Seismic Simulation of Bridge Systems Under Multi-directional Motions

Seismic Simulation of Bridge Systems Under Multi-directional

Motions

Seismic Simulation of Bridge Systems Under Multi-directional

Motions

Jian ZhangAssistant Professor

Yuchuan Tang and Shi-Yu XuGraduate Student Researcher

Department of Civil and Environment EngineeringUniversity of California, Los Angeles

2

UCLA Progress & Scope of WorkUCLA Progress & Scope of Work Selected 4 ground motion suites that

incorporate the site-dependent probabilistic hazard analysis and ground motion disaggregation analysis.

Selected 2 bridge prototypes that are distinctive in terms of structural characteristics and dynamic properties.

Conducted linear and nonlinear time history analysis of prototype bridges subjected to multi-directional ground shakings and evaluate the effect of vertical motions on seismic demand.

Implement nonlinear structural and foundation elements to realistically capture the response under multi-directional ground shakings.

3

Ground Motion SelectionGround Motion Selection Selection Procedure

Select the Los Angeles Bulk Mail Building (LABMB) site used by PEER Building Benchmark project for prototype bridges (NEHRP Class D)

Conduct site-specific Probabilistic Seismic Hazard Analysis (PSHA) using HAZ software to evaluate the probability of exceeding a given intensity measure within a given time periodMultiple Hazard Levels: 2% in 50 Years and 50% in 50 YearsStructural Period of Interest: T=0.5s (Bridge #4) and T=1.5s

(Bridge #8) Conduct dis-aggregation analysis to select ground motion

records that reasonably represent possible future realizations of ground shaking for the appropriate ground intensity measure levelMaginitude (M), Distance (r) and Epsilon (ε)Fault Type, Directivity and Site Condition

4

Uniform Hazard CurvesUniform Hazard Curves

Structure

Period (s)

Spectral Acceleration (g)

2% in 50 yrs

50% in 50 yrs

0 0.58 0.25

0.1 1.14 0.46

0.2 1.48 0.58

0.3 1.47 0.58

0.4 1.35 0.51

0.5 1.24 0.47

0.75 0.99 0.38

1.0 0.82 0.30

1.25 0.69 0.26

1.5 0.61 0.22

2 0.47 0.18

Note: 5% damping

Uniform Hazard at LABMB Site

5

Ground Motion Record Selection CriteriaGround Motion Record Selection Criteria

Magnitude (M) and Site-Source Distance Range (r) Epsilon (ε)

The physical interpretation of ε is the offset between the value of the record’s intensity measure and the expected value from an attenuation relationship.

Parameter ε is model dependent. Attenuation relationship by Abrahamson and Silva (1997) is used to quantify ε.

Positive ε (“peak record”) motions lead to reduced seismic demand as building softens.

Negative ε (“valley record”) motions lead to larger seismic demand as building softens.

Scaling Factor Scaling is needed to enforce a consistent value of target

intensity measure Scaling factor is obtained from the geometric mean of a

single recording and applied equally to all components of the recorded motions

6

Seismic Hazard Disaggregation (T=0.5s)Seismic Hazard Disaggregation (T=0.5s)

0-10

10-2

0

20-3

0

30-4

0

40-5

0

50-6

0

60-7

0

70-8

0

80-9

0

90-1

00

100-

1000

5.0-5.5

5.5-6.06.0-6.5

6.5-7.07.0-7.5

7.5-8.08.0-8.5

0.00E+00

2.00E-02

4.00E-02

6.00E-02

8.00E-02

1.00E-01

1.20E-01

1.40E-01

1.60E-01

1.80E-01

2.00E-01

Rel

ativ

e C

on

trib

uti

on

Distance

Magnitude

Hazard Level: 2% in 50 Years (Targeted PGA=1.24g)

5.0-5.5

6.0-6.5

7.0-7.5

8.0-8.5

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

Distance

Magnitude

For most hazard levels, the intensity measure is dominated by two clusters of magnitude-distance combinations: Cluster A: Small r and small M Cluster B: large r and large M


7

Seismic Hazard Disaggregation (T=1.5s)Seismic Hazard Disaggregation (T=1.5s)

For most hazard levels, the intensity measure is dominated by two clusters of magnitude-distance combinations: Cluster A: Small r and small M Cluster B: large r and large M

5.0-5.5

6.0-6.5

7.0-7.5

8.0-8.5

0.00E+00

2.00E-02

4.00E-02

6.00E-02

8.00E-02

1.00E-01

1.20E-01

1.40E-01

1.60E-01

1.80E-01

2.00E-01

Distance

Magnitude

5.0-5.5

6.0-6.5

7.0-7.5

8.0-8.5

0.00E+00

2.00E-02

4.00E-02

6.00E-02

8.00E-02

1.00E-01

1.20E-01

1.40E-01

1.60E-01

1.80E-01

2.00E-01

Distance

Magnitude



8

Selected Earthquake MotionsSelected Earthquake Motions

Earthquake Station Peak Ground Acceleration (g) Scaling

Factor

Horizontal-X

Horizontal-Y

Vertical

1987 Whittier Narrows

Studio City – Coldwater

0.177 0.231 0.067 2.79


N. Hollywood 0.101 0.250 0.059 3.42


Santa Fe Springs 0.336 0.378 0.206 1.20


Rancho Los Cerritos

0.159 0.189 0.083 2.84

1994 Northridge 90013 Beverly Hills

0.416 0.516 0.326 0.74

1992 Cape Mendocino

Rio Dell Overpass 0.249 0.529 0.131 1.57


Campton - Castlegate

0.297 0.333 0.137 2.10

1986 Chalfant Valley

Zack Brothers Ranch

0.447 0.400 0.321 1.04

1983 Coalinga Pleasant Valley P.P.

0.592 0.551 0.293 0.89

1992 Cape Mendocino

89156 Petrolia 0.586 0.662 0.163 1.06

1994 Northridge Sepulveda VA Hospital

0.532 0.669 0.467 0.79

1986 N. Palm Springs

Whitewater Trout Farm

0.492 0.612 0.471 1.04

Hazard Level: 2% in 50 Years; Dissaggregation Period: 0.5s

9



Factor

Horizontal-X

Horizontal-Y

Vertical


Desert Hot Springs

0.331 0.271 - 0.93

1989 Loma Prieta

Hollister Diff. Array

0.211 0.251 0.154 0.72

1979 Imperial Valley

SAHOP Casa Flores

0.287 0.496 0.379 0.68

1971 San Fernando

Lake Hughes #1 0.145 0.11 0.098 1.85


Campton - Castlegate

0.297 0.333 0.137 0.8


Obregon Park 0.322 0.400 0.144 1.02


Zack Brothers Ranch

0.447 0.4 0.321 0.39


6621 Chihuahua 0.27 0.254 0.218 0.87

1983 Coalinga Parkfield – Fault Zone

0.282 0.274 0.097 0.83

1992 Cape Mendocino

Rio Dell Overpass 0.244 0.529 0.131 0.59

1994 Northridge LA – Saturn St 0.475 0.413 0.078 0.46


Whitewater Trout Farm

0.492 0.612 0.471 0.39


10

Acceleration Spectra of Motions Selected for T=0.5sAcceleration Spectra of Motions Selected for T=0.5s

Hazard Level: 2% in 50 Yrs

Hazard Level: 50% in 50 YrsA=1.24g

A=0.47g

11



Factor

Horizontal-X

Horizontal-Y

Vertical

1984 Morgan Hill

Hollister City Hall 0.071 0.071 0.118 5.39


Fletcher Drive 0.171 0.213 0.103 6.11

1983 Coalinga Parkfield – Fault Zone

0.282 0.274 0.097 1.87



0.594 0.694 0.435 2.64


6621 Chihuahua 0.27 0.254 0.218 3.11


Zack Brothers Ranch

0.447 0.4 0.321 2.02

1994 Northridge 90013 Beverly Hills

0.416 0.516 0.326 1.07

1999 ChiChi Taiwan

HWA011 0.102 0.089 0.039 2.71

1999 ChiChi Taiwan

KAU020 0.078 0.055 0.02 3.15

1999 ChiChi Taiwan

HWA013 0.118 0.142 0.064 2.57

1999 Kocaeli Turkey

Ambarli Termil Santrali

0.249 0.184 0.079 2.32


12


Earthquake Station Name Peak Ground Acceleration (g) Scaling

Factor

Horizontal-X

Horizontal-Y

Vertical

1983 Coalinga Parkfield – Vineyard

0.167 0.23 0.082 1.37


Whittier N. Dam 0.229 0.316 0.505 2.68

1994 Northridge Century City CC North

0.256 0.222 0.116 1.00

1971 San Fernando

Lake Hughes #1 0.145 0.11 0.098 1.92

1992 Landers Yermo Fire Station

0.245 0.152 0.136 0.65


Zack Brothers Ranch

0.447 0.4 0.321 0.73

1999 Kocaeli Turkey

Iznik Karayollari Sefligi

0.136 0.098 0.079 0.79

1999 Kocaeli Turkey

Havaalani 0.09 0.083 0.055 1.95

1989 Loma Prieta

APEEL 2E 0.171 0.139 0.095 1.47

1999 Kocaeli Turkey

Bursa Tofas Fabrikasi

0.103 0.108 0.048 1.41

1992 Landers Indio – Coachella Canal

0.104 0.109 0.042 1.68

1999 ChiChi Taiwan

KAU020 0.078 0.055 0.02 1.14


13

Acceleration Spectra of Motions Selected for T=1.5sAcceleration Spectra of Motions Selected for T=1.5s

A=0.61g

A=0.22gHazard Level: 2% in 50 Yrs

Hazard Level: 50% in 50 Yrs

14

Prototype BridgesPrototype Bridges Two box girder concrete bridges (FHWA Bridge #4

and 8) are selected as prototype bridges for analysis

Structural Charateristics

Design Example #4 Design Example #8

Span/Span LengthThree-span continuous, 320 ft long

Five-span continuous, 500 ft long

Pier TypeTwo-column integral bent, monolithic at column top, pinned at base

Two-column integral bent, monolithic at column top and base

Abutment Type SeatStub abutment with diaphragm

Foundation Type Spread Footing Pile foundation

Expansion JointsExpansion bearings & Shear Keys

Expansion Bearings

Force Resisting Mechanism

Longitudinal: intermediate bent columns & free longitudinal movement at abutmentsTransverse: intermediate bent columns & abutments

Longitudinal: intermediate bent columns and abutment backfillTransverse: intermediate bent columns and abutment backfill

15

Bridge #4 – Structural DetailsBridge #4 – Structural Details

16

Bridge #4 – Pier DetailsBridge #4 – Pier Details

Bent #1 Bent #2

Pier height (ft)

20 20

Foundation (ft)

14 x 14 14 x 14

Pier Cross Section

48”

34 #11 bars

Moment-Curvature Curve

17

Bridge #4 – Surface Foundation DetailsBridge #4 – Surface Foundation Details

Half of footing plan dimension : L = B = 7 ft

Spring and dashpot coefficients based on elastic half-space model by Meek & Wolf (1993)

K11= 1.50E9 N/m =1.03E5 kips/ft, C11= 1.56E7 N.s/m K22= 1.50E9 N/m = 1.03E5 kips/ft, C22= 1.56E7 N.s/m K33= 1.38E9 N/m = 9.44E4 kips/ft, C33= 2.46E7 N.s/m K44= 9.66E9 N*m/rad = 7.12E6 kip*ft/rad C44= 1.08E7 N*m*s/rad K55= 9.66E9 N*m/rad = 7.12E6 kip*ft/rad C55= 1.08E7 N*m*s/rad K66= 1.56E10 N*m/rad = 1.15E7 kip*ft/rad C66= 1.45E7 N*m*s/rad

Equivalent Radii : R = (4*L*B/π)^0.5 = 7.9 ft

18

Bridge #4 – Dashpot of Surface FoundationBridge #4 – Dashpot of Surface Foundation

)1(2

)( 0 aczz

21

)1(2

32

3)(

3

0

aczz

)2(8

)( 0 acxx

32

3)( 0

ac x

sec/10*4563.2)(*** 7

0 m

NacACC zzpzz

sec/10*0752.1)(*** 7

0 rad

mNacICC xpx

sec/10*5589.1)(*** 7

0 m

NacACC xxpxx

sec/10*4548.1)(*** 7

0 rad

mNacICC zpz

Cross area : A = 2L*2B = 18.209 m^2

Thickness : D = 3.5ft = 1.067 m

Soil density : ρ = 1.835 Mg/m^3

Shear wave velocity : Cs = 360 m/sec ; Cp=2*Cs

(Soil Type II, SPT N=50)

Poisson’s ratio : ν = 0.35

19

Bridge #4 – Abutment Modeling (Bin4)Bridge #4 – Abutment Modeling (Bin4)

EQ Strain G1(N/m2) η Kh (N/m) Ch(N*s/

m) Kv (N/m) Cv(N*s/

m) SFA-CAS000 1.00E-03 3.97E+07 0.347471 5.67E+08 1.96E+07 1.91E+09 3.92E+07 2.10

A-CAS270 1.38E-03 3.35E+07 0.384445 4.79E+08 1.81E+07 1.62E+09 3.62E+07 3.13

A-CO2092 7.01E-04 4.74E+07 0.302051 6.78E+08 2.62E+07 2.29E+09 5.23E+07 2.79

A-CO2182 8.45E-04 4.32E+07 0.32642 6.18E+08 2.19E+07 2.09E+09 4.38E+07 2.79

A-CWC180 3.37E-04 6.39E+07 0.21669 9.14E+08 4.35E+07 3.09E+09 8.70E+07 3.42

A-CWC270 1.52E-03 3.14E+07 0.396957 4.49E+08 1.82E+07 1.52E+09 3.63E+07 3.42

A-EJS048 7.87E-04 4.48E+07 0.317294 6.40E+08 2.32E+07 2.16E+09 4.65E+07 1.20

A-EJS318 8.76E-04 4.25E+07 0.330623 6.08E+08 2.13E+07 2.05E+09 4.27E+07 1.20

A-LBR000 5.33E-04 5.35E+07 0.268455 7.65E+08 3.52E+07 2.58E+09 7.04E+07 2.84

A-LBR090 9.03E-04 4.19E+07 0.334072 5.99E+08 2.09E+07 2.02E+09 4.18E+07 2.84

A-ZAK270 7.96E-04 4.45E+07 0.319122 6.36E+08 2.30E+07 2.15E+09 4.59E+07 1.04

A-ZAK360 8.87E-04 4.22E+07 0.332241 6.04E+08 2.11E+07 2.04E+09 4.23E+07 1.45

H-PVY045 6.70E-04 4.83E+07 0.297031 6.91E+08 2.73E+07 2.33E+09 5.46E+07 0.89

H-PVY135 7.85E-04 4.48E+07 0.31702 6.41E+08 2.33E+07 2.16E+09 4.66E+07 0.89

MUL009 3.96E-04 6.03E+07 0.23374 8.62E+08 4.41E+07 2.91E+09 8.82E+07 0.74

MUL279 4.96E-04 5.51E+07 0.259936 7.88E+08 3.78E+07 2.66E+09 7.57E+07 0.74

PET000 8.34E-04 4.35E+07 0.324841 6.22E+08 2.21E+07 2.10E+09 4.42E+07 1.06

PET090 8.88E-04 4.21E+07 0.332943 6.02E+08 2.10E+07 2.03E+09 4.21E+07 1.06

RIO270 8.63E-04 4.29E+07 0.328576 6.13E+08 2.16E+07 2.07E+09 4.32E+07 1.57

RIO360 2.91E-04 6.74E+07 0.200787 9.64E+08 3.89E+07 3.25E+09 7.77E+07 0.71

SPV270 6.47E-04 4.91E+07 0.292623 7.02E+08 2.83E+07 2.37E+09 5.66E+07 0.79

SPV360 1.59E-03 3.04E+07 0.402835 4.35E+08 1.82E+07 1.47E+09 3.65E+07 0.79

WWT180 1.40E-03 3.29E+07 0.387839 4.71E+08 1.81E+07 1.59E+09 3.62E+07 1.04

WWT270 1.28E-03 3.46E+07 0.377415 4.95E+08 1.82E+07 1.67E+09 3.63E+07 1.20

Bin-4 AVG= 6.43E+08 2.55E+07 2.17E+09 5.09E+07

Z0= 3.5814 m Bc= 14.3256 m Gmax=1.15E+0

8 N/m2

S= 1/2 H= 9.144 m Vs=2.50E+0

2 m/s

mu= 0.35

rou= 1835 kg/m3

20

Bridge #4 – Natural Frequencies and ModesBridge #4 – Natural Frequencies and Modes

Mode #1, T=0.81s

Mode #2, T=0.51s

Mode #3, T=0.40s

Mode #4, T=0.32s

Mode #5, T=0.22s

Mode #6, T=0.21s

21

Bridge #4 – Max. response vs. PGABridge #4 – Max. response vs. PGA

0 0.4 0.8 1.2

PG A -x ; P G A -y ; P G A -z

0

0.5

1

1.5

2

2.5

max

Acc

eler

atio

n @

CIP

, g

Long i.(A 1 - x)

Verti. (A 2 - y)

T rans.(A3 - z)

F it 1 : L inear

F it 1 : L inear

F it 1 : L inear

0 0.4 0.8 1.2


0

0.05

0.1

0.15

0.2

0.25

max

Re

l. D

ispl

acem

ent

@co

l_to

p, m

Long i.(U 1 - x)

Verti. (U 2 - y)

T rans.(U 3 - z)

F it 1 : L inear

F it 1 : L inear

F it 1 : L inear

B rid g e 4 w ith lin ea r M -P h i re la tio n sh ip (w ith V -E Q + H -E Q )

0 0.4 0.8 1.2


0E+000

2E+006

4E+006

6E+006

8E+006

1E+007

max

Sec

tion

For

ce @

col,

N

n2 (S F2 - x)

Verti. (SF1 - y)

n1 (S F3 - z)

F it 1 : L inear

F it 1 : L inear

F it 1 : L inear

0 0.4 0.8 1.2


0E+000

5E+006

1E+007

2E+007

2E+007

3E+007

max

Sec

tion

Mom

ent @

col,

N*m

@ n1 (SM 1 - x)

@ n2 (SM 2 - z)

@ vert.(SM 3 - y)

F it 1 : L inear

F it 1 : L inear

F it 1 : L inear


n1

n2x

z

(Linear, 3EQ case)

PGA along x, y, and z directions




Max

Acc

eler

atio

n (

g)M

ax R

elat

ive

Dis

pla

cem

ent

(m)

Max

Sec

tion

For

ce (

N)

Max

Sec

tion

Mom

ent

(N-m

)

22

Bridge #4 – Response Ratio vs. PGA RatioBridge #4 – Response Ratio vs. PGA Ratio

Linear(3EQ/2EQ)

Linear(3EQ/2EQ)

0 0.4 0.8 1.2 1.6

V ertica l to H orizonta l P G A ra tio(P G A -y/x ; P G A -y/z)

0

0.4

0.8

1.2

1.6

ma

x S

ectio

n F

orc

e R

atio

@co

lw

ith V

-EQ

/ w

itho

ut V

-EQ

n2 (S F2 - y /x)

Verti.(S F1 - y /x)

Verti.(S F1 - y /z)

n1 (S F3 - y /z)

F it 1 : Pow er

F it 1 : Pow er

0 0.4 0.8 1.2 1.6


0

0.4

0.8

1.2

ma

x S

ect

ion

Mo

me

nt @

col_

bas

ew

ith V

-EQ

/ w

itho

ut V

-EQ

@ n1 (SM 1 - y/x)

@ vert.(SM 3 - y/x)

@ vert.(SM 3 - y/z)

@ n2 (SM 2 - y/z)

B rid g e 4 w ith lin ea r M -P h i re la tio n sh ip (w ith V -E Q / w ith o u t V -E Q )

0 0.4 0 .8 1 .2 1 .6


0

20

40

60

ma

x A

cce

lera

tion

ratio

@C

IPw

ith V

-EQ

/ w

itho

ut V

-EQ

Long i.(A 1 - y/x)

V erti. (A 2 - y /x)

V erti. (A 2 - y /z)

T rans.(A 3 - y /z)

F it 1 : P ow er

F it 1 : P ow er

0 0.4 0 .8 1 .2 1 .6


0

0 .4

0 .8

1 .2

1 .6

max

Re

l. D

isp

lace

men

t R

atio

@co

l_to

pw

ith V

-EQ

/ w

itho

ut V

-EQ

Long i.(U 1 - y/x)

V erti. (U 2 - y/x)

V erti. (U 2 - y/z)

T rans.(U 3 - y/z)

F it 1 : P ow er

F it 1 : P ow er

Location o f m ax A 2 response changes !


Vertical to Horizontal PGA Ratios




Max

Acc

eler

atio

n R

atio

Max

Dis

pla

cem

ent

Rat

io

Max

Sec

tion

For

ce R

atio

Max

Sec

tion

Mom

ent

Rat

io

23

0 0.4 0 .8 1 .2

P G A -x ; P G A -y ; P G A -z

0E +000

2E +006

4E +006

6E +006

8E +006

1E +007

max

Sec

tion

For

ce @

col,

N

n2 (S F2 - x)

V erti. (S F1 - y)

n1 (S F3 - z)

F it 1 : L inear

F it 1 : L inear

F it 1 : L inear

0 0.4 0 .8 1 .2


0E +000

2E +006

4E +006

6E +006

8E +006

1E +007

max

Sec

tion

Mom

ent @

col,

N

@ n1 (S M 1 - x)

@ n2 (S M 2 - z)

@ vert.(S M 3 - y)

F it 1 : L inear

F it 1 : L inear

F it 1 : L inear

B rid g e 4 w ith n o n -lin ea r M -P h i re la tio n sh ip (w ith V -E Q + H -E Q )

n1

n2x

z


Bridge #4 – Max. response vs. PGABridge #4 – Max. response vs. PGA(non-Linear, 3EQ case)

0 0.4 0.8 1.2


0

0.4

0.8

1.2

1 .6

2

max

Acc

eler

atio

n @

CIP

, g

Long i.(A 1 - x)

V erti. (A 2 - y)

T rans.(A 3 - z)

F it 1 : L inear

F it 1 : L inear

F it 1 : L inear

0 0.4 0.8 1 .2


0

0.04

0.08

0.12

0.16

max

Rel

. Dis

plac

emen

t @co

l_to

p, m

Long i.(U 1 - x)

V erti. (U 2 - y)

T rans.(U 3 - z)

F it 1 : L inear

F it 1 : L inear

F it 1 : L inear

B rid ge 4 w ith n on -lin ear M -P h i re la tion sh ip (w ith V -E Q + H -E Q )M

ax A

ccel

erat

ion

(g)

Max

Rel

ativ

e D

isp

lace

men

t (m

)

Max

Sec

tion

For

ce (

N)

Max

Sec

tion

Mom

ent

(N-m

)




24


Non-Linear(3EQ/2EQ)

Non-Linear(3EQ/2EQ)

0 0.4 0 .8 1 .2 1 .6


0

0 .25

0.5

0 .75

1

1.25

1.5

max

Sec

tion

For

ce R

atio

@co

lw

ith V

-EQ

/ w

ithou

t V-E

Q

n2 (S F2 - y /x)

V erti.(S F1 - y /x)

V erti.(S F1 - y /z)

n1 (S F3 - y /z)

F it 1 : P ow er

F it 1 : P ow er

0 0.4 0 .8 1 .2 1 .6


0

0 .25

0.5

0 .75

1

1.25

max

Sec

tion

Mom

ent @

col

with

V-E

Q /

with

out V

-EQ

@ n1 (S M 1 - y /x)

@ vert.(S M 3 - y/x)

@ vert.(S M 3 - y/z)

@ n2 (S M 2 - y/z)

B rid g e 4 w ith n o n -lin ea r M -P h i re la tio n sh ip (w ith V -E Q / w ith o u t V -E Q )

0 0.4 0 .8 1 .2 1 .6


0

10

20

30

ma

x A

cce

lera

tion

ratio

@C

IPw

ith V

-EQ

/ w

itho

ut V

-EQ

Long i.(A 1 - y/x)

V erti. (A 2 - y/x)

V erti. (A 2 - y/z)

T rans.(A 3 - y/z)

F it 1 : P ow er

F it 1 : P ow er

0 0.4 0 .8 1 .2 1 .6


0

0 .4

0 .8

1 .2

1 .6

max

Re

l. D

isp

lace

men

t R

atio

@co

l_to

pw

ith V

-EQ

/ w

itho

ut V

-EQ

Long i.(U 1 - y/x)

V erti. (U 2 - y/x)

V erti. (U 2 - y/z)

T rans.(U 3 - y/z)

F it 1 : P ow er

F it 1 : P ow er



Vertical to Horizontal PGA Ratios Vertical to Horizontal PGA Ratios


Max

Acc

eler

atio

n R

atio

Max

Dis

pla

cem

ent

Rat

io

Max

Sec

tion

For

ce R

atio

Max

Sec

tion

Mom

ent

Rat

io

25

Bridge #4 – Response Ratio vs. PGABridge #4 – Response Ratio vs. PGANon-

LinearLinear

Non-LinearLinear

0 0.4 0.8 1.2


0

0.4

0.8

1.2

max

Sec

tion

For

ce R

atio

@co

lno

n-lin

ear

/ lin

ear

n2 (S F2 - x )

V erti. (S F1 - y)

n1 (S F3 - z )

0 0.4 0 .8 1 .2


0

0.4

0.8

1.2

max

Sec

tion

Mom

ent R

atio

@co

lno

n-lin

ear

/ lin

ear

@ n1 (S M 1 - x)

@ n2 (S M 2 - z)

@ vert.(S M 3 - y)

B rid ge 4 : n on -lin ear / lin ear resp on se ( w ith V -E Q )

n1

n2x

z

0 0.4 0 .8 1 .2


0

0.4

0 .8

1 .2

max

Acc

eler

atio

n R

atio

@C

IPno

n-lin

ear

/ lin

ear

Long i.(A 1 - x)

V erti. (A 2 - y)

T rans.(A 3 - z)

0 0.4 0 .8 1 .2


0

0.4

0 .8

1 .2

max

Rel

. Dis

plac

emen

t Rat

io @

col_

top

non-

linea

r / l

inea

r

Long i.(U 1 - x)

V erti. (U 2 - y)

T rans.(U 3 - z)

B rid g e 4 : n on -lin ear / lin ear resp on se ( w ith V -E Q )M

ax A

ccel

erat

ion

Rat

ioM

ax D

isp

lace

men

t R

atio

Max

Sec

tion

For

ce R

atio

Max

Sec

tion

Mom

ent

Rat

io


PGA along x, y, and z directions PGA along x, y, and z directions


26

Bridge #4 – Section Moment-Curvature CurveBridge #4 – Section Moment-Curvature Curve

0 0.05 0.1 0.15C urvature (rad/m )

-8000000

-4000000

0

4000000

8000000

Mom

ent

(N

-m)

M -ph i : A baqus

M -ph i : R esponse2000

M -ph i : H and & FEM A

27

Bridge #4 – Column Pushover CurveBridge #4 – Column Pushover Curve

28

0 0.4 0 .8 1 .2


0

0.5

1

1.5

2

2.5

max

Acc

eler

atio

n R

atio

@C

IPw

ith H

inge

/ w

ithou

t Hin

ge

Long i.(A 1 - x)

V erti. (A 2 - y)

T rans.(A 3 - z)

0 0.4 0 .8 1 .2


0

2

4

6

max

Rel

. Dis

plac

emen

t Rat

io @

col_

top

with

Hin

ge /

with

out H

inge

Long i.(U 1 - x)

V erti. (U 2 - y)

T rans.(U 3 - z)

B rid g e 4 : w ith lin ea r M - re la tion sh ip ( w ith H in ge /w ith ou t H in ge )

0 0.4 0.8 1.2


0

0.4

0.8

1.2

1 .6

2

max

Sec

tion

For

ce R

atio

@co

lw

ith H

inge

/ w

ithou

t Hin

ge

n2 (S F2 - x )

V erti. (S F1 - y)

n1 (S F3 - z )

0 0.4 0 .8 1 .2


0

0.4

0.8

1.2

1 .6

max

Sec

tion

Mom

ent R

atio

@co

lw

ith H

inge

/ w

ithou

t Hin

ge

@ n1 (S M 1 - x)

@ n2 (S M 2 - z)

@ vert.(S M 3 - y)

B rid g e 4 : w ith lin ear M - re la tion sh ip ( w ith H in ge /w ith ou t H in ge )

n1

n2x

z

Bridge #4 – Response Ratio vs. PGABridge #4 – Response Ratio vs. PGAWith

HingeW/O

Hinge

With HingeW/O

Hinge

(Linear)

(Linear)



Max

Acc

eler

atio

n R

atio

Max

Dis

pla

cem

ent

Rat

io

Max

Sec

tion

For

ce R

atio

Max

Sec

tion

Mom

ent

Rat

io

29

0 0.4 0.8 1.2


0

0.4

0.8

1.2

1.6

2

max

Acc

eler

atio

n R

atio

@C

IPw

ith H

inge

/ w

ithou

t Hin

ge

Long i.(A1 - x)

Verti. (A2 - y)

T rans.(A3 - z)

0 0.4 0.8 1.2


0

1

2

3

4

5

max

Rel

. Dis

plac

emen

t Rat

io @

col_

top

with

Hin

ge /

with

out H

inge

Long i.(U 1 - x)

Verti. (U 2 - y)

T rans.(U 3 - z)

B rid ge 4 : w ith n on -lin ear M - re la tion sh ip (w ith H in g e / w ith o u t H in g e)

0 0.4 0 .8 1 .2


0

0.4

0 .8

1 .2

1 .6

max

Sec

tion

For

ce R

atio

@co

lw

ith H

inge

/ w

ithou

t Hin

ge

n2 (S F2 - x )

V erti. (S F1 - y)

n1 (S F3 - z )

0 0.4 0 .8 1 .2


0

0.4

0 .8

1 .2

max

Sec

tion

Mom

ent R

atio

@co

lw

ith H

inge

/ w

ithou

t Hin

ge

@ n1 (S M 1 - x)

@ n2 (S M 2 - z)

@ vert.(S M 3 - y)

B rid g e 4 : w ith n o n -lin ea r M - re la tio n sh ip (w ith H in g e / w ith o u t H in g e)

n1

n2x

z

Bridge #4 – Response Ratio vs. PGABridge #4 – Response Ratio vs. PGAWith

HingeW/O

Hinge

With HingeW/O

Hinge

(non-Linear)(non-

Linear)



Max

Acc

eler

atio

n R

atio

Max

Dis

pla

cem

ent

Rat

io

Max

Sec

tion

For

ce R

atio

Max

Sec

tion

Mom

ent

Rat

io

30

Bridge #8 – Structural DetailsBridge #8 – Structural Details

31

Bridge #8 – Pier DetailsBridge #8 – Pier Details

48”

20 #10 bars

Bent #1 Bent #2 Bent #3 Bent #4

Pier height(ft)

30 45 50 45

Pile length(ft)

170 155 150 155

Pier Cross Section

32

Bridge #8 - Pile Foundation DetailsBridge #8 - Pile Foundation Details

Spacing between piles: Sx = Sy = 8 ft

Spring and dashpot coefficients based on model by Makris and Gazetas (1993)

Kx= 1.1497e+009 N/m =7.8869E4 kips/ft, Cx= 3.5792e+007 N.s/m = 2.4553E3 kips.s/ft,

Ky= 3.1174e+009 N/m = 2.1385E5 kips/ft, Cy= 1.0927e+008 N.s/m = 7.4959E3 kips.s/ft,

Kz= 1.1510e+009 N/m = 7.8959E4 kips/ft, Cz= 3.0441e+007 N.s/m = 2.0883E3 kips.s/ft.

CIP concrete pile with steel casingPile diameter: d=2 ft; Pile cross section area(including

transformed area of steel casin): A=673 in2

x

z

46’-0”

22’-

0”

33

Bridge #8 – Natural Frequencies and ModesBridge #8 – Natural Frequencies and Modes

Mode #1, T=1.62s

Mode #2, T=1.38s

Mode #3, T=1.05s

Mode #4, T=0.68s

Mode #5, T=0.45s

Mode #6, T=0.29s

34

-2.5E+03

-2.0E+03

-1.5E+03

-1.0E+03

-5.0E+02

0.0E+00

5.0E+02

1.0E+03

0.0 5.0 10.0 15.0 20.0

time(s)

axia

l fo

rce(

kip

)

-1.5E+02

-1.0E+02

-5.0E+01

0.0E+00

5.0E+01

1.0E+02

1.5E+02

0.0 5.0 10.0 15.0 20.0

time(s)

shea

r fo

rce_

x(ki

p)

-8.0E+02

-6.0E+02

-4.0E+02

-2.0E+02

0.0E+00

2.0E+02

4.0E+02

6.0E+02

8.0E+02

0.0 5.0 10.0 15.0 20.0

time(s)

shea

r fo

rce_

z(ki

p)

At bottom node of Column in Bent#3

At top node of Column in Bent#1

At bottom node of Column in Bent#1

Structural Response of Bridge #8Structural Response of Bridge #8

-1.5E-02

-1.0E-02

-5.0E-03

0.0E+00

5.0E-03

0.0 5.0 10.0 15.0 20.0

time(s)

axia

l re

lati

ve d

isp

.(ft

)

-1.0E-01

-5.0E-02

0.0E+00

5.0E-02

1.0E-01

0.0 5.0 10.0 15.0 20.0

time(s)

rela

tive

dis

p._

x(ft

)

-6.0E-01

-4.0E-01

-2.0E-01

0.0E+00

2.0E-01

4.0E-01

6.0E-01

8.0E-01

0.0 5.0 10.0 15.0 20.0

time(s)

rela

tive

dis

p._

z(ft

)

Column in Bent#3

Column in Bent#1

Column in Bent#1

Force Demand Displacement Demand

1986 N. Palm Springs Earthquake

Tension

35

Bridge #8 – Max. response vs. PGABridge #8 – Max. response vs. PGA(Linear, 3EQ case)

0 0.4 0 .8 1.2 1.6 2


0E +000

2E +006

4E +006

6E +006

8E +006

1E +007

max

Sec

tion

For

ce @

col,

N

n2 (S F2 - x )

V erti. (S F1 - y)

n1 (S F3 - z )

F it 1 : L inear

F it 1 : ln (Y )=B *ln (X )+A

F it 1 : L inear

0 0.4 0 .8 1.2 1.6 2


0E +000

1E +007

2E +007

3E +007

max

Sec

tion

Mom

ent @

col,

N*m

@ n1 (S M 1 - x)

@ n2 (S M 2 - z)

@ vert.(S M 3 - y)

F it 1 : Y =B *ln (X )+A

F it 1 : L inear

F it 1 : L inear

B rid ge 8 w ith lin ear M -P h i re la tio n sh ip (w ith V -E Q + H -E Q )

x

z n1

n2

0 0.4 0.8 1.2 1.6 2


0

1

2

3

ma

x A

ccel

era

tion

@C

IP, g

Long i.(A1 - x)

Verti. (A2 - y)

T rans.(A3 - z)

F it 1 : L inear

F it 1 : L inear

F it 1 : L inear

0 0.4 0.8 1.2 1.6 2


0

0.2

0.4

0.6

0.8

max

Re

l. D

ispl

ace

men

t @

col_

top,

m

Long i.(U 1 - x)

Verti. (U 2 - y)

T rans.(U 3 - z)

F it 1 : L inear

F it 1 : L inear

F it 1 : Y=B*ln(X )+A


Pga-x,y,zPGA along x, y, and z directions PGA along x, y, and z directions


Max

Acc

eler

atio

n (

g)M

ax R

elat

ive

Dis

pla

cem

ent

(m)

Max

Sec

tion

For

ce (

N)

Max

Sec

tion

Mom

ent

(N-m

)

36


Linear(3EQ/2EQ)

Linear(3EQ/2EQ)

0 0.5 1 1.5 2 2.5


0

2

4

6

8

ma

x S

ectio

n F

orc

e R

atio

@co

lw

ith V

-EQ

/ w

itho

ut V

-EQ

n2 (S F2 - y /x)

Verti.(S F1 - y /x)

Verti.(S F1 - y /z)

n1 (S F3 - y /z)

F it 1 : Pow er

F it 1 : Pow er

0 0.5 1 1.5 2 2.5


0

0.4

0.8

1.2

ma

x S

ect

ion

Mo

me

nt @

col_

bas

ew

ith V

-EQ

/ w

itho

ut V

-EQ

@ n1 (SM 1 - y/x)

@ vert.(SM 3 - y/x)

@ vert.(SM 3 - y/z)

@ n2 (SM 2 - y/z)


x

z n1

n2

0 0.5 1 1.5 2 2.5


0

20

40

60

80

100

ma

x A

cce

lera

tion

ratio

@C

IPw

ith V

-EQ

/ w

itho

ut V

-EQ

Long i.(A 1 - y/x)

V erti. (A 2 - y /x)

V erti. (A 2 - y /z)

T rans.(A 3 - y /z)

F it 1 : P ow er

F it 1 : P ow er

0 0.5 1 1.5 2 2.5


0

2

4

6

8

max

Re

l. D

isp

lace

men

t R

atio

@co

l_to

pw

ith V

-EQ

/ w

itho

ut V

-EQ

Long i.(U 1 - y/x)

V erti. (U 2 - y/x)

V erti. (U 2 - y/z)

T rans.(U 3 - y/z)

F it 1 : P ow er

F it 1 : P ow er





Max

Acc

eler

atio

n R

atio

Max

Dis

pla

cem

ent

Rat

io

Max

Sec

tion

For

ce R

atio

Max

Sec

tion

Mom

ent

Rat

io

37

0 0.4 0 .8 1.2 1.6 2


0

1

2

3

max

Acc

eler

atio

n @

CIP

, g

Long i.(A 1 - x)

V erti. (A 2 - y)

T rans.(A 3 - z)

F it 1 : L inear

F it 1 : L inear

F it 1 : Y =B *ln (X )+A

0 0.4 0 .8 1.2 1.6 2


0

0.1

0 .2

0 .3

0 .4

max

Rel

. Dis

plac

emen

t @co

l_to

p, m

Long i.(U 1 - x)

V erti. (U 2 - y)

T rans.(U 3 - z)

F it 1 : L inear

F it 1 : L inear

F it 1 : Y =B *ln (X )+A

B rid ge 8 w ith n on -lin ear M -P h i re la tion sh ip (w ith V -E Q + H -E Q )

0 0.4 0 .8 1.2 1.6 2


0E +000

2E +006

4E +006

6E +006

8E +006

1E +007

max

Sec

tion

For

ce @

col,

N

n2 (S F2 - x)

V erti. (S F1 - y)

n1 (S F3 - z)

F it 1 : ln (Y )=B *ln (X )+A

F it 1 : ln (Y )=B *ln (X )+A

F it 1 : ln (Y )=B *ln (X )+A

0 0.4 0 .8 1.2 1.6 2


0E +000

4E +006

8E +006

1E +007

2E +007

max

Sec

tion

Mom

ent @

col,

N

@ n1 (S M 1 - x)

@ n2 (S M 2 - z)

@ vert.(S M 3 - y)

F it 1 : ln (Y )=B *ln (X )+A

F it 1 : ln (Y )=B *ln (X )+A

F it 1 : ln (Y )=B *ln (X )+A

B rid g e 8 w ith n o n -lin ea r M -P h i re la tio n sh ip (w ith V -E Q + H -E Q )

x

z n1

n2

Bridge #8 – Max. response vs. PGABridge #8 – Max. response vs. PGANon-

Linear(3EQ case)

Non-Linear(3EQ case)



Max

Acc

eler

atio

n (

g)M

ax R

elat

ive

Dis

pla

cem

ent

(m)

Max

Sec

tion

For

ce (

N)

Max

Sec

tion

Mom

ent

(N-m

)

38

0 0.5 1 1.5 2 2.5


0

20

40

60

80

100

ma

x A

cce

lera

tion

ratio

@C

IPw

ith V

-EQ

/ w

itho

ut V

-EQ

Long i.(A 1 - y/x)

V erti. (A 2 - y/x)

V erti. (A 2 - y/z)

T rans.(A 3 - y/z)

0 0 .5 1 1.5 2 2.5


0

1

2

3

4

5

max

Re

l. D

isp

lace

men

t R

atio

@co

l_to

pw

ith V

-EQ

/ w

itho

ut V

-EQ

Long i.(U 1 - y/x)

V erti. (U 2 - y/x)

V erti. (U 2 - y/z)

T rans.(U 3 - y/z)



0 0.5 1 1.5 2 2.5


0

1

2

3

4

5

max

Sec

tion

For

ce R

atio

@co

lw

ith V

-EQ

/ w

ithou

t V-E

Q

n2 (S F2 - y /x)

V erti.(S F1 - y /x)

V erti.(S F1 - y /z)

n1 (S F3 - y /z)

0 0 .5 1 1.5 2 2.5


0

0 .25

0.5

0 .75

1

1.25

max

Sec

tion

Mom

ent @

col

with

V-E

Q /

with

out V

-EQ

@ n1 (S M 1 - y /x)

@ vert.(S M 3 - y/x)

@ vert.(S M 3 - y/z)

@ n2 (S M 2 - y/z)


x

z n1

n2


Non-Linear(3EQ/2EQ)

Non-Linear(3EQ/2EQ)



Max

Acc

eler

atio

n R

atio

Max

Dis

pla

cem

ent

Rat

io

Max

Sec

tion

For

ce R

atio

Max

Sec

tion

Mom

ent

Rat

io

39

0 0.4 0 .8 1.2 1.6 2


0

0.4

0 .8

1 .2

max

Acc

eler

atio

n R

atio

@C

IPno

n-lin

ear

/ lin

ear

Long i.(A 1 - x)

V erti. (A 2 - y)

T rans.(A 3 - z)

0 0 .4 0 .8 1.2 1.6 2


0

0.4

0 .8

1 .2

1 .6

max

Rel

. Dis

plac

emen

t Rat

io @

col_

top

non-

linea

r / l

inea

r

Long i.(U 1 - x)

V erti. (U 2 - y)

T rans.(U 3 - z)

B rid g e 8 : n o n -lin ea r / lin ea r resp o n se ( w ith V -E Q )

0 0.4 0 .8 1.2 1.6 2


0

0.4

0 .8

1 .2

1 .6

max

Sec

tion

For

ce R

atio

@co

lno

n-lin

ear

/ lin

ear

n2 (S F2 - x)

V erti. (S F1 - y)

n1 (S F3 - z)

0 0 .4 0 .8 1.2 1.6 2


0

0.5

1

1.5

2

2.5

max

Sec

tion

Mom

ent R

atio

@co

lno

n-lin

ear

/ lin

ear

@ n1 (S M 1 - x)

@ n2 (S M 2 - z)

@ vert.(S M 3 - y)

B rid g e 8 : n o n -lin ea r / lin ea r resp o n se ( w ith V -E Q )

x

z n1

n2

Bridge #8 – Response Ratio vs. PGABridge #8 – Response Ratio vs. PGANon-

LinearLinear

Non-LinearLinear

Max

Acc

eler

atio

n R

atio

Max

Dis

pla

cem

ent

Rat

io

Max

Sec

tion

For

ce R

atio

Max

Sec

tion

Mom

ent

Rat

io




40

Bridge #8 – Section Moment-Curvature CurveBridge #8 – Section Moment-Curvature Curve

0 0.05 0.1 0.15C urvature (rad/m )

-4000000

-2000000

0

2000000

4000000

6000000

Mom

ent

(N

-m)

M -ph i : A baqus

M -ph i : R esponse2000

M -ph i : H and & FEM A

41

Bridge #4 – Bending vs Torsional Moment RatioBridge #4 – Bending vs Torsional Moment Ratio

Bridge#4 3EQ –

Linear

M@n1 M@n2 T T/M1 T/M2 M1/T M2/T

SM1_col SM2_col SM3_col SM3/SM1 SM3/SM2 SM1/SM3 SM2/SM3

Bin4

A-CO2 6.73E+06 9.74E+06 6.63E+02 9.85E-05 6.81E-05 1.02E+04 1.47E+04A-CWC 8.18E+06 8.90E+06 5.62E+02 6.87E-05 6.31E-05 1.46E+04 1.58E+04A-EJS 8.64E+06 7.54E+06 4.91E+02 5.68E-05 6.51E-05 1.76E+04 1.54E+04A-LBR 1.51E+07 1.53E+07 5.85E+02 3.88E-05 3.83E-05 2.58E+04 2.61E+04MUL 1.20E+07 1.20E+07 4.04E+02 3.37E-05 3.36E-05 2.97E+04 2.98E+04RIO 1.32E+07 8.94E+06 4.33E+02 3.29E-05 4.84E-05 3.04E+04 2.06E+04

A-CAS 1.62E+07 1.61E+07 6.98E+02 4.32E-05 4.34E-05 2.31E+04 2.30E+04A-ZAK 8.14E+06 7.49E+06 4.89E+02 6.01E-05 6.53E-05 1.66E+04 1.53E+04H-PVY 1.22E+07 6.33E+06 3.69E+02 3.03E-05 5.83E-05 3.30E+04 1.72E+04PET 2.21E+07 1.81E+07 4.65E+02 2.10E-05 2.57E-05 4.76E+04 3.90E+04SPV 1.64E+07 1.05E+07 5.86E+02 3.56E-05 5.57E-05 2.81E+04 1.80E+04

WWT 1.01E+07 7.09E+06 5.63E+02 5.60E-05 7.95E-05 1.79E+04 1.26E+04

Bin7

HDA 6.60E+06 6.47E+06 1.98E+02 3.00E-05 3.06E-05 3.33E+04 3.26E+04H-SHP 3.16E+06 3.57E+06 2.98E+02 9.45E-05 8.35E-05 1.06E+04 1.20E+04L01 8.64E+06 4.38E+06 1.28E+02 1.48E-05 2.92E-05 6.76E+04 3.43E+04

A-CAS 6.13E+06 6.07E+06 2.69E+02 4.38E-05 4.43E-05 2.28E+04 2.26E+04A-OBR 4.15E+06 3.20E+06 3.87E+02 9.33E-05 1.21E-04 1.07E+04 8.26E+03A-ZAK 3.04E+06 2.80E+06 1.90E+02 6.25E-05 6.77E-05 1.60E+04 1.48E+04H-Z14 6.48E+06 5.04E+06 1.06E+02 1.64E-05 2.11E-05 6.09E+04 4.74E+04

RIO 4.93E+06 3.38E+06 1.66E+02 3.38E-05 4.92E-05 2.96E+04 2.03E+04STN 4.30E+06 2.80E+06 1.82E+02 4.24E-05 6.51E-05 2.36E+04 1.54E+04WWT 3.37E+06 2.46E+06 2.12E+02 6.29E-05 8.60E-05 1.59E+04 1.16E+04

* Note : Moment is taken at the middle of column.

42


Bridge#4 3EQ – non-

linear



Bin4

A-CO2 5.68E+06 6.92E+06 6.11E+02 1.07E-04 8.83E-05 9.30E+03 1.13E+04A-CWC 6.63E+06 6.97E+06 4.99E+02 7.52E-05 7.16E-05 1.33E+04 1.40E+04A-EJS 6.51E+06 6.19E+06 4.56E+02 7.00E-05 7.37E-05 1.43E+04 1.36E+04A-LBR 6.62E+06 7.05E+06 5.68E+02 8.58E-05 8.06E-05 1.17E+04 1.24E+04MUL 6.50E+06 7.05E+06 3.53E+02 5.43E-05 5.01E-05 1.84E+04 2.00E+04RIO 7.05E+06 6.81E+06 3.42E+02 4.85E-05 5.02E-05 2.06E+04 1.99E+04

A-CAS 7.05E+06 7.03E+06 6.92E+02 9.82E-05 9.84E-05 1.02E+04 1.02E+04A-ZAK 6.11E+06 6.48E+06 4.66E+02 7.62E-05 7.19E-05 1.31E+04 1.39E+04H-PVY 7.05E+06 5.89E+06 3.66E+02 5.19E-05 6.21E-05 1.93E+04 1.61E+04PET 7.05E+06 7.05E+06 4.59E+02 6.51E-05 6.51E-05 1.54E+04 1.54E+04SPV 7.05E+06 7.02E+06 5.47E+02 7.76E-05 7.79E-05 1.29E+04 1.28E+04

WWT 6.86E+06 5.77E+06 5.26E+02 7.67E-05 9.12E-05 1.30E+04 1.10E+04

Bin7

HDA 4.68E+06 5.91E+06 1.95E+02 4.16E-05 3.29E-05 2.40E+04 3.04E+04H-SHP 2.55E+06 2.89E+06 3.06E+02 1.20E-04 1.06E-04 8.31E+03 9.44E+03L01 6.40E+06 4.01E+06 1.23E+02 1.91E-05 3.05E-05 5.23E+04 3.28E+04

A-CAS 5.05E+06 4.64E+06 2.64E+02 5.22E-05 5.68E-05 1.92E+04 1.76E+04A-OBR 3.29E+06 3.12E+06 3.91E+02 1.19E-04 1.25E-04 8.43E+03 7.99E+03A-ZAK 2.59E+06 2.80E+06 1.79E+02 6.90E-05 6.40E-05 1.45E+04 1.56E+04H-Z14 5.10E+06 4.16E+06 1.01E+02 1.98E-05 2.43E-05 5.05E+04 4.12E+04

RIO 4.27E+06 3.06E+06 1.50E+02 3.51E-05 4.90E-05 2.85E+04 2.04E+04STN 3.28E+06 2.57E+06 1.71E+02 5.22E-05 6.65E-05 1.91E+04 1.50E+04WWT 2.87E+06 2.25E+06 2.05E+02 7.15E-05 9.12E-05 1.40E+04 1.10E+04

* Note : Moment is taken at the middle of column.

43


Bridge#8 3EQ – Linear

Mx Mz T T/Mx T/Mz Mx/T Mz/T


Bin4

A-FLE 1.85E+07 7.17E+06 6.97E+05 3.77E-02 9.72E-02 26.55 10.29 ATS 2.47E+07 5.68E+06 9.58E+05 3.88E-02 1.69E-01 25.76 5.93

A-ZAC 3.00E+07 5.09E+06 1.13E+06 3.77E-02 2.22E-01 26.53 4.50 HCH 1.78E+07 4.39E+06 7.24E+05 4.07E-02 1.65E-01 24.59 6.06

HWA011 1.60E+07 3.96E+06 6.14E+05 3.85E-02 1.55E-01 26.00 6.46 HWA013 2.89E+07 4.87E+06 9.60E+05 3.32E-02 1.97E-01 30.09 5.07 H-Z14 1.62E+07 5.57E+06 5.88E+05 3.62E-02 1.06E-01 27.61 9.47 KAU020 1.82E+07 3.09E+06 6.14E+05 3.38E-02 1.99E-01 29.57 5.04 MUL 2.22E+07 3.64E+06 8.08E+05 3.64E-02 2.22E-01 27.48 4.50 NPS 1.75E+07 1.33E+07 7.02E+05 4.01E-02 5.28E-02 24.96 18.94

Bin7

A2E 7.76E+06 1.74E+06 3.08E+05 3.97E-02 1.77E-01 25.18 5.66 A-WHD 6.96E+06 3.78E+06 2.70E+05 3.88E-02 7.15E-02 25.80 13.99 A-ZAC 1.08E+07 1.84E+06 4.08E+05 3.77E-02 2.22E-01 26.53 4.50 BUR 1.02E+07 1.43E+06 3.65E+05 3.56E-02 2.56E-01 28.06 3.91 CCN 5.77E+06 1.73E+06 2.56E+05 4.43E-02 1.48E-01 22.59 6.77 DHM 8.61E+06 1.95E+06 3.19E+05 3.70E-02 1.63E-01 27.01 6.12

H-PV1 8.00E+06 2.10E+06 2.53E+05 3.16E-02 1.20E-01 31.69 8.31 IND 6.96E+06 1.03E+06 2.58E+05 3.70E-02 2.51E-01 27.00 3.98 IZN 6.15E+06 1.57E+06 2.02E+05 3.28E-02 1.29E-01 30.52 7.76 KAU 6.57E+06 1.12E+06 2.22E+05 3.38E-02 1.99E-01 29.57 5.04 L01 7.52E+06 2.10E+06 3.28E+05 4.36E-02 1.57E-01 22.92 6.38 YER 4.29E+06 1.76E+06 1.62E+05 3.78E-02 9.23E-02 26.46 10.84

* Note : Moment is taken at base of column.

44


Bridge#83EQ – non-

linear

Mx Mz T T/Mx T/Mz Mx/T Mz/T


Bin4

A-FLE 1.29E+07 1.13E+07 4.52E+05 3.49E-02 3.98E-02 28.62 25.11 ATS 9.04E+06 6.77E+06 4.15E+05 4.59E-02 6.13E-02 21.77 16.30 A-ZAC 1.09E+07 8.49E+06 5.74E+05 5.26E-02 6.76E-02 19.02 14.79 HCH 8.92E+06 5.54E+06 3.67E+05 4.11E-02 6.62E-02 24.31 15.10 HWA011 8.89E+06 6.29E+06 3.10E+05 3.49E-02 4.93E-02 28.66 20.30 HWA013 9.11E+06 6.20E+06 4.53E+05 4.97E-02 7.30E-02 20.10 13.69 H-Z14 9.53E+06 8.22E+06 3.03E+05 3.18E-02 3.69E-02 31.45 27.13 KAU020 8.11E+06 4.95E+06 2.65E+05 3.27E-02 5.35E-02 30.61 18.68 MUL 9.41E+06 7.41E+06 5.06E+05 5.37E-02 6.82E-02 18.62 14.66 NPS 1.39E+07 1.25E+07 5.37E+05 3.86E-02 4.30E-02 25.88 23.23

Bin7

A2E 7.15E+06 3.03E+06 1.32E+05 1.84E-02 4.34E-02 54.34 23.04 A-WHD 8.01E+06 4.44E+06 1.83E+05 2.29E-02 4.13E-02 43.73 24.23 A-ZAC 8.21E+06 3.65E+06 2.19E+05 2.67E-02 6.01E-02 37.42 16.63 BUR 7.91E+06 2.53E+06 2.02E+05 2.56E-02 8.01E-02 39.04 12.48 CCN 7.35E+06 2.83E+06 1.79E+05 2.43E-02 6.32E-02 41.11 15.82 DHM 7.11E+06 3.59E+06 1.70E+05 2.40E-02 4.75E-02 41.71 21.06 H-PV1 8.10E+06 3.93E+06 2.33E+05 2.88E-02 5.94E-02 34.71 16.83 IND 7.72E+06 2.33E+06 2.13E+05 2.76E-02 9.12E-02 36.29 10.96 IZN 4.15E+06 2.40E+06 7.46E+04 1.80E-02 3.10E-02 55.62 32.22 KAU 7.36E+06 2.00E+06 1.28E+05 1.74E-02 6.44E-02 57.33 15.54 L01 7.48E+06 4.21E+06 2.07E+05 2.77E-02 4.93E-02 36.07 20.29 YER 5.34E+06 2.91E+06 1.11E+05 2.08E-02 3.83E-02 48.03 26.14

45


Bridge#4No Hinge

3EQ – Linear



Bin4

A-CO2 2.36E+07 2.01E+07 2.37E+05 1.00E-02 1.18E-02 99.6 84.8 A-CWC 2.41E+07 2.18E+07 3.25E+05 1.35E-02 1.49E-02 74.1 67.0 A-EJS 2.52E+07 1.27E+07 2.21E+05 8.76E-03 1.75E-02 114.1 57.3 A-LBR 2.38E+07 1.53E+07 2.20E+05 9.24E-03 1.44E-02 108.2 69.7 MUL 1.89E+07 7.64E+06 1.54E+05 8.17E-03 2.02E-02 122.4 49.6 RIO 2.60E+07 1.67E+07 2.01E+05 7.74E-03 1.20E-02 129.3 83.4 A-CAS 2.88E+07 1.44E+07 3.85E+05 1.34E-02 2.67E-02 74.7 37.4 A-ZAK 2.26E+07 1.71E+07 2.47E+05 1.09E-02 1.45E-02 91.7 69.2 H-PVY 2.82E+07 1.59E+07 2.71E+05 9.62E-03 1.71E-02 103.9 58.6 PET 2.21E+07 1.40E+07 2.73E+05 1.24E-02 1.95E-02 80.7 51.3 SPV 2.21E+07 1.49E+07 3.09E+05 1.40E-02 2.07E-02 71.4 48.3 WWT 2.27E+07 2.91E+07 4.94E+05 2.18E-02 1.70E-02 45.9 58.9

Bin7

HDA 6.15E+06 5.31E+06 8.66E+04 1.41E-02 1.63E-02 71.1 61.3 H-SHP 5.23E+06 6.49E+06 1.36E+05 2.60E-02 2.10E-02 38.4 47.7 L01 7.49E+06 5.94E+06 9.55E+04 1.28E-02 1.61E-02 78.4 62.2 A-CAS 1.09E+07 5.46E+06 1.46E+05 1.34E-02 2.68E-02 74.8 37.4 A-OBR 8.54E+06 6.65E+06 1.14E+05 1.33E-02 1.71E-02 75.3 58.6 A-ZAK 8.50E+06 6.40E+06 9.37E+04 1.10E-02 1.47E-02 90.7 68.2 H-Z14 8.39E+06 6.01E+06 9.43E+04 1.12E-02 1.57E-02 88.9 63.7 RIO 9.77E+06 6.31E+06 7.70E+04 7.88E-03 1.22E-02 127.0 81.9 STN 9.40E+06 6.70E+06 1.13E+05 1.21E-02 1.69E-02 82.8 59.0 WWT 7.36E+06 1.04E+07 1.83E+05 2.49E-02 1.76E-02 40.2 56.9

* Note : Moment is taken in the middle of column.

46


Bridge#4 No Hinge

3EQ – non-

Linear



Bin4

A-CO2 2.19E+07 2.04E+07 2.63E+05 1.20E-02 1.29E-02 83.4 77.6 A-CWC 2.35E+07 2.17E+07 3.03E+05 1.29E-02 1.40E-02 77.5 71.5 A-EJS 2.60E+07 1.25E+07 2.02E+05 7.75E-03 1.62E-02 129.1 61.9 A-LBR 2.17E+07 1.49E+07 2.22E+05 1.02E-02 1.49E-02 97.9 67.0 MUL 1.96E+07 8.05E+06 1.58E+05 8.06E-03 1.96E-02 124.0 51.0 RIO 2.62E+07 1.74E+07 2.07E+05 7.90E-03 1.19E-02 126.5 84.0 A-CAS 2.73E+07 1.50E+07 3.87E+05 1.41E-02 2.58E-02 70.7 38.7 A-ZAK 2.38E+07 1.77E+07 2.53E+05 1.06E-02 1.43E-02 94.3 70.1 H-PVY 3.20E+07 1.51E+07 2.66E+05 8.31E-03 1.76E-02 120.4 56.8 PET 2.27E+07 1.37E+07 2.83E+05 1.25E-02 2.06E-02 80.2 48.6 SPV 2.20E+07 1.47E+07 3.08E+05 1.40E-02 2.10E-02 71.5 47.6 WWT 2.31E+07 2.84E+07 5.27E+05 2.28E-02 1.86E-02 43.9 53.8

Bin7

HDA 6.08E+06 5.09E+06 9.34E+04 1.54E-02 1.83E-02 65.0 54.5 H-SHP 5.38E+06 5.76E+06 1.35E+05 2.51E-02 2.34E-02 39.8 42.7 L01 7.74E+06 5.65E+06 8.85E+04 1.14E-02 1.57E-02 87.4 63.8 A-CAS 1.04E+07 5.67E+06 1.47E+05 1.42E-02 2.59E-02 70.7 38.6 A-OBR 7.94E+06 6.43E+06 1.14E+05 1.44E-02 1.78E-02 69.4 56.2 A-ZAK 9.00E+06 6.63E+06 9.63E+04 1.07E-02 1.45E-02 93.4 68.8 H-Z14 8.33E+06 5.97E+06 1.06E+05 1.28E-02 1.78E-02 78.4 56.1 RIO 9.72E+06 6.58E+06 7.97E+04 8.20E-03 1.21E-02 122.0 82.6 STN 9.23E+06 6.80E+06 1.12E+05 1.21E-02 1.64E-02 82.6 60.8 WWT 7.45E+06 1.02E+07 1.97E+05 2.64E-02 1.92E-02 37.9 52.1

* Note : Moment is taken in the middle of column.

47

Preliminary ConclusionsPreliminary Conclusions

Vertical Motion Effects Only affect vertical response. Vertical response ratio increase as vertical to

horizontal PGA ratio increases, except for max section moment.

Vertical responses increase almost linearly with max vertical PGA.

Non-linear Flexural Behavior Effects Not significant in transverse direction. Max longitudinal response ratio decreases as

PGA increases, which means the non-linearity effects is more significant in strong earthquakes than in small ones.

48

Future Research PlanFuture Research Plan Perform high quality pretest simulations

of test specimens with realistic loading and boundary conditions Provide guidance for tests conducted at UIUC Optimize number and parameters of test

specimens Identify realistic loading and boundary

conditions Integrate various analytical models into the

framework of UI-Simcor for pseudo-dynamic hybrid testing

49

UCLA Contribution: Post-test Model DevelopmentUCLA Contribution: Post-test Model Development Use test results to develop accurate

shear-flexure interaction and axial-shear-flexure models for beam-column elements Improve existing models with better shear-

flexure interaction representation Investigate the effect of shear-axial-flexure

interaction in the presence of high vertical motion

Parametric analytical studies to develop design equations and procedures

Parametric assessment and improvement of code shear equations

50

UCLA Contribution: Post-test System AnalysisUCLA Contribution: Post-test System Analysis Perform system analysis of bridge

systems using the improved component models of columns

Derive probabilistic fragility relationships for RC bridges including axial-shear-flexure interaction

Develop recommendations for bridge column design to account for reduced shear capacity due to combined loading conditions

Documents

Seismic Simulation of Bridge Systems Under Multi-directional Motions