- Prepared a 2D stick model of the bridge in SAP2000 using the properties mentioned in the FHWA Bridge document - Designed the bridge for linear and non-linear structural models to conduct analyses - Performed different analyses on the bridge – multimode analysis, pushover analysis, time history analysis and capacity spectrum analysis - Compared the shear force, bending moment, axial force and displacement values for each abutment and pier from all analyses and critically assessed the bridge performance

1. Analysis of FHWA Example 5 Bridge at Tacoma
by
Lemuria Pathfinders
Supratik Bose
Sathvika Meenakshisundaram
Sharath Chandra Ranganath
Sandhya Ravindran
Amy Ruby
May 2014

2. 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

3. Introduction

4. Introduction
CSEE DEPARTMENT, UNIVERSITY AT BUFFALO
Plan View of the Eight Span Steel Girder Continuous Bridge
4
Details of Bridge

5. Objectives

6. Objectives
CSEE DEPARTMENT, UNIVERSITY AT BUFFALO 6
 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

7. Modeling
Assumptions

8. Modeling Assumptions
CSEE DEPARTMENT, UNIVERSITY AT BUFFALO 8
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

9. Modeling Assumptions…
CSEE DEPARTMENT, UNIVERSITY AT BUFFALO 9
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

10. Modeling Assumptions…
CSEE DEPARTMENT, UNIVERSITY AT BUFFALO 10
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

11. Response Spectra
and Scaling

12. Response Spectra
CSEE DEPARTMENT, UNIVERSITY AT BUFFALO 12
Response Spectra of the Site
 MCEER/ATC 49 report suggests 2 level of earthquakes for analysis
Maximum Credible Earthquake Expected Earthquake

13. Scaling of GMs
CSEE DEPARTMENT, UNIVERSITY AT BUFFALO 13
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
MCE
1
Cape
Mendocino
828 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

14. Analysis Procedure
and Results

15. Analysis
CSEE DEPARTMENT, UNIVERSITY AT BUFFALO 15
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 L
K
v 


sup
16011.2
18271.2
long super piers long
trans er piers trans
W W W kips
W W W kips


  
  
2m
W
T
Kg
 e d
W
P 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

16. Analysis…
CSEE DEPARTMENT, UNIVERSITY AT BUFFALO 16
Multimode Method
 Modal analysis was carried out in SAP 2000 program
Mode
Period
(s)
Cumulative Modal Mass Participation
Mode 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

17. Analysis…
CSEE DEPARTMENT, UNIVERSITY AT BUFFALO 17
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 Transverse
Axial
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

18. Analysis…
CSEE DEPARTMENT, UNIVERSITY AT BUFFALO 18
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

19. Analysis…
CSEE DEPARTMENT, UNIVERSITY AT BUFFALO 19
Pushover Curves…
70 feet - Transverse
0
500
1000
1500
2000
2500
0 5 10 15 20 25
LateralForce(kips)
Displacement (inches)
0
5 10
5
1 106
1.5 10
6
0 0.005 0.01 0.015 0.02 0.025
Moment(kips-inches)
Rotation (radians)
0
200
400
600
800
1000
0 5 10 15 20 25
LatrealForce(kips)
Displacement (inches)
0
1 105
2 10
5
3 10
5
4 10
5
5 10
5
0 0.005 0.01 0.015 0.02 0.025
Moment(kips-inches)
Rotation (radians)
70 feet - Longitudinal
0
5000
10000
15000
20000
25000
30000
0 2 4 6 8
LateralForce(kips)
Displacement (feet)
Entire bridge - Transverse
0
1000
2000
3000
4000
5000
0 2 4 6 8
LateralForce(kips)
Displacement (feet)
Entire bridge - Longitudinal

20. Analysis…
CSEE DEPARTMENT, UNIVERSITY AT BUFFALO 20
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.

21. Analysis…
CSEE DEPARTMENT, UNIVERSITY AT BUFFALO 21
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)
MCE
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

22. Analysis…
CSEE DEPARTMENT, UNIVERSITY AT BUFFALO 22
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

23. Analysis…
CSEE DEPARTMENT, UNIVERSITY AT BUFFALO 23
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

24. Analysis…
CSEE DEPARTMENT, UNIVERSITY AT BUFFALO 24
Capacity Spectrum Analysis
2
1
2 1
2
v n
C c
L y
gF S V
C 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

25. Analysis Results…
CSEE DEPARTMENT, UNIVERSITY AT BUFFALO 25
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
Inelastic
THA
1150 1959 104900 47930 0.46 0.37 2064 3403 147300 116600 1.31 1.12
Comparison of results from various analysis procedure

26. Analysis Results…
CSEE DEPARTMENT, UNIVERSITY AT BUFFALO 26
Performance of the bridge
 Demands obtained from linear analysis were divided by R-factor
1 ( 1)
1.25
B B
S
T
R 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.

27. Recommendations

28. Recommendations
CSEE DEPARTMENT, UNIVERSITY AT BUFFALO 28
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

29. Thank You

30. References
CSEE DEPARTMENT, UNIVERSITY AT BUFFALO 30
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.