.05 Evalua5on Changes with Amplitude




ROOF

-15

-10

-5

0

5

10

15

0 5 10 15 20 25 30 35 40Time [s]

Displ. [cm]


8TH FLOOR

-15

-10

-5

0

5

10

15

0 5 10 15 20 25 30 35 40Time [s]

Disp. [cm]


2ND FLOOR

-15

-10

-5

0

5

10

15

0 5 10 15 20 25 30 35 40Time [s]

Disp. [cm]


BASE

-15

-10

-5

0

5

10

15

0 5 10 15 20 25 30 35 40Time [s]

Disp. [cm]

CHAN10 - CHAN10

Computed



ROOF

-15

-10

-5

0

5

10

15

0 5 10 15 20 25 30 35 40Time [s]

Displ. [cm]


8TH FLOOR

-15

-10

-5

0

5

10

15

0 5 10 15 20 25 30 35 40Time [s]

Disp. [cm]


2ND FLOOR

-15

-10

-5

0

5

10

15

0 5 10 15 20 25 30 35 40Time [s]

Disp. [cm]


BASE

-15

-10

-5

0

5

10

15

0 5 10 15 20 25 30 35 40Time [s]

Disp. [cm]

CHAN10 - CHAN10

Computed




Earthquake Date Mw Epic.1Dist1[km] Roof1displ.1[in] RDR1Long.1Ewref ξ T T/TWT ξ/ξWT

Whittier 1-Oct-87 6.1 38 4.92 0.00250 0.040 2.54 1.00 1.00

Landers 28-Jun-92 7.3 187 4.88 0.00248 0.045 2.52 0.99 1.13

Northridge 17-Jan-94 6.7 9 12.87 0.00640 0.050 2.92 1.15 1.25

0.00#

0.01#

0.02#

0.03#

0.04#

0.05#

0.06#

0.07#

0.08#

0.000# 0.001# 0.002# 0.003# 0.004# 0.005# 0.006# 0.007#

ξ"

Roof#Dri2#Ra4o#

NR WT

LD

About three 5mes the amplitude of response and somewhat similar level of damping


CSMIP Station: 24601 Earthquake: Landers Building parameters:

Location: Los Angeles Component: EWref T1 = 0.94 [ = 0.031 D0 = 1.4Number of stories: 17 Lateral Resisting System: Shear Walls

Use/Type: Residential Building

ROOF

-6.0

-4.5

-3.0

-1.5

0.0

1.5

3.0

4.5

6.0

0 5 10 15 20 25 30 35 40 45 50 55 60Time [s]

Displ. [cm]

CHAN12 - CHAN04

Computed

13th FLOOR

-6.0

-4.5

-3.0

-1.5

0.0

1.5

3.0

4.5

6.0

0 5 10 15 20 25 30 35 40 45 50 55 60Time [s]

Disp. [cm]

CHAN09 - CHAN04

Computed

7th FLOOR

-6.0

-4.5

-3.0

-1.5

0.0

1.5

3.0

4.5

6.0

0 5 10 15 20 25 30 35 40 45 50 55 60Time [s]

Disp. [cm]

CHAN07 - CHAN04

Computed

BASE

-6.0

-4.5

-3.0

-1.5

0.0

1.5

3.0

4.5

6.0

0 5 10 15 20 25 30 35 40 45 50 55 60Time [s]

Disp. [cm]

CHAN04 - CHAN04

Computed


28





ROOF

-6.0

-4.5

-3.0

-1.5

0.0

1.5

3.0

4.5

6.0

0 5 10 15 20 25 30 35 40 45 50 55 60Time [s]

Displ. [cm]

CHAN12 - CHAN04

Computed

13th FLOOR

-6.0

-4.5

-3.0

-1.5

0.0

1.5

3.0

4.5

6.0

0 5 10 15 20 25 30 35 40 45 50 55 60Time [s]

Disp. [cm]

CHAN09 - CHAN04

Computed

7th FLOOR

-6.0

-4.5

-3.0

-1.5

0.0

1.5

3.0

4.5

6.0

0 5 10 15 20 25 30 35 40 45 50 55 60Time [s]

Disp. [cm]

CHAN07 - CHAN04

Computed

BASE

-6.0

-4.5

-3.0

-1.5

0.0

1.5

3.0

4.5

6.0

0 5 10 15 20 25 30 35 40 45 50 55 60Time [s]

Disp. [cm]

CHAN04 - CHAN04

Computed




ROOF

-6.0

-4.5

-3.0

-1.5

0.0

1.5

3.0

4.5

6.0

0 5 10 15 20 25 30 35 40 45 50 55 60Time [s]

Displ. [cm]

CHAN12 - CHAN04

Computed

13th FLOOR

-6.0

-4.5

-3.0

-1.5

0.0

1.5

3.0

4.5

6.0

0 5 10 15 20 25 30 35 40 45 50 55 60Time [s]

Disp. [cm]

CHAN09 - CHAN04

Computed

7th FLOOR

-6.0

-4.5

-3.0

-1.5

0.0

1.5

3.0

4.5

6.0

0 5 10 15 20 25 30 35 40 45 50 55 60Time [s]

Disp. [cm]

CHAN07 - CHAN04

Computed

BASE

-6.0

-4.5

-3.0

-1.5

0.0

1.5

3.0

4.5

6.0

0 5 10 15 20 25 30 35 40 45 50 55 60Time [s]

Disp. [cm]

CHAN04 - CHAN04

Computed



ξ = 0.033

CSMIP Station: 24601 Earthquake: Northridge Building parameters:



ROOF

-12

-9

-6

-3

0

3

6

9

12

0 5 10 15 20 25 30 35 40 45 50 55 60Time [s]

Displ. [cm]

CHAN12 - CHAN04

Computed

13th FLOOR

-12

-9

-6

-3

0

3

6

9

12

0 5 10 15 20 25 30 35 40 45 50 55 60Time [s]

Disp. [cm]

CHAN09 - CHAN04

Computed

7th FLOOR

-12

-9

-6

-3

0

3

6

9

12

0 5 10 15 20 25 30 35 40 45 50 55 60Time [s]

Disp. [cm]

CHAN07 - CHAN04

Computed

BASE

-12

-9

-6

-3

0

3

6

9

12

0 5 10 15 20 25 30 35 40 45 50 55 60Time [s]

Disp. [cm]

CHAN04 - CHAN04

Computed

CSMIP Station: 24601 Earthquake: Northridge Building parameters:



ROOF

-12

-9

-6

-3

0

3

6

9

12

0 5 10 15 20 25 30 35 40 45 50 55 60Time [s]

Displ. [cm]

CHAN12 - CHAN04

Computed

13th FLOOR

-12

-9

-6

-3

0

3

6

9

12

0 5 10 15 20 25 30 35 40 45 50 55 60Time [s]

Disp. [cm]

CHAN09 - CHAN04

Computed

7th FLOOR

-12

-9

-6

-3

0

3

6

9

12

0 5 10 15 20 25 30 35 40 45 50 55 60Time [s]

Disp. [cm]

CHAN07 - CHAN04

Computed

BASE

-12

-9

-6

-3

0

3

6

9

12

0 5 10 15 20 25 30 35 40 45 50 55 60Time [s]

Disp. [cm]

CHAN04 - CHAN04

Computed



ξ = 0.035 CSMIP Station: 24601 Earthquake: Sierra Madre Building parameters: 1.9

Location: Los Angeles Component: EWref T1 = 0.95 [ = 0.035 D0 = 0.3 Manual



ROOF

0

250

500

750

1000

0.0 1.0 2.0 3.0 4.0 5.0 6.0PERIOD [s]

Accel. [cm/s2]


ROOF

-160-120

-80-40

04080

120160

0 5 10 15 20 25 30 35 40 45 50 55 60Time [s]

Accel. [cm/s2]

CHAN12Computed

13th FLOOR

-160

-120

-80

-40

0

40

80

120

160

0 5 10 15 20 25 30 35 40 45 50 55 60Time [s]

Accel. [cm/s2]

CHAN09Computed

7th FLOOR

-160

-120

-80

-40

0

40

80

120

160

0 5 10 15 20 25 30 35 40 45 50 55 60Time [s]

Accel. [cm/s2]

CHAN07Computed

13th FLOOR

0

250

500

750

1000

0.0 1.0 2.0 3.0 4.0 5.0 6.0PERIOD [s]

Accel. [cm/s2]


7th FLOOR

0

250

500

750

1000

0.0 1.0 2.0 3.0 4.0 5.0 6.0PERIOD [s]

Accel. [cm/s2]


0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

0 1 2 3 4PFA / PGA

x=z/H

Recorded Computed

BASE

-160

-120

-80

-40

0

40

80

120

160

0 5 10 15 20 25 30 35 40 45 50 55 60Time [s]


BASE

0

250

500

750

1000

0.0 1.0 2.0 3.0 4.0 5.0 6.0PERIOD [s]

Accel. [cm/s2]


CSMIP Station: 24601 Earthquake: Sierra Madre Building parameters:



ROOF

-4

-3

-2

-1

0

1

2

3

4

0 5 10 15 20 25 30 35 40 45 50 55 60Time [s]

Displ. [cm]

CHAN12 - CHAN04

Computed

13th FLOOR

-4

-3

-2

-1

0

1

2

3

4

0 5 10 15 20 25 30 35 40 45 50 55 60Time [s]

Disp. [cm]

CHAN09 - CHAN04

Computed

7th FLOOR

-4

-3

-2

-1

0

1

2

3

4

0 5 10 15 20 25 30 35 40 45 50 55 60Time [s]

Disp. [cm]

CHAN07 - CHAN04

Computed

BASE

-4

-3

-2

-1

0

1

2

3

4

0 5 10 15 20 25 30 35 40 45 50 55 60Time [s]

Disp. [cm]

CHAN04 - CHAN04

Computed



Earthquake Date Mw Epic.1Dist1[km] Roof1displ.1[in] RDR1Long.1Ewref ξ T

Sierra Madre 28-Jun-91 5.8 32 1.06 0.0006 0.035 0.95

Landers 28-Jun-92 7.3 168 1.18 0.0007 0.031 0.94

Northridge 17-Jan-94 6.7 32 3.94 0.0022 0.033 1.08


0.00#

0.01#

0.02#

0.03#

0.04#

0.05#

0.06#

0.07#

0.08#

0.0000# 0.0005# 0.0010# 0.0015# 0.0020# 0.0025#

ξ"

Roof#Dri2#Ra4o#

NR SM

LD

Almost four 5mes the amplitude of response and yet similar level of damping

29


Changes in damping ra8o in structures tested in shake tables

(Ager ATC 72-‐2)


2-46 2: General Nonlinear Modeling PEER/ATC-72-1

undergone modest levels of shaking (less than 1% drift) and sustained slight

damage (i.e., hairline cracking, minor spalling), damping values increase to

about 4%. Following significant damage, damping increases beyond 5% up

to a maximum measured value of 11% of critical. In steel braced frames,

damping in the undamaged state is about 0.7% to 1.3% of critical, or about

half of that measured in the reinforced concrete structures.

Table 2-2 Measured Damping versus Level of Damage from Shaking Table Tests

Test Description Measured Damping (% critical)

versus Level of Damage Reference

RC Frames (2) 1-story, 3-bay (1/2 scale)

Undamaged: 1.4% to 1.9% Yielded: 2.1% to 3.7% Significant: 3.9% to 5.4%

Elwood and Moehle (2003)

RC Wall-Frame 7-story (1/5 scale)

Undamaged: 1.9% to 2.2% Slight: 3.5% to 3.7% Significant: 6.9% to 7.5%

Aktan et al. (1983); Bertero et al. (1984)

RC Flat Plate-Frame 2-story, 3-bay (1/3 scale)

Undamaged: 1.2% to 1.7% (negligible drift) Slight: 2.4% to 2.6% (0.002 to 0.011 drift) Moderate: 5.0% (0.017 to 0.034 drift) Significant: 7.2% (0.053 drift)

Diebold and Moehle (1984)

RC Frame 2-story, 1-bay (1/3 scale)

Undamaged: 1.9 to 2.2% Damaged: 3.9 to 5.3%

Oliva (1980)

RC Frame 3- to 6-story, 2-bay (1/3 scale)

Undamaged: 2.7% to 3.7% (0.001 to 0.003 drift) Moderate: 4.9% to 6.4% (0.012 drift) Significant: 9.6% to 11.1% (0.015 to 0.02 drift)

Shahrooz and Moehle, (1987)

RC Frames (12) 1-story, 3-bay (1/3 scale)

Undamaged: 1.4% to 2.9% (2.1% avg., 0.31 COV)

Shin and Moehle (2007)

RC Frame 3-story, 3-bay, (1/3 scale)

Undamaged: 1.9% Moehle et al. (2006)

Steel EBF 1 bay, 6-story (1/3 scale)

Undamaged: 0.7% Whittaker et al. (1987)

Steel CBF 1 bay, 6-story (1/3 scale)

Undamaged: 0.7% to 1.3% Whittaker et al. (1988)

Damping effects measured in shaking table tests can also be inferred from

comparisons with nonlinear analyses of the tests. For example, nonlinear

analyses with 2% viscous damping resulted in accurate comparisons to the

shake table tests by Shin and Moehle (2007). For shaking table tests of a

reinforced concrete bridge pier, Petrini et al. (2008) compared various

viscous damping assumptions made using fiber-type and plastic hinge





1985 1991


(Ager Miranda, 1991) Fundamental period more than 50% longer. Small ambient vibra5on more than two 5mes larger than the EQ inferred lateral s5ffness (about 55% of the lateral s5ffness “vanished”)


30


Changes in period of vibra8on in structures tested in shake tables

(Ager Miranda, 1991)



ξ =c

2mω

Evalua5on Changes with Amplitude From the defini8on of damping ra8o

Suppose that my period changes 15% with higher amplitude of response

1ω

Small amplitude Large amplitude

1.15ω

Subs8tu8ng

ξ =c

2mωSmall amplitude

1.15ξ = 1.15c2mω

Large amplitude

Assuming the mass is the same (a reasonable assump5on) then a period elonga5on lead to an equal increase in damping ra5o, but your damping coefficient, c, (what you actually use in your analysis) has not increased !


Period Elonga8on


Amplitude of Response

Most of the change (increase) in period occurs at very small levels of lateral deforma5on

(Ager Duran and Miranda, 1998)



(Ager Mosquera and Miranda, 2006)

31


Evalua5on Changes with Amplitude Period Elonga8on

Roof Drig Ra8o

Period Elonga8on

Roof Drig Ra8o

Roof Drig Ra8o Roof Drig Ra8o

Most of the change (increase) in period occurs at very small levels of lateral deforma5on (Ager Mosquera and Miranda, 2006)



clear evidence of a strongly linear and decreasing trend with noapparent plateau over the range of amplitudes considered.

As discussed in the previous section, the discrepancies betweenpredicted and in-situ natural frequencies for Building 2 could beattributed to numerous modeling assumptions. For example, giventhe age of the building, it is quite likely that the degree of crackingincluded in finite element models intended to represent thestructure at key design limit states are not yet realized in thestructure at present. To observe if the structure’s frequencies havereduced with time as the result of the natural process of cracking,Building 2’s frequency estimates are presented with time in Fig. 5.While there is potentially a slight softening evident from thisfigure, given the comparatively limited time span of these observa-tions in comparison with the expected life cycle of the building, a

definitive conclusion on the evolution of permanent softeningcannot be reached.

6.2. Overall trends in damping ratios

The resulting damping values for Buildings 1, 2 and 3 arepresented in Figs. 6, 7 and 8, respectively. As expected, the dampingestimates show significantly more scatter than the frequencyestimates for all three buildings and, consistent with the observa-tions in Section 5, the scatter is more pronounced for HPBW. This ofcourse emphasizes the importance of evaluating damping over asuite of events. To facilitate discussion, the average damping valuesfor each building are reported in Table 4. The average dampingestimate for Building 1 is within approximately 10% for the two

0.176

0.177

0.178

0.179

0.18

0.181

0.182

0.183

0.184

0.185

0.170.1720.1740.1760.178

0.180.1820.1840.1860.188

0.19

0 0.1 0.2 0.3 0.4 0.5

HPBWRDTFEM

0 0.2 0.4 0.6 0.8

Normalized Acceleration Normalized Acceleration

Freq

uenc

y (H

z)

Fig. 3. Natural frequency estimates for Building 2 in the in fundamental x-sway mode (left) and y-sway mode (right). The FEM estimated natural frequency for x-sway(not shown) is 0.148 Hz.

0.115

0.116

0.117

0.118

0.119

0.12

0.121

0.122

0 1 2 3 4 50.115

0.116

0.117

0.118

0.119

0.12

0.121

0.122

0.123

0.124

0 1 2 3 4 5

HPBWRDTFEM

Normalized Acceleration Normalized Acceleration

Freq

uenc

y (H

z)

Fig. 4. Natural frequency estimates for Building 3 in the fundamental x-sway mode (left) and y-sway mode (right).

0.176

0.177

0.178

0.179

0.18

0.181

0.182

0.183

0.184

0.185

10/2002 6/2003 3/2004 11/2004 7/2005 3/2006 11/2006 8/2007

Date of Event

10/2002 6/2003 3/2004 11/2004 7/2005 3/2006 11/2006 8/2007

Date of Event

HPBWRDT

0.17

0.172

0.174

0.176

0.178

0.18

0.182

0.184

0.186

0.188

0.19HPBWRDT

Freq

uenc

y (H

z)

Fig. 5. Fundamental frequency estimates for Building 2 plotted against date of event for x-sway mode (left) and y-sway mode (right).

R. Bashor et al. / J. Wind Eng. Ind. Aerodyn. 104–106 (2012) 88–9792

(Ager Bashor et al, 2012)

Most of the change (increase) in period occurs at very small levels of lateral deforma5on

dependence may be evidenced by the fact that RDT dampingvalues in the y-axis of all three buildings are larger in Event 2 thanEvent 1.

In previous analysis of the data from these buildings, dampingvalues similar to the RDT results reported here were observed forBuilding 1, which tends to manifest comparable levels of dampingon both axes. In the case of Building 2, y-sway damping valueswere previously observed to be larger than x-sway (Kijewski-Correa and Pirnia, 2007), and this was affirmed by the RDT resultsin this study. While Building 2 would be generally expected tohave greater damping than Building 1, by virtue of its use ofconcrete, what is more interesting is the stark difference indamping values between the two axes of this concrete building.Reasons for this variation in damping along the two axes of thisbuilding were explored in Kijewski-Correa and Pirnia (2007) forthis building and for other buildings in Erwin et al. (2007) andBentz and Kijewski-Correa (2008). These studies have demon-strated that structural systems with greater degrees of frameaction tend to dissipate more energy than systems that aredominated by cantilever action (member level axial deforma-tions). In Building 2, shear walls and outriggers engage theexterior columns to achieve global cantilever action in thex-direction, whereas the y-direction is dominated by compara-tively more frame action as the beams and slabs are the primarymechanisms to engage the lateral resistance of the building.Therefore the in-situ observations reported herein are consistentwith the hypothesis that frame-dominated systems yield higherlevels of damping. Even when comparing the RDT damping levelsin the two steel buildings, one may hypothesize that Building 1,which has been observed to be dominated by cantilever action asan essentially pure tube (Bentz and Kijewski-Correa, 2008) wouldhave less damping than Building 3, whose panel zone sheardeformations have been extensively studied (Bentz et al., 2010).In total these observations help to provide a more rational basisfor the levels of damping to be assumed in design, as opposed tothe crude respective assumptions of 1% or 2% critical for steel andconcrete.

5.2. Comparison of results with finite element models

One of the primary objectives of the CFSMP is to validateassumptions made in the development of finite element modelsused in design by comparing their predictions and in-situ values.Comparisons of the results in Tables 2 and 3 to the designpredictions in Table 1 affirms that Building 1’s in-situ funda-mental sway frequencies show excellent agreement with thedesign predictions, which may be explained by the fact that, asmentioned previously, the structure’s elements are engagedprimarily axially as a structural tube and may thereby be less

susceptible to uncertainties in modeling material, section orconnection details. Building 2 is 20% stiffer in-situ in the x-direction and 13% stiffer in-situ in the y-direction than originallypredicted by the finite element model, while the converse is truefor Building 3 (11% softer in-situ), reaffirming observations inprevious studies (Kijewski-Correa et al., 2006). Moreover, the in-situ values for Building 2 suggest a greater consistency betweenthe fundamental mode frequencies in sway than predicted byfinite element models. A variety of sources have been andcontinue to be explored to determine the causes of this discre-pancy, from rigid off sets in connection modeling, to the influenceof panel zones, to the assumptions regarding in-situ materialproperties and the degree of cracking in concrete elements(Kijewski-Correa et al., 2006; Bentz et al., 2010).

6. Analysis of overall trends in dynamic properties

In the following, several hundred wind events were identifiedas stationary, i.e., having 80% of triggered data in a given eventpass the aforementioned tests, and were analyzed using the samesystem identification approaches discussed previously. The num-ber of records available for analysis varies for each building,depending on the number of times it triggers. In this study, 500events will be analyzed for Building 1 and 200 for each ofBuildings 2 and 3—events are defined as those having at leastfive triggered 1 h time histories.

6.1. Overall trends in frequency estimates

The natural frequency estimates for Buildings 1, 2, and 3 fromboth HPBW and RDT are shown in Figs. 2, 3 and 4, respectively.For reference, the natural frequency assumed for the finiteelement model is indicated in the figures by a thick horizontalline except in instances where discrepancies between in-situ dataand predictions are so great that they cannot be reasonablyshown on the same figure. It should be noted that the amplitudeof responses for each of the buildings varies widely, as does thenumber of triggered events displayed. While more pronouncedscattering may be evident with increasing amplitude, particularlywith Building 2, this cannot be fully concluded given the limitedamount of data. Still, clear evidence of amplitude dependence andsoftening with increased response is displayed for all threebuildings, consistent with initial observations from a narrowersubset of CFSMP data in Kijewski-Correa and Pirnia (2007).Interestingly, in some cases, though recognizing the limitedextent of the amplitude ranges available for analysis here, thefrequency softening appears to plateau (see Building 1 x-axis andboth axes of Building 2), whereas in the case of Building 3, there is

0.202

0.203

0.204

0.205

0.206

0.207

0.208

0.209

0.21

0 0.2 0.4 0.6 0.8Normalized Acceleration Normalized Acceleration

Freq

uenc

y (H

z)

0.14

0.141

0.142

0.143

0.144

0.145

0.146

0 0.5 1 1.5 2 2.5

HPBWRDTFEM

Fig. 2. Natural frequency estimates for Building 1 in fundamental x-sway mode (left) and y-sway mode (right).

R. Bashor et al. / J. Wind Eng. Ind. Aerodyn. 104–106 (2012) 88–97 91



(Ager Fang et al, 1999)

Several wind studies have also documented that increments in period and damping tend to saturate once you reach a certain amplitude

2-44 2: General Nonlinear Modeling PEER/ATC-72-1

focus of wind studies, there are more data available for tall buildings

subjected to wind vibrations than to earthquake shaking, worldwide.

Information from these studies, however, is still limited by the number of

instrumented buildings and relatively small displacement amplitudes.

Moreover, there are some differences in the loading effects between wind

and earthquakes that can affect response. For example, wind introduces

aero-elastic damping associated with fluid dynamics of airflow, which is not

present under earthquake shaking. Also, nonlinearities in the soil-

foundation-structure interface are expected to have a larger effect on

earthquake-induced motions than wind-induced motions.

The amplitude dependence of damping for wind vibration in buildings has

been well established by Jeary (1986) and others. Figure 2-26 shows a plot

of damping measured by Fang et al. (1999) in a 30-story (120 meter)

building that demonstrates the typical amplitude dependence considered in

wind engineering. In this example, damping was calculated from wind

vibration data collected over a two year period, which provided

measurements at various amplitudes. As shown, damping increases from

negligible amounts, to about 0.5% critical damping in the so-called “high

amplitude plateau.”

It should be noted, however, that even the largest recorded amplitudes in the

high amplitude plateau are on the order of 0.02% roof drift. This is well

below the amplitudes associated with serviceability or safety limit states for

strong ground motions (i.e., drifts on the order of yield-level drifts of 0.5% to

1%). Unfortunately, there are no studies relating damping at the high

amplitude plateau for wind loading to damping at larger drifts expected under

earthquake shaking.

Figure 2-26 Illustration of amplitude dependence of measured damping

under wind loading (Fang et al., 1999).


Summary and Conclusions

•  Results from a comprehensive study on damping ra8os inferred from records obtained in instrumented buildings subjected to earthquakes.

•  This study is different from previous studies in a number of ways: o  It exclusively uses data from earthquake loading that was large enough to

digi8ze the analog data. o  Much larger number of data points both in number of buildings and number of

damping ra8os o  All data was inferred using a common method for all data which avoids mixing

data from different methods. o  Uses a system ID which is directly relevant to how most structural engineers

will be using the data (modal response history analysis assuming a fixed-‐base).

•  Damping ra8os are characterized by very large variability, which means that recommending or using “a value” could lead to significant errors. A simple but smarter approach is to contemplate a range of values (not necessarily max and min, it could be plus or minus one standard devia8on).

•  Damping ra8os are highly skewed to larger values which together with the large

variability means than mean values can be quite a bit larger than median values.

32


Summary and Conclusions

•  Mean damping ra8os from RC building are sta8s8cally higher than concrete buildings, indica8ng that the common prac8ce of assuming 5% damping for all buildings is not very good.

•  Similar to previous studies, this study has shown there is an important decrease in damping ra8os with height. This reduc8on is primarily due to reduc8on in radia8on damping with decreasing frequency (increasing period) and increasing slenderness ra8o.

•  Results from this study suggest that recent recommenda8ons of using 2 or 2.5% for very tall buildings may lead to overes8ma8ons of the level of damping present in very tall buildings.

•  Data does not support the common idea of important increments in level of damping with increasing response amplitude. Although increments do occur, a significant por8on of this increment in damping ra5o occurs at very small levels of deforma8on and is possibly due to period elonga8ons in these ranges of amplitudes but are not necessarily increments in the actual level of damping in the structure.


Some references on previous work

Hart, G. C., & Vasudevan, R. (1975). Earthquake design of buildings: damping.Journal of the Structural Division, 101(1), 11-‐30. Haviland, R. (1976). A study of the uncertain8es in the fundamental transla8onal periods and damping values for real buildings. Massachuse;s Ins8tute of Technology, Department of Civil Engineering, Constructed Facili8es Division. Lagomarsino, S. (1993). Forecast models for damping and vibra8on periods of buildings. Journal of Wind Engineering and Industrial Aerodynamics, 48(2), 221-‐239. Tamura, Y., & Suganuma, S. Y. (1996). Evalua8on of amplitude-‐dependent damping and natural frequency of buildings during strong winds. Journal of wind engineering and industrial aerodynamics, 59(2), 115-‐130. Suda, K., Satake, N., Ono, J., & Sasaki, A. (1996). Damping proper8es of buildings in Japan. Journal of wind engineering and industrial aerodynamics,59(2), 383-‐392.


Some references on previous work

Goel, R. K., & Chopra, A. K. (1997). Vibra8on proper8es of buildings determined from recorded earthquake mo8ons. Earthquake Engineering Research Center, University of California. Satake, N., Suda, K. I., Arakawa, T., Sasaki, A., & Tamura, Y. (2003). Damping evalua8on using full-‐scale data of buildings in Japan. Journal of structural engineering, 129(4), 470-‐477. Fritz, W. P., Jones, N. P., & Igusa, T. (2009). Predic8ve models for the median and variability of building period and damping. Journal of structural engineering,135(5), 576-‐586. Smith, R., Merello, R., & Willford, M. (2010). Intrinsic and supplementary damping in tall buildings. Proceedings of the ICE-‐Structures and Buildings,163(2), 111-‐118.

miranda damping ratios v5 for seaonc

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