Uhm cee-03-03

Computer Modeling of the Proposed Kealakaha Stream Bridge

Jennifer B.J. Chang

Ian N. Robertson

Research Report UHM/CEE/03-03 May 2003

iii

ABSTRACT

The studies described in this report focus on the short-term structural performance

of a new replacement Kealakaha Bridge scheduled for construction in Fall 2003.

A new three span, 220-meter concrete bridge will be built to replace an existing

six span concrete bridge spanning the Kealakaha Stream on the island of Hawaii. During

and after construction, fiber optic strain gages, accelerometers, Linear Variable

Displacement Transducers (LVDTs) and other instrumentation will be installed to

monitor the structural response during ambient traffic and future seismic activity. This

will be the first seismic instrumentation of a major bridge structure in the State of Hawaii.

The studies reported here use computer modeling to predict bridge deformations

under thermal and static truck loading. Mode shapes and modal periods are also studied

to see how the bridge would react under seismic activity. Using SAP2000, a finite

element program, a 2-D bridge model was created to perform modal analysis, and study

vertical deformations due to static truck loads. A 3-D bridge model was also created in

SAP2000 to include the horizontal curve and vertical slope of the bridge. This model is

compared with the 2-D SAP2000 model to evaluate the effect of these and other

parameters on the structural response.

In addition, a 3-D Solid Finite Element Model was created using ANSYS to study

thermal loadings, longitudinal strains, modal analysis, and deformations. This model was

compared with the SAP2000 model and generally shows good agreement under static

truck loading and modal analysis. In addition, the 3-D ANSYS solid finite element model

gave reasonable predictions for the bridge under thermal loadings. These models will be

used as a reference for comparison with the measured response after the bridge is built.

iv

ACKNOWLEDGEMENTS

This report is based on a Masters Plan B report prepared by Jennifer Chang under

the direction of Ian Robertson. The authors wish to express their gratitude to Drs Si-

Hwan Park and Phillip Ooi for their effort in reviewing this report.

This project was funded by the Hawaii Department of Transportation (HDOT)

and the Federal Highway Administration (FHWA) program for Innovative Bridge

Research and Construction (IBRC) as part of the seismic instrumentation of the

Kealakaha Stream Bridge. This support is gratefully acknowledged. The content of this

report reflects the views of the authors, who are responsible for the facts and the accuracy

of the data presented herein. The contents do not necessarily reflect the official views or

policies of the State of Hawaii, Department of Transportation, or the Federal Highway

Administration. This report does not constitute a standard, specification or regulation.

v

TABLE OF CONTENTS Abstract…………………………………………………………………………. iii Acknowledgements……………………………………………………………… iv Table of Contents……………………………………………………………….. v List of Tables……………………………………………………………….…… vii List of Figures…………………………………………………………………… viii Chapter 1 INTRODUCTION…..…………………………………………… 1

1.1 Project Description……………………………………………….. 1 1.2 Project Scope……………………………………………………… 5

Chapter 2 DESIGN CRITERIA FOR KEALAKAHA BRIDGE…………… 7 2.1 Geometric Data…………………………………………………… 7 2.2 Linear Soil Stiffness Data………………………………………… 7 2.3 Material Properties………………………………………………… 11 2.4 Boundary Conditions of Bridge…………………………………… 11 2.5 Bridge Cross Section……………………………………………… 11

Chapter 3 SAP2000 FRAME ELEMENT MODELS ……………………… 13

3.1 Development of SAP2000 Frame Element Models……………… 13 3.2 Element Sizes used for SAP2000 Models………………………… 16 3.3 Results of Frame Element Model Comparisons…………………… 18

3.3.1 Natural Frequencies…………………………………………18 3.3.2 Static Load Deformations………………………………….. 18

Chapter 4 ANSYS SOLID MODEL ………………………………………… 25

4.1 ANSYS Solid Model Development………………………………. 25 4.2 Finite Element Analysis: ANSYS, an Overview ..……………….. 26 4.3 Solid Model Geometry…………………………………………… 26 4.4 Development of Solid Model Geometry…………………………. 29 4.5 Meshing in ANSYS………………………………………………. 33 4.6 Test Beam: Determining Finite Element Type and Mesh for

Thermal Loading…………………………………………………. 34 4.7 Analytical Solution For Test Beam………………………………. 37 4.8 Comparison of ANSYS to Theoretical Result: Thermal Loading… 38

4.9 Comparison of ANSYS to Theoretical Result: Static Point Loading.39 4.10 Mesh Generation for Kealakaha Bridge Model……………………. 42 4.11 Convergence of 4 Meter Mesh…………………………………….. 42

Chapter 5 ANSYS SOLID MODEL ANALYSIS …………………………… 45

5.1 Truck Loading Conditions…………………………………………. 45 5.2 Truck Loading Results…………………………………………….. 46 5.2.1 Single 320 kN (72 Kip) Point Load……………………….. 46

5.2.2 Distributed Single Truck Load……………………………. 48 5.2.3 2x2 Truck Loading……………………………………….. 50

vi

5.2.4 4 Truck Loading Creating Torsion Effects………………… 52 Chapter 6 TEMPERATURE ANALYSIS …………………………………… 57

6.1 Temperature Gradient……………………………………………… 57 6.2 Results of Temperature Gradient………………………………….. 58 6.3 Strain Distribution…………………………………………………. 64

Chapter 7 MODAL ANALYSIS …………………………………………….. 67

7.1 Modal Periods……………………………………………………… 67 7.1.1 Modal Periods: 2-D vs. 3D Models…….…………………. 67 7.1.2 Modal Periods: Gross Section vs. Transformed Section….. 68 7.1.3 Modal Periods: Linear Soil Spring vs. Fixed Support….… 68 7.1.4 Modal Periods: SAP2000 vs. ANSYS….…………………. 69

7.2 Mode Shapes………………………………………………………. 70 Chapter 8 CONCLUSIONS AND SUMMARY……………………………… 79 8.1 Summary………………….………………………………………. 79 8.2 Conclusions……………………………………………………….. 79 8.3 Sources of Possible Error………………………………………….. 80 8.4 Suggestions for Further Study…………………………………….. 81 References …………………………………………………………………….. 83 Appendix A – Model Input Data ………………………………………………… 85 Coordinates of SAP2000 2-D Model …………………………………….. 85

Coordinates of SAP2000 3-D Model …………………………………….. 86 SAP2000 Cross Section Properties ………………………………………. 88 Material Properties used in SAP2000 ……………………………………. 89 ANSYS Solid Model – Coordinates ……………………………………… 90 ANSYS Solid Model – Cross-Section Depths …………………………… 91

vii

LIST OF TABLES 2.1 Kealakaha Bridge Geometric Data……………….……………………….. 7 2.2 Linear Soil Stiffness Data………………………………………………….. 8 3.1 Comparison of Vertical Deflections For Fixed Support…………………… 21 3.2 Comparison between Fixed Supports and Soil Springs ..…………………. 24 4.1 Vertical Deflection at Midspan on Test Beam: Thermal Loading…………. 39 4.2 Vertical Deflection at Midspan on Test Beam: 10 N Point Load…………. 41 4.3 Comparison between Four and Six Meter Mesh for ANSYS Model……… 44 5.1 Results of Single 320 kN Truck Point Load ….…………………………… 46 5.2 Vertical Deflection at Center of Bridge due to Single Truck

Load (Actual Wheels Modeled) .………………………………………….. 48 5.3 Vertical Deflection of Bridge due to 2x2 Truck Load

(Actual Wheels Modeled)………………………………………………….. 50 5.4 Vertical Deflection of Bridge due to 4 Truck Loading at Edge of Bridge

(Actual Wheels Modeled)…………………………………………………. 55 6.1 Vertical Deflection due to Temperature Gradient .……………………….. 62 7.1.1 Modal Periods: 2-D vs. 3D ……………………………………………… 67 7.1.2 Modal Periods: Gross Section vs. Transformed Section………………… 68 7.1.3 Modal Periods: Linear Soil Spring Support vs. Fixed Supports………… 69 7.1.4 Modal Periods: SAP2000 vs. ANSYS…………………………………… 69

viii

LIST OF FIGURES 1.1 Location of Project………………………………………………………… 1 1.2 Elevation, Section and Plan of Kealakaha Bridge ..….……………………. 2 1.3 UBC 1997 Seismic Zonation ..…………………….….…………………… 3 1.4 Horizontal Ground Acceleration (% g) at a 0.2 Second Period with 2%

Probability of Exceedance in 50 Years……………….……………………. 4 1.5 Horizontal Ground Accelerations (% g) at a 0.2 Second Period with 10%

Probability of Exceedance in 50 Years……………………………………. 5 2.1 Lateral Stiffness (Longitudinal Direction)……………………..………….. 9 2.2 Lateral Stiffness (Transverse Direction)………………………..…………. 9 2.3 Rotational Stiffness (Longitudinal Direction)…………………..…………. 10 2.4 Rotational Stiffness (Transverse Direction)……………………..………….10 2.5 Design Cross Section of Kealakaha Bridge…………………….………….. 12 3.1 SAP2000 2-D Frame Element Model (Schematic)………………………… 14 3.2 SAP2000 2-D Frame Element Model (Screen Capture)..………………….. 14 3.3 SAP2000 3-D Frame Element Model (Schematic)………………………… 15 3.4 SAP2000 3-D Frame Element Model (Screen Capture).………………….. 15 3.5 Element Lengths in SAP2000 Models……………………………..….…… 17 3.6 Convergence of Original and Half Size Finite Elements………….…….…. 18 3.7 Schematic Drawing of a Single HS20 Truck Load ………………..……… 19 3.8 Single HS20 Truck Load used in Chapter 3 ………………………..……... 19 3.9 Deformed Shape due to Single Truck Load ..……………………………… 20 3.10 Comparisons Between 2-D and 3-D Model .…………………………….... 21 3.11 Comparison of Gross and Transformed Section Properties for 2-D

Model Results ..……………………………………………………………. 22 3.12 Comparison of Gross and Transformed Section Properties for 3-D

Model Results …..…………………………………………………………. 22 3.13 Difference Between Fixed Support and Soil Springs: 2-D Model …..…… 23 3.14 Difference Between Fixed Support and Soil Springs: 3-D Model …...…… 24 4.1 Side View of a Portion of the Kealakaha Bridge……………………….…. 28 4.2.1 Design Cross Section………………………………………………….…… 30 4.2.2 Simplified Cross Section……………………………………………….….. 30 4.3 ANSYS Solid Model Cross Section View before Meshing…………….…. 31 4.4 Kealakaha Bridge before Meshing, Elevation ……………………………. 32 4.5 Kealakaha Bridge before Meshing, Isometric View………………………. 32 4.6 Solid 45, Eight Node Structural Solid (ANSYS) ….……………………… 34 4.7 Solid 92, Ten Node Tetrahedral Structural Solid (ANSYS) ..…………….. 34 4.8 Square Test Beam – Thermal Loading ……………………………………. 35 4.9 Thermal Distribution in Test Beam……………………………………….. 36 4.10 Test Beam Deflection under 10° C Temperature Gradient (Auto Mesh) … 38 4.11 Square Test Beam – Point Loading .………………………………………. 39 4.12 Four Meter Mesh Size, Kealakaha Bridge (Part of Bridge)……………….. 43 4.13 Six Meter Mesh Size, Kealakaha Bridge (Part of Bridge)…………………. 43 4.14 Convergence of Four and Six Meter Mesh for ANSYS Model …………… 44 5.1 Distribution of Truck Loads…………………………………….…………. 45

ix

5.2 ANSYS Layout of Single Truck Point Load…………………………….… 47 5.3 SAP2000 vs. ANSYS, Single Truck Point Load…………………...……… 47 5.4 Viaduct Section Showing Single Truck Load……………………………… 48 5.5 Layout of Wheel Placement for Single Truck………………………..……. 49 5.6 SAP2000 vs. ANSYS, Single Truck Modeled with Wheels…………...….. 49 5.7 Location of Axle Loads for the 2x2 Truck Configuration ……………..…. 50 5.8 Viaduct Section showing 2x2 Truck Configuration……………………..… 51 5.9 ANSYS Placement of 2x2 Truck Load ………………….………………… 51 5.10 SAP2000 vs. ANSYS, 2x2 Trucks Modeled with Wheels……………….... 52 5.11 Location of Axle Loads for Four Trucks in a Row……………………….... 52 5.12 Viaduct Section showing Four Trucks in a Row…………………..………. 53 5.13 ANSYS Layout of Four Trucks in a Row………………………….……… 53 5.14 Deflected and Non-Deflected Cross Section……………………….……… 54 5.15 Torsion Effects, Four Trucks in a Row………………………………….… 54 5.16 Isometric View of Vertical Deflection under Torsion Loading………..….. 55 6.1 ANSYS Applied Temperature Gradient………………………………….... 57 6.2 Bridge End Span Showing Effect of Thermal Gradient……………….…... 58 6.3 Deformation due to 10 Degrees Temperature Gradient……………….…... 59 6.4 Isometric View of Bridge Deformation due to Thermal Loading……....…. 59 6.5 Side View of Bridge Deformation due to Thermal Loading………..…..…. 60 6.6 Locations of Reported Deformation due to Thermal Loading…...………... 61 6.7 Vertical Deflection of Bridge due to Ten Degree Temperature Gradient…. 62 6.8 Combination of Temperature and Truck Loading…………………………. 63 6.9 Strain Distribution through Box Girder Depth near Pier………………..… 64 6.10 Strain Distribution through Box Girder Depth near Midspan……………... 64 6.11 Strain Output Locations……………………………………………….…… 65 6.12 Longitudinal Strains at Locations A and B …………………………..…… 66 6.13 Longitudinal Strains at Locations C and D …………………………..……. 66 7.1 ANSYS Mode 2……………………………………………………….…… 70 7.2 SAP2000 Mode 1………………………………………………………..…. 70 7.3 ANSYS Mode 1………………………………………………………….… 71 7.4 SAP2000 Mode 2……………………………………………………….….. 71 7.5 ANSYS Mode 3……………………………………………………………. 72 7.6 SAP2000 Mode 3……………………………………….……………….…. 72 7.7 ANSYS Mode 4………………………………………….………………… 73 7.8 SAP2000 Mode 4………………………………………….…………….…. 73 7.9 ANSYS Mode 5…………………………………………….……………… 74 7.10 SAP2000 Mode 5…………………………………………….………….…. 74 7.11 ANSYS Mode 6……………………………………………….…………… 75 7.12 SAP2000 Mode 6………………………………………………………..…. 75 7.13 ANSYS Mode 7……………………………………………….…………… 76 7.14 SAP2000 Mode 7……………………………………………….……….…. 76 7.15 ANSYS Mode 8………………………………………………….………… 77 7.16 SAP2000 Mode 8………………………………………….…………….…. 77 7.17 ANSYS Mode 9………………………………………….………………… 78 7.18 SAP 2000 Mode 9……………………………………….……………….… 78

x

1

CHAPTER 1

INTRODUCTION 1.1 Project Description

The project site is located along Mamalahoa Highway (Hawaii Belt Road) over

the Kealakaha stream in the District of Hamakua on the Island of Hawaii. The existing

bridge, a six span concrete bridge crossing the Kealakaha Stream is scheduled for

replacement in Fall 2003. The new replacement bridge will be built on the north side of

the existing bridge and will reduce the horizontal curve and increase the roadway width

of the existing bridge. The new bridge has been designed to withstand the anticipated

seismic activity whereas the existing bridge is seismically inadequate. Figure 1.1 shows

the location of the project on the Big Island of Hawaii.

Figure 1.1: Location of Project

2

The new prestressed concrete bridge will be a 3 span bridge and is approximately

220 meters long and 15 meters wide and will be designed to withstand earthquake and all

other anticipated loads. The new bridge will consist of three spans supported by two

intermediate piers and two abutments (Figure 1.2). The center span will be a cast-in-

place concrete segmental span of about 110 meters and the two outside spans will be

about 55 meters resulting in a balanced cantilever system. During and after construction,

fiber optic strain gages, accelerometers, Linear Variable Displacement Transducers

(LVDT’s) and other instrumentation will be installed to monitor the structural response

during ambient traffic and future seismic activity. This will be the first seismic

instrumentation of a major bridge structure in the State of Hawaii.

Figure 1.2: Elevation, Section and Plan of Kealakaha Bridge

3

The new bridge is in an ideal location for a seismic study because of the

earthquake activity on the island of Hawaii. The Island of Hawaii is in zone 4, the

highest zone of seismic activity categorized in the “1997 Uniform Building Code.”

Figure 1.3 shows the map of the “UBC 1997 Seismic Zonation” for the State of Hawaii.

Figure 1.3: UBC 1997 Seismic Zonation

Figures 1.4 and 1.5 show the peak ground acceleration maps included in the

International Building Code, IBC (2000). These maps are based on the USGS National

Seismic Hazard Mapping Project (USGS 1996). The maps show earthquake ground

motions that have a specified probability of being exceeded in 50 years. These ground

motion values are used for reference in construction design for earthquake resistance.

The maps show peak horizontal ground acceleration (PGA) at a 0.2 second period with

5% of critical damping. There are two probability levels: 2% (Fig. 1.4) and 10% (Fig.

1.5) probabilities of exceedence (PE) in 50 years. These correspond to return periods of

about 500 and 2500 years, respectively. The maps assume that the earthquake hazard is

independent of time.

4

The location of the Kealakaha bridge shows approximately 65% g with a 2%

probability of exceedance in 50 years (Fig. 1.4) and 35% g with a 10% probability of

exceedance in 50 years (Fig. 1.5). The acceleration due to gravity, g, is 980 cm/sec2.

Figure 1.4: Horizontal Ground Acceleration (%g) at a 0.2 Second Period With 2% Probability of Exceedance in 50 Years (USGS, 1996)

5

Figure 1.5: Horizontal Ground Acceleration (%g) at a 0.2 Second Period With 10% Probability of Exceedance in 50 Years (USGS 1996)

1.2 Project Scope

A number of computer models of the Kealakaha Bridge were created, analyzed

and compared to evaluate the structural response of the bridge to various loading

conditions. All models were linear elastic simulations in either SAP2000 (CSI 1997) or

ANSYS (ANSYS, 2002).

6

Frame element models were created in SAP2000 to determine the following:

1) Vertical deflection of the viaduct due to static truck loads.

2) Mode shapes and modal periods.

3) Effects of different degrees of modeling accuracy:

a. 3-D model compared with 2-D model.

b. Inclusion of linear soil stiffness properties (soil springs vs. fixed

supports.)

c. Inclusion of prestressing steel (transformed section vs. gross section

properties.)

d. Beam element size to produce convergence of results.

A three-dimensional solid model was created in ANSYS to determine the

following:

1) Deformation and strains of the viaduct due to thermal loads.

2) Deformation and strains of the viaduct due to truck loads.

3) Comparison of mode shapes and modal periods, and vertical deformations

under truck loads, with the SAP2000 frame element models.

7

CHAPTER 2

DESIGN CRITERIA FOR KEALAKAHA BRIDGE

The design specifications used for the Kealakaha bridge are the AASHTO LRFD

Bridge Design Specification – Second Edition (1998) including the 1999 and 2000

interim revisions (AASHTO, 1998). A geotechnical investigation was performed by

Geolabs, Inc. in 2001 and the report was available for this study (Geolabs, 2001a)..

Structural bridge data was obtained from Sato and Associates, the bridge design

engineers, and from the State of Hawaii project plans titled “Kealakaha Stream Bridge

Replacement, Federal Aid Project No. BR-019 2(26)” dated July 2001.

2.1 Geometric Data

The geometric data of the Kealakaha bridge are shown in Table 2.1. The bridge

radius and slopes were not modeled in the 2-D SAP2000 and the ANSYS models. The

bridge radius, longitudinal slope, and cross slope were included in the SAP2000 3-D

model.

Table 2.1: Kealakaha Bridge Geometric Data

Design Speed 80 km/hour Span Lengths 55 m – 110 m – 55m Typical Overall Structure Width 14.90 m (constant width) Bridge Radius constant radius of 548.64 m Bridge Deck constant cross slope of 6.2% Vertical Longitudinal Slope Vertical curve changing to a constant

longitudinal slope of -3.46%

2.2 Linear Soil Stiffness Data

The only geotechnical information available for this study was the data provided

by Geolabs, Inc. in the project geotechnical report (Geolabs-Hawaii W.O. 3885-00

November 17, 1998). The study was done for Sato and Associates, Inc. and the State of

8

Hawaii Department of Transportation. The report summarized the findings and

geotechnical recommendations based on field exploration, laboratory testing, and

engineering analyses for the proposed bridge replacement project. The recommendations

were intended for the design of foundations, retaining structures, site grading and

pavements.

Geolabs, Inc. provided the design engineers with linear soil stiffness during

service conditions and extreme earthquake events using the secant modulus (Geolabs,

2001). A future proposed soil investigation and a soil-structure interaction-modeling

program will determine the non-linear and dynamic properties of the foundation material.

Figures 2.1 to 2.4 show plots of the secant modulus used to determine these linear

soil spring stiffness. Figure 2.1 shows the estimated secant modulus for lateral soil

stiffness in the bridge longitudinal direction with a lateral deflection of 0.0088 meters and

a lateral load of 18,750 kN. Figure 2.2 shows the secant modulus for the transverse

direction. The rotational stiffness in the bridge longitudinal direction was determined

from the secant modulus at a rotational displacement of 0.0054 rad and a moment of

165,000 kN-m (Figure 2.3). Figure 2.4 shows the secant modulus for the rotational

stiffness in the bridge transverse direction. These stiffness values are used for the soil

springs in the SAP2000 frame element models at the base of both piers. The values are

shown in Table 2.2.

Table 2.2: Linear Soil Stiffness Data

Lateral Stiffness Longitudinal 2.12 X 106 kN/m Transverse 1.89 X 106 kN/m Rotational Stiffness Longitudinal 3.29 X 108 kN-m/rad Transverse 3.56 X 108 kN-m/rad

9

Lateral Stiffness (Longitudinal)Calculating Secant Modulus

Data from Geolabs, Inc. 1/29/2001

0

2000

4000

6000

8000

10000

12000

14000

16000

18000

20000

0 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009 0.01

Lateral Deflection (meters)

Late

ral L

oad

(kN

)

Fitted Curve

Secant Modulus

2.12X106 kN/m (Extreme Event)

2.9X106 kN/m (Service)

Figure 2.1: Lateral Stiffness (Longitudinal Direction)

Lateral Stiffness (Transverse)Calculating Secant Modulus


02000400060008000

100001200014000160001800020000

0 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009 0.01

Lateral Deflection (meters)

Late

ral L

oad

(kN

)

Secant Modulus

1.89X106 kN/m (Extreme Event)

Figure 2.2: Lateral Stiffness (Transverse Direction)

10

Rotational Stiffness (Longitudinal)Calculating Secant Modulus


0

20000

40000

60000

80000

100000

120000

140000

160000

180000

0 0.001 0.002 0.003 0.004 0.005 0.006

Rotation (Rad)

Mom

ent (

kN-m

)

Fitted CurveSecant Modulus

3.29X108 kN-m/rad (Extreme Event)

3.59X108 kN/m (Service)

Figure 2.3: Rotational Stiffness (Longitudinal Direction)

Rotational Stiffness (Transverse)Calculating Secant Modulus


0

50000

100000

150000

200000

250000

300000

350000

0 0.0001 0.0002 0.0003 0.0004 0.0005 0.0006 0.0007 0.0008 0.0009 0.001

Rotation (Rad)

Mom

ent (

kN-m

)

Secant Modulus

3.56X108 kN-m/rad (Extreme Event)

Figure 2.4: Rotational Stiffness (Transverse Direction)

11

2.3 Material Properties

Based on the design documents obtained from Sato and Associates, three different

types of concrete were used to model the structure in the frame element models. Super-

structure concrete was used for the bridge span, sub-structure concrete was used for the

concrete piers and abutments, and weightless concrete was used for the dummy

connectors between the pier and the bridge girder in the SAP2000 frame element models.

Poisson’s ratio of 0.20 was used throughout the bridge. The Elastic Modulus was taken

as 2.4 x 107 kN/m2 for the bridge superstructure and 2.1 x 107 kN/m2 for the piers and

abutments.

2.4 Boundary Conditions of Bridge

For most computer models, the bases of the two piers were modeled as fully

fixed. In the SAP2000 soil spring model, rotational, horizontal, and vertical linear soil

springs were incorporated at the base of the piers. In all computer models, the abutments

at each end of the bridge were modeled as roller supports in the bridge longitudinal

direction, free to rotate about all axes, but restrained against vertical and transverse

displacement.

2.5 Bridge Cross Section

Figure 2.5 shows the design cross section of the Kealakaha bridge box girder.

From this cross section, centroidal coordinates, moments of inertia, torsion constants, and

cross-sectional areas were calculated for the SAP2000 models. All dimensions are

constant throughout the length of the bridge except the box girder depth, h, and the

bottom slab thickness, T. These values are listed in Appendix A for the end of each

bridge segment. The cross section in Figure 2.5 is referred to as the design cross section.

12

Modifications were made to simplify the cross-section for the ANSYS solid model as

explained in Chapter 4.

Figure 2.5: Design Cross Section of Kealakaha Bridge

13

CHAPTER 3

SAP2000 FRAME ELEMENT MODELS

3.1 Development of SAP2000 Frame Element Models

SAP2000 (CSI, 1997) was used to create the frame element models. Figures 3.1

and 3.2 show elevation, plan and isometric views of the 2-D model. This model ignores

the horizontal curve, longitudinal slope and cross slope. Note that although the roadway

is horizontal, the girder frame elements follow the centerline of the varying depth box

girder and are therefore curved in the vertical plane.

Figures 3.3 and 3.4 show elevation, plan and isometric 3-D views of the 3-D

model. In the 3-D model, the horizontal curve with radius of 548.64 m and the vertical

curve are modeled. The vertical curve begins as a varying slope until the center of the

bridge where it becomes a constant slope of –3.46 %. To model the bridge deck constant

cross slope of 6.2%, moments of inertia, and centerline coordinates were recalculated for

the 3-D model.

14

Figure 3.1: SAP2000 2-D Frame Element Model (Schematic)

Figure 3.2: SAP2000 2-D Frame Element Model (Screen Capture)

15

Figure 3.3: SAP2000 3-D Frame Element Model (Schematic)

Figure 3.4: SAP2000 3-D Frame Element Model (Screen Capture)

16

Eight frame element models were created based on these 2-D and 3-D geometries.

• 2-D frame element model (slopes and curve of bridge not considered)

1) Gross section properties neglecting the effect of prestressing steel

a) Fixed Supports

b) With linear soil springs at base of piers

2) Transformed section properties including prestressing steel

a) Fixed Supports


• 3-D frame element model (slopes and curve of bridge included).

1) Gross section properties neglecting the effect of prestressing steel

a) Fixed Supports


2) Transformed section properties including prestressing steel

a) Fixed Supports


3.2 Element Sizes used for SAP2000 Models

To model the varying cross section along the length of the bridge, the box girder

was modeled using frame element segments. Each segment had the same section and

properties. The mass of each segment was computed automatically by SAP2000 based

the cross sectional area, concrete density, and frame element length.

The frame element size was based on the construction segment length throughout the

bridge. For the majority of the bridge length, 5.25 meter long elements were used. Three

1.5 meter long elements were used above each pier and abutment, and three 1 meter long

17

elements were used at the closure segment at the center of the middle span. Elements

used to model the piers varied in length from 1 m to 6.45 m. Figure 3.5 shows the

SAP2000 2-D model.

Figure 3.5: Element Lengths in SAP2000 models

These element sizes were small enough to produce valid results. An analysis using finite

element sizes 50% smaller produced the same deflection results under a single truck

loading and the same modal frequencies. Figure 3.6 shows the results of the vertical

deflection under a single truck loading.

5.25

1.5 m

1 m

18

Sap2000 Frame Element ModelVertical Deflection with Single Truck Loading at CenterConvergence of Original and Half Size Finite Elements

2-D No Steel Model

-7

-6

-5

-4

-3

-2

-1

0

1

2

0 50 100 150 200

Along Length of Bridge (meters)

Vert

ical

Def

lect

ion

(mm

)

Original Size Elements

Half Size Elements

Figure 3.6: Convergence of Original and Half Size Finite Elements

3.3 Results of Frame Element Model Comparisons

3.3.1 Natural Frequencies

Natural frequencies, modal periods and mode shapes were determined for the first

nine modes for each of the eight SAP2000 frame element models. These results are

presented in Chapter six along with those from the ANSYS analysis.

3.3.2 Static Load Deformations

In order to evaluate the anticipated structural response to vehicle traffic, a number

of truck loading conditions were considered. This section presents the deflected shape

resulting from a single AASHTO HS20 truck located at midspan of the center span. This

loading condition is used to compare the various SAP2000 models. A single truck weighs

a total of 72 Kips or 320 kN. The truck scale dimensions are shown in Figure 3.7.

19

Figure 3.7: Schematic Drawing of a Single HS20 Truck Load

Chapter 4 shows results from modeling each axle or wheel for the HS20 loading

of Figure 3.7. In this section, a single point load of 320 kN is used to represent a single

truckload for comparisons of different computer modeling techniques as shown in Figure

3.8.

Figure 3.8: Single HS20 Truck Load Used in Chapter 3

20

Figure 3.9 shows the deflected shape of the bridge when subjected to a single

truck load at the center of the middle span using the 2-D SAP2000 model.

Figure 3.9: Deformed Shape due to Single Truck Load

21

Sap2000 Frame Element ModelVertical Deflection with Single Truck loading at center of bridge

Fixed Foundation SupportGross Section Properties

-7

-6

-5

-4

-3

-2

-1

0

1

2

0 50 100 150 200


Vert

ical

Def

lect

ion

(mm

)

2-D

3-D

Figure 3.10: Comparison between 2-D and 3-D Models

Figure 3.10 shows that differences between the 2-D model and the 3-D model are

minimal for static deflections. At the center of the bridge, the maximum deflections

differ by only 0.07 mm between the 2-D and 3-D model as shown in Table 3.1.

Table 3.1: Comparison of Vertical Deflections For Fixed Support

Fixed Support Models

2-D Model (mm)

3-D Model (mm)

Effect of Model Type

Gross Section 5.92 5.85 0.07 (1.2 %) Transformed Section

5.139

5.07

0.07 ( 1.3 %)

Effect of Prestressing Steel (mm)

0.78 (13.2 %)

0.78 (13.3 %)

22

2-D Sap2000 Frame Element ModelVertical Deflection With Single Truck Loading at Center

Fixed Support Model With (Transformed) or Without (Gross) Prestressing Steel

-7

-6

-5

-4

-3

-2

-1

0

1

2

0 50 100 150 200


Vert

ical

Def

lect

ion

(mm

)

2-D Model (Gross Section)

2-D Model (TransformedSection)

Figure 3.11: Comparison of Gross and Transformed Section Properties for 2-D Model Results

3-D Sap2000 Frame Element ModelVertical Deflection With Single Truck Loading at Center

Fixed Support Model With (Transformed) or Without (Gross) Prestressing Steel

-7

-6

-5

-4

-3

-2

-1

0

1

2

0 50 100 150 200


Vert

ical

Def

lect

ion

(mm

)

3-D Model (Gross Section)

3-D Model (TransformedSection)

Figure 3.12: Comparison of Gross and Transformed Section Properties for 3-D

Model Results

23

When comparing the models with and without the prestressing steel, the

differences are more significant. Figures 3.11 and 3.12 show the comparison between

gross section and transformed section properties for the 2-D and 3-D models respectively.

Table 3.1 lists the maximum midspan deflections for each model showing differences of

0.78 mm (13.2%) and 0.78 mm (13.3%) for the 2-D and 3-D models respectively.

2-D Sap2000 Frame Element ModelVertical Deflection with Single Truck Loading at Center of Bridge

2-D Models With or Without Linear Soil Spring

-7

-6

-5

-4

-3

-2

-1

0

1

2

0 50 100 150 200


Vert

ical

Def

lect

ion

(mm

)

Gross Section Without Linear SoilSpringsGross Section With Linear SoilSprings

Figure 3.13: Differences Between Fixed Supports and Soil Springs: 2-D Model

24

3-D Sap2000 Frame Element ModelVertical Deflection with Single Truck Loading at Center of Bridge

3-D Models With or Without Linear Soil Springs

-7

-6

-5

-4

-3

-2

-1

0

1

2

0 50 100 150 200


Vert

ical

Def

lect

ion

(mm

)

Gross Section Without LinearSoil SpringsGross Section With Linear SoilSprings

Figure 3.14: Difference Between Fixed Supports and Soil Springs: 3-D Model

Figures 3.13 and 3.14 show the differences between the fixed support and linear

soil springs used at the foundation of the piers for the 2-D and 3-D model respectively.

As stated previously, the soil springs are modeled with linear soil properties, and may not

accurately reflect actual soil response to different forces. Table 3.2 shows that there are

minimal differences in the vertical deflection between the fixed and spring foundation

and minimal differences between the 2-D and 3-D model. For this reason, and to keep the

ANSYS solid model under 32,000 nodes, the solid model was generated as a straight

model (equivalent to the SAP2000 2-D fixed geometry) using fixed supports at the piers.

Table 3.2: Comparison between Fixed Supports and Soil Springs

2-D Model (mm)

3-D Model (mm)

Effect of Model Type

Linear Soil Spring 5.98 5.92 0.06 (1%) Fixed Foundation

5.92

5.85 0.07 (1.2%)

Effect of Soil Springs

0.06 (1%)

0.07 (1%)

25

CHAPTER 4

ANSYS SOLID MODEL

4.1 ANSYS Solid Model Development

Reasons for creating a solid model in ANSYS include:

• More detailed representation than a frame element model

• Output strain values for use in designing a strain-based deflection system

• Study torsion effects of eccentric truck loads

• Predict thermal deformations

• ANSYS has nonlinear modeling capabilities for use in future seismic analysis.

Several software programs were considered for analyzing the solid model.

• Sap 2000 Version 8 (CSI 2002)

• ANSYS Version 6.1 (ANSYS Inc, 2002)

• Abaqus-Standard Version 6.0 (Abaqus, Inc. 2002)

• I-deas

ANSYS was the choice of software for creating the solid model. SAP2000 did not have

the capability of creating a box girder bridge with a varying cross section. SAP2000 did

not have adequate meshing capabilities and could only mesh solid models in linear

elements. I-deas was used previously to create solid bridge models of the H-3 (Ao 1999)

but the College of Engineering at the University of Hawaii no longer has a license for

I-deas. Between Abaqus and ANSYS, ANSYS appeared to be the more “user friendly”

software with a simple tutorial and CAD input capabilities.

26

4.2 Finite Element Analysis: ANSYS, an Overview

ANSYS is a finite element analysis program used for solid modeling. It has

extensive capabilities in thermal, and structural analysis.

The solid model consists of key points/nodes, lines, areas and volumes with

increasing complexity in that order. Careful thought needs to be put into the model

before building the entire model. Once the model is meshed, volumes, areas, or lines

cannot be deleted if they are connected to existing meshed elements. The aspect ratio and

type of mesh must also be decided depending on the size and shape of the complete solid

model.

ANSYS contains many solid finite elements to choose from, each having its own

specialty. First, the type of analysis must be chosen which ranges from structural

analysis, thermal analysis, or fluid analysis. Once the type of analysis is determined, an

element type needs to be chosen ranging from beam, plate, shell, 2-D solid, 3-D solid,

contact, couple-field, specialty, and explicit dynamics. Each element has unique

capabilities and consists of tetrahedral, triangle, brick, 10 node, or 20 node finite

elements both in 2-D or 3-D analysis.

4.3 Solid Model Geometry

There are three ways to create a model in any finite element program for solid modeling.

1) Direct (manual) generation

• Specify the location of nodes

• Define which nodes make up an element

• Used for simple problems that can be modeled with line elements

(links, beams, pipes)

27

• For objects made of simple geometry (rectangles)

• Not recommended for complex solid structures

2) Importing Geometry

• Geometry created in a CAD system like Autodesk Inventor

• Saved as an import file such as an IGES file.

• Inaccuracies occur during the import, and the model may not

import correctly.

3) Solid Modeling Approach

• The model is created from simple primitives (rectangles, circles,

polygons, blocks, cylinders, etc.)

• Boolean operations are used to combine primitives.

Direct manual generation was the approach used to create the SAP2000 frame

element models. However when creating a solid model that contains over 20,000 nodes,

this approach is not recommended.

Using a CAD program such as Autodesk Inventor to create the solid model was

also investigated. Autodesk Inventor had a very good CAD capability compared to

creating the model in the ANSYS CAD environment. However, attempts to import the

IGES file into ANSYS were unsuccessful. The model did not import correctly due to

software incompatibility.

The solid modeling approach was used to create the Kealakaha Bridge. Creating

the top slab of the bridge with the “extrude” command was easy because it was the same

shape throughout the bridge. However, when creating the box girder, the cross section

varied throughout the length of the bridge. ANSYS did not have good CAD capabilities

28

to create many volumes in 3-D space with a varying cross section. When creating the

solid volume for the box girder, each solid element had to be created using only 8 nodes

at a time by using the “create volumes arbitrary by nodes” command. Creation of the

final bridge model was accomplished by dividing the bridge into many volumes and

combining them together. Figure 4.1 shows the side view of portion of the bridge. Each

color represents a different area and block volume that had to be created and joined

together using the Boolean operation. Due to symmetry, the reflect and copy command

was used to create the other half of the bridge.

1

X

Y

Z

FEB 19 200311:00:21

AREAS

AREA NUM

Figure 4.1: Side View of a Portion of the Kealakaha Bridge

29

4.4 Development of Solid Model Geometry

The program that was used to analyze the solid model was ANSYS/University

High Option, Version 6.1. Limitations to this software include the maximum number of

nodes which is set at 32,000 nodes. To keep the number of nodes below this limit, the

original cross section could not be used without having a large aspect ratio during

meshing. To reduce the amount of nodes as well as computation time, the cross section

model had to be simplified. Weng Ao (1999) performed a similar study on the North

Halawa Valley Viaduct (NHVV), which is part of the H-3 freeway. The NHVV box

girder shape was very similar to the Kealakaha bridge box girder. Ao used simpler cross

sections than the original box girder and compared the predicted to measured results.

Even with simplification of the cross sections, the analytical results using the I-deas solid

modeling program showed good agreement with actual results for both thermal and truck

loading conditions.

The simplified cross section shown in Figure 4.2.2 was created by averaging the

top and bottom slab thickness of the design cross section to create an equivalent area in

the simplified cross section. The moment of inertia was changed by no more than 3% in

the lateral direction and 11% in the vertical direction.

Figure 4.2.1 shows the design cross section that was used to compute section properties

for the frame element models in SAP2000. Figure 4.2.2 shows the simplified cross

section used for the solid model in ANSYS. The depths and heights that vary are listed in

the Appendix.

30

Figure 4.2.1: Design Cross Section

Figure 4.2.2 Simplified Cross Section

31

1

X

Y

Z

FEB 19 200311:02:06

VOLUMES

TYPE NUM

Figure 4.3: ANSYS Solid Model Cross Section before Meshing

Figure 4.3 shows a close up view of the simplified cross section in ANSYS. Figures 4.4

and 4.5 show the completed solid model before meshing. The piers have fixed supports

while the abutment ends are restrained against vertical and lateral movement

perpendicular to the bridge.

32

1

X

Y

Z

FEB 20 200311:27:15

VOLUMES

TYPE NUM

U

Figure 4.4: Kealakaha Bridge before Meshing, Elevation

1

X

Y

Z

FEB 20 200311:26:02

VOLUMES

TYPE NUM

U

Figure 4.5: Kealakaha Bridge before Meshing, Isometric View

33

4.5 Meshing in ANSYS

Meshing in ANSYS can be applied manually or automatically. The element type

selected (Linear vs. Tetrahedral), and the mesh size can affect the accuracy of the results

of the analysis. Due to the large model size, automatic meshing was not possible for the

entire Kealakaha bridge. In automatic meshing, ANSYS automatically chooses a

meshing size based on the shape of the model. This resulted in more elements than

permitted by the University High Option of ANSYS. Manual meshing allows the user to

define the maximum size of the elements.

To guide the selection of element type, a test beam was created in ANSYS to

determine what solid finite element produced the best results for deflection under thermal

loading. There are two types of elements in ANSYS that have both structural and

thermal capabilities for solid modeling. They are Solid 45 which is an eight node brick

(cube shaped) element (Fig. 4.6) and Solid 92 which is a 10 node tetrahedral element

(Fig. 4.7). These elements were tested under thermal and static loads on a test beam to

determine which element produced the best results when compared to the theoretical

values.

34

Figure 4.6: Solid 45, Eight Node Structural Solid (ANSYS)

Figure 4.7: Solid 92, Ten Node Tetrahedral Structural Solid (ANSYS)

4.6 Test Beam: Determining Finite Element Type and Mesh for Thermal Loading

Solid 45 and Solid 92 were evaluated using a test beam that was 10 meters long

by one meter thick and one meter high. The sample test beam was also created to test the

performance of ANSYS under thermal loading conditions. Simply supported end

conditions were used for the test beam as shown in Figure 4.8.

35

10 Degrees 10 m

1 m

Temp Gradient

Figure 4.8: Square Test Beam-Thermal Loading

A 10-degree temperature gradient was produced by applying two different

temperatures at the top and bottom surfaces of the beam. A temperature gradient is

anticipated for the top slab of the Kealakaha bridge during solar heating similar to the H-

3 study (Ao 1999). The thermal expansion coefficient was arbitrarily chosen as 10-5 per

degrees Celsius for this test beam. Figure 4.9 shows the distribution of the temperature

that was applied throughout the beam. The red indicates a temperature of 10 degrees C,

while the blue represents a temperature of 0 degrees C. The actual thermal expansion

coefficient used in the Kealakaha bridge model will be based on concrete cylinder tests

and is expected to be in the range of 10 to 11X10-5 per degree Celsius. For the thermal

analysis performed in this study, a value of 11X10-5 per degree Celsius was used for the

Kealakaha bridge model. Concrete properties similar to the top slab of the Kealakaha

bridge was used for the test beam.

36

1

MN

MXX

Y

Z

0

1.1112.222

3.3334.444

5.5566.667

7.7788.889

10

FEB 19 200311:33:04

NODAL SOLUTION

STEP=1SUB =1TIME=1BFETEMP (AVG)RSYS=0DMX =.001304SMX =10

Figure 4.9: Thermal Distribution in Test Beam

37

4.7 Analytical Solution For Test Beam

The deformation due to a linear temperature change can be expressed as:

hT

dxdv

dxd ∆= α

where v = Vertical Deflection

α = Coefficient of Thermal Expansion

= 10-5/°C in the test beam

∆T = Change in temperature between top and bottom surfaces

= 10 °C in the test beam

h = Depth of the beam

= 1 meter in the test beam

Therefore,

hT

dxdv ∆= α x + A

BAxxhTv ++∆= 2

21 α

where A and B are integration constants.

Applying boundary conditions: At x=0, v(0)=0 and at x=10, v(10)=0 and substituting the

numerical values into the equation, we obtain:

=v (50-5x)x*10-5

At the midspan, x = 5 meters therefore:

=v 0.00125 meters

There should be a maximum deflection of 0.00125 meters at the center of the test beam.

38

Figure 4.10 shows the deflection result of the test beam in ANSYS due to the 10 degrees

temperature gradient using the solid 92 element. The automatic meshing tool was used

which produced element sizes close to 0.5 meters.

1

X

Y

Z

FEB 19 200311:32:31

DISPLACEMENT

STEP=1SUB =1TIME=1DMX =.001304

Figure 4.10: Test beam deflection under 10° Celcius Temperature Gradient

(Automatic Mesh)

4.8 Comparison of ANSYS to Theoretical Result: Thermal Loading

Table 4.1 shows the comparison between Solid 45 and Solid 92 for the thermal

loading conditions. Varying the element size from 0.25 to 1 meter had very little effect

on the vertical deflection under thermal loading. The theoretical result is 1.25 mm for the

vertical deflection at midspan. The percentage error in Table 4.1 is the error compared to

the theoretical result.

39

Table 4.1: Vertical Deflection at Midspan on Test Beam: Thermal Loading

Vertical Deflection at Midspan (mm)

Percentage Error

Theoretical Result 1.25 -

Solid45 Eight Node Structural Solid (Brick Node)

1.128 9.8%

Solid 92 Ten Node Structural Solid Tetrahedral Shaped

1.304 4.3%

Solid 92 gave the lowest percentage error of 4.3% when compared with the analytical

result.

4.9 Comparison of ANSYS to Theoretical Result: Static Point Loading

A static point load of 10 Newton applied to the midspan of the test beam

using different element types and sizes as shown in Figure 4.11.

10 N (at midspan of beam)

1 m

10 m

Figure 4.11: Square Test Beam – Point Loading

40

For a simply supported beam under a midspan point load, the theoretical deflection is:

Vertical Deflection EI

PL48

3

−=∆

where P = Load at midspan

= 10 N on test beam

L = Length of beam

= 10 m for test beam

E = Modulus of Elasticity

= 2.4X107 kN/m2 for test beam

I = Moment of Inertia = 12

3bh

= 121 m4for test beam

Substituting the numerical values produces the following theoretical result:

∆ = 1.041X10-7 m down

Table 4.2 lists the comparisons between the Solid 45 and Solid 92 elements for

the vertical deflection at the midspan due to a 10 N point load. The theoretical result will

not match the result from ANSYS because the theoretical result does not include shear

deformation. However, the % difference between the theoretical and ANSYS will be

used. The results show that Solid 92 consistently predicted deflections close to the

theoretical result with the percent difference ranging from 3.2 to 5.4%. The solid 45

results range from 5.76 to 62 percent and are highly dependant on the mesh element size.

For this reason, Solid 92 would be the better choice under a static load.

41

Table 4.2: Vertical Deflection at Midspan on Test Beam: 10 N Point Load

Element Size

Solid45 Eight Node Structural Solid

(Brick Node)

Solid 92 Ten Node Structural Solid

Tetrahedral Shaped

Vertical Deflection at

Midspan (X10-7m)

% Difference

From Theoretical

Vertical Deflection at

Midspan (X10-7m)

% Difference

From Theoretical

Automatic Meshing 1.128 8.3 1.09 4.7 0.25 meters 1.178 13.2 1.08 3.7 0.5 meters 0.961 7.7 1.09 4.7 1 meter 0.472 55 1.1 5.6 Theoretical Result 1.041 X10-7m 1.041 X10-7m

Structural Solid 92 was selected for meshing the Kealakaha Bridge model.

Solid 92 has a quadratic displacement behavior and is well suited to model irregular

geometries as shown in Figure 4.7. The element can model plasticity, creep, swelling,

stress stiffening, large deflection, and large strain conditions.

When applying a thermal load, a thermal solid element must also be selected.

ANSYS automatically chose Thermal Solid 87 for both test beam and bridge models.

Thermal analysis is done separately in ANSYS, and is saved as a .rth file in the working

directory. In thermal analysis, one must transfer the element type from a structural

element to thermal element so that thermal loads can be applied linearly. This is

important because if the program is in structural element mode, the temperatures will

only be applied at the surface of the beam, and will not be applied linearly throughout the

entire beam. After running the thermal analysis, the .rth file must be imported into the

structural element mode with Solid 92 and applied as a “temperature from thermal

analysis.” After running the structural analysis, structural deformation/stress/strain results

are produced.

42

4.10 Mesh Generation for Kealakaha Bridge Model

ANSYS has the capability of doing automatic meshing where it automatically

picks an element size. However, automatic meshing may not produce the best results and

cannot be used for the 220 meter Kealakaha bridge because it will produce over 32,000

nodes which exceeds the University program capability. The “mesh tool” command must

be used to specify the element size.

Based on the specified element size, ANSYS will mesh the model to produce the

best results. The element size will not be the same for all elements, but all elements will

be smaller than the specified size.

The mesh size used for the Kealakaha bridge was 4 meters. A similar mesh size

of 12 feet was used in the NHVV study by Weng Ao (1999), and produced good results

when compared with measured deflections. Figure 4.12 shows the 4 meter mesh for a

portion of the bridge. The full bridge consisted of 24,576 nodes and 12,246 elements.

4.11 Convergence of 4 Meter Mesh

To confirm that the four-meter mesh converges with a larger size mesh, a six

meter mesh was created and the response to a single truck load was compared. See

Figure 3.8 for a description of the single truck load. The four-meter mesh is seen in

Figure 4.12 and the six-meter mesh is shown in Figure 4.13.

43

1

FEB 20 200311:14:11

ELEMENTS

Figure 4.12: Four Meter Mesh Size, Kealakaha Bridge (Part of Bridge)

1

ELEMENTS

Figure 4.13: Six Meter Mesh Size, Kealakaha Bridge (Part of Bridge)

44

ANSYS Solid ModelVertical Deflection with Single Truck loading at center of bridge

Convergence of Four Meter Mesh Vs. Six Meter Mesh

-7

-6

-5

-4

-3

-2

-1

0

1

2

0 50 100 150 200

Distance Along Bridge (meters)

Vert

ical

Def

lect

ion

(mm

)

4 Meter Mesh

6 Meter Mesh

Figure 4.14: Convergence of Four and Six Meter Mesh for ANSYS Model

Table 4.3: Comparison between Four and Six Meter Mesh for ANSYS Model

Six Meter Mesh Vertical

Deflection (mm)

Four Meter Mesh Vertical Deflection

(mm)

Difference (%)

Maximum End Span Deflection

0.94 0.96 0.02 (2.1%)

Maximum Center Span Deflection

-5.73 -5.73

0 (0%)

The results plotted in Figure 4.14 show convergence between a four meter mesh

and a six meter mesh. The results at the maximum deflection for the end span and center

span under a single truck loading are shown in Table 4.3. In Table 4.3, there is a 0%

difference in the center span deflection, and only a 2.1% difference in the end span

deflection. Therefore, a four-meter mesh is adequate for this analysis.

45

CHAPTER 5

ANSYS SOLID MODEL ANALYSIS

5.1 Truck Loading Conditions

According to the design criteria on the construction plans, a typical truck weighs a

total of 320 kN or 72 Kips with the dimensions shown in Figure 5.1.

Figure 5.1: Distribution of Truck Loads

Each 320 kN truck has six wheels and the load is divided among all six wheels for

the ANSYS solid model. The total axle load shown in Figure 5.1 is divided by two to get

the load for each wheel. In ANSYS, loads can only be applied to existing nodes

produced by the mesh. The mesh size used was 4 meters, so the loads were placed at the

closest possible node to produce the actual wheel location.

Three different truck-loading conditions were considered in this analysis. In all of

these analyses, the truck placement was symmetrical about the midspan of the center span

of the bridge. The three loading conditions are:

46

• Single Truck Load on centerline of roadway

• Four Trucks (Two rows of two trucks each, 2x2 Truck Load) on centerline

of roadway

• Four Trucks (All four trucks in a single line) at edge of roadway

In ANSYS, each wheel was modeled as a load, however in the SAP2000 frame

element analysis, each axle was modeled as a load. ANSYS and SAP2000 model results

are compared in the following sections.

In addition, the SAP2000 frame element model and the ANSYS solid model were

also compared when a single 320 kN point load was applied at the center of the roadway

at midspan of the center span.

5.2 Truck Loading Results

5.2.1 Single 320 kN (72 Kip) Point Load

Figure 5.2 shows the single 320 kN truck point load applied to the top slab of the

ANSYS model. Figure 5.3 shows a comparison between SAP2000 and ANSYS while

Table 5.1 shows the vertical displacement under the 320 kN point load.

The maximum deflection from the SAP2000 model is less than the ANSYS

model, but at all other nodes the ANSYS model yielded slightly less deflections. The

local deformation of the top slab under the single concentrated load does not correctly

represent the effect of the truck loading.

Table 5.1: Results of Single 320 kN Truck Point Load Sap2000

Single Truck Load ANSYS

Single Truck Load Difference

Vertical Deflection at Center of Bridge Span (mm)

-5.92

-6.32

0.4 (6.7%)

Maximum End Span Deflection (mm) 1.04 1.01

0.03 (2.9%)

47

1 2

3

X

YZ

X

Y

Z

ELEMENTS ELEMENTS

ELEMENTS

UF

UF

UF

Figure 5.2: ANSYS Layout of Single Truck Point Load

SAP2000 Vs. ANSYSSingle Truck (Point Load) at Center of Bridge

-7

-6

-5

-4

-3

-2

-1

0

1

2

0 50 100 150 200


Vert

ical

Def

lect

ion

(mm

)

ANSYS

SAP2000

Figure 5.3: SAP2000 vs. ANSYS, Single Truck Point Load

48

5.2.2 Distributed Single Truck Load

Figure 5.4 shows the viaduct section with a single truck loading placed at the

center of the section and at the center span along the length of the bridge. Isometric, top

and side views are shown in ANSYS in Figure 5.5. The results for the vertical deflection

due to the single truck load are shown in Figure 5.6. Wheels were modeled to conform to

Figure 5.1 but dimensions of the truck wheels vary according to the node locations in the

solid model. The results for deflections are shown in table 5.2

Table 5.2: Vertical Deflection at Center of Bridge due to Single Truck Load, Actual Wheels Modeled

Vertical Deflection at Center of Bridge (mm)

SAP2000 Each Axle Modeled

ANSYS Each Wheel

Modeled

Difference (mm)


-5.69

-5.73 0.04 mm (0.6%)

Maximum End Span Deflection (mm)

0.98

0.97

0.2 mm (3.2%)

Figure 5.4 Viaduct Section Showing Single Truck Load

49

1 2

3

X

YZ

X

Y

Z

ELEMENTS ELEMENTS

ELEMENTS

UF

UF

UF

Figure 5.5: Layout of Wheel Placement for Single Truck

SAP2000 Vs. Ansys Single Truck Load at Center Of Bridge

ANSYS: Each Wheel Modeled SAP2000: Each Axle Modeled

-7

-6

-5

-4

-3

-2

-1

0

1

2

0 50 100 150 200


Vert

ical

Def

lect

ion

(mm

)

ANSYS

SAP2000

Figure 5.6: SAP2000 vs. Ansys, Single Truck Modeled with Wheels

3.12 m

5.25 m

10.38 m

50

5.2.3 2x2 Truck Loading

Figure 5.7 shows the locations of the axles for the 2x2 truck loading. Figure 5.8

shows the viaduct section under the 2x2 truck loading. The trucks are placed

symmetrically about the center span to reduce computational time for the analysis and

produce symmetrical deflected shapes. The axle spacing is larger than as shown in

Figure 5.1 due to limited node locations available for applying the loads. Figure 5.9

shows the layout of the 2x2 truck loading in ANSYS. The vertical deflection results are

shown in Figure 5.10 and Table 5.3.

Table 5.3: Vertical Deflection of Bridge Due to 2x2 Truck Load (Actual Wheels Modeled)

Vertical Deflection at Center of Bridge (mm)

SAP2000 Each Axle Modeled

ANSYS Each Wheel

Modeled

Difference (mm)


-19.49

-19.17

0.32 mm (1.6%)


3.77

3.61 0.16 mm (4.2%)

Midspan of Bridge Center Span

Figure 5.7: Location of Axle Loads for the 2x2 Truck Configuration

51

Figure 5.8: Viaduct Section showing 2x2 Truck Configuration

1 2

3

X

YZ

X

Y

Z

ELEMENTS ELEMENTS

ELEMENTS

UF

UF

UF

Figure 5.9: ANSYS Placement of 2x2 Truck Load

52

SAP2000 Vs ANSYS 2X2 Truck Load, 4 Trucks Total ANSYS: Each Wheel ModeledSAP2000: Each Axle Modeled

-25

-20

-15

-10

-5

0

5

0 50 100 150 200

Length Along Bridge (meters)

Vert

ical

Def

lect

ion

(mm

)

ANSYS

SAP2000

Figure 5.10: SAP2000 vs. ANSYS, 2x2 Truck Modeled with Wheels

5.2.4 4 Truck Loading Creating Torsion Effects.

4 truck loads were placed at the edge of the viaduct cross section to study torsion

effects due to eccentric loading. Figure 5.11 shows the locations of the axle loadings for

the trucks. The trucks are placed symmetrically about the center span of the bridge to

reduce the computational time for the analysis and to generate a symmetrical deflected

shape.

Midspan of bridge center span

Figure 5.11: Location of Axle Loads for Four Trucks in a Row

53

The 4 trucks modeled at the right edge of the viaduct section are shown in Figure

5.12. Figure 5.12 show the locations “A,” “B,” and “C,” where the vertical deflections

were recorded. Location “C” is at the middle of the cross section. Location “B” is on the

side of the truck loading above the box girder stem and location “A” is on the opposite

side above the box girder stem. Figure 5.13 shows the layout of the 4 trucks in ANSYS.

The loads are applied at the nodes.

Figure 5.12: Viaduct Section showing Four Trucks in a Row

1 2

3

X

YZ

X

Y

Z

ELEMENTS ELEMENTS

ELEMENTS

UF

UF

UF

Figure 5.13: ANSYS Layout of Four Trucks in a Row

54

Figure 5.14 shows the deflected and non-deflected shape of the cross section modeled in

ANSYS at midspan of the center span of the bridge, the legend at the bottom shows the

vertical deflection in meters. Locations “A,” “B,” and “C” are shown at the top of the

slab (See Figure 5.12 for more precise locations). The result of the vertical deflection

due to the truck load are shown in Figure 5.15.

1

X

Y

Z

-.02163-.018763

-.015896-.013029

-.010162-.007295

-.004427-.00156

.001307.004174

Figure 5.14: Deflected and Non-Deflected Cross Section

ANSYS: Torsion Effects 4 Trucks in a Row at Edge of Bridge

ANSYS: Each Wheel Represented By One Load

-20

-15

-10

-5

0

5

0 50 100 150 200


Vert

ical

Def

lect

ion

(mm

)

Location A

Location B

Location C(Center)

Figure 5.15: Torsion Effects, Four Trucks in a Row

CB

A

Truck

55

Table 5.4 shows the results of the vertical deflections at locations “A,” “B,” and

“C.” The torsion effect shows that there is a 2.43 mm difference between the left and

right sides of the bridge cross section at the center span and a 0.57 mm difference in the

maximum end span deflections.

Table 5.4: Vertical Deflection of Bridge due to 4 Truck Loading at Edge of Bridge (Actual Wheels Modeled)

Vertical Deflection in Cross Section Points A and B (mm)

ANSYS Location A

(Left)

ANSYS Location B

(Right)

% Difference (torsion effect)


-16.20

-18.63

2.43 (13.0%)


3.71

3.14

0.57 (15.4%)

Figure 5.16 shows an isometric view of the bridge with color contours for the

vertical deflection of the bridge. The torsion effect can be seen by the different colors.

The legend shows the deflection in meters.

1

MN

MX

X

Y

Z

-.02163

-.018763-.015896

-.013029-.010162

-.007295-.004427

-.00156.001307

.004174

NODAL SOLUTION

STEP=1SUB =1TIME=1UY (AVG)RSYS=0DMX =.021714SMN =-.02163SMX =.004174

Figure 5.16: Isometric View of Vertical Deflection under Torsion Loading

56

57

CHAPTER 6

TEMPERATURE ANALYSIS 6.1 Temperature Gradient

Figure 6.1: ANSYS Applied Temperature Gradient

Figure 6.1 show the temperature gradient applied to the ANSYS solid model. A

10 degrees Celsius linear temperature gradient is applied through the 0.35 m thick top

slab. The temperature gradient was based on temperature measurements from the NHVV

(Ao, 1999). Below the top slab, the temperature was assumed constant at zero degrees

throughout the box girder, and piers. This thermal loading develops by mid afternoon

due to solar radiation on the top surface of the bridge. Thermocouples will be installed in

the Kealakaha Bridge to record the exact temperature gradients after the bridge is built.

The coefficient of thermal expansion used for this analysis was 11X10-5 per

degrees Celsius.

58

1

MX

0

1.1112.222

3.3334.444

5.5566.667

7.7788.889

10

NODAL SOLUTION

STEP=1SUB =1TIME=1BFETEMP (AVG)RSYS=0DMX =.008688SMX =10

Figure 6.2: Bridge End Span Showing Effect of Thermal Gradient

6.2 Results of Temperature Gradient

Figure 6.2 shows the temperature gradient applied through the top slab of the

bridge and the resulting exaggerated deformed shape. Figure 6.3 shows the deformation

of the bridge due to the 10 degree temperature gradient. Figures 6.4 and 6.5 show

isometric and side views of the deformation of the bridge.

59

1 2

3 4

X

Y

Z

X

YZ

X

Y

Z

X

Y

Z

DISPLACEMENT DISPLACEMENT






Figure 6.3: Deformation due to 10 Degree Temperature Gradient

1

X

Y

Z

DISPLACEMENT


Figure 6.4: Isometric View of Bridge Deformation due to Thermal Loading

60

1

X

Y

Z

DISPLACEMENT


Figure 6.5: Side View of Bridge Deformation due to Thermal Loading

61

The deflected shape is plotted along the middle of the top slab (location “a”),

along the top of the box stems (“b”) and along the edge of the top slab cantilevers (“c”).

Locations “a” and “c” are affected by longitudinal and transverse deformations as seen in

Figure 6.5, hence location “b,” above the box girder stems, is assumed to be the best

representation of the deformed shape of the bridge spans. Comparisons with measured

deflections based on the field instrumentation will confirm whether these predicted

deflections are accurate.

Figure 6.6 shows the approximate locations “a,” “b,” and “c” in the cross section

view indicated by the circles.

X

Y

Z

-.008667-.007468

-.006269-.005071

-.003872-.002674

-.001475-.276E-03

.922E-03.002121

Figure 6.6: Locations of Reported Deformation due to Thermal Loading

b b

c c

a

62

ANSYS Solid ModelVertical Deflection due to Gradient Temperature of 10 Degrees Celcius through top

slab

-10

-8

-6

-4

-2

0

2

4

0 50 100 150 200

Distance Along Bridge (meters)

Vert

ical

Def

lect

ion

(mm

)Deflection along roadway centerline (a)

Deflection above base stems (b)

Deflection at end of cantilever (c)

Figure 6.7: Vertical Deflection of Bridge due to Ten Degree Temperature Gradient

Table 6.1: Vertical Deflection due to Temperature Gradient Distance Along Bridge (meters)

Deflection (mm) Along Roadway

Centerline “a”

Deflection (mm) Above Base Stems

“b”

Deflection (mm) at End of

Cantilever “c”

16.75 m and 203.25 m

2.1 1.79 1.19

110 m -5.08 -5.48 -8.66

Figure 6.7 shows the vertical deflections at points a, b, and c. The results at the

center span and maximum deflections in the end spans are shown in Table 6.1. Results

show that at 110 meters, the greatest deflection occurs downwards. At 16.75 and 203.25

meters, the greatest upward deflection occurs. Location “b” best represents the deformed

shape of the bridge span. The top slab curls upwards at the center “a” while the left and

right cantilevers “c” deflect downwards due to the temperature applied at the top

surface.

63

ANSYS Solid ModelCombination of Temperature and Truck Loading

-14

-12

-10

-8

-6

-4

-2

0

2

4

0 50 100 150 200

Along Length Of Bridge (meters)

Vert

ical

Def

lect

ion

(mm

)

Temperature Only (10 DegreesCelcius)One Truck Loading Only

Combined

Figure 6.8: Combination of Temperature and Truck Loading

Figure 6.8 shows the combination of the temperature and the truck loading. Note

that the vertical deflection due to thermal gradient of 10° C is similar to that caused by a

single truck load. Since, this is a linear elastic analysis, the deformation due to the

“temperature only” and the “truck loading only” can be added using superpositioning to

determine the deformation due to the combined temperature and truck loading. For this

reason, any results used from the truck loading analysis in the previous section can be

added to the “temperature only” analysis to get the deformations for both temperature and

truck loading simultaneously. While monitoring deflections of the bridge under ambient

traffic, it will be necessary also to measure the thermal gradient through the top slab so as

to adjust for the deflections due to thermal loading.

64

6.3 Strain Distribution

The strain distribution through the box girder depth under a single truck load is

shown near the pier support in Figure 6.9 and at the midspan of the center span in Figure

6.10.

Strain Distribution Through Box Girder Depth Near Pier Along Length of Bridge (Single Truck Load)

-6

-5

-4

-3

-2

-1

0

-6 -4 -2 0 2 4 6 8

Microstrain

Dep

th o

f Brid

ge (m

)

Tension

Compression

Figure 6.9: Strain Distribution through Box Girder Depth near Pier

Strain Distribution Through Box Girder DepthNear Centerspan Along Length of Bridge (Single Truck load)

-3

-2.5

-2

-1.5

-1

-0.5

0

-18 -13 -8 -3 2 7 12

Microstrain

Dep

th o

f Brid

ge (m

)

Compression

Tension

Figure 6.10: Strain Distribution through Box Girder Depth near Midspan

65

Figure 6.11: Strain Output Locations

Figure 6.11 shows the locations where future strain gages will be installed after

the bridge is built to monitor longitudinal strain in the box girder. These gages will be

used in a strain based deflection system under development at the University of Hawaii

(Fung, 2003). The gages selected for this system must have sufficient resolution to

monitor the anticipated strains.

The locations are represented with the letters A, B, C, and D. Locations A and B

are at the inside top of the box girder, while locations C and D are located at the inside

bottom of the box girder. The longitudinal strains due to a single truck at midspan of the

center span and due to a 10 degree temperature gradient throughout the top slab are

shown in Figures 6.12 and 6.13.

In order to measure these strains, the gages will need a production of 1

microstrain. It will also be important to monitor the slab temperature so as to separate the

thermal effects from the loading effects.

66

ANSYS Solid ModelLongitudinal Strain at Location A and B Along Length of Bridge

-20

-10

0

10

20

30

40

50

60

70

0 50 100 150 200


Long

itudi

nal S

trai

n (C

ompr

essi

on +

) (m

icro

stra

in)

Temperature Only (10 DegreesCelcius)One Truck Loading Only

Combined

Figure 6.12: Longitudinal Strains at Locations A and B

ANSYS Solid ModelLongitudinal Strain at Location C and D Along Length Of Bridge

-20

-10

0

10

20

30

40

50

0 50 100 150 200


Long

itudi

nal S

trai

n (c

ompr

essi

on +

) m

icro

stra

in

Temperature Only (10 Degrees Celcius)Truck Loading OnlyCombined

Figure 6.13: Longitudinal Strains at Locations C and D

67

CHAPTER 7

MODAL ANALYSIS 7.1 Modal Periods

The first nine modal periods of the Kealakaha bridge were obtained from the

SAP2000 and ANSYS models. The objective of this study was to obtain the basic mode

shapes to confirm the locations of the strain gages and accelerometers during the

construction of the bridge. The accelerometers and strain gages will measure structural

response to ambient traffic, thermal loading, and seismic activity. The modal periods

from the different SAP2000 models are compared in Tables 7.1.1, 7.1.2, and 7.1.3. Table

7.1.4 shows the comparison between the SAP2000 model and the equivalent ANSYS

model. The mode shapes are shown in Figures 7.1 to 7.18.

7.1.1 Modal Periods: 2-D vs. 3-D Models

Table 7.1.1 shows the comparison of modal periods between the 2-D and 3-D

models for the SAP2000 frame element models, using the gross section properties. There

was less than a 1% difference in periods between the 2-D and 3-D models.

Table 7.1.1: Modal Periods: 2-D vs. 3-D

Mode 2-D no steel 3-D no steel % Difference1 0.951 0.954 -0.2 2 0.912 0.905 0.7 3 0.660 0.658 0.4 4 0.410 0.408 0.5 5 0.340 0.340 -0.1 6 0.319 0.317 0.6 7 0.274 0.273 0.3 8 0.255 0.254 0.5 9 0.187 0.186 0.4

68

7.1.2 Modal Periods: Gross Section vs. Transformed Section

As seen in Table 7.1.2, there is also very little difference between modal periods

for models with gross section (no prestressing steel) and transformed properties

including (prestressing steel). Therefore, including the prestressing steel resulted in less

than 2.2% difference in the modal periods.

Table 7.1.2: Modal Periods: Gross Section vs. Transformed Section

Mode 2-D no steel 2-D with steel % Difference1 0.951 0.965 -1.5 2 0.912 0.891 2.2 3 0.660 0.674 -2.1 4 0.410 0.401 2.2 5 0.340 0.345 -1.5 6 0.319 0.319 0.0 7 0.274 0.275 -0.6 8 0.255 0.250 2.0 9 0.187 0.187 -0.2

7.1.3 Modal Periods: Linear Soil Spring vs. Fixed Support

Table 7.1.3 shows the modal period comparison between the 2-D SAP2000 model

with linear soil springs versus fixed supports. For most mode shapes, the modal periods

were similar for the SAP2000 models with or without linear soil springs. However, in

modes with significant transverse pier displacement, the modal periods for models with

soil springs were up to 21% larger than models without soil springs. There was a high

percent difference in modes 3, 5 and 7 which are shown in Figures 7.6, 7.10, and 7.14

respectively. This is due to the lateral soil springs, which are less stiff than the fixed

supports. It will be important in future studies to determine the nonlinear and dynamic

properties of the soil to obtain the accurate soil stiffness for seismic analysis.

69

Table 7.1.3: Modal Periods: Linear Soil Spring Supports vs. Fixed Support

Mode 2-D no steel,

Fixed Support 2-D no steel, Soil Springs % Difference

1 0.951 1.002 -5.3 2 0.912 0.918 -0.7 3 0.660 0.776 -17.5 4 0.410 0.414 -1.0 5 0.340 0.413 -21.5 6 0.319 0.320 -0.2 7 0.274 0.296 -8.1 8 0.255 0.255 -0.1 9 0.187 0.187 0.0

7.1.4 Modal Periods, SAP2000 vs. ANSYS

Table 7.1.4 shows the comparison between SAP2000 and ANSYS for the first 9

mode shapes. Mode 1 from the ANSYS model corresponds to mode 2 from SAP2000.

There is a significant difference in modal periods for mode shapes 5,7 and 9, which have

substantial torsion in the box girder as detected in the ANSYS runs. The torsional cross-

section properties used in the SAP2000 models may not accurately represent the box-

girder.

Table 7.1.4: Modal Periods, SAP2000 vs. ANSYS Mode SAP2000

(sec.) ANSYS

(sec.) % Difference

1 0.951 0.889 4.5 2 0.912 0.901 1.2 3 0.660 0.703 6.1 4 0.409 0.418 1.9 5 0.340 0.401 15.2 6 0.319 0.333 4.1 7 0.274 0.329 16.8 8 0.255 0.271 5.9 9 0.187 0.207 9.8

7.2 Mode Shapes

The first nine mode shapes obtained from the SAP2000 and ANSYS models are

shown in Figures 7.1 to 7.18.

70

1 2

3

X

Y

Z

X

YZ

X

Y

Z


DISPLACEMENT

STEP=1SUB =2FREQ=1.124RSYS=0DMX =.420E-03



Figure 7.1: ANSYS Mode 2

Figure 7.2: SAP2000 Mode 1

71

1 2

3

X

Y

Z

X

YZ

X

Y

Z


DISPLACEMENT






72

1 2

3

X

Y

Z

X

YZ

X

Y

Z


DISPLACEMENT






73

1 2

3

X

Y

Z

X

YZ

X

Y

Z


DISPLACEMENT






74

1 2

3

X

Y

Z

X

YZ

X

Y

Z


DISPLACEMENT






75

1 2

3

X

Y

Z

X

YZ

X

Y

Z


DISPLACEMENT






76

1 2

3

X

Y

Z

X

YZ

X

Y

Z


DISPLACEMENT






77

1 2

3

X

Y

Z

X

YZ

X

Y

Z


DISPLACEMENT






78

1 2

3

X

Y

Z

X

YZ

X

Y

Z


DISPLACEMENT






79

CHAPTER 8

SUMMARY AND CONCLUSIONS

8.1 Summary

The studies described in this report focus on the short-term structural performance

of a new replacement Kealakaha Bridge scheduled for construction in Fall 2003.

A new three span, 220-meter concrete bridge will be built to replace an existing

six span concrete bridge spanning the Kealakaha Stream on the island of Hawaii. During

and after construction, fiber optic strain gages, accelerometers, Linear Variable

Displacement Transducers (LVDT’s) and other instrumentation will be installed to

monitor the structural response during ambient traffic and future seismic activity. This

will be the first seismic instrumentation of a major bridge structure in the State of Hawaii.

The studies reported here use computer modeling to predict bridge deformations under

thermal and static truck loading. Mode shapes and modal periods are also studied to see

how the bridge would react under seismic activity.

SAP2000 was used to generate 2-D and 3-D frame element models while ANSYS

was used to generate a full 3-D solid model of the bridge structure.

Results from this study will be used to confirm the locations of the strain gages

and accelerometers during the construction of the bridge. The accelerometers and strain

gages will measure structural response to ambient traffic, thermal loading and seismic

activity. Various computer modeling techniques were investigated in this study to aid in

the development of future models of the bridge for dynamic and nonlinear analysis.

80

8.2 Conclusions

Conclusions from the SAP2000 frame element analysis include the following:

• Differences between the SAP2000 2-D and 3-D models are minimal therefore a

2-D model is sufficient for estimating deflections under static loads and for modal

analysis.

• Including prestressing steel in the SAP2000 models has a significant effect on

vertical deflections under static truck loads but little effect on the modal analysis.

• Including linear soil springs in place of fixed supports did not affect vertical

deflections due to static loads but did affect certain modal periods and will

therefore affect modal analysis of seismic response.

• Further soil investigation should provide non-linear soil properties which will

enhance soil spring modeling.

Conclusions from the ANSYS Solid modeling include the following:

• ANSYS and SAP2000 produced similar deflections under static truck load with

less than a 4% difference.

• Thermal loading of a 10° Celsius gradient through the top slab of the box girder

produced significant deformations of both the top slab and overall box girder.

Thermal effects should therefore be considered in all future analysis of the bridge

and when processing measured deformations.

• Strain gages installed to monitor longitudinal strains must have a 1 microstrain

resolution in order to record the full effects of a single truck load or 10° Celsius

thermal gradient.

81

Conclusions from the modal analysis include the following:

• ANSYS and SAP2000 produced equivalent modal shapes and modal periods for

all modes. Differences of up to 16 % were noted in modes with significant

torsion in the box girder.

• Including the prestressing steel had little effect on the modal periods.

• For most mode shapes, the modal periods were similar for the SAP2000 models

with or without linear soil springs. However, in modes with significant transverse

pier displacement, the modal periods for models with soil springs were up to 21%

larger than models without soil springs.

8.3 Sources of Possible Error

Several assumptions were made in the computer modeling.

• All models assume linear elastic material properties for both concrete and soil

elements.

• For the thermal analysis, a linear temperature gradient of 10 ° Celsius was

assumed through the top 0.35 meter thick slab. This temperature gradient was

estimated based on monitoring of the H-3 Freeway.

• Material properties were based on the design plans. The actual material

properties used during construction should be investigated and included in these

models for post construction analysis.

• Abutment supports were assumed as rollers, while the actual bridge bearings will

develop frictional forces.

82

8.4 Suggestions for Further Study

• Include nonlinear and dynamic soil properties for bridge modeling.

• Obtain exact temperatures from the bridge thermocouples after bridge

construction to study thermal loading.

• Use the accelerometers for system identification to determine the actual modal

periods.

• Perform truck loading and thermal studies on the bridge after construction to

compare with computer modeling predictions.

83

REFERENCES AASHTO “LRFD Bridge Design Specification-Metric Units” First Edition (1994) including the 1996 and 1997 Interm Revisions. ANSYS. ANSYS Inc (1970-2002) Version 6.1, Canonsburg, PA. Ao, Weng and Robertson, Ian (1999), “Investigation of Thermal Effects and Truck Loading on the North Halawa Valley Viaduct”, Report UHM/CE/99-05, Honolulu, HI.

Computers and Structures, Inc., SAP2000 NonLinear Version 7.40, Berkeley, CA, 2000. Department of Transportation, “Highways Division, Plans for Hawaii Belt Road Kealakaha Stream Bridge Replacement,” Federal Aid Project No. BR-019-2(26), District of North Hilo, HI, July 2001. Fung, Stephanie S.Y. and Robertson, Ian (2003), “Seismic Monitoring of Dynamic Bridge Deformations using Strain Measurements”, Research Report UHM/CEE/03-02, May 2003, Honolulu, HI.

Geolabs (2001), “Correspondence with Sato and Associates dated January 29, 2001”, Geolabs Inc. Honolulu, HI. Geolabs-Hawaii, Geotechnical Engineering Exploration, Kealakaha Stream Bridge Replacement, Project No. BR-19-2(24), Kealakaha, Hamakua, Hawaii, November 17, 1998. Sato and Associates, Kealakaha Bridge Seismic Instrumentation, Job No. 96048.02, “Design Criteria Document, Bruco Model and Section Properties, Seisab Model and Section Properties, Pier Springs”, Feb. 14, 2002 Correspondence. USGS (1996) Earthquake Hazards Program, National Seismic Mapping Project, http://geohazards.cr.usgs.gov/eq/. UBC (1997), “Uniform Building Code, 1997,” International Conference of Building Officials, ICBO, Los Angeles, CA.

84

85

Coordinates Of Sap2000 2-D Model Kealahaha Bridge `

Node Section Number

Length of Segment

(m) X (m) Y(m) Z(m) Node Section Number

Length of Segment

(m) X (m) Y(m) Z(m)1 2.00 -2.0000 0 -1.100 39 1 5.25 166.50 0 -2.5352 11 1.00 0.0000 0 -1.100 40 2 5.25 171.75 0 -2.2343 11 5.25 1.0000 0 -1.100 41 3 5.25 177.00 0 -1.9664 10 5.25 6.2500 0 -1.111 42 4 5.25 182.25 0 -1.7305 9 5.25 11.500 0 -1.146 43 5 5.25 187.50 0 -1.5256 8 5.25 16.750 0 -1.204 44 6 5.25 192.75 0 -1.3937 7 5.25 22.000 0 -1.286 45 7 5.25 198.00 0 -1.2868 6 5.25 27.250 0 -1.393 46 8 5.25 203.25 0 -1.2049 5 5.25 32.500 0 -1.525 47 9 5.25 208.50 0 -1.14610 4 5.25 37.750 0 -1.730 48 10 5.25 213.75 0 -1.11111 3 5.25 43.000 0 -1.966 49 11 1 219.00 0 -1.10012 2 5.25 48.250 0 -2.234 50 11 2 220.00 0 -1.10013 1 1.50 53.500 0 -2.535 51 11 3.46 222.00 0 -1.10014 1 1.50 55.000 0 -2.535 52 Not Used 15 1 5.25 56.500 0 -2.535 53 13 6.45 55.00 0 -6.00016 2 5.25 61.750 0 -2.234 54 12 2.5 55.00 0 -12.45017 3 5.25 67.000 0 -1.966 55 12 3.46 55.00 0 -18.90018 4 5.25 72.250 0 -1.730 56 12 6.45 55.00 0 -21.40019 5 5.25 77.500 0 -1.525 57 13 6.45 165.0 0 -6.00020 6 5.25 82.750 0 -1.393 58 12 6.45 165.0 0 -12.45021 7 5.25 88.000 0 -1.286 59 12 2.5 165.0 0 -18.90022 8 5.25 93.250 0 -1.204 60 12 --- 165.0 0 -21.40023 9 5.25 98.500 0 -1.14624 10 5.25 103.75 0 -1.11125 11 1.00 109.00 0 -1.10026 11 1.00 110.00 0 -1.10027 11 5.25 111.00 0 -1.10028 10 5.25 116.25 0 -1.11129 9 5.25 121.50 0 -1.14630 8 5.25 126.75 0 -1.20431 7 5.25 132.00 0 -1.28632 6 5.25 137.25 0 -1.39333 5 5.25 142.50 0 -1.52534 4 5.25 147.75 0 -1.73035 3 5.25 153.00 0 -1.96636 2 5.25 158.25 0 -2.23437 1 1.50 163.50 0 -2.53538 1 1.50 165.00 0 -2.535

* Nodes 1 to 51 are on the center line of the box girder from left to right in the SAP models

* Nodes 53-56 are on the center line of the left pier from top to bottom

* Nodes 57-60 are on the center line of the right pier from top to bottom

APPENDIX AMODEL INPUT DATA

86

Coordinates of Sap2000 3-D Model Kealahaha Bridge

Node Section Number

X coordinate of centroid

(Longitudinal direction)

(m)

Y coordinate of centroid

(Transverse direction)

(m)

Z coordinate of centroid (Vertical

Direction)(m)

1 0 0 0 2 11 0.920 -0.274 -0.014 3 11 1.896 -0.555 -0.026 4 10 6.934 -1.972 -0.111 5 9 11.991 -3.341 -0.225 6 8 17.057 -4.657 -0.367 7 7 22.135 -5.928 -0.541 8 6 27.225 -7.154 -0.745 9 5 32.324 -8.324 -0.980

10 4 37.432 -9.452 -1.295 11 3 42.556 -10.525 -1.648 12 2 47.683 -11.549 -2.037 13 1 52.825 -12.530 -2.466 14 1 54.321 -12.805 -2.503 15 1 55.821 -13.076 -2.539 16 2 60.978 -13.978 -2.359 17 3 66.139 -14.825 -2.217 18 4 71.308 -15.630 -2.115 19 5 76.493 -16.380 -2.047 20 6 81.674 -17.087 -2.059 21 7 86.868 -17.739 -2.103 22 8 92.065 -18.340 -2.179 23 9 97.265 -18.898 -2.285 24 10 102.474 -19.404 -2.419 25 11 107.686 -19.858 -2.583 26 11 108.698 -19.937 -2.618 27 11 109.710 -20.022 -2.653 28 10 114.928 -20.403 -2.846 29 9 120.152 -20.742 -3.064 30 8 125.379 -21.028 -3.304 31 7 130.607 -21.266 -3.569 32 6 135.834 -21.452 -3.862 33 5 141.064 -21.589 -4.181 34 4 146.295 -21.677 -4.572 35 3 151.528 -21.714 -4.995 36 2 156.762 -21.702 -5.466 37 1 161.995 -21.638 -5.941 38 1 163.522 -21.610 -5.994 39 1 165.046 -21.580 -6.047 40 2 170.277 -21.437 -5.919 41 3 175.504 -21.238 -5.824 42 4 180.731 -21.004 -5.763

87

Coordinates Of Sap2000 3-D Model – Cont. Kealahaha Bridge

Node Section Number

X coordinate of centroid

(Longitudinal direction)

(m)

Y coordinate of centroid

(Transverse direction)

(m)

Z coordinate of centroid (Vertical

Direction) (m)

43 5 185.962 -20.711 -5.734 44 6 191.180 -20.373 -5.778 45 7 196.398 -19.974 -5.849 46 8 201.610 -19.541 -5.944 47 9 206.819 -19.050 -6.066 48 10 212.022 -18.511 -6.210 49 11 217.222 -17.910 -6.379 50 11 218.212 -17.794 -6.415 51 11 219.237 -17.678 -6.450 52 Not Used 53 13 54.321 -12.805 -5.968 54 12 54.321 -12.805 -12.418 55 12 54.321 -12.805 -18.868 56 12 54.321 -12.805 -21.399 57 13 163.522 -21.610 -9.459 58 12 163.522 -21.610 -15.909 59 12 163.522 -21.610 -22.359 60 12 163.522 -21.610 -24.859

88

SAP2000 Cross Section Properties Kealakaha Bridge Cross Section Properties at Segment Joints

Section Number

Box Girder Depth

(m) Width (m)

Centroid Distance from top

(m)

Cross Sectional

Area (m2)

Torsional Constant

(m4)

Moment of Inertia about

3 Axis (Ix) (m4)

Moment of Inertia about

2 Axis (Iy)(m4)

1 6 14.6 2.535 13.025 88.943 72.994 150.321 2 5.43 14.6 2.234 12.307 72.833 56.178 144.523 3 4.92 14.6 1.966 11.643 59.340 43.187 139.305 4 4.47 14.6 1.730 11.033 48.461 33.249 134.667 5 4.08 14.6 1.525 10.477 39.245 25.721 130.609 6 3.75 14.6 1.393 10.180 33.444 21.026 127.419 7 3.48 14.6 1.286 9.937 28.962 17.579 124.809 8 3.27 14.6 1.204 9.748 25.651 15.138 122.778 9 3.12 14.6 1.146 9.613 23.383 13.520 121.328 10 3.03 14.6 1.111 9.532 22.063 12.598 120.458 11 3 14.6 1.100 9.283 21.630 11.993 114.855 12 2 7 14 18.667 4.667 57.167 13 203 1 1 1

Section 13 is a weightless member which acts as a rigid link between the pier and the box girder

Material Properties used in SAP2000 Units are kilonewtons and meters Mass per

unit volume (kg/m3)X103

Weight per unit volume (kN/m3)

Modulus of Elasticity (kN/m2)

Poissons Ratio

Coeff. Of thermal expansion (per degree C)

Shear Modulus(kN/m2)

Reinforcing Yield Stress, Fy (kPa)

Concrete Strength, fc (kPa)

Shear steel yield stress Fyv

Super-Structure Concrete (Box Girder)

2.5586 25.1 24000000 0.2 0.000011 8750000 413686 41369 413686

Sub-Structure Concrete (Piers)

2.5586 25.1 21000000 0.2 0.000011 8750000 413686 42000 413686

Weightless (Connector)

0 0 * Rigid Link

0.2 0.000011 1.2E+07 413686 27580 413686

* The rigid link Modulus of Elasticity is 4 times the stiffness of the piers.

89

90

ANSYS Solid Model - Coordinates Distance Along Length of Bridge (meters)

Section Number

Length of Section (meters)

0.0000 11 Start 1.0000 11 1.00 6.2500 10 5.25 11.500 9 5.25 16.750 8 5.25 22.000 7 5.25 27.250 6 5.25 32.500 5 5.25 37.750 4 5.25 43.000 3 5.25 48.250 2 5.25 53.500 1 5.25 55.000 1 1.50 56.500 1 1.50 61.750 2 5.25 67.000 3 5.25 72.250 4 5.25 77.500 5 5.25 82.750 6 5.25 88.000 7 5.25 93.250 8 5.25 98.500 9 5.25 103.75 10 5.25 109.00 11 5.25 110.00 11 1.00 111.00 11 1.00 116.25 10 5.25 121.50 9 5.25 126.75 8 5.25 132.00 7 5.25 137.25 6 5.25 142.50 5 5.25 147.75 4 5.25 153.00 3 5.25 158.25 2 5.25 163.50 1 5.25 165.00 1 1.50 166.50 1 1.50 171.75 2 5.25 177.00 3 5.25 182.25 4 5.25 187.50 5 5.25 192.75 6 5.25 198.00 7 5.25 203.25 8 5.25 208.50 9 5.25 213.75 10 5.25 219.00 11 5.25 220.00 11 1.00

91

ANSYS Solid Model - Cross Section Depths

Design Cross Section (Figure 2.5 and Figure 4.2.1)

Simplified Cross Section (Figure 4.2.2)

Section Number

Slab Thickness T (meters)

Height h (meters)

Slab Thickness t (meters)

1 0.45 -6.00 0.45 2 0.4 -5.47 0.43 3 0.35 -4.90 0.40 4 0.3 -4.39 0.38 5 0.25 -3.95 0.35 6 0.25 -3.62 0.35 7 0.25 -3.35 0.35 8 0.25 -3.14 0.35 9 0.25 -3.12 0.35

10 0.25 -3.03 0.35 11 0.25 -3.00 0.33

Technology

Uhm cee-03-03