Floor Response Spectra for Ultimate and

Serviceability Limit States of Earthquakes

SR Uma (Presenting Author) John Zhao

Andrew King

GNS Science

Outline

• Acceleration demand on Non-structural components

• Under two limit states:

- Ultimate limit state (ULS)

- Serviceability limit state (SLS)

• Adequacy of NZ standard provisions

- in NZS 1170.5 / NZS 4219

Does the force design for ULS always take

care of forces in SLS conditions?

GNS Science

New Zealand - Gisborne Earthquake, Dec 2007

(M 6.6)

Failure of suspended

components

< 50% of Design earthquake

GNS Science

What demand is on NSC?

Period of component

F1

F2

F3

F4

PGA

PFA2

PFA1

PFA3

PFA4

PFA

Acceleration history Response spectra

G

GNS Science

Period of component

Sac/P

FA

Design approach

Floor Height

Coefficient

(FHC)

Component

Amplification Factor

(CAF)

PFA i / PGA

PFA1

PGA

PFA2

PFA3

PFA4

GNS Science

Parameters for design provisions

Floor Height Coefficients Component Amplification factor

0

0.2

0.4

0.6

0.8

1

0 1 2 3 4

Floor Height Coefficient

h/H

Low -rise

High-rise

(NZS)

0

0.2

0.4

0.6

0.8

1

0 1 2 3 4

Floor Height Coefficient

h/H

(IBC)

0

0.5

1

1.5

2

2.5

3

0 1 2 3

Component Period, Tp

Am

plifica

tio

n fa

cto

r,C

i(T

p)

0

0.5

1

1.5

2

2.5

3

0 1 2 3

Component Period, (Tp /TB)

Am

plifica

tio

n fa

cto

r,C

i(T

p)

(NEHRP)

0p p Hi i pC T C C C T

Basic design force (NZS)

GNS Science

NZS Provisions with International Standards

• Maximum limit on design coefficient

– NZS: 3.6 Wp

– IBC: 1.6 SDsIp Wp

• Performance factors or Reduction factor

– NZS: 0.45 to 0.85

– IBC: 0.08 to 1.0

GNS Science

RECORD

NAME

COMP. STATION NAME EARTHQUAKE NAME MW R (KM)

500 year return period (Ultimate Limit State)

ARC2 EW Arcelik 1999 Kocaeli, Turkey 7.3 14

DUZ2 270 Duzce 1999 Kocaeli, Turkey 7.3 15

ELC2 270 El Centro 1940 El Centro 7.0 7

LAU1 NS La Union 1985 Michoacan 8.1 121

LUC1 260 Lucern 1992 Landers 7.3 2

K0392 NS HKD085 2003-09-26 Japan 8.3 45

TAB2 NS Tabas 1978 Tabas, Iran 7.4 2

50 year return period (Serviceability Limit State)

A-IV1/2 90/360 Wildlife Liquef. Array 1987 Superstition Hills 6.2 18

B-BRA1/2 225/315 Brawley Airport 1987 Superstition Hills 5.8 17

B-LAD1/2 180/270 Bishop - LADWP 1986 Chalfant Valley 5.8 23

H-PTS1/2 225/315 Parachute Test Site 1979 Imperial Valley 6.5 12

Earthquake record components

• Deaggregation analyses

• Scaled to the design spectrum• Wellington, Shallow soil site

GNS Science

Building model

P-Delta

column• Plastic hinges

3 storey and 10 storey (with a roof) buildings, Ductility = 6

Two dimensional Models

SAP 2000

Nonlinear link elements (Takeda) at plastic hinges

Modal Periods: 3 storey building – 1.1s and 0.35s

10 storey building - 2.3s and 0.75s

1

3

2

R

GNS Science

3 storey 10 storey

Floor height coefficient, HiC

0

1

2

3

4

0.0 1.0 2.0 3.0 4.0 5.0

PFA/C(0)

Flo

or

leve

l

ULS

ULS-84

SLS

SLS-84

NZS

RC30

1

2

3

4

5

6

7

8

9

10

11

0.0 1.0 2.0 3.0 4.0 5.0

PFA/C(0)

Flo

or

leve

l

ULS

ULS-84

SLS

SLS-84

NZS

RC10

PFA (Analysis)

(i) Constant up the height

(ii) << Code provisions

Reasons

• High frequency components filtered

• De-amplification due to non-linear behaviour

• Code provisions – maximum responses

ULS : 0.4g

SLS : 0.2g

NZS NZS

GNS Science

Component amplification - ULS

3 Storey Building 10 Storey Building

0.0

1.0

2.0

3.0

4.0

5.0

6.0

0.0 0.5 1.0 1.5 2.0

Tp/TB1

Sac/C

(0)

1st

4th

7th

10th

NZS

NZS-inel

RC10

ULS

0.0

1.0

2.0

3.0

4.0

5.0

6.0

0.0 0.5 1.0 1.5 2.0 2.5 3.0

Tp/TB1

Sac/C

(0)

1st

2nd

3rd

Roof

NZS

NZS-inel

RC3

ULS

Design envelopes for:

(1) Non- ductile components

(2) Ductile fixing and braced to the structure – “performance factor”, Cph is used

0.45 < Cph < 0.85

conservative conservative

NZS_NonDuctile

NZS_Ductile

NZS_NonDuctile

NZS_Ductile

GNS Science

Component amplification - SLS

(Lower

storeys)

0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

0.0 0.5 1.0 1.5 2.0 2.5 3.0

Tp/TB1

Sac/C

(0)

3rd

3rd-84th

Roof

Roof-84th

NZS

RC3

SLS

0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

0.0 0.5 1.0 1.5 2.0 2.5 3.0

Tp/TB1

Sac/C

(0)

1st

1st-84th

2nd

2nd-84th

NZS

RC3

SLS

0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

0.0 0.5 1.0 1.5 2.0

Tp/TB1

Sac/C

(0)

1st

1st-84th

NZS-1st

RC10

SLS

0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

0.0 0.5 1.0 1.5 2.0

Tp/TB1

Sac/C

(0)

7th

7th-84th

10th

10th-84th

NZS

RC10

SLS

• “Resonance effect” at modal periods

• Design envelopes with performance factors =1

(Upper

storeys)

3 storey 10 storey

NZSNZS

NZS

NZS

GNS Science

Acceleration demand for Low-rise building

Short period components Long period components

ULS

SLS

0P P Hi i PC T C C C T

NZ Standard

Overall coefficient

√√

? ?

√ ?- Conservative - Marginal/

Unconservative

1

2

3

4

0.0 5.0 10.0 15.0 20.0 25.0 30.0 35.0

Cp (Tp)

Flo

or

leve

l

Med 84th NZS

RC3

SM

ULS

1

2

3

4

0.0 5.0 10.0 15.0

Cp (Tp)

Flo

or

leve

l

Med 84th NZS

RC3

SM

SLS

1

2

3

4

0 5 10 15 20 25 30 35

Cp (Tp)

Flo

or

leve

l

Med 84th NZS

RC3

FM

ULS

1

2

3

4

0.0 5.0 10.0 15.0

Cp (Tp)

Flo

or

leve

l

Med 84th NZS

RC3

FM

SLS

NZS NZS

NZS

NZS

GNS Science

Long period components Short period components

ULS

SLS

0P P Hi i PC T C C C TOverall coefficient

?

√

NZ Standard√ ?- Conservative - Marginal/

Unconservative

Acceleration demand for High-rise building

1

2

3

4

5

6

7

8

9

10

11

0.0 5.0 10.0 15.0 20.0 25.0 30.0 35.0

Cp (Tp)

Flo

or

leve

l

Med 84th NZS

RC10

SM

ULS

1

2

3

4

5

6

7

8

9

10

11

0.0 5.0 10.0 15.0

Cp (Tp)

Flo

or

leve

l

Med 84th NZS

RC10

SM

SLS

√

√

1

2

3

4

5

6

7

8

9

10

11

0.0 5.0 10.0 15.0 20.0 25.0 30.0 35.0

Cp (Tp)

Flo

or

leve

l

Med 84th NZS

RC10

FM

ULS

1

2

3

4

5

6

7

8

9

10

11

0.0 5.0 10.0 15.0

Cp (Tp)

Flo

or

leve

l

Med 84th NZS

RC10

FM

SLS

NZSNZS

NZS

NZS

GNS Science

Low cycle fatigue at high frequency?

Response of a component with a natural period of 0.36s

-15

-10

-5

0

5

10

15

0 5 10 15 20 25 30Time (s)

Tota

l accele

ration (

m/s

2)

Component damp ratio 5%

Response of a component with a natural period of 0.36s

-25

-20

-15

-10

-5

0

5

10

15

20

25

0 5 10 15 20 25 30

Time (s)

Tota

l accele

ration (

m/s

2) Component damp ratio 2%

5 % damping 2 % damping

(Serviceability limit state earthquake at 2nd floor of 3 storey building)

Damage accumulation due to low cycle fatigue?

Reduced damping ratio at SLS

Design acceleration Design accelerationNZS

NZS

NZS

NZS

GNS Science

Practical implications on components at SLS

Rigid mounted (Tp < 0.06s) Braced to the structure Vibration isolated

• Non ductile

• Overly conservative design

in ULS

• “ductile” performance

expected

• lesser damping at SLS

• Low cycle fatigue

• knowledge on (Tp/TB)

appears to be essential

to avoid “Resonance

effect” at least for low-

rise buildings with

TB < 0.75

GNS Science

NZS design provisions

Component Period, Tp LS Low-rise High-rise

ShortULS

SLS

LongULS

SLS

√

?

?

√√

?

?- Conservative - Unconservative

√ √

√

GNS Science

Conclusions

• Constant Peak Floor Acceleration up the height except the roof

– Quite different from the current provisions

– Is current provisions overly conservative for very rigid components, i.e.

Tp closer to zero

• “Resonance effect” more pronounced in SLS

– not represented in NZ design standards

• Spectral amplification exceeds the design envelope

– At building periods

– More in SLS earthquakes

• Adequacy of design standards for overall Cp (Tp)

– Likely to exceed the standard’s provisions in SLS conditions

– Adequate in ULS conditions

GNS Science

Does the force design for ULS always take

care of forces in SLS conditions?

Not Always…

GNS Science

Thank you!

GNS Science

Earthquake loss

• Losses due to

– Structural Damage

– Non-structural components/ contents Damage

• Study of NSC – important component of PBEE

Typical investments in building construction (after E. Miranda)

GNS Science

Response of flexible components in tall

buildings

• Flexible components – such as spring mounted

components – or very flexible and lightly

damped components – vibration associated with

the resonance of these flexible systems with the

harmonic vibration of buildings, particularly tall

buildings, can be catastrophic and special

design is required – NZS 1170.5 commentary