Presentation CIE619

Analysis of FHWA Example 5 Bridge at Tacoma

by

Lemuria Pathfinders

Supratik Bose

Sathvika Meenakshisundaram

Sharath Chandra Ranganath

Sandhya Ravindran

Amy Ruby

May 2014

Outline

Introduction

Motivation and Objectives

Response Spectra and Scaling of GM

Modeling Assumptions

Analysis Procedure and Results

Conclusions and Recommendations

CSEE DEPARTMENT, UNIVERSITY AT BUFFALO 2

Introduction

Introduction

CSEE DEPARTMENT, UNIVERSITY AT BUFFALO

Plan View of the Eight Span Steel Girder Continuous Bridge

4

Details of Bridge

Objectives

Objectives


Primary objective was to evaluate the bridge response using various

analysis procedures given MCEER/ATC 49 report

Comparison of the results obtained from various analysis

Critical assessment of performance of the bridge based on those results

Recommendations for improvement of performance during future

seismic event




SAP 2000 Model

2D Bridge model was developed in SAP 2000 v. 16.0.1 program

Uniformly distributed load (DL) on superstructure = 9.3 kips/feet

Superstructure : Equivalent concrete cross-section with same area

and inertia of composite structure

Centroid of the superstructure taken 8 feet above the top of the pier to

account for bearing height

Modeling Assumptions…


Modeling of Substructure: Piers

Modelled as three 2D frame

elements

Foundation spring stiffness

attached to the bottommost

nodes of the piers

Pinned piers: node 6XX transfers

shears but longitudinal moment

(M3) released

Sliding piers: Only transverse

shear transferred and M3, V2

released

Relationship between actual pier and stick model

Details of sliding bearings

Modeling Assumptions…


Foundation springs and abutment

Foundation stiffness calculated in

FHWA- example was used as the soil

conditions are similar

Abutments modelled as simple nodes

with vertical translation and torsional

rotation restraint and transverse

equivalent spring

Spring Foundation Model

Abutment Support Model

k11 2.66 × 104 Kip/ft

k22 7.847 × 105 Kip/ft

k33 1.70× 104 Kip/ft

k44 7.96 × 107 Kip-ft/rad

k55 4.785 × 106 Kip-ft/rad

K66 9.628 × 107 Kip-ft/rad

Response Spectra and Scaling

Response Spectra


Response Spectra of the Site

MCEER/ATC 49 report suggests 2 level of earthquakes for analysis

Maximum Credible Earthquake Expected Earthquake

Scaling of GMs


Selected GMs

Selected ground motions are scaled such that

Geometric mean spectra never lies below 15% of design spectra

Average ratio of mean and target spectra not less than unity over

the period range of significance.

Selected Ground Motions

No Ground Motion NGA# Scale M Year Station

MC

E

1Cape

Mendocino828 1.0 7.01 1992 Petrolia

2 North Ridge 960 1.0 6.69 1994 Canyon Country-W Lost Cany

3 Loma-Prieto 753 1.0 6.93 1989 Corralitos

EE

1 North Ridge 1048 0.38 6.69 1994 North Ridge 17645 Saticoy St

2 Imperial Valley 181 0.47 6.53 1979 El-Centro #6

3 Kobe Japan 1116 0.72 6.90 1995 Shin-Osake

Analysis Procedure and Results

Analysis


Uniform Load Method

Maximum displacement (vs-max) obtained by assigning Po of 1 kip/ft,

Pe, K and Tm calculated based on these equations

max

o

s

P LK

v

sup

16011.2

18271.2

long super piers long

trans er piers trans

W W W kips

W W W kips

2m

WT

Kg

e d

WP C

L

Direction of applied load

Transverse Longitudinal

Max displacement (ft) 0.037 0.144

Lateral Stiffness (kip/ft) 36808.5 9631.17

Time Period (s) 0.78 1.43

Hazard level EE MCE EE MCE

Cd 0.2486 0.8825 0.133 0.47

Pe (kip/ft) 3.281 11.65 1.5386 5.437

Base Shear (kips) 4542.22 16124.33 2129.49 7525.26

Maximum Moment (kips-feet) 5698.64 20234.42 2704.91 9558.44

Max Displacement after Pe (ft) 0.124 0.442 0.228 0.775

Analysis…


Multimode Method

Modal analysis was carried out in SAP 2000 program

ModePeriod

(s)

Cumulative Modal Mass ParticipationMode of

VibrationTranslational Rotational

UX UY UZ RX RY RZ

1.00 1.54 0.57 0.00 0.00 0.00 0.00 0.06 Longitudinal

2.00 0.88 0.00 0.59 0.00 0.02 0.00 0.00 Transverse

3.00 0.75 0.05 0.00 0.00 0.00 0.00 0.54 Torsion

Direction Analytical Calculation (kip/feet) Modal Analysis (kip/feet)

Longitudinal (Local X) 8484 8277

Transverse (Local Y) 28793 28927

Comparison of bridge stiffness obtained analytically and from modal analysis

Analysis…


Multimode Method…

Modes were combined using CQC method and the directional effects

were considered by 100%-40% combination rule

Ambient damping of 5% was considered

Results obtained from multimode response spectrum analysis at MCE

MCE Pier No.

Longitudinal TransverseAxial ForceShear Moment Shear Moment

1L

+ 0

.4T Pier 1 993.8 37327.5 221. 9 114662.1 55.6

Pier 2 1322.1 68960.6 2330.0 125658.3 32.4

Pier 3 699.8 35743.1 2301.7 159105.4 64.9

Pier 4 437.2 20518.7 2693.0 186280.0 26.3

1T

+ 0

.4L Pier 1 1413.3 53082.6 1587.5 79300.8 90.6

Pier 2 2325.7 124775.3 1573.5 84425.7 48.9

Pier 3 1310.0 71479.4 1372.0 91656.7 101.2

Pier 4 1092.5 51280.3 1078.0 74358.5 10.5

Analysis…


Pushover Analysis

Fiber PMM hinges were used to define non linearity

Simplified bilinear behaviour assumed for concrete and steel

Triangular loading pattern was used

Individual piers: Hinges only at the bottom of the members

Entire structure: Hinges considered at the base and the neck of the

trapezoidal part of the piers

Stiffness (kips/feet)Longitudinal Transverse

Pushover Analytical Pushover Analytical

70 feet pier 5872 5022 1728 1259

50 feet pier 8100 7841 3375 2983

Stiffness (kips/feet) Chord Radial

Bridge 10500 10331 28889 29521

Comparison of stiffness obtained analytically and calculated from pushover analysis

Analysis…


Pushover Curves…

70 feet - Transverse

0

500

1000

1500

2000

2500

0 5 10 15 20 25

La

tera

l F

orc

e (

kip

s)

Displacement (inches)

0

5 105

1 106

1.5 106

0 0.005 0.01 0.015 0.02 0.025

Mo

me

nt

(kip

s-i

nch

es)

Rotation (radians)

0

200

400

600

800

1000

0 5 10 15 20 25

La

tre

al F

orc

e (

kip

s)

Displacement (inches)

0

1 105

2 105

3 105

4 105

5 105

0 0.005 0.01 0.015 0.02 0.025

Mom

en

t (k

ips-i

nch

es)

Rotation (radians)

70 feet - Longitudinal

0

5000

10000

15000

20000

25000

30000

0 2 4 6 8

La

tera

l F

orc

e (

kip

s)

Displacement (feet)

Entire bridge - Transverse

0

1000

2000

3000

4000

5000

0 2 4 6 8

La

tera

l F

orc

e (

kip

s)

Displacement (feet)

Entire bridge - Longitudinal

Analysis…


Linear Elastic Time History Analysis (THA)

Linear elastic THA carried out both in NONLIN and SAP 2000

Hazard

Level

Base Shear (kips) Displacement (feet)

Long Trans Long Trans

NON SAP NON SAP NON SAP NON SAP

MCE 8426.75 12130 20743.9 32080 0.81 1.16 0.70 1.33

EE 4051.63 5731 6803.53 10250 0.39 0.34 0.23 0.35

Comparison of maximum results from SAP 2000 and NONLIN

EE has lesser demand on the structure and hence impose smaller

displacement on the piers as compared to MCE

20% difference in results obtained from SAP2000 and NONLIN.

Analysis…


Non Linear SDoF Time History Analysis (THA)

Nonlinear SDoF THA was carried out in NONLIN

Simplified bilinear behaviour was assumed with K2 = 0

Yield strength obtained from pushover analysis

Hazard Level

GM

Global X Linear Global X Nonlinear

Global Y Linear

Global Y Nonlinear

Shear (kips)

Disp. (feet)

Shear (kips)

Disp. (feet)

Shear (kips)

Disp. (feet)

Shear (kips)

Disp. (feet)

MC

E NGA 753-FN 2757 0.27 2757 0.27 7356 0.25 7356 0.25

NGA 753-FP 6905 0.67 4250 0.72 20409 0.69 20409 0.69

NGA 828-FN 4165 0.40 4165 0.40 18876 0.64 18876 0.64

EE

NGA 1048-FP 3105 0.30 3105 0.30 5007 0.17 5007 0.17

NGA 1116-FP 2297 0.22 2297 0.22 5644 0.19 5644 0.19

NGA 1116-FP 4052 0.39 4052 0.39 6282 0.21 6282 0.21

Comparison of results from linear and nonlinear analysis in NONLIN

Analysis…


Non Linear MDoF Time History Analysis

Same nonlinear model as used in pushover analysis

Newmark Beta direct integration procedure was used

Maximum displacement response during NR-GM Hysteretic begaviour during NR-GM

Analysis…


Non Linear MDoF Time History Analysis

Lesser demands observed at EE for linear and nonlinear analysis.

Structure remain within the elastic range at EE hazard level

In MCE for some of the GMs, the structure reached the inelastic zone

Maximum displacement recorded from MDoF analysis in SAP 2000

program was higher compared to SDoF analysis in NONLIN.

Max

Moment (kips-ft)

Shear (kips) Disp. (ft)

Trans Long Long Trans Long Trans

P1 86000 27670 754 1858 0.175 0.234

P2 101300 47930 1150 1959 0.460 0.280

P3 104700 36240 666 1584 0.439 0.363

P4 104900 28210 617 1634 0.331 0.369

Max

Moment (kips-ft)

Shear (kips) Disp. (ft)

Trans Long Long Trans Long Trans

P1 141500 53740 1728 3403 0.699 0.647

P2 145800 56600 1413 3275 0.853 0.801

P3 140700 51320 2064 2325 0.915 1.106

P4 147300 43820 1824 2462 1.305 1.124

Expected Earthquake Maximum Credible Earthquake

Analysis…


Capacity Spectrum Analysis

2

12 1

2v n

C c

L y

gF S VC C

B W

BL obtained from Table 5.4.1.1-1 of MCEER/ATC 49

MCE

y θpH 0.25CCH Modified CC Modified Vn

Long Trans Long Trans Long Trans Long Trans Long Trans

Operational 13.7 2.3 1.75 1.75 4.2 25.3 1.1 2.6 33722 33722

Life Safety 5.4 0.9 1.75 1.75 4.2 25.3 2.6 - 13174 -

Hazard Level

Operational Life Safety

Long Trans Long Trans

EE SAFE

MCE UNSAFE UNSAFE UNSAFE SAFE

Analysis Results…


Comparison of results of various analysis

Shear forces and displacements obtained are in close agreement

Bending moment in some of the cases are different and the possible

reason is the irregular curved geometry of the bridge

Max

Expected earthquake Maximum Credible earthquake

Shear (kips)

Moment (kips-feet)

Displacement (feet)

Shear (kips)

Moment (kips-feet)

Displacement (feet)

Long Trans Trans Long Long Trans Long Trans Trans Long Long Trans

ULM 793 624 45482 45988 0.24 0.12 2217 2802 161485 162499 0.85 0.44

MM 761 657 52668 35293 0.18 0.15 2326 2693 186280 124783 0.64 0.51

Elastic THA

672 2058 127500 42417 0.34 0.35 2850 7810 495833 152500 1.33 1.16

InelasticTHA

1150 1959 104900 47930 0.46 0.37 2064 3403 147300 116600 1.31 1.12

Comparison of results from various analysis procedure

Analysis Results…


Performance of the bridge

Demands obtained from linear analysis were divided by R-factor

1 ( 1)1.25

B B

S

TR R R

T RB obtained from Table 4.7.1 of MCEER/ATC 49

Analysis

Expected Earthquake Maximum Credible Earthquake

Longitudinal Transverse Longitudinal Transverse

LS OP LS OP LS OP LS OP

ULM Safe Safe Safe Safe Unsafe Unsafe Safe Unsafe

MM Safe Safe Safe Safe Unsafe Unsafe Unsafe Unsafe

Elastic THA Safe Unsafe Safe Safe Safe Unsafe Safe Unsafe

Inelastic THA Unsafe Unsafe Unsafe Unsafe Unsafe Unsafe Unsafe Unsafe

Therefore it can be concluded that performance of bridge remains

operational in case of EE but leads to possible failure in MCE.

Recommendations

Recommendations


Recommendation for improvement of bridge performance at MCE:

Seismic isolation bearings can be used to accommodate the excess

displacement demands during high seismic event.

Sliding friction pendulum bearings can be a good alternative to those

used in the present model to ensure better performance at MCE.

Use of dampers along with the isolators can also improve the

performance of the bridge at large earthquakes.

All the piers can be converted to sliding piers to accommodate the

high displacement demands expected at MCE

Thank You

References


CSI., 2009. Integrated Software for Structural Analysis and Design, SAP 2000. CSI.

FHWA-SA-97-010. Seismic Design of Bridges, Design Example No. 5, Nine Span Viaduct Steel Girder Bridge.

BERGER/ABAM Engineers. Federal Highway Administration. 1996.

MCEER/ATC 49. Recommended LFRD Guidelines for the Seismic Design of Highway Bridges, Part I: Specifications. ATC MCEER Joint Venture. 2003

MCEER/ATC 49. Recommended LFRD Guidelines for the Seismic Design of Highway Bridges, Part II: Commentary and Appendices. ATC MCEER Joint Venture. 2003

Bruneau, M., Uang, C. M. and Sabelli, R. 2010. Ductile Design of Steel Structures. Second Edition

Lawson, R.S., Vance, V. and Krawinkler, H. 1994. Nonlinear static pushover analysis: Why, When and How?.

Proceedings of 5th US National Conference on Earthquake Engineering, July 10-14, 1994, Chicago.

Chopra, A. K. (2012). Earthquake Response of Linear Systems. Dynamics of Structures: Theory and Applications to Earthquake Engineering (). Upper Saddle River, NJ: Pearson Education Inc.

Villaverde, R., 2009. Fundamental Concepts of Earthquake Engineering.

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