Stresses in Steel Girder Bridges - College of Engineering

ReportNumber 96-28MN DEPT OF TRANSPORTATION

3 0314 00023 6876

Ak

V

Stresses in Steel Girder BridgesCTSTG315.G361996

UNIVERSITY OF MINNESOTA

CENTER FOR

STUDIES

Technical Report Documentation Page1. Report No. 2. 3. Recipient's Accession No.

MN/RC - 96/28

4. Title and Subtitle 5. Report Date

STRESSES IN STEEL CURVED GIRDER BRIDGES August 1996

6.

7. Author(s) 8. Performing Organization Report No.

Theodore V. Galambos, Jerome F. Hajjar, Roberto T. Leon, Wen-Hsen Huang, Brian E. Pulver, and Brian J. Rudie

9. Performing Organization Name and Address 10. Project/Task/Work Unit No.

Department of Civil EngineeringInstitute of Technology 11. Contract (C) or Grant (G) No.University of MinnesotaMinneapolis, Minnesota 55455-0220 (C) 72443 TOC #155

12. Sponsoring Organization Name and Address 13. Type of Report and Period Covered

Minnesota Department of Transportation Final Report 1994-1996395 John Ireland Boulevard Mail Stop 330 14. Sponsoring Agency CodeSt. Paul, Minnesota 55155

15. Supplementary Notes

16. Abstract (Limit: 200 words)

Steel curved I-girder bridge systems may be more susceptible to instability during construction than bridges constructedof straight I-girders. The primary goal of this project is to study the behavior of the steel superstructure of curved steel I-girder bridge systems during all phases of construction, and to ascertain whether the linear elastic analysis software usedby Mn/DOT during the design process represents well the actual stresses in the bridge. Sixty vibrating wire strain gageswere applied to a two-span, four-girder bridge, and the resulting stresses and deflections were compared to computationalresults for the full construction sequence of the bridge. The computational results from the Mn/DOT analysis software werefirst shown to compare well with results from a program developed specifically for this project (called the "UM program"),since the latter permits more detailed specification of actual loading conditions on the bridge during construction. The UMprogram, in turn, correlated well with the field measurements, especially for the primary flexural stresses. Warping stressesinduced in the girders, and the stresses in the crossframes, were more erratic, but showed reasonable correlation. It isconcluded that Mn/DOT's analysis software captures the behavior well for these types of curved girder bridge systems,and that the stresses in these bridges may be relatively low if their design is controlled largely by stiffness.

17. Document Analysis/Descriptors 18. Availability Statement

Bridges Lateral-torsional Buckling No restrictions. Document available from:Curved Steel I-girder Warping National Technical Information Services,Diaphragm Structural Stability Springfield, Virginia 22161Crossframe Construction SequenceComposite Deck Field MeasurementTorsion Vibrating Wire Strain Gage

19. Security Class (this report) 20. Security Class (this page) 21. No. of Pages 22. Price

Unclassified Unclassified 345

Stresses in Steel Curved Girder Bridges

Final Report

Prepared by

Theodore V. Galambos

Department of Civil Engineering

University of Minnesota

Minneapolis, Minnesota 55455

Wen-Hsen Huang

Virginia Dept. of Transportation

Div. of Structures and Bridges

Richmond, Virginia

Jerome F. Hajjar

Department of Civil Engineering


Minneapolis, Minnesota 55455

Brian E. Pulver

Wiss, Janney, Elstner Associates

330 Pfingsten Road

Northbrook, Illinois 60062

Roberto T. Leon

Sch. of Civil and Environ. Eng.

Georgia Institute of Technology

Atlanta, Georgia 30332

Brian J. Rudie

Minn. Dept. of Transportation

Office of Bridges and Structures

Roseville, Minnesota 55113

August 1996

Published by

Minnesota Department of TransportationOffice of Research Administration

Transportation Building395 John Ireland Boulevard

St. Paul, Minnesota 55155-1899

This report does not constitute a standard, specification, or regulation. The findings and conclusionsexpressed in this publication are those of the authors and not necessarily the Minnesota Department ofTransportation or the Center for Transportation Studies. The authors, the Minnesota Department ofTransportation, and the Center for Transportation Studies do not endorse products or manufacturers.Trade or manufacturers' names appear herein solely because they are considered essential to this report.

ACKNOWLEDGMENTS

The authors would like to express their sincere appreciation to the Offices of Bridges and

Structures, Materials, and Research Administration at the Minnesota Department of

Transportation for support of this research on steel curved girder bridges. The authors would

also like to give special thanks to the PDM Bridge Company, fabricators of the curved girder

bridge; the Lunda Construction Company, the general contractors on the bridge construction; and

High Five Erectors, the erectors of the steel superstructure of the bridge. Without their extensive

cooperation, this research would not have been possible. In particular, the authors would like to

thank the following individuals for their substantial contributions to this project:

Minnesota Department of Transportation:

Offices of Bridges and Structures, Materials, and Research Administration

D. Flemming, G. Peterson, P. Rowekamp, S. Ellis, K. Anderson, T. Nieman, J. Southward

Minnesota Department of Transportation: Field Office

D. Reinsch, L. Lillie, P. Koff, J. Michaels

The PDM Bridge Company, Eau Claire, Wisconsin

J. Bates, R. Cisco

Lunda Construction Company, Rosemount. Minnesota

D. Davick

High Five Erectors, Shakopee. Minnesota

B. Theis


J. Millman, A. Staples, P. Bergson

TABLE OF CONTENTS

CHAPTER 1 INTRODUCTION ................................................. 1

1.1 Objectives ................................................................ 2

1.2 Background on Curved Girder Analysis Approaches ............................... 3

1.3 Scope ................................................................. 4

1.4 Outline of Report ....................................................... 5

CHAPTER 2 INSTRUMENTATION OF THE GIRDERS ........................ 7

2.1 Bridge Layout and Gage Placement Design ................................ 7

2.2 Data Acquisition System ........................... ............ ... ....... . 8

2.3 Field Instrumentation of Girders .................... ......................... 11

CHAPTER 3 FIELD MEASUREMENTS DURING CONSTRUCTION OF THE BRIDGE. 21

3.1 Introduction ........................................................... 21

3.2 Erection and Construction Procedure and Sequencing .......................... 22

3.3 Construction Stresses ............ . .... .................................. 25

CHAPTER 4 FIELD MEASUREMENTS DURING LIVE LOADING OF THE BRIDGE .. 37

4.1 Introduction.............................................................. 37

4.2 Two Trucks Side by Side at the Quarter Points of the Bridge ....................... 38

4.3 One Truck at the Quarter Points of the Bridge ................................... 39

4.4 Two Trucks End to End at the Midspan of Each Span ............................. 40

4.5 One Truck at the Midspan of Each Span Simultaneously .......................... 40

CHAPTER 5 FINITE ELEMENT MODEL ...................................... 43

5.1 Introduction ............................................................. 43

5.2 The Grillage Method..................................... ................. .. 43

5.3 Comparison Between DESCUS-I and the UM Program .......................... 48

CHAPTER 6 COMPARISON BETWEEN COMPUTATIONAL ANALYSIS AND

THE FIELD MEASUREMENTS .................................... 61

6.1 Structural Loading ........................................................ 61

6.2 Comparison of Field Measurements and Finite Element Analyses ................... 62

6.3 Stresses in the Crossframes Near the Skew Supports .............................. 73

CHAPTER 7 CONCLUSIONS ............................................... 117

REFERENCES ....... ..................................................... . 119

APPENDIX A

APPENDIX B

APPENDIX C

APPENDIX D

APPENDIX E

APPENDIX F

APPENDIX G

APPENDIX H

STRESSES DUE TO CONSTRUCTION

STRESSES DUE TO THE POURING OF THE CONCRETE DECK

STRESSES DUE TO THE TRUCK LIVE LOADING

DETAILED CONSTRUCTION SEQUENCE

CALCULATION OF DEAD LOADS FOR ANALYSIS

TRANSFER OF VERTICAL LOADS

BACKGROUND ON ANALYSIS OF STEEL CURVED GIRDER BRIDGE

SYSTEMS

SPECIFICATIONS OF THE VIBRATING WIRE STRAIN GAGE

List of Tables

Table 2.1 Difference between the zero readings at PDM and on the construction site ....... 15

Table 5.1 Nodal degrees-of-freedom .......................................... 51

Table 5.2 Percentage difference between MN/DOT DESCUS-I and UM programs due to

bare steel subjected to steel weight and wet concrete ........................ 52

Table 5.3 Percentage difference between MN/DOT DESCUS-I and UM programs due to

composite structure (N=24) subjected to superimposed dead loads ............. 53

Table 6.1 Loading condition and the corresponding structures ......................... 75

Table 6.2 Vertical loading distribution factors ................................... 76

Table 6.3 Deflection comparison after pouring of the concrete deck .................... 77

Table 6.4 Deflection comparison during truck loading ............................. 78

Table 6.5 Comparison of axial rotation angles obtained from field tests at Beam 4 on the

midspan of the north span .......................................... 79

List of Figures

Figure 2.1

Figure 2.2

Figure 2.3

Figure 2.4

Figure 2.5

Figure 3.1

Figure 3.2

Figure 3.3

Figure 3.4

Figure 4.1

Figure 5.1

Figure 5.2

Figure 5.3

Figure 5.4

Figure 5.5

Figure 5.6

Figure 5.7

Figure 6.1

Figure 6.2

Figure 6.3

Figure 6.4

Figure 6.5

Figure 6.6

Framing plan ...................................... 16

Superstructure profiles ................................ 17

Elevation of intermediate cross frame diaphragms . . . . . . . . . . . . . . . . 18

Plan view of the girders displaying the girder nomenclature . . . . . . . . . 19

Nomenclature used to describe gage locations, girders, and diaphragms . . 20

Come-along device .................................. 34

Right triangular bar support with plywood formwork .............. 34

Plan view of the bridge displaying the progression of the pouring of the

concrete deck ...................................... 35

Example of girder stresses varying across the width of the bridge's cross

section ............ ................... ... ........ 36

Plan of field tests for cases 1 to 6 ......................... 42

Grillage model and bridge profiles ......................... 54

Elements in the grillage method .......................... 55

Modeling of the grid system ............................. 56

Comparison of vertical deflections between DESCUS and UM programs for

non-composite analysis (Beam 3) .......................... 57

Comparison of bending moment diagrams between DESCUS and UM

programs for non-composite analysis (Beam 4) . . . . . . . .. . . . . . . 58

Comparison of vertical deflections between DESCUS and UM programs for

composite analysis (N=24, Beam 2) . . . . . . . . . . . . . . . . . . . . . . . . 59

Comparison of bending moment diagrams between DESCUS and UM

programs for composite analysis (N=24, Beam 4) . . . . . . . . . . . . . . . 60

Instrumentation of strain gages ............ ............... 80

The designation of strain gages . .......................... 81

Locations of deflection and rotation measuring . . . . . . . . . . . . . .. .. .. 82

MN/DOT snow plowing truck 1, unit weight = 48.1 kips . . . ...... .. 83

MN/DOT snow plowing truck 2, unit weight = 49.4 kips .......... .. 84

Stress comparison at three gage lines for Step 1-1 . . . . . . . . . . . . .. .. 85

Figure 6.7

Figure 6.8

Figure 6.9

Figure 6.10

Figure 6.11

Figure 6.12

Figure 6.13

Figure 6.14

Figure 6.15

Figure 6.16

Figure 6.17

Figure 6.18

Figure 6.19

Figure 6.20

Figure 6.21

Figure 6.22

Figure 6.23

Figure 6.24

Figure 6.25

Figure 6.26

Figure 6.27

Figure 6.28

Figure 6.29

Figure 6.30

Figure 6.31

Figure 6.32

Figure 6.33

Figure 6.34

Figure 6.35

Figure 6.36

Figure 6.37

Stress comparison at three gage lines for Step 1-2 . . . . . . . . . . . . . . .

Stress comparison at three gage lines for Step 1-3 . . . . . . . . . . . . . . .

Stress comparison

Stress comparison

Stress comparison

Stress comparison

Stress comparison

Stress comparison

Stress comparison

Stress comparison

Stress comparison

at three gage lines for Step









2-1 . . . . . . . . . . . . . . .

2-2 ..... .... ......

2-3a . ..............

2-3b . ..............

3-1 ................

3-2 ...............

3-3a . ..............

3-3b . ..............

3-3c .................

Stress comparison at three gage lines for Step 4-1 (N=8) . . . . . . . . . . .

Stress comparison at three gage lines for Step 1-2 (N=8) . . . . . . . . . . .

Plan of field tests for cases 1 to 6 . ........................

Plan of field tests for cases 7 to 9 . .......................

Plan of field tests for cases 10 to 15 .......................

Stress comparison at three gage lines for truck load Case 2 . . . . . . . . .

Stress comparison at three gage lines for truck load Case 3 . . . . . . . . .

Stress comparison at three gage lines for truck load Case 7 .... . . . . .

Stress comparison at three gage lines for truck load Case 8 ..... . . . .

Stress comparison at three gage lines for truck load Case 13 .... . . . .

Stress variations due to truck loads in crossframe 39 . . . . . . . . . . . . .





Stress variations due to truck loads in crossframe 28 . . . . . . . . .....

Stress variations due to truck loads in crossframe 48 . . . . . . .. . . ......



Stress variations due to truck loads in crossframe 47 . . . . . . . . . . . ..

86

87

88

89

90

91

92

93

94

95

96

97

98

99

100

101

102

103

104

105

106

107

108

109

110

111

112

113

114

115

116

Figure A-1

Figure A-2

Figure A-3

Figure A-4

Figure A-5

Figure A-6

Figure A-7

Figure A-8

Figure A-9

Figure A-10

Figure A- 11

Figure A-12

Figure A-13

Figure A-14

Figure A-15

Figure A-16

Figure A-17

Figure A-18

Figure A-19

Plan view of the girders displaying the girder nomenclature . . . . . ... .. A-6

Nomenclature used to describe gage locations, girders, and diaphragms . A-7

Magnitude of girder stresses after erection of span 1 . . . . . . . . . . .. .. A-9

Change in girder stresses between the erection of span 1 and the erection of

half of span 2 ..................................... A-11

Magnitude of girder stresses after the erection of half of span 2 .... . A-13

Change in girder stresses between erection of half of span 2 and all of the

girder and diaphragms in place with bolts loose . . . . . . . . . . . . . .. .. A-15

Magnitude of girder stresses after all of the girders and diaphragms were in

place with the bolts loose ............................. A-17

Change in girder stresses between the erection of all of the girders and

diaphragms with the bolts loose and after the structure was "rattled

up" . ... ...... . . . ..... ... .. ...... . . . .. . . . ... ... A -19

Magnitude of girder stresses after all of the girders and diaphragms were

erected and the structure was "rattled up" . . . . . . . . . . . . . . . . ... . A-21

Change in girder stresses between the "rattled up" structure and after the

placement of the formwork ............................ A-23

Magnitude in girder stresses after the placement of the formwork . . . . . A-25

Change in girder stresses between the placement of the formwork and the

placement of the reinforcement .......................... A-28

Magnitude of girder stresses after the placement of the reinforcement . . A-29

Change in girder stresses between the placement of the reinforcement and the

pouring of the reinforced concrete deck . . . . . . . . . . . . . . . . . . .. . A-31

Magnitude of girder stresses after the pouring of the reinforced concrete

deck . ......................................... A-33

Change in girder stresses between the pouring of the reinforced concrete deck

and the pouring of the parapet walls . .. . .. . . . . . . . . . . . . . . . ... A-35

Magnitude of girder stresses after the pouring of the parapet walls . . . . A-37

Change in girder stresses between the pouring of the parapet walls and the

final state of stress of the bridge before being opened for service .. . . . A-39

Magnitude of girder stresses before the bridge was opened for service . . A-41

Figure B-1

Figure B-2

Figure B-3

Figure B-4

Figure B-5

Figure B-6

Figure B-7

Figure B-8

Figure B-9

Figure B-10

Figure B-11

Figure B-12

Figure B-13

Figure B-14

Figure B-15

Figure B-16

Figure B-17

Figure B-18

Figure B-19

Figure B-20

Figure B-21

Figure B-22

Figure B-23

Plan view of the bridge displaying the progression of the pouring of the

concrete deck ..................................... B-5

Change in girder stresses between the initial reading and stage 1 . . . . . B-10

Magnitude of girder stresses for stage 1 reading (4:45 a.m.)

Change in girder stresses between stage 1 and stage 2 . . . .

Magnitude of girder stresses for stage 2 (5:15 a.m.) . . . . .













. . . . . . B-11

. . . . . . . B-13

. . . . . . B-14

. . . . . . . B-16

. . . . . . B-17

. . . . . . . B-19

. . . . . . B-20

. . . . . . B-22

. . . . . . B-23

. . . . . . . B-25

. . . . . . B-26

. . . . . . . B-28

. . . . . . B-29

. . . . . . . B-31

. . . . . . . B-32

Change in stress for gages 1A-6A during the pouring of the concrete

deck . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . .


deck . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .


deck . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .


deck . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Change in stress for gages 1B-6B during the pouring of the concrete

deck . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . .


deck . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

S.B-35

S.B-36

S.B-37

. .B-38

. .B-39

.B-40

Figure B-24

Figure B-25

Figure B-26

Figure B-27

Figure B-28

Figure B-29

Figure B-30

Figure B-31

Figure B-32

Figure B-33

Figure B-34

Figure B-35

Figure B-36

Figure B-37

Figure B-38


deck ................ ......... ............ . .... B-41


deck .......................................... B-42

Change in stress for gages 1C-4C during the pouring of the concrete

deck .......................................... B-43


deck .......................................... B-44


deck .......................................... B-45

Magnitude of stress for gages 1A-6A measured during the pouring of the

concrete deck ..................................... B-49


concrete deck ..................................... B-50


concrete deck ..................................... B-51


concrete deck ..................................... B-52

Magnitude of stress for gages 1B-6B measured during the pouring of the

concrete deck ...... ............................... B-53


concrete deck ..................................... B-54


concrete deck ................. .................... B-55


concrete block .................................... B-56

Magnitude of stress for gages 1C-4C measured during the pouring of the

concrete deck ..................................... B-57


concrete deck ........................... . . ...... B-58

Figure B-39

Figure

Figure

Figure

Figure

C-la

C-lb

C-lc

C-2

Figure C-3

Figure C-4

Figure C-5

Figure C-6

Figure C-7

Figure C-8

Figure C-9

Figure C-10

Figure C-11

Figure C-12

Figure C-13

Figure C-14


concrete deck ..................................... B-59

Plan of field tests for cases 1 to 6 . ....................... C-7

Plan of field tests for cases 7 to 9 . ....................... C-8

Plan of field tests for cases 10 to 15 ....................... C-9

Change in stress for two 50 kip trucks placed side by side at the first quarter

point of span 1 .................................... C-11

Change in stress for two kip trucks placed side by side at the midspan of

span 1 ...................... ................... C-13

Change in stress for two 50 kip trucks placed side by side at the third quarter

point of span 1 ................. . .................. C-15

Change in stress for two 50 kip trucks placed side by side at the first quarter

point of span 2 .................................... C-17

Change in stress for two 50 kip trucks placed side by side at the midspan of

span 2 ......................................... C-19

Change in stress for two 50 kip trucks placed side by side at the third quarter

point of span 2 . ................................... C-21

Change in stress for gages

at the quarter points of the


at the quarter points of the


at the quarter points

Change in stress for



the quarter points of




of the

gages

of the

gages

1A-6A with two 50 kip trucks placed side by side

bridge ... ..................... C-25


bridge ........................ C-26


bridge ........................ C-27

19A-24A with two 50 kip trucks side by side placed

bridge ........................ C-28

1B-6B with two 50 kip trucks placed side by side at

the bridge ...... . .................... C-29

gages 7B-12B with two 50 kip trucks placed side by side

of the bridge ........................ C-30

gages 13B-18B with two 50 kip trucks placed side by side

at the quarter points of the bridge ......................... C-31

Figure C-15

Figure C-16

Figure C-17

Figure C-18

Figure C-19

Figure C-20

Figure C-21

Figure C-22

Figure C-23

Figure C-24

Figure C-25

Figure C-26

Figure C-27

Figure C-28

Figure C-29

Figure C-30

Figure C-31

Change in stress for gages 19B-24B with two 50 kip trucks side by side at the

quarter points of the bridge ............................. C-32

Change in stress for gages 1C-4C with two 50 kip trucks placed side by side at

the quarter points of the bridge .......................... C-33

Change in stress for gages 5C-8C with two 50 kip trucks placed side by side at

the quarter points of the bridge .......................... C-34

Change in stress for gages 9C-12C with two 50 kip trucks placed side by side

at the quarter points of the bridge ........................ C-35

Change in stress for one 50 kip truck placed at the first quarter point of

span 1 .................................. ....... C-39

Change in stress for one 50 kip truck placed at the midspan of span 1 . . C-41

Change in stress for one 50 kip truck placed at the third quarter point of

span 1 ......................................... C-43

Change in stress for one 50 kip truck placed at the first quarter point of

span 2 ......................................... C-45

Change in stress for one 50 kip truck placed at the midspan of span 2 . . C-47

Change in stress for one 50 kip truck placed at the third quarter point of

span 2 ......................................... C-49

Change in stress for gages 1A-6A with one 50 kip trucks placed at the quarter

points of the bridge ................................. C-52

Change in stress for gages 7A-12A with one 50 kip truck placed at the quarter


Change in stress for gages 13A-18A with one 50 kip placed at the quarter


Change in stress for gages 19A-24A with one 50 kip truck placed at the

quarter points of the bridge ............................ C-55

Change in stress for gages 1B-6B with one 50 kip truck placed at the quarter



points of the bridge ................................... C-57


Figure C-32

Figure C-33

Figure C-34

Figure C-35

Figure C-36

Figure C-37

Figure C-38

Figure D-1

Figure F-1

Figure F-2

Figure G-1

Figure G-2

Figure G-4

Figure G-5

Figure G-6

Figure G-7

Figure G-8

Figure G-9

points of the bridge . . . . . . . . . . . . . . . . . . . . ........ C-58



Change in stress for gages 1C-4C with one 50 kip truck placed at the quarter

points of the bridge .......................... ...... . C-60





Change in stress for two 50 kip trucks placed end to end at the midspan of

span 1 ......................................... C-66

Change in stress for two 50 kip trucks placed end to end at the midspan of

span 2 . ........................................ C-68

Change in stress for two 50 kip trucks one placed at eh midspan of both span

1 and 2 ......................................... C-70

Designation for erection sequence of the skeleton . . . . . . .. . . . ......

Distribution of vertical dead loads . . . . . . . . . . . . . . . . . . . . . . .

Distribution of truck loads ............................

Loading of curved girder .............................

Additional effects due to torsion ........................

Flange acting as laterally loaded beam ....................

Three-dimensional method - six degrees of freedom . . . . . . . . . ...

Single curved orthotropic plate . ........................

System of curved orthotropic plates . . . . . . . . . . . . . . . . . . . . . .

Rigorous analysis - distortion of girders and beams . . . . . . . . . . . . .

D-10

. F-7

. F-8

.G-14

.G-15

.G-16

.G-17

.G-18

.G-18

.G-19

Differential element of flange under assumed lateral load . . . . . . . . . G-19

EXECUTIVE SUMMARY

Composite, I-shaped, steel curved girder bridges are relatively stiff and strong when the structure

is completely erected and subjected to service loading resulting from daily traffic. However, the

structure may be quite flexible and potentially susceptible to stability problems during

construction, prior to its stabilization after hardening of the concrete deck. When designing these

types of bridges, linear elastic analysis software is typically used to determine the stresses and

deflections in the steel members due to wet weight of the concrete, and after hardening of the

concrete deck. In order to insure safe design, it is vital that the stresses and deflections resulting

from such analyses be representative of the stress state in the actual bridge structure. In addition,

it is important to know whether the stress state in this type of bridge at other points in the

construction process may be represented computationally, to insure that no unusual stress states

occur which are possibly being neglected in current design practice. Curved girder bridge systems

exhibit special behavior as compared to bridge systems with straight girders. Such unique

behavior includes, for example, the effect of warping restraint on the behavior of the I-girders, the

behavior of crossframes in a curved girder system, and the potential susceptibility of these bridges

to lateral-torsional buckling during construction, due to the initial curvature of the girders. These

added considerations require special care to be taken regarding the accuracy of the computational

simulations used to obtain forces for design. In spite of this, to date there have been few

measurements of actual stresses in these girders recorded during construction. Consequently, this

project seeks to determine the range of stresses exhibited in a typical steel curved girder bridge

during all stages of construction, and to compare these stresses with results obtained using linear

elastic analysis software commonly used for design.

The Minnesota Department of Transportation (MN/DOT) uses an analysis program, DESCUS-I,

to determine the stresses for the design of steel curved I-girder bridge systems. The primary

objective of this research involves instrumenting and monitoring the strains and stresses in the

steel superstructure of a two-span curved I-girder bridge (MN/DOT Bridge No. 27998) during its

entire construction process, and comparing these field measurements with results obtained from

two analysis programs: MN/DOT's DESCUS-I, and the University of Minnesota Steel Curved

Girder Bridge System Analysis Program (referred to herein as the UM program), which was

developed specifically for this project and which permits more detailed specification of loading

and assessment of stress states. These two software programs are first compared to insure they

yield the same results for similar bridge topology, properties, and loading. Subsequently, results

from the UM software are compared to the field measurements to determine the capability of

these types of programs to simulate actual stress distributions measured during construction.

Conclusions drawn from this study include: 1) This bridge was shored in the early stages of

construction of the steel superstructure, and the bridge design was controlled by stiffness, not

strength. Therefore, stresses well below the yield stress occurred throughout construction. 2)

Computational results consistently matched well qualitatively and often quantitatively with

measured results, both for stresses and deflections. The bridge behavior was predictable at all

stages. 3) The primary difference between measured and computed results was due mainly to the

erratic effects in the field of warping restraint and weak axis bending on the measured results. 4)

Fit-up stresses were measured in the crossframes, but they dissipated as construction progressed,

and they remained below 6 ksi. 5) The MN/DOT curved girder program, DESCUS-I, compares

well to the UM program, which in turn compares well to the field measurements. Consequently,

it may be concluded that the DESCUS-I program represents construction and final live load

stresses and deflections well, both for the bare steel and the composite bridge system. It should

be emphasized that while the ability to make direct comparisons between DESCUS-I and the field

measurements is somewhat limited (due to constraints of specifying actual loading, etc. in

DESCUS-I), it may be concluded that stresses obtained from DESCUS-I are representative of

what is seen in the field for the type of studied in this project. 6) It is recommended that a

minimum of 20 to 30 psf live loading for construction be included in analyses to capture maximum

stresses. Future research in this area should include further tests with increased live loading. Two

trucks placed on this structure induced only approximately 2 ksi in the measured members. If

additional trucks are placed on the structure, more substantial and reliable strain readings may be

made, which will provide firmer evidence of the service load behavior of these types of structures.

In addition, it may be possible to ascertain whether composite behavior diminishes over time.

CHAPTER 1

INTRODUCTION

Composite, I-shaped, steel curved girder bridges are relatively stiff and strong when the structure

is completely erected and subjected to service loading resulting from daily traffic. However, the

structure may be quite flexible and potentially susceptible to stability problems during

construction, prior to its stabilization after hardening of the concrete deck. When designing these

types of bridges, linear elastic analysis software is typically used to determine the stresses and

deflections in the steel members at two points during the construction process and useful life of

the bridge: 1) due to dead load just after the pouring of the concrete deck, but prior to the deck

hardening; and 2) due to live load on the finished bridge structure. In order to insure safe design

according to the American Association of State Highway and Transportation Officials (AASHTO)

provisions [1], it is vital that the stresses and deflections resulting from such analyses be

representative of the service-level stress state in the actual bridge structure; this insures that

appropriate stress distributions are used for member design according to either Working Stress or

Load and Resistance Factor Design methodologies, and that serviceability limit states are

evaluated accurately. In addition, it is important to know whether the stress state in this type of

bridge at other points in the construction process may be represented computationally, to insure

that no unusual stress states occur which are possibly being neglected in current design practice.

Curved girder bridge systems exhibit special behavior as compared to bridge systems with straight

girders [2]. Such unique behavior includes, for example, the effect of warping restraint on the

behavior of the I-girders, the behavior of crossframes in a curved girder system, and the potential

susceptibility of these bridges to lateral-torsional buckling during construction, due to the initial

curvature of the girders. These added considerations require special care to be taken regarding

the accuracy of the computational simulations used to obtain forces for design. In spite of this, to

date there have been few measurements of actual stresses in these girders recorded during

construction. Consequently, this project seeks to determine the range of stresses exhibited in a

typical steel curved girder bridge system during all stages of construction, and to compare these

stresses with computational results obtained using linear elastic analysis software commonly used

for design.

1.1 OBJECTIVE

The Minnesota Department of Transportation (MN/DOT) uses an analysis program, DESCUS-I

[3], to determine the stresses for the design of steel curved I-girder bridge systems. As is the case

with all analysis programs, assumptions must be made regarding the idealization of these

structures. In addition, these programs do not account explicitly for the stresses and deflections

induced by fabrication and construction practices. The primary objective of this research involves

instrumenting and monitoring the strains and stresses in the steel superstructure of a two-span

curved I-girder bridge during its entire construction process [4], and comparing these field

measurements with results obtained from two analysis programs: MN/DOT's DESCUS-I, and

the University of Minnesota Steel Curved Girder Bridge System Analysis Program (referred to

herein as the UM program), which was developed specifically for this project and which permits

more detailed specification of loading and assessment of stress states [5]. For this project,

MN/DOT Bridge No. 27998 was selected for the research. Specific objectives of this project

include:

1. Measure the strains in the steel superstructure of this curved I-girder bridge system, beginning

at the fabrication yard, and track of these strains through the transportation of the girders and

crossframes to the site, erection of the steel structure, casting of the deck, and application of

live load to the completed bridge.

2. Conduct detailed analyses of the bridge to determine the stresses (derived from the strain

readings) and deflections during the different phases of construction, as well as due to live

loading on the completed structure. These analyzes use both MN/DOT's DESCUS-I analysis

program and the UM software. These two software programs are first compared to insure

they yield similar results for similar bridge topology, properties, and loading. Subsequently,

results from the UM software are compared to the field measurements to determine the

capability of these types of programs to simulate actual stress distributions measured during

construction. Once these comparisons are made, conclusions are drawn regarding the

suitability of DESCUS-I to determine stresses for design.

1.2 BACKGROUND ON CURVED GIRDER ANALYSIS APPROACHES

There are many commercial, proprietary, and in-house computer programs available for the

analysis of curved girder bridges. Stegmann and Galambos [6] and Zureick et al. [7] summarize

common methods of analysis for curved steel girder bridges. In addition, three texts present the

theory for the development of these analytical and computational approaches, including

Dabrowski [8], Heins [9], and Nakai and Yoo [10]. These references range in time from 1975 to

1993, and they reflect the work performed predominantly in the late 1960-s and the early 1970-s

under the sponsorship of the Federal Highway Administration by the Consortium of University

Research Teams (CURT).

This section provides a brief background on analysis methods for steel curved girder bridge

systems. The reader is referred to Appendix G for further detail, and to Zureick et al. [7].

Zureick et al. [7] indicate that there are two basic types of computational approaches for

analyzing curved bridge girder systems: approximate methods and refined methods. The

approximate methods include: a) the plane grid method; b) the space frame method; and c) the V-

load method. Refined techniques include: a) direct analytical solution of the differential equation

governing the behavior of the curved girders (for analyzing isolated girders); b) the finite

difference method; c) the finite strip method; d) the slope-deflection method; and e) the finite

element method. The approximate methods are suitable for design, while the refined methods are

best used for a detailed evaluation of the behavior of a final design or of an existing structure.

3

In addition, Stegmann and Galambos [6] classify these analysis methods as: Level I methods

(most sophisticated research tools); Level II methods (for final design and investigation of existing

bridges); and Level III methods (for preliminary design). The program DESCUS-I may be

classified as a Level II, refined approach utilizing the finite element method. This software

effectively takes into account both the flexural and warping normal stresses in the curved girders,

which are the main stresses governing the design of steel curved girder bridges. The UM program

is of essentially the same degree of sophistication, although it has several additional features,

including nonlinear analysis capabilities [5], not discussed in this report. Chapter 5 provides

further details of these two software programs.

1.3 SCOPE

Because of the substantial coordination required to measure strains in an actual bridge system

from fabrication through opening of the bridge, only one curved I-girder bridge was included in

this project. The conclusions resulting from this project must therefore be interpreted within the

context of the specific type of bridge selected. MN/DOT Bridge No. 27998 is an off-ramp from

an interstate highway, and it has a general layout that is similar to that used throughout the

country for these types of bridges. A main distinguishing feature of the bridge is that it includes

four concentric I-girders, each of differing depth ranging from 50 to 70 inches. Each beam differs

in depth in order to maximize the webs depths while maintaining the superelevation and while

minimizing the vertical clearance over the interstate highway below. The bridge girders are

divided into three segments over two spans, with one central support (see Chapter 2). The spans

range from 139 to 155 feet each, and the girders are continuous over the center support. The in-

plane radius of curvature of the bridge is relatively small, varying from approximately 270 feet to

300 feet. In addition, two of the three supports have substantial skews relative to the tangential

axis of the bridge at the point of support. Thus, the complex behavior typical of these types of

common curved bridge systems is well represented by this bridge. In addition, its design was

controlled mainly by insuring adequately small live load deflection (L/800), which is common in

these types of bridges. The construction process went relatively smoothly, as did the field

measurements (i.e., there were no substantial anomalies which biased the results), and for these

4

reasons it is felt that the scope of this project is justifiably broad, such that the conclusions are

relevant for the type and scale of curved I-girder bridge system studied in this work.

Nevertheless, it is important to recognize that the conclusions drawn in this report are based upon

the results of studying only a single bridge.

1.4 OUTLINE OF THE REPORT

Chapter 2 begins with a description of the curved girder bridge. It then outlines in detail the

instrumentation strategy of the bridge. Chapter 3 follows with a detailed summary of the strains

recorded on the bridge. These include strains recorded at key points in time during construction,

as well as strains recorded on a nearly continuous basis during the pouring of the concrete deck.

Chapter 4 summarizes the strains recorded due to controlled live loading on the bridge: two

trucks of known weight were placed at various positions on the bridge, which was otherwise

closed to traffic. Chapter 5 outlines the details of the finite element models used to compare to

the field measurements, and it compares the DESCUS-I software of MN/DOT with the UM

software to show that they yield essentially identical results for similar structural models. Chapter

6 compares the UM software analysis results to the field measurements, and also reports the two

sets of deflection measurements made in the field. Conclusions are drawn in Chapter 7.

Appendices A through C contain the complete set of strain data measured during the entire

project. Appendix D outlines in detail the construction sequence of the steel superstructure.

Appendix E details the calculations made to determine the dead loads applied to the bridge in the

analyses. Appendix F outlines the manner in which gravity loads were assigned as point loads to

the four I-girders in the analysis programs. Appendix G provides more detailed background on

techniques for analyzing steel curved girder bridge systems. Appendix H presents the

specification of the gage used for strain measurements on this project.

CHAPTER 2

INSTRUMENTATION OF THE GIRDERS

2.1 BRIDGE LAYOUT AND GAGE PLACEMENT

This chapter outlines the instrumentation strategy for measuring the strains in the curved girder

bridge system. Figures 2.1 and 2.2 show plan and elevation views, respectively, of MN/DOT

Bridge No. 27998 [11]. Relevant dimensional information is included in these figures. The

location of the crossframes, end diaphragms, and supports, including the orientation of their skew,

is clear in Figure 2.1. Figures 2.2 and 2.3, in turn, show the girder and deck dimensions

(including the differing depths of the four I-girders -- Figure 2.2), as well as the topology of a

typical crossframe (Figure 2.3). Also, as seen in Figure 2.2, stiff I-shaped end diaphragms are

used in lieu of crossframes at the two ends of the bridge.

2.1.1 GAGE PLACEMENT DESIGN

Sixty gages were attached to the steel superstructure of the bridge. This number was felt to be

optimal given the budget and time constraints present for this project. Figures 2.4 and 2.5 (and,

equivalently, Figures A.1 and A.2) show the position of these gages. Twenty-four gages were

placed along a section at the midspan of span 1 (i.e., the southern span) in order to determine the

stresses occurring in the positive moment region of span one. Span one was selected since it was

to be erected first. In the positive moment region, the stresses are expected to be negative

(compressive) in the top flanges and positive (tensile) in the bottom flanges. This section was

labeled as Gage Line A and the gages were numbered as 1A, 2A,...24A starting with the outside

facia girder and progressing to the inside facia girder (see Figure 2.5) 3. Six gages, three on the

top and three on the bottom, were attached to each of the four girders to determine the stresses in

3 Note that girder 1 is labeled as the outside facia girder in Figure 2.5 and in all strainmeasurements reported herein, while the MN/DOT drawing (Figure 2.1) labeled the outside faciagirder as "beam 4".

the top and bottom flanges. The three gages on a given flange and neighboring web determine the

changes in stress occurring across the width of the flanges so as to determine the effects of

warping. For each girder, four gages were placed, two on the bottom of the top flange and two

on the top of the bottom flange, as close to the edges of the flanges as possible. The last two

gages were affixed to the web approximately 1.5 inches away from the flange since it was not

possible to affix the gages directly to the center of the flanges. These web gages are most

appropriate for tracking the predominant strong axis flexural forces in the girders. Twenty-four

gages were also placed along a section over the middle pier in order to determine the stresses

occurring in the negative moment region. In the negative moment region, the stresses are

expected to be positive in the top flanges and negative in the bottom flanges. This section was

labeled as Gage Line B and the gages were numbered from 1B to 24B in the same manner as

described for Gage Line A. The location of the gages for Gage Line B was the same as Gage

Line A (Figure 2.5). The final twelve gages were located at a section where diagonal crossframes

were present. The crossframes consist of four angle sections, two horizontal and two diagonal,

welded to gusset plates that are bolted to the curved girders. A gage was attached to each angle

section to monitor the axial stress present in each of the members. This section was labeled Gage

Line C, and the gages were numbered 1C to 12C, starting with the top horizontal member

connected to the outside facia girder and the next inside girder and proceeding down and towards

the inside facia girder. Note that the gages and wires were purposely located in areas of the

girders which would not interfere with the construction or erection of the girders. These

locations were based on information received during a series of planning meetings held with the

erector and construction crews. The following section details the data acquisition system

developed to collect the information desired.

2.2 DATA ACQUISITION SYSTEM

The data acquisition system consists of the Geokon VK-4100 Vibrating Wire Strain Gage, Belden

8730 Wire, AMP Five Pin Soft Shelled Connectors, the Geokon GK-403 Vibrating Wire Readout

Box, and a fabricated termination box. The following sections outline each of the components of

the data acquisition system.

8

2.2.1 Geokon VK-4100 Vibrating Wire Strain Gage

The strains of the curved girders were measured using vibrating wire strain gages. Vibrating wire

strain gages have a known length of wire within the gage. This wire is tensioned between the two

ends of the gage. These two ends are then affixed to the surface of the girder, the wire is plucked

by an electromagnetic coil present in the gage cover, and the resonant frequency of vibration of

the wire is measured. This initial reading is the zero reading for that gage. As load is applied to

the structure, deformations occur in the members of the structure. This causes the affixed ends to

move relative to one another and this changes the tension in the wire. The wire is plucked once

again, and the change in frequency is measured, thus indicating directly the new strain reflective of

the deformations present. Using the zero readings, a strain due to a given loading can be

calculated and converted to stress using Young's modulus of elasticity (if linear elastic behavior is

assumed, which is appropriate for this project, as will be discussed when the field measurements

are reported in Chapters 3 and 4). Vibrating wire gages have an advantage over standard foil

gages because once the gage is attached, the zero reading is not lost if the power supply is

removed. This is important for this project since the gages were attached prior to transport of the

girders to the construction site. In addition, these gages providing accurate strain readings over a

long period of time with little to no drift, which is another key advantage these particular gages.

The type of vibrating wire strain gage used was the Geokon VK-4100 Vibrating Wire Strain Gage

[12] (see Appendix H for the gage specifications). These gages are designed primarily for

measuring strains in steel bridges and other types of steel members. The range of strain that can

be measured is 2500 microstrain with a sensitivity of one microstrain. The gage length is 2.5

inches while a total length of the gage coil housing is 3 inches. The total height of the gage is 1/2

inches, and its width is 7/8 inches. The operational temperature range of the gage is -40 oC to

+250 °C. The thermal coefficient of expansion is 12 ppm/ °C, which is the same as that of steel.

This is important because the girders will expand/contract due to the heating/cooling of the

structure. If the gages did not respond at an equivalent rate, erroneous strain readings would

result since the strain registered could reflect the change in temperature, the change in the loading

condition, or a combination of both. The temperature differential between the girders and the

9

gages would have to be known to determine the amount of strain induced by the temperature

change. This residual strain would then have to be subtracted from the total reading to indicate

the strain due to that particular loading stage. While the temperature was registered during each

of the gage readings, the above correction was not deemed to be necessary in this work because

of the similar thermal properties of the gage and the steel members.

Included with the gage is an electromagnetic plucking coil, which resides in the coil housing,

which is the reading device for the gage. The coil housing has a ten foot "pigtail" of wire

included. At the end of the "pigtail" is a female AMP connector.

2.2.2 Belden 8730 Wire

The Belden 8730 wire is a shielded, four condition wire. It consists of four separate coated wires

and an uncoated ground wire. The wire coatings are colored white green, black, and red. The

colors of the wire represent, respectively, the negative thermistor lead, the positive thermistor

lead, the negative vibrating wire lead, and the positive vibrating wire lead. At one end of the wire

is a male AMP connector that attaches to the "pigtail", while the other end is attached to a female

AMP connector, which is located in the termination box (see below).

2.2.3 AMP Five Pin Soft Shelled Connector

The AMP five pin soft shelled connectors are constructed by stripping the wire coating from the

Belden 8730 wire and crimping the appropriate individual male or female contact pin to the end of

each of the five wires. The contact pins are then inserted into the connector shells to complete the

construction of the connectors. These connectors allow for quick and easy connection of the

wires to the "pigtails" and termination box in the field because the male and female connectors

snap together securely.

2.2.4 Geokon GK-403 Vibrating Wire Readout Box

The GK-403 Readout Box may be used with all of the models of vibrating wire strain gages that

Geokon produces (see Appendix H for the specifications of the readout box). There are six

10

different settings, A-F, that allow the different strain gages to be read. The VK-4100 gage is read

using channel E. The readout box, when attached to the wires leading from a gages,

automatically causes the electromagnetic coil to "pluck" the wire of the gage, making it vibrate.

The frequency of the wire is then measured. This frequency is transmitted to the readout box, and

it is converted within the readout box to microstrain. The calculation used for channel E is:

RE = (F2 * 10-)*0.39102 (2.1)

with F equaling the frequency in Hertz. Up to 256 readings may be stored in a storage array in

the readout box, which can later be downloaded as an ASCII file to a personal computer using the

communications program, Procomm, which is included by Geokon with the readout box.

2.2.5 Termination Box

The termination box, designed and fabricated at the University of Minnesota, is a waterproof box

constructed using sheet metal and aluminum. The box has an access hole to the back of a panel

which holds sixty connectors labeled for each gage. This box consolidates the wires from the

sixty gages on the bridge, and makes it possible to read all sixty gages at one convenient location.

With this box, all sixty gages could be read and recorded in approximately five minutes. The

termination box is located on top of the southern abutment, just under the bridge deck at that

ocation. It is kept covered with plastic, and is accessed with a 16 foot extension ladder.

2.3 FIELD INSTRUMENTATION OF GIRDERS

2.3.1 Gage Attachment Procedure

The steel superstructure was fabricated at the PDM Bridge Company (PDM) in Eau Claire,

Wisconsin. After its fabrication, the structure were shipped in pieces by truck to the job site for

erection. To insure an accurate zero reading, with as close to zero stress in the girders as

possible, the strain gages were attached on site at PDM, and the zero readings were taken at

PDM. The areas on the girders where the strain gages were to be attached were masked off to

prevent painting in those areas. Once the priming and painting of the girders was completed, they

11

were moved out to a storage yard where the attachment of the gages occurred. In some cases,

the surface of the steel where the gages were to be attached had paint, rust, or dirt present. In

those cases the surface was ground smooth to the bare steel, and a fine grit sand paper was used

to further smooth the surface. The surface was then cleaned and degreased. The location of each

gage was measured and marked with a straight edge and pencil to insure the alignment of the

gage. Each gage was then held in place, and the gage was welded to the member using a

capacitance spot welder. The welder was a Micromeasurements Model 700 Portable Strain

Gage Welding and Soldering Unit. Approximately 34 spots were welded per gage to hold the

gage in place. Approximately 40 watt-seconds of energy per weld was used to properly weld

each gage to the steel.

After the welding process was completed, the tabs of the gage were waterproofed. A drop of

cyanoacrylate glue was applied to the tabs of the gage. The glue wicks underneath the tab to

protect against corrosion. Micromeasurements M-Coat F, an acrylic waterproofing compound,

was then applied to the top of the tabs to waterproof the welds. After the waterproofing was dry,

the plucking coil was welded into place over the gage. Two straps hold the plucking coil in place

with ten welds per strap. Before the coil was put into place, Dow Corning RTV-3145 silicone

rubber was placed on the underside of the coil to add another layer of waterproofing protection

against corrosion. The same waterproofing techniques were used to protect the welds on the

straps that hold the coil housing in place over the gage. Additional silicone was placed around the

coil housing for added protection.

For gage line B and C, the AMP female connectors at the "pigtail" ends were wrapped in plastic

and left in place for transport. For gage line A, the "pigtail" was connected at PDM to the AMP

male end connector, which in turn was attached to the Belden wire, which was coiled for

transport. When the girders were erected, the coiled wire at the end of the girders was run to the

termination box, as is described in the next section.

12

2.3.2 Wire Placement

The frequency values that represent the strain measurements are transferred to the readout box via

Belden 8730 wire. After discussions with MN/DOT and Lunda Construction, it was agreed that

it would be most efficient to attach the wires for the gages to the girders before their

transportation to the construction site. The wire layout was tailored to insure that the wires

would be safe and unobtrusive during transportation and construction. In particular, at PDM, the

ends of the wires for Gage Lines A, B, and C were coiled and attached to adhesive bases with

locking tie wraps, and the adhesive bases were affixed to the girders in unobtrusive locations.

The wires for Gage Line A were routed from the gages directly to the bottom flange, where they

were collected, bundled with tie wraps, and routed back along the web-flange intersection to the

end of the girder to be placed at the southern abutment. For additional protection, where it was

possible the wires were passed through the notch in the stiffeners where the flange and web meet.

Since there is a splice present in span one, the wires for Gage Line B could not be attached

directly to their girders (over the middle pier) until after transportation occurred. Instead, the

wires for Gage Line B were put in their proper place on the girders which contain Gage Line A,

since all wires of Gage Line B must pass by Gage Line A on their way to the termination box.

The length of wire needed to reach the gages over the middle pier was coiled and attached to the

girder at a location near the splice. The wires were then routed to the gages and connected to the

Gage Line B "pigtails" after the erection of the girders. The wires for Gage Line C were similarly

bundled with the other wires of Gage Lines A and B, and connected to the crossframe gages after

their erection process.

2.3.3 Zero Readings

Readings were taken after the gages were attached at PDM. The support conditions of the

girders, including wood blocking, were noted for these readings. Once the girders were delivered

to the construction site, a second set of zero readings was taken. Table 2.1 provides a

comparison of the zero readings taken at PDM, and the readings taken after the girders were

delivered to the job site while they were sitting on the ground. When the readings were taken at

PDM, not all of the temperatures were recorded. Therefore a comparison was made to determine

13

the effect this might have on the readings. The largest discrepancy occurred with the zero

readings for girder 312D2 which were taken inside the paint shop at PDM Bridge, but out in the

sun at the construction site. The greatest percent difference was 5.32% on this girder. Most of

the other readings did not vary by more than 2 to 3 percent. The zero readings for the other

girders were taken in the sun both at PDM and the construction site. The effects of the sun could

thus be a reason for some of the larger discrepancies (i.e., 4 to 5 percent) found in some of the

gages. However, the difference between the two readings is generally small, and the PDM

readings were used as the zero for this project.

2.3.4 Gage Damage and Replacement

Two gages were damaged during the erection and construction of the bridge. These problems

resulted from miscommunication between the University of Minnesota researchers and the

different construction crews, or within the construction crews. During the erection of the girders,

the gage labeled 11B was damaged by a "come along". A "come along" is a device used to keep

the curved girder vertical when it is lifted from the ground. The attachment of the "come along"

to the top flange of the girder at its midspan crushed gage 11 lB. The other top flange gages were

spared by chance. The use of the "come along" was not discussed during the planning meetings,

and should be accounted for in future projects of this nature. The second gage, gage 1A, was

damaged when the cantilever supports for the formwork were put into place. This formwork

consists of a 4 x 4 board wedged between the girder's top flange and the cantilever supports, and

then 3/4" plywood is placed on top of the supports. It was the wedging of the board between the

flange and the support that damaged the gage. The construction crew placing the formwork was

not informed about the location of the gages, and the gages were not visible from above the

girders. This lead to the damaging of the gage. Both of these gages were replaced. It should be

noted that on the whole, the cooperation of MN/DOT personnel, the erectors, and the

construction crews was exceptional, which was directly related to the success of this field

instrumentation study.

14

Table 2.1. Difference Between the Zero Readings at PDM and on the Construction Site

nirtial Strain Readings At PDM on 7/13/95Temperature 3, C

Member Gage Number Strain (*10' 6 )

308D1

307C1

306B1

305A1

312D2

31102

31082

309A2

1A

2A3A4A

5A6A

7A

8A9A10A11A12A

13A14A15A16A17A18A

19A20A21A22A23A24A

182B3B4B8

5B68

7B

889B10811B128

138148158

168178188

198208218B228

238248B

2173.61991.51957.51991.62379.41938.7

2193.52488.31722.82172.22431.22281.2

2355.82200.62239.91657.52192.51832.1

2426.52105.42163.01567.52476.41802.8

1228.51895.12144.81691.71670.32592.3

1440.32179.92376.02188.41910.61785.3

2191.42327.72605.22224.91601.82589.6

1658.02059.62192.32599.01643.32262.9

5 9/71/7 & 7/1 8195 on Construction

Site on the Ground

Strain ('10 " ) Temperature ( C)

2231.12010.01946.22027.92389.71921.1

2255.72537.91757.72223.32485.92298.3

2352.32213.72230.01648.02222.01850.8

2430.22155.22130.01545.72485.91796.3

1280.01960.52169.01781.71681.92663.4

1459.22194.02413.22208.61928.31861.8

2209.82345.72647.32257.61524.92647.5

1668.02075.82217.32641.51659.82326.1

35.535.735.632.834.331.2

36.436.444.244.536.233.7

32.031.137.937.432.529.5

32.632.2

31.532.329.3

34.734.333.732.234.936.3

34.734.133.631.735.136.9

32.332.031.729.932.036.9

32.132.031.229.531.735.5

% Diff % Diff

ZeroStrain

Difference

57.518.5

-11.336.310.3

-17.6

62.249.634.951.154.717.1

-3.513.1-9.9-9.529.518.7

3.749.8-33.0-21.89.5-6.5

51.565.424.290.011.671.1

18.914.137.220.217.776.5

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15

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CHAPTER 3

FIELD MEASUREMENTS DURING

CONSTRUCTION OF THE BRIDGE

3.1 INTRODUCTION

This section contains a description of the stresses resulting from the construction and erection of

the bridge. Figures 2.1 through 2.5 display a plan of the bridge and the girder nomenclature. The

construction sequence is divided into different loading stages designed to examine the stresses

present during what was determined to be the critical stages of the construction of the bridge.

This allowed for the observation of the stresses the structure experienced during the construction

of the bridge. The following list details the loading stages after which readings were taken:

1. The erection of span 1

2. Half of span 2 was erected

3. All girders and crossframes erected (bolts loose on all crossframes)

4. All girders and crossframes erected (all bolts "rattled up" into their tightened position)

5. All deck formwork in place

6. All deck formwork and reinforcement in place

7. During the pouring of the reinforced concrete deck

8. Parapet walls poured

9. During truck live loading

The readings from these stages are arranged into two sections to make the results easier to

analyze. The two sections are classified as: Stresses due to Construction, and Stresses During

21

the Pouring of the Reinforced Concrete Deck The Stresses During the Truck Live Loading will

be discussed in Chapter 4.

At each of the loading stages detailed above, strain readings were taken, and the data was stored

in the readout box. Zero readings, recorded at PDM on July 13, 1995, were used as a base line of

"zero" stress to which the remaining readings were compared (see Chapter 2).

3.2 ERECTION AND CONSTRUCTION PROCEDURE AND SEQUENCING

The following is a description of the erection and construction procedure. This section provides a

general overview of how the structure was constructed, and how this procedure affected the

stresses in the structure. A detailed construction sequence of the bridge is included in Appendix

D.

3.2.1 Erection of the Curved Girders and Crossframes

The erection of the bridge began on July 17, 1995 in span 1 (i.e., the southern span) with the

innermost girders. Girders 305A1, 309A2, 306B1, and 310B2 (see Figure 2.4) were delivered to

the construction site in the morning by PDM. They were placed on the ground until the evening

when the erection began. The erection of the girders occurred from 11:00 p.m. to 7:00 a.m. to

reduce traffic congestion. Two 100 ton crawler cranes and one 50 ton 4-wheel crane were used

to lift the girders and crossframes into place. Girder 305A1 was hoisted by a 100 ton crane, using

a 20 foot spreader bar (which allowed for two lifting points), and the 50 ton crane, using a single

lifting point, and the southern end of the girder was placed on the southern abutment (There

were some fit-up problems that occurred resulting from an improperly sized hole in the girder

bearing plate. This problem was fixed after the erection was completed.) The other 100 ton

crane then hoisted girder 309A2 using a "come-along" and a 30 foot spreader, and aligned it,

with the help of the some workers, with girder 305A1. The "come-along" is a device shown in

Figure 3.1. The "come-along" prevents the girder from tilting out of the vertical plane, and this

helps the fit up of the two girders. With the two girders being in alignment, the bolts for the

splice were put into place and the nuts were tightened using an air pump driver. While this was

22

being done, a shoring tower was placed approximately at the midspan of span 1 to support the

bottom flange and increase the stability of the girders. The shoring tower helps to control the

vertical geometry of the structure so that it acts as a unit until all girders are connected by

crossframes, and it also improves the alignment of the total structure, which helps during the

attachment of the crossframes. A shoring tower was used for each girder during the erection of

both spans 1 and 2. Note that while MN/DOT did anticipate the possible use of shoring towers,

and thus provided shoring tower locations, this structure was actually designed presuming no

shoring towers were to be used -- it was the steel erector that opted to use them.

After the splice was tightened, the 100 ton and 50 ton crane holding girder 305A1 were released,

and the two cranes lifted girder 306B1 into place while the second 100 ton crane continued to

support girder 309A2. After the girder was placed on the southern abutment, the 50 ton crane

was released, and it began to lift crossframes which were connected between girders 305A1 and

306B1. A crossframe was placed at approximately the quarter point of the span and at the

southern end of the span. These two crossframes were held in place with four bolts (one per

gusset plate). The second 100 ton crane released girder 309A2 and hoisted girder 310B2, once

again using the "come-along". This girder was then aligned with 306B1, and the splice

connecting the two girders was tightened. The remaining crossframes for that span were placed

and secured. The following night, girders 307C1, 311C2, 308D1, and 312D2 were erected in a

similar manner. This is the point at which the first set of strain readings were taken. During July

24 and July 25, 1995, the four girders in span 2 (northern span) were erected. The erection began

with the outermost girder and proceeded towards the innermost girder. The 100 ton and the 50

ton crane were employed to hoist the girders and crossframes into place. Note that the four

shoring towers were moved from span 1 to span 2 during the day of July 25 (after two of the four

girders of span 2 were erected). Following each night's erection, all of the bolts were placed for

all of the crossframes. In some cases the bolts were pounded into place with a sledge hammer

which could have induced stresses in the structure. After the entire steel structure was erected,

the entire structure was "rattled up". The "rattling up" procedure involved the final tightening of

23

all bolts, connecting the crossframes to the girders, along with the removal of all the shoring

towers. This was the final state of the structure before the formwork was constructed.

3.2.2 Construction of the Formwork and Placement of Reinforcement

After the erection of the girders and crossframes, the placement of the formwork began. The

formwork consists of whalers, 2" x 10" boards with end clamps attached to the top flange of the

girders, supporting 3/4" plywood decking spanning between the girders. Outside the two

outermost girders, right triangle bar supports were spaced approximately every five feet, and 2" x

6" boards supported the formwork for the concrete to be poured outside of the girders. These

supports are cantilevers wedged against the underside of the top flange with a 4"x 4" board in

order to force the tip of the triangle against the web to create a reaction against the weight of the

forms. Figure 3.2 shows a such a support, with the dark lines being the girder and triangular

support, and the gray being the board and formwork.

Other loading resulted from the weight of the workers and their equipment. In general there were

five to ten workers and two air compressors weighing 2,784 lb. each on the bridge during the

construction. After the formwork was finished, the shear connectors were welded to the top flanges of

the girders. These shear connectors allow the steel girders and the reinforced concrete to act

compositely to resist the forces in the positive moment regions. The final preparation of the structure

before the pouring of the concrete deck involved the placement of the reinforcement. The bottom layer

of steel was in the longitudinal direction. Next the transverse steel was placed followed by the top

layer of longitudinal reinforcement. The concrete deck was poured on August 11, 1995. After the

deck was allowed to properly cure, the reinforcement cage for the parapet walls (i.e., the concrete

traffic bariers) was fabricated. Once this task was completed, a slip former was used to form the

parapet walls. The slip former was the shape of the parapet walls. The concrete was pumped directly

into the slip former, and this allowed the walls to be fabricated as the slip former progressed along the

bridge. The final step in the construction of the bridge was the pouring of the two inch low slump

concrete overlay. Once all of this construction was completed, the bridge was opened to traffic.

24

3.3 CONSTRUCTION STRESSES

This section contains observations of the data acquired during the various construction stages.

When describing a particular stress, the given location of the stress may be classified in different

ways depending on how specific a reference is required. The convention used to reference these

locations is as follows. Starting with the outside facia girder and proceeding towards the inside

facia girder, the girders are labeled as girder 1, girder 2, girder 3, and girder 4. If an individual

girder is referenced, then the designations from the structural plans are used, i.e., girders 308D1,

312D2, and 316D3 are spliced together to form girder 1. If a more exact is location needed, then

the gage line can be specified. Finally, the actual gage number can furnish an exact location. The

same notation is used when describing the crossframes, except that crossframe 323CF15 is called

crossframe 1, crossframe 324CF13 is called crossframe 2, and crossframe 325CF13 is called

crossframe 3. Figures 2.4 and 2.5 illustrate all of these designations described above. When

describing a stress value, a negative value indicates compression and a positive value indicates

tension. Units of kilo-pounds (kips) per square inch, ksi, will be used throughout this report to

display the values of stress observed.

The strains obtained from the field measurements are longitudinal (i.e., they are oriented along the

primary axis of the member), and are linearly related to longitudinal stress by Young's modulus of

elasticity, which for the steel in this project is taken as 29,000 ksi. This calculation of stress from

strain, based upon linear elastic behavior, presupposes there is no yielding or significant

geometric nonlinearity in any member during construction. For this structure, the nominal yield

stress of the steel members is 50 ksi.

3.3.1 Stresses During Construction of the Steel Superstructure

This section summarizes the stresses observed at each of the loading stages detailed above. At

each stage of construction a complete set of strain readings was taken, and the data was reduced

to observe the stresses relating to that stage. In Appendices A, B, and C, the cross-sectional

stresses for all sixty gages are displayed on one sheet per one set of readings. A cover sheet

detailing the loading condition, reading objective, and general observations accompanies each data

25

sheet. The change in stress between each loading stage was also examined. This allowed the

correlation of the resulting stresses to the additional loading for that stage. Another cover sheet

accompanied the data sheet that detailed the changes in stress. An overview follows that

discusses the general behavior observed during the erection and construction of the bridge. Refer

to Appendices A, B, and C for the detailed results.

There was little obvious correlation of stresses to loading in the first two loading stages. These

readings were taken during the erection of the steel girders and crossframes (see Appendix A).

There was not enough dead load to induced significant stress in the girders. The largest stress,

5.88 ksi, was observed in a member of the crossframes. This stress probably resulted from the

placement of the bolts. As described earlier, the alignment between the girders and the

crossframes was not exact. The day following the erection of the girders, the remaining bolts

were placed. In many cases, the bolts were hammered into place to allow proper fit up. This fit

up process could have induced these stresses. The largest stresses otherwise were -3.77 ksi in

compression and 3.27 ksi in tension. All of the observed values are minimal compared to the total

allowable stress of the members. In the July 24 readings, girder 312D2 does exhibit clear strong

axis bending behavior, plus the effects of warping, which is to be expected since this is the sole

girder at the time contributing to the negative moment across the full span. On July 24, stresses

could also have been induced by the crane when hoisting the girders into place, which could be

another possible explanation for these erratic stresses.

Clearer stress distributions resulted on July 26, after erection of the full steel skeleton, loosely

bolted. Once all of the girders were in place with all of the bolts still loose, the general trend of

the behavior of the girders, except for girder 1 at the middle pier, was as expected. At this

loading stage, the maximum and minimum stresses were -4.34 and 6.5 ksi, which are fairly

minimal.

Once all of the bolts were in place, the whole structure was "rattled up" which involved the final

aligning of the structure through the tightening of all of the bolts. The change in stress observed

26

for this loading stage ranged from -0.87 ksi to 1.15 ksi. As can be observed, the "rattling up" of

the structure did not significantly increase the stresses. This illustrates that the majority of the

erection induced stresses (as opposed to stresses due to self weight) resulted from the alignment

corrections that allowed the placement of the crossframe bolts. Aside from four gages (i.e.,

girders 2 and 3 at the midspan), the behavior of the girders is as expected. The range of stresses

present in the structure resulting from the erection of the steel members were:

midspan: -3.78 ksi to 2.87 ksi

middle pier: -4.75 ksi to 6.74 ksi

crossframes: -3.04 ksi to 4.41 ksi

After the formwork was placed, the largest stress increase ranged from -1.75 to 1.27 ksi. There

was one isolated increase that was not within this range, in which girder 309A2 had a change in

stress of 3.08 ksi. The reason for this isolated increase is not explainable, although it may relate

to an odd eccentricity present in the construction live load in that area.

The next reading was taken after the reinforcement was placed. The stresses did not increase

much, with the changes ranging from -0.66 to 0.65 ksi. The largest values of stress present before

the pouring of the concrete deck were:




The girders behaved as expected at the midspan (i.e., for girders in a positive moment region) and

the middle pier (i.e., for girders in a negative moment region) due to the loading of the reinforced

concrete deck. The loads were finally sufficient to yield consistent behavior of the stresses; any

anomolies due to fitup and small load eccentricities were overwhelmed by the increase in

27

deadweight on the bridge. The change in stress due to the pouring of the concrete deck ranged

from -7.87 to 6.00 ksi. The greatest magnitude of stresses present at this stage were:




The pouring of the concrete parapet walls (August 25) induced stresses whose magnitudes were

consistent with the expected behavior at the midspan and middle pier. However, several of the

midspan top flange gages picked up a tiny amount of tension during the parapet wall pour. This

could be due to the stresses redistributing across the cross section of the bridge due to the

additional loading along the outer edges of the deck, or the composite action of the bridge at the

midspan. In general, once the deck hardened, the top flange gages at the midspan showed much

less change in stress than the bottom flange, and these results from the parapet wall pour show

that the neutral axis of the girders due to strong axis bending was probably near or in the top of

the girder top flanges. The stress envelope for this load stage is:




The final construction stress reading was taken after the 2 inch concrete overlay was poured.

This was the final state of the bridge before it was opened to traffic. The behavior of the girder

flanges was as predicted at the midspan and middle pier, although the crossframe behavior was

less predictable, as was customary throughout the construction process. The final state of stresses

for the bridge before being put into service were:


28



These values are well within the allowable stresses of the structure, and they are comparable to

the computer predicted values, as will be shown in Chapter 6. For the final three loading stages at

the middle pier, the largest compressive stress occurred at the top inside flange tip of the inside

facia girder, and the largest tensile stress occurred at the bottom inside flange tip of the same

girder. In the crossframes, the largest tensile stress occurred in the top horizontal of crossframe 1

while the largest compressive stress occurred in the bottom horizontal of crossframe 1. The

largest stresses at the midspan varied with each loading stage.

3.3.2 Stresses During the Pouring of the Reinforced Concrete Deck

The following section contains the data taken during the pouring of the concrete bridge deck.

Each loading stage occurred at thirty minute intervals, and at every loading stage a complete

reading of all sixty gages was recorded. In an attempt to record as readings continuously as

possible, sixteen gages (1A, 4A, 5A, 6A, 13A, 16A, 17A, 18A, 1B, 4B, 5B, 6B, 13B, 16B, 17B,

and 18B) were read approximately every ten minutes. The pouring of the bridge deck began at

4:15 a.m. at the north abutment. Concrete locations are referenced from the north abutment for

the loading condition for each loading stage. There were ten to fourteen workers at a given time

working the concrete. These workers' various duties included directing the wet concrete with the

concrete pump, spreading the concrete, vibrating the concrete, hand finishing the concrete, and

running the finishing machine. A break was taken by the workers from 6:10 a.m. to 6:40 a.m.

The following defines the time of each loading stage:

Stage 0:4:15 a.m. - The girders with the formwork and reinforcement in placeStage 1: 4:45 a.m. - The concrete deck located at the first quarter point of span twoStage 2: 5:15 a.m. - The concrete deck located at the midspan of span twoStage 3: 5:45 a.m. - The concrete deck located at the middle pierStage 4: 6:15 a.m. - The concrete deck located at the first quarter point of span oneStage 5: 7:00 a.m. - The concrete deck located at the midspan of span oneStage 6: 7:30 a.m. - The concrete deck located at the third quarter point of span oneStage 7:7:50 a.m. - The entire concrete was finishedStage 8: 8:15 a.m. - Reading taken to determine the stress change after thirty minutes

29

Figure 3.3 (and, equivalently, Figure B.1) details the location of each loading stage on a plan view

of the bridge. The following section summarizes the data recorded for each of the loading stages

during the pouring of the concrete deck. Appendix B contains these stresses. For each loading

stage, there is a cover sheet describing the loading condition, reading objective, and general

observations, followed by two sheets: one displaying the change in stress between each stage and

the other the actual stress present. The observations on the cover sheets describe the changes in

the stresses from load stage to load stage. This approach permits the observation of the behavior

of the girders as the pour progressed along the bridge, regardless of the in-situ stresses at the time

of the reading. In addition, Appendix B contains graphs showing the total stress and the change

in stress in each gage as a function of time.

Stages 1. 2. & 3: In a two span bridge when the loading is in one span, a negative moment region

is created in the other span. Except for girder 4, the girder stresses at the midspan of span 1

exhibited behavior expected in a negative moment region, which is tension in the top flange and

compression in the bottom flange. Girder 4 experienced compression in the top flange and

tension in the bottom flange. This is due to an apparent moment or differential deflection acting

across the width of the girders. Beginning at the outside facia girder, the stresses are the largest.

At each respective gage location, the stress decreases, and ultimately reverses sign as the inside

facia girder is approached. Figure 3.4 illustrates this point. The girders at the middle pier are also

experiencing stresses indicative of a negative moment region, which is expected.

As the pour continued to the midspan of span 2 the girders, with the exception of girder 4,

continued to respond with the stress pattern observed in the previous loading stage. The

differential behavior across the width of the deck continued to be observed. The stress changes at

the midspan increased, in most cases, by 2 to 2.5 times that of the increase observed in load stage

1. At the middle pier, the largest increase in stress was 2.8 times that of the stress changes in load

stage 1. The change in stress in the crossframes was approximately of the same magnitude as that

of the girders, and the diagonals in the crossframes continued to display compression in the top

members, except for gage 10C, and tension in the bottom members.

30

At stage 3 the pour had reached the middle pier. The change in stress continued with the same

expected pattern. The range of the stress change from stage 2 to 3 at the midspan was 0.07 to

0.65 ksi (tension) and -0.06 to -0.19 ksi (compression), and the range of stress change from stage

2 to 3 at the middle pier was 0.14 to 1.01 ksi (tension) and -0.19 to -0.78 ksi (compression). The

change in the stresses in the crossframes was 0.02 to 0.67 ksi and -0.07 to -0.49 ksi. The

envelope of the magnitude of stresses present after the pouring of the second span (from the

beginning of the pour) was:




Stages 4.5.6. & 7: The next four loading stages observed the behavior of the girders when the

concrete was poured in the first span. There was a thirty minute break between the completion of

the pour in span 2 and the start of the span 1 pour. When the concrete had reached the first

quarter point there-was not much change in the stresses. Except for a few gage locations, the

beginning of a stress reversal at the midspan was observed, which is expected since the midspan

will be a positive moment region. The middle pier stresses continued to respond as gages in a

negative moment region. A stress reversal was also observed in the diagonals of the crossframes.

The top two members displayed a change in tensile stress with the bottom two members

exhibiting a change in compressive stress. The range of stress changes for the cross sections were

-0.98 ksi to 76 ksi for the crossframes and -0.59 ksi to 0.39 ksi for the girders.

When the concrete reached the midspan of span 1 a definite increase in stress was observed. At

the midspan, the top flanges displayed an increase in compressive stress and the bottom flanges an

increase in tensile stress. The opposite behavior was occurring at the middle pier, and the

previously described behavior in the crossframes continued. The stress change envelope at the

midspan was -3.12 ksi to 1.31 ksi. The stress change envelope at the middle pier was -1.47 ksi to

31

1.65 ksi. The stress change envelope in the crossframes was -2.94 ksi to 3.21 ksi (there was a

value of greater magnitude, but it was extrapolated from nearby data, since a crossframe gage

temporarily did not read, and therefore this value is not used here as the largest tensile stress).

The trend in the stresses continued when the pour reached the third quarter point. The stress

changes ranged -6.05 ksi to 2.80 ksi at the midspan, -1.30 ksi to 1.28 ksi at the middle pier, and

-3.73 ksi to 2.12 ksi in the crossframes.

The stresses did not change significantly when the concrete pour was finished and had reached the

southern abutment. Twenty-five minutes after the pour was finished, another set of readings was

taken to observe any changes in stress that might occur due to composite action beginning to

form. There was no significant change in stress to confirm the onset of composite action. The

final state of stress of the bridge with wet concrete and no composite action was:




In addition to these "snapshots" of the stresses, plots were prepared displaying the stresses as the

pour progressed. Plots displaying both the magnitude of stress and the change in stress observed

during the pouring of the concrete deck are located in Appendix B. These plots were developed

to display the bridge stresses versus the time line of the pouring of the deck. Each plot displays

the cross section for a single member at a given location, i.e., the first plot is of girder 1 at the

midspan of span 1 (gages 1A-6A). As stated above, two plots were constructed for each of these

cross sections: one displaying the change in stress versus time, and the other displaying the actual

stress versus time. The abscissa displays the actual time of day, and the ordinate displays the

stress in units of kips per square inch (ksi). The pouring of the concrete deck began at 4:15 a.m.

at the northern abutment, progressed through span 2 to span 1, and was completed at the

southern abutment at 7:50 a.m. When examining these plots, the left end of the abscissa

32

represents the north abutment and the right end the south abutment. Icons displaying the

progression of the pour are included on Figure B-18 to mark each loading stage on the time line.

Once the pouring of the deck began, a full set of readings was taken every thirty minutes. These

readings are represented by a solid line. The continuous readings taken for sixteen of the gages

(see the gage numbers listed previously) are represented by a dashed line.

As documented above, the top flanges for the midspan gages generally experienced tensile stress

while the bottom flanges experienced compressive stresses when the concrete was being placed in

span 2. This was due to the negative moment created at this location in span 1. At 7:00 a.m.,

when the pour had progressed to the midspan of span 1, a reversal of stress occurred due to the

positive moment created by the load of the wet concrete. The top flanges then experienced

compressive stress while the bottom flanges experienced tensile stress. Throughout the entire

pour, a negative moment region was located at the middle pier, so the top flanges experienced

tension and the bottom flanges experienced compression. These stresses increased as the

concrete pouring progressed to the southern abutment. The bottom two members in the

crossframes experienced tension when the wet concrete was in span 2, and underwent a reversal

of stress to compression once the concrete entered span 1. The top two members displayed the

opposite behavior. When the concrete was in span 2, the stress experienced was compressive

which increased in tension once the concrete entered span 1. There are interruptions in the lines

in the plots of the crossframe stresses. This occurred because there were times when a gage did

not read, so that data point was omitted

The behavior of the girders and crossframe observed during the pouring of the concrete deck was

as expected. The range of the stresses were also of the magnitude that was expected before the

pouring of the deck began. None of the stresses observed were extraordinary, and they were well

within the capacity of stress that the bridge could support. This is significant since this is a critical

portion of the construction of the bridge. The steel girders must support this large load without

the benefit of composite action that the cured concrete deck will provide once the bridge is placed

in service.

33

Tensioned Chain

Figure 3.1. Come-along device

Figure 3.2. Right triangular bar support with plywood formwork

34

4.

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Figure 3.4. Example of girder stresses varying across the width of the bridge's cross section

36

CHAPTER 4

FIELD MEASUREMENTS DURING

LIVE LOADING OF THE BRIDGE

4.1 INTRODUCTION

The final stage of this project was observing the behavior of the bridge under live load. The

method for applying live load involved using two dump trucks weighing approximately 50 kips

each. The beds of the trucks were loaded with sand, and their actual weights were measured with

truck scales. Four basic loading configurations were selected including:

* Two Trucks Side by Side at the Quarter Points of the Bridge

* One Truck at the Quarter Points of the Bridge

* Two Trucks End to End at the Midspan of Each Span

* One Truck at the Midspan of Each Span Simultaneously

In all of the above cases, the trucks were centered along the width of the bridge. The quarter

points, including the midspan, were measured and marked on the deck of the bridge. The trucks

were guided to these areas, and the front tires of the trucks were located so that their center of

gravity were as close to the quarter points as possible.

At each loading position a complete set of readings was taken, and they are displayed in Appendix

C. Again, a cover sheet is included to describe the stresses observed. In addition to these

separate readings, plots were made for the first two loading configurations, i.e., the trucks being

located at the quarter points for each span. These plots display the member stresses for a given

truck location, and allow the observation of how the stresses change as a vehicle travels along the

37

bridge. In all of the stress readings taken, the change in stress was monitored. Before the trucks

were placed on the bridge, a set of readings was taken to document the final unloaded stress state

of the bridge. These readings were used as the baseline for comparing the stresses induced from

the trucks. This was done to observe the behavior of the bridge without the stresses from

construction affecting the readings. The locations where the trucks were placed were labeled

from 1 to 6, and actually corresponded to specific crossframe positions at the approximate quarter

points of the bridge (see Figure 4.1). The placement of the trucks started from the southern

abutment and continued towards the northern abutment. Figure C-1 shows the exact locations of

all fifteen cases of truck loading measured. Cases 1 through 6 correspond to two trucks placed

side by side at the six locations, and cases 10 through 15 correspond to one truck placed at the six

locations. Case 7 placed one truck on each span. Cases 8 and 9 had two trucks placed end to end

on each span. In the following four sections the results from the truck live loading are discussed.

4.2 TWO TRUCKS SIDE BY SIDE AT THE QUARTER POINTS OF THE BRIDGE

For this loading condition the two trucks were placed side by side on the bridge deck at each of

the bridge's quarter points. In general, the behavior of the girders was as expected. When the

trucks were located in span 1, a positive moment region was created at the midspan, and a

negative moment region was created at the middle pier support. Except for gage 19A, the inside

tip of the top flange of the inside facia girder, the top flanges experienced compressive stress, and

the bottom flanges experienced tensile stress. The maximum stresses for both flanges were

observed when the two trucks were placed at truck location 2 which was directly over the gages

at the midspan of span 1. As the placement of the trucks continued away from truck location 2,

these stresses decreased until a reversal in the stresses occurred at truck location 4. At this

location the trucks were in span 2, so a negative moment region was created at the midspan of

span 1. This produced tension in the top flanges and compression in the bottom flanges. When

compared to the stresses observed when the trucks were in span 1, these stresses were fairly

minimal. The stresses observed for the top flanges were minimal throughout this loading stage

because of the composite action present in the midspans of the bridge. In these regions, the steel

girders had the assistance of the concrete deck, through the shear connectors, in resisting the

38

truck live loading. These stresses ranged between approximately 0.10 ksi and approximately -

0.30 ksi. The bottom flange stresses ranged between approximately 1.50 ksi and approximately -

0.30 ksi. The largest stress observed during this loading stage was 1.48 ksi at gage location 12A.

At the middle pier gage line, the top flanges experienced tensile stress and the bottom flanges

experienced compressive stress at all of the truck loading locations. This behavior was expected

because this line of gages is located at the middle pier, and loading in either of the spans would

cause this area of the bridge to be a negative moment region. The stresses in both the bottom and

top flanges increased and reached a maximum as truck location 3 was approached. The stresses

decreased at truck location 4. This was probably a result of the loading being directly resisted by

the middle pier and not transferring the load to gage line B. The stresses increased and

approached the previously observed magnitudes at truck location 3 when the trucks were at

location 5. The top flange stresses were once again minimal when compared with the values of

stress in the bottom flanges. It appears that some composite action is occurring with the top

flange and concrete deck even though no shear connectors are present in this area. This could be

a result of bond between the concrete and steel. The stress for the top flanges was not greater

than approximately 0.15 ksi, and the stress for the bottom flanges was not greater than

approximately -0.75 ksi. The largest stress observed at the middle pier was -0.72 ksi. The

stresses observed in the crossframes ranged from approximately -1.75 ksi to 1.00 ksi. The largest

stress observed during the loading occurred at truck location 3 and had a value of -1.76 ksi. The

diagonal members of the crossframes experienced the largest tensile and compressive stress with

the horizontal members experiencing values in between. For these small loadings, there was not

always an observable pattern or explanation for the individual behavior of the members of the

crossframes.

4.3 ONE TRUCK AT THE QUARTER POINTS OF THE BRIDGE

The next loading condition involved the placement of one 50 kip truck at each quarter point of the

two spans. The truck was centered along the width of the bridge. Equivalent behavior was

generally observed as described for the two trucks placed side by side. In some cases though, the

load from one truck was insufficient to induce the expected behavior in a negative or positive

39

moment region. The same basic trends in the stresses were observed (i.e., maximum stresses

occurred at truck location 3, with a stress reversal at truck location 4), but sometimes a stress that

was expected to be compressive was observed to be a tensile stress. This behavior was observed

more for the inside girders 3 and 4. It appears that the stiffer two girders 1 and 2 were resisting a

greater portion of the stress, which caused the inside girders to experience a warping stress which

caused some of the top flanges to experience tension instead of compression. The same behavior

was also observed at the middle pier gages. The maximum stresses observed ranged from

approximately -0.15 ksi to approximately 0.80 ksi at the midspan and approximately -0.45 ksi to

approximately 0.10 ksi. Once again there was not an explainable pattern to the behavior of the

crossframes. The range of stress experienced was approximately -1.00 ksi to approximately 0.30

ksi. These results show that greater loading is required if a definitive bridge behavior is to emerge

from truck live loading.

4.4 TWO TRUCKS END TO END AT THE MIDSPAN OF EACH SPAN

In this loading stage, the two 50 kip trucks were placed end to end and centered at the midspan of

each span. The trucks were also centered along the width of the bridge. This loading stage had

an equivalent effect to that of the two trucks side by side at truck locations 2 and 5. Positive

moment action was generated at the midspan of span 1 when the two trucks were located in span

1, and negative moment action was generated at the midspan of span 1 when the two trucks were

located in span 2. A negative moment region was present at the middle pier gage line for both

truck loading locations. The largest tensile stress was observed at the midspan of span 1 with the

trucks in span 1 and equaled 1.37 ksi. The largest compressive stress located at the middle pier

with the two trucks in span one equaled -0.68 ksi. The largest stresses in the crossframes were -

1.81 ksi and 0.82 ksi. These stresses occurred with the two trucks in span 1.

4.5 ONE TRUCK AT THE MIDSPAN OF EACH SPAN SIMULTANEOUSLY

This loading stage involved placing one 50 kip truck at the midspan of each span at the same time.

The stresses observed were not as significant as those in the previous loading stage. Again a

positive moment region was observed at gage line A and a negative moment region was at gage

40

line B. The largest tensile stress in the bottom flanges at the midspan was 0.66 ksi, and the largest

compressive stress observed in the bottom flanges at the middle pier was -0.75 ksi. The range of

stresses observed in the crossframes was -0.79 ksi to 0.38 ksi.

41

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CHAPTER 5

FINITE ELEMENT MODEL

5.1 INTRODUCTION

This chapter outlines the finite element models used to obtain computational results to compare to the

field measurements. To permit detailed modeling of the specific topology and loading of this bridge

during all phases of construction, the research team developed the University of Minnesota Steel

Curved Girder Bridge System Analysis Program (i.e., the UM program). Before using this program to

compare analysis results to the field measurements, the results from the program are compared to those

obtained using DESCUS-I. In this way, conclusions may be drawn about the level of stresses seen in

the subject bridge during construction, and about the ability of the software programs to reproduce

these stresses accurately.

5.2 THE GRILIAGE METHOD

Among all the methods available for analyzing curved girder bridge systems, the Grillage Method,

based on using a planar grid model, is most appropriate for practical use. This is the basic type of

analysis used by the UM program, and is similar in its essentials to the type of analysis used in

DESCUS-I. The basic idea of the Grillage Method is to use a two-dimensional finite element model to

simulate the three-dimensional effects of bridge superstructures. Figure 5.1a illustrates the grillage

model of this research, which uses four types of structural members, including longitudinal curved I-

girders, crossframes, abutment beams, and transverse grids, for the curved steel I-girder bridge system.

Figure 5. b shows a cross section view of this bridge system. A primary difference between the

Grillage Method and the Grid Method (which is commonly used for straight girder bridge systems) is

that the Grillage Method includes a warping degree-of-freedom in the analysis.

43

The Grillage Method is a stiffness-based finite element procedure which first assembles the system

stiffness matrix by adding all element stiffnesses directly from the referenced nodal degrees-of-freedom.

Once the global stiffness matrix is formed, an equation solver, based on the Cholesky decomposition

algorithm, is used to solve the simultaneous equations for the displacements. Warping effects of open

sections are taken into consideration, similar to the way proposed by Mondkar and Powell [13]. This

section describes the basic assumptions and element library of the Grillage Method followed by a

discussion of the modeling and boundary conditions of the MN/DOT bridge.

5.2.1 Basic Assumptions

The basic assumptions in the Grillage Method are as follows:

1. All members have a monosymmetric cross section.

2. The structure behaves like a grillage: any force or displacement vector acting at a node has four

components, or degrees-of-freedom, including one translational component normal to the plane of

grillage, two rotational components about axes in the plane of grillage, and one additional

component, referred to as the twisting rate, to account for the warping effect.

3. The interaction behavior among all grillage members is obtained with respect to the average plane,

which is referred to as the grillage plane, defined by the principal centroidal axes of the curved

girders. However, members other than the curved girders which have their centroidal axes at a

different level from the grillage plane are permitted in this method by accounting for their offsets

from this plane, so that the analysis can be practical and flexible, yet mathematically consistent.

4. Shear deformation is neglected.

5. Nonuniform torsion (warping) is included.

6. Support conditions are idealized as either fixed or pinned.

44

7. Straight members such as crossframes, abutment beams, and supports may be either radially

positioned or skewed.

8. Girder spacing and member section may be varied.

9. Composite construction is considered.

10. Loading applied to the girder can include any number of concentrated and/or uniformly distributed

loads.

5.2.2 Element library

This section briefly describes the different finite element models included in the grillage method.

5.2.2.1 Curved I-Girder

The curved I-girders are represented by a three-dimensional two-node curved beam element with seven

degrees-of-freedom at each node. In a curved steel I-girder bridge, the in-plane (in the plane of

curvature) displacements, including the two translational displacements in the plane of the bridge, and

one rotational displacement about the axis perpendicular to the plane of the bridge, are small compared

to the out-of-plane displacements, and may be neglected. This is the principal idea behind the Grillage

Method, which generally assumes four degrees-of-freedom at each node as shown in Figure 5.2a. The

girder members may vary in depth, width, or other cross section dimensions along their length. The

composite action with the concrete deck on top of the girder is only considered in the positive moment

region or in the regions with shear studs. The program output gives stress resultants, including vertical

shear force, torsion, bending moments, and bimoments corresponding to each degree-of-freedom,

respectively. The computer program also provides information suitable for computing the normal

(longitudinal) stresses in the girders.

45

5.2.2.2 Crossframes

In Figure 5.2b, crossframes of the X-bracing type are shown to be modeled as of truss frames made up

of four pinned-end truss elements, for which only axial force is assumed. Noncomposite construction

is considered in each crossframe since there are no shear studs connecting the crossframe members to

the concrete slab. The axial force and its associated stress are calculated for each truss member of the

crossframe in this method.

5.2.23. End Abutment Beams and/or Transverse Grids

End abutment beam and transverse grid elements are assumed to use the same type of straight beam

finite element formulations in this analysis. End abutment beams are assumed not to be integral with

the concrete slab since the spacing between longitudinal girders is in general not large. Therefore, the

abutment beam is predominantly subject to negative moments which are not able to develop the

composite behavior. Transverse grid elements, used to simulate the transverse behavior of the concrete

deck, are assumed as straight beams with an effective width of concrete, and they are assumed to be

attached on the top of the crossframes, spanning from girder to girder. Although the transverse grid

and the crossframe share the same nodes in the analysis model, they are assumed to deform

independently, except for the nodal continuity at their ends. Accordingly, noncomposite construction

is considered for the transverse grids. Figure 5.2c shows the reduced degrees-of-freedom of the

straight beam element. Output for this element includes the nodal displacements corresponding to the

nodal degrees-of-freedom, and the stress resultants (member forces) at the beam ends. Bending normal

stresses at top and bottom edges of the beam are also provided.

5.2.3 Modeling and Joint Conditions of The Project Bridge

This section describes the finite element model used in the analyses for this project.

5.23.1 Modeling

The structural analyses were performed by modeling the two-span curved I-girder system as a grid,

shown in Figure 5.3. The south span, span 1, and the north span, span 2, are identified in the figure.

There are 104 nodes, 100 curved girder elements, 58 crossframes, and 6 end crossframes for the mesh

46

of the bare steel structure in this figure. An extra non-structural node number 105 is required for the

reference center of curvature. The curved girder elements may also have composite properties if

composite behavior is active, and in such cases the additional transverse reinforced concrete beam

members are also considered as part of the crossframes acting on the top of crossframes. The nodes

are located at points of crossframes, splices, supports and changes of cross section. Figure 5.3 also

shows all the geometry required for the mesh modeling, such as the radius of curvature and arc length

for each girder.

5.23.2 Joint Conditions

As described in Section 5.2.1, four degrees-of-freedom at each joint are appropriate for the analysis of

curved I-girder bridges. However, a fifth and sixth degree-of-freedom are incorporated into these

analyses for the following reasons. First, for consideration of thermal expansion, the use of vulcanized

expansion bearings is necessary. The girders are allowed to displace in their longitudinal direction, and

the skew end crossframes at both abutments thus induce axial forces when reacting against the curved

girders. To better track the structural response of the project bridge, the axial degree-of-freedom is

included at each joint in all analyses conducted with the UM program. The five degrees-of-freedom

(dl to d5) include: two translational components, where dl is oriented along the axial direction of

girders and d2 is oriented normal to the plane of the grillage; two rotational components about axes in

the plane of the grillage, where d3 is oriented about the axial direction and d4 is oriented about the axis

normal to the plane generated by dl and d2; and one component referred to as the twisting rate to

account for the warping effect, referred to as d5. For convenience, the boundary conditions at all

supports for the subsequent structural analyses are assumed to be fixed for degrees-of-freedom d2 and

d3, which means that the vertical deflection and the axial twist are restrained. Degree-of-freedom dl,

representing the axial translation, is also fixed at the interior pier, since the fixed bearings are

designed here. The joint conditions at all modeling nodes are tabulated in Table 5.1.

Second, the restraint of lateral (transverse) displacements provides artificial support at the nodal joints,

thus affecting the analysis results in the crossframes. To investigate the stresses in the crossframes, a

sixth degree-of freedom was often included in the UM program analyses (i.e., a degree-of-freedom in

47

the transverse direction of the bridge at each node). These analyses are identified accordingly in

Chapter 6.

In order to model pin connections, end force release codes may be employed on the straight beam

elements in accordance with the connection types or other physical considerations between these

elements and the girder elements. In the following analyses, all the straight beam elements, including

the end crossframes and the transverse grid members, are considered not to transfer bending moments

about the minor axes of their cross sections. In addition, the skew end diaphragms at both abutments

are further considered not to transfer bending moments about the major axes.

5.3 COMPARISON BETWEEN DESCUS-I AND THE UM PROGRAM

In order to compare to field measurements during construction, it is necessary to be able to model

detailed topological and loading conditions of the bridge, so as to match conditions in the field. The

UM program provides much more control over these issues than DESCUS-I, and it is for this reason

that it is used to compare to the field measurements. In order to be able to draw conclusions about the

quality of the DESCUS-I program, the results from both of these programs are compared in this

section. The differences between the two programs are compared first, followed by sample results

from the comparison.

5.3.1 Differences in Formulation Between DESCUS-I and the UM Program

The methodology behind these two computer programs have differences described as follows:

1. Polynomial functions are chosen as the displacement shape functions in DESCUS-I while

displacement solutions which are a combination of hyperbolic and trigonometric functions are used

in the UM program.

2. The spacing of crossframes is defined as the width of the concrete grid elements in DESCUS-I,

while only three tenths of this spacing is selected in the UM program to account for the shear lag,

as described in Hambly [14].

48

3. The warping normal stresses are computed by interpolating between the fixed and the pinned end

conditions in each girder element in DESCUS-I, while they are calculated from the bimoments in

the UM program, since an additional degree-of-freedom for warping is considered in the grillage

method of the UM program.

In addition, in the DESCUS-I analyses, the torsional rigidity of the girders was neglected, and the top

chord of each crossframe was considered to have zero cross-sectional area. This was consistent with

the modeling used for this bridge's design. These quantities were all calculated in the UM program.

5.3.2 Comparison of Computational Results

Two types of structural behavior are compared between the two programs. Noncomposite behavior is

applied initially until the concrete hardens. This is followed by composite behavior, once the concrete

strength is developed. The example of the noncomposite analysis being discussed is the bare steel

structure subjected to the self weight of the steel and the wet concrete slab. Figure 5.4 depicts the

vertical deflection of Beam 3 (the second to the outermost girder) along its length. Figure 5.5 shows a

typical bending moment diagram of Beam 4, which is the outermost girder. The difference between

the results obtained from DESCUS-I and the UM program is quite small. The percentage differences

for the vertical deflections and the bending moments between these two programs are tabulated in

Table 5.2. The maximum difference is found to be 9.43% in Beam 4 for vertical deflections and 5.23%

in Beam 1 for bending moments, but most results are much closer.

The composite analysis models the composite structure with the ratio of the steel modulus to the

concrete modulus, N, equal to 24 to account for long-term loading under superimposed dead loads

(SDL) of 0.3775 k/ft uniformly distributed on each girder. This SDL includes the parapet, a two inch

overlay, and the wearing surface. Results of the vertical deflection of Beam 2 and the bending moment

of Beam 4 are shown in Figures 5.6 and 5.7, respectively. The percentage difference for this case is

tabulated in Table 5.3, and the maximum difference is found to be 9.76% in Beam 4 for vertical

deflections and 5.97% in Beam 1 for bending moments, although most errors are much smaller. The

49

major differences occur at the innermost girder for bending moment and at the outermost girder for

vertical deflections. The deflection differences are caused primarily by difference #3 (as listed in

Section 5.3.1) of the methodology behind these two programs outlined earlier. The difference is found

to be very minimal on the two interior girders where the torsional effects are relatively insignificant.

Because the two programs compare well for the two primary phases of construction typically analyzed

during the design process, the UM program is utilized in this research to compare to field

measurements. Subsequently, conclusions may then be drawn regarding the ability of DESCUS-I to

provide a reasonable representation of the stresses in curved girder bridge systems.

50

Table 5.1 Nodal degrees-of-freedom

Conditions Node No. di. d2 d3 d4 d5 Notes

Abutments 1-4, 101-104 1 0 0 1 1 0- fixed, 1-free

Pier 48, 52, 56, 60 0 0 0 1 1 0-fixed, 1-free

Fixed point 105 0 0 0 0 0 0- fixed, 1-free

Free nodes others 1 1 1 1 1 0- fixed, 1-free

Notes: The degrees-of-freedom dl to d5 are defined as

dl- the linear component along the axial direction

d2- the linear component normal to the plane of the grid

d3- the rotational component about the axial direction

d4- the rotational component about the other axis normal to the plane entailing

dl and d2.

d5- the component regarding warping degree-of-freedom

51

Table 5.2 Percentage difference between MN/DOT DESCUS-I and UM programs due to baresteel subjected to steel weight and wet concrete

Span No. Beam 1 Beam 2 Beam 3 Beam 4 Average

1 D 0.0 -1.97 -3.81 -3.13 -3.0- 0.0

M -2.78 -0.52 -3.85 -4.44 -2.9

2 D -3.34 -1.07 2.31 9.43 -2.2- 5.9

M -5.23 -3.02 -3.05 -0.27 -2.9

Notes: Percentage Difference = (MN/DOT - UM) / UM * 100%

D- Deflection; M- Bending Moment

52

Table 5.3 Percentage difference between MN/DOT DESCUS-I and UM programs due tocomposite structure (N=24) subjected to superimposed dead loads

Span No. Beam 1 Beam 2 Beam 3 Beam 4 Average

1 D -2.33 0.0 2.5 9.76 -2.3- 6.1

M -3.17 -0.98 1.28 0.86 -2.1- 1.1

2 D 3.57 0.0 -1.89 1.89 -1.9- 2.7

M 5.97 -0.79 4.78 -0.57 -0.7- 5.4

Notes: N= EJEc

Percentage Difference = (MN/DOT - UM) / UM * 100%

D- Deflection; M- Bending Moment

53

Transverse arid

kUI VcULI 1 I I UtI

(a) Typical

End diaphragm

Crossframes

lode

grillage model

I (DU

d i aphragm

ntermediatei aphragm

Steel curved I-girders

(b) Profiles of diaphragms

Figure 5.1. Grillage model and bridge profiles

54

n Avk 2%. vlý24ýAO% L &% I. I.,

Two nodes per element Reduced nodal degrees of freedom

(a) Curved I-girders

Four bracing members per frame

(b) Crossfra

Two nodes per element

Two-force member on each bracing

imes

2 4

Reduced element degrees of freedom

(c) Abutment end diaphragms and/or transverse grids

Figure 5.2. Elements in the Grillage Method

55

C0

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56

Am".

z

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Figure 5.4. Comparison of vertical deflections between DESCUS and UM

programs for non-composite analysis (Beam 3)

57

U.

U/)I-zw

00z

a

DISTANCE TO SOUTH ABUTMENT (FT)

Figure 5.5. Comparison of bending moment diagrams between DESCUS and UM

programs for non-composite analysis (Beam 4)

58

Composite Structure Under SDL

DISTANCE TO SOUTH ABUTMENT (FT)

Figure 5.6. Comparison of vertical deflections between DESCUS and UM

programs for composite analysis (N=24, Beam 2)

59

z00

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Composite Structure Under SDL

Figure 5.7. Comparison of bending moment diagrams between DESCUS and UM

programs for composite analysis (N =24, Beam 4)

60

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ca

CHAPTER 6

COMPARISON BETWEEN THECOMPUTATIONAL ANALYSIS AND

THE FIELD MEASUREMENTS

This chapter compares the results of analyses using the UM program with stresses obtained from field

measurements of strain conducted on MN/DOT Bridge No. 27998. Prior to comparing results, the

loading applied within the different analyses is detailed first.

6.1 STRUCTURAL LOADING

For comparisons of computed and field stresses, the finite element model and loading of the bridge

structure are modified at each critical stage of construction to track the changes in the bridge. Table

6.1 tabulates the model used in each structural analysis, along with the corresponding loads considered

for each construction-phase. There are five construction steps listed in this table, including the final live

loading test.

For simplicity, the applied loads due to formwork, concrete pouring, and equipment loads are defined

in terms of uniformly distributed floor loads. These are computed in Appendix E. In the grillage

method, the applied loads can be either concentrated loads input at nodal points, or uniformly

distributed linear loads input on the girder elements, as mentioned previously in assumption (10) of

Section 5.2.1. Accordingly, an appropriate lateral transfer of uniform floor load to each girder of the

bridge system must be considered before the structural analysis. Simple distribution factors based on

tributary area may be satisfactory if the girders are uniform in their cross sections. However, more

rigorous distribution factors are required for a curved I-girder system, since the depth of the I-girder

varies from the innermost girder to the outermost girder to provide an adequate superelevation for the

curved roadway alignment. The distribution factors obtained using both approaches are listed in Table

61

6.2, and the derivation of these factors is outlined in Appendix F, including the distribution factors for

floor loads, parapets, and test trucks. The rigorous distribution factors consider the behavior of the

bridge cross section as a whole, considering are used for the analyses below.

The self-weight of the girders and the crossframes can be either implicitly generated by a special input

key, or considered as applied loads and explicitly input for each girder element. The self-weight of the

end diaphragms transmitted directly to the abutment bearings is not considered in the structural analysis

unless the support reactions and/or the maximum stresses in the end diaphragms need to be

determined. An additional 20% of the crossframe self-weight is added to the girder self-weight to

account for the stiffeners connecting crossframes on the webs of the girders.

6.2 COMPARISON OF FIELD MEASUREMENTS AND FINITE ELEMENT ANALYSES

Chapter 2 describes the instrumentation strategy and measurements taken in the field as part of this

research. Details of the gage locations are repeated for convenience in Figure 6.1. Gage locations are

designated in Figure 6.2. Deflection measurements, including vertical displacements and flexural

rotations of the girders, were also made. The displacement measurements were obtained by taking the

elevation with a surveying rod and level with an accuracy of plus or minus 1/16". The rotation angles

were obtained during erection by measuring the relative lateral displacements with a carpenter level,

which proved to be too inaccurate for the magnitude of rotation seen in this work. The rotations

during loading from the two trucks were obtained by taking voltage readings from an inclinometer,

which has a more appropriate sensitivity of plus or minus 0.0001 degree (1.75 microradian) or better.

Locations of the measuring points for deflection and rotation are shown in Figure 6.3.

To be consistent with the construction sequence, four steps are classified in the following. From step 1

to step 3, the structure being analyzed is a bare steel frame. The loading includes the self-weight of the

steel structure, the falsework, the wet weight of the concrete, and the equipment plus workers,

depending on the progress of the construction. In step 4, the superimposed dead loads, including

parapets and the concrete overlay, are applied to the composite structure, which consists of the steel

frame and the concrete slab (note that the stiffness of the overlay itself is neglected in all composite

62

models in this work, since its stiffness is low; only the weight of the overlay is included in the models).

Finally, two test trucks, weighing between 48 and 50 kips each, were used to simulate the service load

on the composite structure. Figures 6.4 and 6.5 describe the weight and axle distance for these trucks.

6.2.1 Stresses During Steel Assembly

Three sets of reading taken during steel erection are investigated here. Self-weight from all steel

members is considered as the applied load in this phase. For the designations of the gages, Figure 6.2

should be referred to.

Step 1-1: The first reading was taken on July 19, 1995, when the girders for span 1 were in place. The

crossframes were in place but held with only three to four bolts. The end diaphragms at the south end

abutment were not erected yet. At approximately midspan were four shoring towers, which were used

during the erection and left in place until the remaining girders were placed. Figure 6.6 illustrates the

stresses predicted by the UM program as well as the field measurements, on the three gage lines. Gage

11B, designated in Figure 6.2, was broken during the erection, so no reading came from this gage.

No direct correlations can be drawn between the computed and the measured stresses in this step. For

example, in gage line A, the computed stresses differs from the measured stresses even for the web

gages, which relate directly to the primary major axis bending moment of the girders. Reasons for this

are twofold: (1) The shoring towers were modeled as supports in the analysis. The rigid model for the

shoring towers in the grillage analysis does not simulate the actually elastic supports. (2) The lateral

bending and the warping behavior may not agree with the linear analysis model since the connection

bolts between the crossframes and girders are not fully tightened -- in other words, the loading on the

girders are so small, that local eccentricities and minor fitup stresses dominate the results. In gage line

B, the bending normal stresses on the webs are correlated better than the warping stresses on the

flanges; however, the flange tip stresses, which are more affected by warping, do not consistently

correlate. In gage line C, high stresses obtained from strain readings show that some initial strain exists

in the crossframes, e.g., 5.88 ksi in gage 1C, probably due to fitup. The significant finding from this

63

reading is that, when shoring towers are used, the stresses in the bridge are minor, as would be

expected (note that the nominal yield stress of the steel is 50 ksi)

Step 1-2: The second reading was taken at 4 a.m. on July 25 during the erection of the second girder

from the outermost girder of span 2, when the girder was being held by the crane and the splice was

being tightened. The end diaphragms on the south abutment were in place. All of the bolts for the

crossframes of span 1 had been put into place, but they were not fully tightened. Stress results and the

structure to be analyzed are shown in Figure 6.7.

At the outermost girder near the middle pier, gages 1B through 6B, stress increases due to the newly

added girders are noticeable in this figure. As can be seen in this girder, the correlations between the

computed and the measured stresses are improved when the stresses are increased. The computed

stresses are less well correlated in gages 7B to 12B, however, with the measured stresses not

increasing as much as the computed. This is not unexpected, as this girder was still being held by the

crane during erection at the time of the reading -- this added support could not be modeled well in the

analysis. Although the measured stresses are somewhat random at this stage, the magnitude of the

stresses are on the same order as the computed stresses (i.e., not more than 3 ksi).

Step 1-3: The third reading was taken at 11 p.m. on July 28 when all the girders were erected in place

and all the crossframes were fully tightened (rattled up). All the shoring towers were removed and the

steel frame became a self-supported structure. In many cases, the bolts of the crossframes were

hammered into place. This may affect the gages on the crossframes but is not considered herein

explicitly in the analysis. Stress results for Step 1-3 are shown in Figure 6.8.

Better correlations may be found in Step 1-3, because the structure skeleton is completed and its

behavior becomes more regulated or predictable. In both gagelines A and B, the primary flexural

bending behavior is consistently correlated between the structural analyses and the field measurements

except for gage 15A, in which the values are 1.36 ksi and -0.67 ksi for the computation and the field

measurement respectively. The warping stresses obtained from analysis on the flanges indicate the

64

direction of twist for each girder is in the same direction, Le., clockwise looking north. However, this

prediction of warping stresses differs from the measurements. In gage line A, the measured stresses

indicate lateral (weak axis) bending on Beam 1 through Beam 3, in which Beam 1 bends in one

direction while Beams 2 and 3 bend in the other direction. In gage line B, Beams 1 and 2 are warping

in the opposite direction from the prediction; warping in Beam 3 is not clear from the measurements

since gage 11B was not functioning at this time. Correlation for warping can be seen in Beam 4 for

both A and B gage lines, which are warped in the same fashion as the prediction from analysis. The

stresses in the crossframes correlate better in the diagonal members than in the top and bottom chords.

Note, however, that the level of stress is still so small that small eccentricities in the field can explain

these variations. The maximum stress increases during the erection of the steel backbones are 6.74 ksi

(measured) versus 4.53 ksi (computed) in gage 1B for girders, and 4.41 ksi (measured) in gage 1C

versus 1.93 ksi (computed) in gage 2C for the crossframes. The linear model for structural analysis

predicts the behavior relatively well in this stage.

6.2.2 Stresses During Placing of the Formwork and the Reinforcing Steel

The completed steel frame is used as the base structure for the analysis including formwork and

reinforcing bar. The estimate of the uniform floor loads in this phase is 5 psf for formwork and 10 psf

for reinforcing as determined in Appendix E. Three sets of readings are selected to compare with the

prediction from structural analyses.

Step 2-1: This reading was taken at 6 a.m. on August 1. The loading includes the formwork, two

generators, and five to ten workers. The formwork was in place from the south abutment to

approximately midspan of span 1, while the joists to support the plywood forms had been placed in

span 1 up to the middle pier. For purpose of analysis, a uniform load of 5 psf was distrtbuted on half

span of span 1 to model the formwork. Comparisons between computed and measured stresses are

shown in Figure 6.9. Gage 1A was found broken by the jamming of the 4"x4" plywood joist.

The computed stresses are all increased by approximately 1.2 ksL The measured stresses, on the other

hand, showed little change, and did not uniformly increase due to the small amount of extra formwork

65

applied to the bridge. Reasons for this could be that the supporting whalers and the joists redistribute

some of the stress and further accentuate local irregularities in the stress distribution.

Step 2-2: The reading was taken at 6:30 a.m. on August 7 when the formwork was completed, the

shear studs were in place, and all equipment had been removed from the structure. A uniformly

distributed floor load of 5 psf was assigned to both spans to model the formwork in the structural

analysis. Stress results are compared in Figure 6.10.

Two gages, designated as 1A and 11B, which were damaged during the erection of steelwork and the

placement of formwork, respectively, were replaced on August 2. Accordingly, it was required to

initialize these two strains and their corresponding datum stresses. The first strain readings after

replacement, Step 2-1, were picked to serve the purpose. As a result, the stress shown on gage 1A and

11B should read as the stress increase after reattachment, rather than the total stress from the

unstressed state.

In Figure 6.10, bending stresses from both sources were increased in gage line B near the middle pier

but were decreased in gage line A as compared to Step 2-1. This is logical, since the primary

difference in loading between Steps 2-1 and 2-2 is the addition of plywood on span 2. Also note that

the measured stress in crossframe gage 1C continued to increase.

Steps 2-3a and 2-3b: Readings were taken on August 10 when all reinforcing steel was in place.

Loading assigned to the bridge is the sum of formwork and the reinforcing, L.e., 15 psf Figure 6.11

shows the comparison of the computed stress and the measured stress.

Better correlation between the computations and the measurements can be found in this step. The

difference of the maximum stress between the analysis and the field measurements for the girders has

changed from 2.21 ksi (6.74-4.53) in Step 1-3 to 0.76 ksi (6.4-5.64) in Step 2-3a. However, the

primary bending behavior of the girders, as seen in the web gages, continues to correlate better than the

66

warping, seen in the flange gages. Nevertheless, most of the beam flanges show clear correlation with

respect to warping behavior. Stresses in the crossframes are still somewhat more random.

To investigate effects of local stresses during this stage of construction, an additional 30 psf uniform

surcharge is considered in case 2-3b to simulate higher point loads and to investigate better correlation

with some higher measured stresses. Stress results for this case using a 45 psf floor load plus steel self-

weight are shown in Figure 6.12. Almost all the computed stresses in the girders are far beyond the

measured stresses, except for the gages 19A and 23B, where the computed stresses are -3.31 and 5.79

ksi respectively and the measured stresses are -4.73 and 7.58 ksL However, the maximum stress is

computed as 7.80 ksi in gage 1B (on the outermost girder) and is measured as 7.58 ksi in gage 23B (on

the innermost girder). Therefore, the additional 30 psf is adequate for computing the maximum stress.

It is thus suggested that at least 20 to 30 psf of uniform surcharge (construction load) is required in

design and analysis of curved I-girder systems subjected to formwork and reinforcing bar loading.

6.2.3 Results During Pouring of The Concrete Deck

During the pouring of the concrete deck on August 11, complete readings were taken once every 30

minutes from 4:15 a.m. to 8&15 a.m. Three typical sets of data are discussed in the following to

compare with the analysis. The distributed floor loads range from 95 psf to 125 psf with the inclusion

of a 0 psf to 30 psf of the surcharge to account for the construction and/or equipment loads. The base

structure throughout this phase is assumed to be bare steel, Le., non-composite behavior, even though

the composite behavior is developing during the concrete pour as the concrete hardens.

Step 3-1: The first set of readings chosen to compare with the analysis results were taken at 5:45 a.m.

when span 2 (north span) concreting was about to be completed. In addition to the self-weight of the

base structure, the distributed floor load consists of 5 psf for the formwork, 10 psf for the

reinforcement, 80 psf for the concrete, and 15 psf for the construction load. Accordingly, the

distributed floor load is 15 psf on span 1 and 110 psf on span 2, where the wet concrete is in place.

The stress comparison is shown in Figure 6.13.

67

In this step, stresses are increased about 2 to 3 ksi. Since only one span is loaded by the concrete

weight, it may be seen that gage line B picks up stress, while gage line A tends to show some

unloading behavior. The correlation of stresses is showing a clear improvement, as the effects of local

fitup stresses are starting to dissipate under the more substantial loading.

Step 3-2: Readings were taken at 7 a.m when the concrete pouring was approximately up to the

midspan of span 1. Loading for the zone with no concrete was still assigned as 15 psf. For the zone

where the wet concrete was in place, there are two loading types: In the whole of span 2 and one

panel of the crossframe over the middle pier, the floor pressure is estimated as 95 psf. For the rest of

the bridge, the floor is assumed to weigh 110 psf since the activity of pouring concrete is taking place

in this region. The stress comparison is recorded in Figure 6.14.

Correlation continues to improve as loading increase. Excellent correlation (less than 15% difference)

can be found in the following gages: (1) 20A, 2B, 9B, 15B, 20B, and 21B for the girder webs, (2)

10A, 17A, 23A, 1B, 11iB, 17B, and 24B for the girder flanges, and (3) 7C and 10C for the crossframe

bracings. Difference of stresses obtained from two sources are attributed to the variations of the

estimated loading magnitude, the construction loads, and the ever-changing location of the placed

concrete.

Step 3-3a., 3-3b. 3-3c: Readings were taken at 7:50 a.m. when the concrete was all in place. Three

levels of floor loads, including 95, 110, and 125 psf, are assigned to cases 3-3a, 3-3b, and 3-3c

respectively, these loads spanning from the south abutment to the midspan of span 1 to investigate the

loading due to the construction equipment and the workers. The 95 psf uniform floor loading is

assigned to the other three quarters of the bridge floor. Stress correlations for these three cases are

shown in Figure 6.15 to 6.17. respectively.

Note that in order to investigate stresses in gage line C, the nodal degree-of-freedom for lateral

displacement was released for this step and all subsequent steps, as mentioned in section 2.3.2.

Releasing these degrees-of-freedom substantially increased the crossframe stresses and brought them

68

more into line with the measured results, although it appears that initially higher stresses in the field are

retained in the crossframes up to this point in the loading.

Overall, better correlations in an average sense are found in Step 3-3a, which has the 95 psf floor load

everywhere. In this loading condition, gages with differences less than 15% of the measured stresses

from the computed stresses may be found in the gages 5A, 17A, 19A, 1B, 11B, 17B, and 24B for the

flanges, 3A, 8A, 20A, 2B, 9B, 15B, 20B and 21B for the webs, and 7C, 9C, and 10C for crossframes.

Both the primary bending behavior and the warping plus minor bending behavior (exhibited in the

girder flanges) generally correlate well in this case. The maximum normal stress is 11.01 ksi measured

in gage 23B in this step. With the 15 psf surcharge in the construction area (case 3-3b), the stress in

gage 23B is computed to be 9.37 ksi as shown in Figure 6.16, while with the 30 psf surcharge around

the same region (case 3-3c), the stress in gage 23B is computed 9.70 ksi. Therefore the best

correlation for determining the maximum stress in the girders is found in loading case 3-3c. As a result,

at least 20 to 30 psf of surcharge is again suggested to account for construction loading during the

concrete casting.

Comparison of Deflections #1: The first set of deflections were correlated at this loading stage. The

initial elevation was surveyed when the steel backbone had just been rattled up. After the concrete

deck was in place, another leveling was performed to get the vertical deflection and the axial rotation

angles at the midspan of each span. Loading to be assigned in this case is a 110 psf uniform floor load,

including live load. The bare steel model was used for the analysis. Results are tabulated in Table 6.3,

in which the deflections are correlated much better than the rotations. Since rotations are so small,

attention is focused on the displacements. As the concrete pouring proceeds into span 1, composite

behavior is developing in span 2, especially during the thirty minute intermission right after the passing

of the middle pier. Ignoring the composite behavior may result in the overestimate of the deflections

on span 1 as compared with field data. However, it was also found that a temperature difference often

to fifteen degrees Centigrade caused a change in deflection on the order of 0.02 feet in the girders.

Thus, temperature alone could explain the difference between the computational and field results. The

average percentage differences of the surveyed deflections from computed deflections are 4% below

69

for span 1 (south) and 19% above for span 2 (north). It is noted that the deflections measured on span

2 were taken five days later than those measured on span 1. Although the hardening of concrete

improves the bridge stiffness, deformation may continue to grow as the concrete hardens, which may

explain the larger measured deflection readings in span 2., although, again, a temperature difference

alone (as compared to the intial deflection measurements when the steel was rattled up) could cause

much of these differences.

6.2.4 Stresses From Parapets and The Overlay

For modeling the parapets, the estimated vertical loads were computed to be 443 plf for the inner

parapet and 578 plf for the outer parapet, respectively. The vertical distribution to each girder is listed

in Table 6.2. The reading was taken with little construction loading on the bridge. Composite

behavior is considered here. A nominal strength of the concrete designed to be 5,000 psi for the deck

was considered to be satisfactory (cylinder strengths from the slab were 5,625, 6,057, and 6,197 psi).

Also, only a 2% of difference was found between using a modulus ratio of steel to concrete of N= 24

as compared to that of N= 8. Figure 6.18 shows the comparison between analysis results and field

measurements using N equal to 8 (Step 4-1). Incremental stresses due to parapet loads, applied on the

composite structure, are computed first. Then the total stresses to date in this figure are accumulated

from step 3-3a in Figure 6.15.

Due to adding the parapets, an approximately 2.0 ksi stress increase can be found in the girders. Stress

redistribution can also be seen in Figure 6.18: the outermost crossframe used to be the most highly

stressed, but now the other two crossframes have picked up more stress. Again, correlation in most of

the web gages is quite good. Correlation in the flange gages also exhibit good correlation, but not as

consistently as the web gages, again showing that the primary bending behavior is more predictable

from analysis than the warping plus minor bending behavior. Excellent correlation between analysis

and experiment (less than 20% error) may be found as follows: (1) In the flanges of the girders, gages

10A, 16A, 17A, 1B, 4B, 5B, and 11B, (2) in the webs, gages 3A, 8A, 20A, 2B, 3B, 9B, and 20B, and

(3) in the crossframes, 7C, 9C, 10C and 11C.

70

Loading of the 2 inch overlay is estimated as a floor pressure of 24 psf over all the bridge, and the

results are collected in Figure 6.19 (Step 4-2). The structural system remains the same, except the

parapet member has developed its strength and is included in the computation of effective width of the

concrete slab for the edge girders. With the addition of overlay on the bridge, in average, the stresses

increased less than 1.0 ksi in the girders.

6.2.5 Truck Loading

After the bridge was opened for traffic, the bridge was closed for a night, and two snow plow trucks

weighing 48.1 kips, denoted as truck 1, and 49.4 kips, denoted as truck 2, were provided by MN/DOT

to permit live load measurements. The axle loads and wheel spacings are shown in Figs. 6.4 and 6.5.

Composite behavior is considered throughout the analysis. A total of fifteen loading cases, including

six cases of two-trucks side by side, three cases of two-trucks in line, and six cases of a single truck

(truck 2) were conducted on the night of October 7, 1995. Five cases are discussed herein. The plan

of the truck loading is shown in Figures 6.20 to 6.22.

It is assumed that the truck weight is transferred to the nodal points surrounding the center of gravity

of the truck. The methodology for distribution of the truck weight is discussed in Section F.3 of

Appendix F. It is also noted that most of the plywood forms underneath the bridge had been removed

before this service loading test. Hence, unloading due to the removal of the forms was considered by

taking a set of readings when the bridge had no vehicles on it. Only the differential stresses from this

reading are reported for the truck loads. To get total values of the current stress state, results of the

previous stress state in Figure 6.19 should be added to the truck load results.

Figure 6.23 shows the differential stresses of case 2, in which two trucks are side by side near the

midspan of span 1. The stresses at the bottom flanges are consistently correlated in gage lines A and B,

while stresses at the top flanges differ between the analysis and the measured results. Reasons for this

could be twofold. First, the deck greatly relieves the stress at the top flange, due both to redistribution

of stress through the slab, and because the top flange is close to the neutral axis of the section in

positive bending. Second, if the stresses in the deck are low and the shear stress to be transferred

71

between the concrete slab and the steel girder's top flange in the negative moment region is smaller than

the friction resistance, the behavior may approach that of a fully composite member. Thus, an analysis

in which the negative moment region is modeled as bare steel, may not be able to precisely describe the

stress distribution in the concrete slab. In order not to lose generality and to be consistent with the

actual service condition that these trucks may place on the bridge, the results will be reported first for a

model in which the negative moment region near the middle pier is governed by non-composite

behavior.

The discussion of the stress correlation focuses on the bottom portion of the girders, since the

measured stress on the top portion is negligibly small for this small loading. Good correlation was

found at the bottom three gages of each girder, and in the crossframes. Since case 2 is a midspan

loading of span 1, better correlation occurs in gage line A. Excellent results, with less than 20%

difference between the computed and measured stresses for this loading condition, are indicated in

gages 9A, 21A, 3B, 15B, and 21B for the webs, 4A, 10A, 12A, 16A, 18B, and 22B for the flanges of

the girders, and 3C and 12C for crossframes.

The results of test cases 3, 7, 8, and 13 are presented in the following figures denoted from Figures

6.24 to 6.27. In Figure 6.24, again better correlations are found at gage line A, such as gages 3A, 4A,

6A, 9A, 10A, 15A, 16A, 21A, and 24A, since this loading condition is more related to the midspan

loading of case 2. However, excellent correlation can still be found in gage lines B and C.

In investigating the possibility that composite action was active over the center support, fully

composite behavior across the entire bridge was used to generate Figures 6.25 to 6.27. Figure 6.25

shows the condition of both spans loaded. This results in good correlation in gage lines A and B, such

as 4A, 9A, 10A, 12A, 15A, and 16A in gage line A and 3B, 6B, 12B, 15B, 21B, and 24B in gage line

B. Also, stresses on the top portion of the girders show better correlation from the analysis of a fully

composite model than that of a non-composite model in the negative moment region. Stresses in the

crossframes are fairly well correlated, except for gages 1C, 5C, and 8C, which exhibit reverse signs of

stress state. Similarly, case 8, the span 1 loaded condition, and case 13, the span 2 loaded condition,

72

yield good correlations in gage lines A and B, respectively. Similarly, excellent correlations are found

in gages 4A, 6A, 9A, 10A, 12A, 15A, 16A, 3B, 15B, and 21B for case 8 (most on line A) and 3A,

24A, 4B, 12B, 15B, 21B, and 24B for case 13 (most on line B) are shown in Figures 6.26 and 6.27,

respectively.

Comparison of deflections #2: Deflections and rotations due to the trucks are discussed in this section.

Two sets of zero surveying readings were taken before and after the field tests separately and were

averaged to get the zero deflections and rotations for the following tests. An inclinometer was used for

measuring the rotation angle at the interseotion of outermost girder, Beam 4, and the fourth crossframe

from the north abutment in span 2, as shown in Figure 6.3. The structure under consideration is fully

composite.

Results are tabulated in Table 6.4 for deflections and Table 6.5 for rotation angles respectively. As far

as the structural behavior is concerned, correlations of the deflections and the rotations from both

sources are excellent even though the values are small. For the comparison of rotation angles, better

correlations are found by using the inclinometer rather than the method of the carpenter level, used in

the previous comparison of rotations.

63 STRESSES IN THE CROSSFRAMES NEAR THE SKEW SUPPORTS

To investigate the possibility that skew supports greatly affect the stress distribution in the crossframes

near the support, the analysis results of two sets of crossframes were studied due to the truck loading.

Figures 6.28 through 6.37 show the total axial stress in each crossframe element due to the 15 cases of

truck loading for crossframes 39, 1, 20, and 40 (near the south abutment, which experience high shear

and low moment), and crossframes 8, 27, 47, and 9, 28, and 48 (near the center support, which

experience both high moment and high shear). These crossframe designations are shown in Figure 5.3

(the crossframes near the center pier are not labeled explicitly in the figure, but the crossframe

numbering scheme is apparent). First, studying crossframes 1,20, and 40, one can see that crossframe

1 has almost three times the stress, primarily due to the dead load (it is apparent that the variation in

stress due to the truck live loading is minimal). In addition, crossframe 39, which is just next to the

73

support, between the inner two girders, also has stresses comparable to crossframe 1. However, if one

looks at Figures 6.32 to 6.37, it is apparent that crossframes 8 and 9, next to the outside girder, have

larger stresses than the other crossframes at their section, even though they are further away from the

skewed support. Thus, it must be concluded for this bridge that, with the exception of a lone

crossframe such as 39, the crossframes in the stiffer region of the bridge, e.g., next to the outer facia

girder for this bridge, attract more force, regardless of their position relative to the skew support.

However, it is interesting to note that the chords are less stressed than the diagonals, potentially

indicating high shearing action. (The computational results of the instrumented crossframe show

similar results, although the measured results themselves were inconsistent in terms of determining

which crossframe members, chords or diagonals, were most stressed -- this may be due to the

instrumented crossframes being susceptible to local irregularities due to their low stress levels.) These

figures also reveal a predictable variation in stress as the trucks move across the bridge, as was

discussed in Section 6.2.5.

In general, however, it should be noted that the stress distribution in crossframes can be complex and

may include flexural as well as axial stress components. The conclusions drawn above from these

analyses regarding the effects of skew on crossframe stresses and the potential dominance of shearing

action cannot be assured to apply to other similar curved girder bridges.

74

Table 6.1 Loading condition and the corresponding structures

Sequence Loading Structure Construction

Step 1 Steel Weight Steel Assembling of thesteel

Step 2 Steel+Formwork+Rebar Steel Formwork and

+Equipment reinforcing

Step 3 Steel+Formwork+Concrete+Eq Steel Pouring of theuipment concrete

Step 4 Parapets+Overlay Steel+Slab Placing parapets

(Composite) and overlay

Field Test Truck weight Steel+Slab Complete

(Composite)

75

Table 6.2 Vertical loading distribution factors

Loading (plt) Beam 1 Beam 2 Beam 3 Beam 4 Multiplier

Floor RD 0.92 0.92 1.021 0.883 qd*Loads(pif) ______

SD 0.87 1.0 1.0 0.87

Parapet (pf) 0.185 0.209 0.279 0.327 Pi+P2

Trucka panel 0.064 0.071 0.091 0.103 W(Ibs) front

panel 0.130 0.144 0.186 0.211rear

Notes:

a- A typical example for truck 2 at location x3= 14.56 ft.

* q- uniform floor pressure (psf)

d- spacing between two girders (ft)

** Pr- uniform weight of the inner parapet, 443 plf

P2- uniform weight of the outer parapet, 578 plf

*** W- truck unit weight in pounds

RD- Rigorous Distribution (used for the analyses in this research)

SD- Simple Distribution by Tributary Areas

76

Table 6.3 Deflection comparison after pouring of the concrete deck

Locations Deflections Beam 1 Beam 2 Beam 3 Beam 4

Span 1 Displacements LA -.108 -.108 -.108 -.116

(South) (FT.) M -.109 -.109 -.103 -.104

Rotations LA .017 .036 0.054 .078

(DEG.) M NA 0 0 .2

Span 2 Displacements LA -.161 -.144 -.125 -.108

(North) (FT.) M -. 183 -.168 -.146 -.140

Rotations LA -.070 -.096 -.094 -.068

(DEG.) M 0 -.3 -.3 -.2

Notes:

1. Bare steel structure is subjected to the loading of concrete and formwork

2. Notations: FT.- Displacement units, Foot; and DEG.- Rotation units, Degree;

LA - Linear Analysis; and M - Measurement

3. The net floor loading is 110 psf

77

Table 6.4 Deflection comparison during truck loading

Deflections (FT.) on Span 1 (South), computed/measured

Loading Beam 1 Beam 2 Beam 3 Beam 4

2 -.021/-.012 -.023/-.012 -.026/-.022 -.027/-.020

5 .005/.008 .007/.018 .012/.013 .015/.010

7 -.007/-.007 -.007/-.007 -.007/-.002 -.007/-.005

8 -.015/-.017 -.019/-.012 -.027/-.027 -.031/-.030

11 -.009/-.007 -.011/-.007 -.013/-.012 -.015/-.015

Deflections (FT.) on Span 2 (North), computed/measured

Loading Beam 1 Beam 2 Beam 3 Beam 4

2 .005/.005 .007/.005 .010/.020 .012/.007

4 -.007/-.000 -.006/00000 -.005/-.000 -.005/-.008

5 -.028/-.020 -.029/-.025 -.029/-.020 -.030/-.023

7 -.011/-.010 -.011/-.015 -.011/-.005 -.011/-.018

9 -.016/-.010 -.017/-.015 -.018/-.010 -.019/-.018

14 -.014/-.010 -.014/-.015 -.015/-.010 -.018/-.008

Note: Downward deflections are negative.

78

Table 6.5 Comparison of axial rotation angles obtained from field tests at

Beam 4 on the midspan of the north span

Loading Case Computed Rotations Measured Rotations(DEG.) (DEG.)

2 -.016 -.009

3 -.018 -.012

4 -.002 .002

5 .013 .006

6 .014 .005

7 .002 .004

8 -.022 -.013

9 .010 .009

10 -.003 -.001

11 -.009 -.005

12 -.010 -.005

13 -.001 .002

14 .009 .006

15 .010 .004

Note: Positive rotation is clockwise looking north.

79

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CHAPTER 7

CONCLUSIONS

This report has outlined: 1) the development of software at the University of Minnesota to analyze

steel curved girder bridge systems; 2) the comparison of this program with the third party software,

DESCUS-I, used by MN/DOT for these types of analyses; and 3) the comparison of this software with

field measurements taken on MN/DOT Bridge No. 27998. Conclusions drawn from this study include:

1. This bridge was shored in the early stages of construction of the steel superstructure, and the

bridge design was controlled by stiffness, not strength. Therefore, stresses well below the

yield stress occurred throughout construction.

2. Computational results consistently matched well qualitatively and often quantitatively with

measured results, both for stresses and deflections. The bridge behavior was predictable at all

stages.

3. The primary difference between measured and computed results was due mainly to the erratic

effects in the field of warping restraint and weak axis bending on the measured results.

4. The MN/DOT curved girder program, DESCUS-I, compares well to the UM program, which

in turn compares well to the field measurements. Consequently, it may be concluded that the

DESCUS-I program represents construction and final live load stresses and deflections well,

both for the bare steel and the composite bridge system. It should be emphasized that

DESCUS-I is geared towards modeling the bridge at just a few specific stages of

construction, and that it makes minor modeling assumptions that are often less appropriate

than those made in the UM program for permitting detailed modeling of a bridge. However,

these assumptions are generally fine for analyses to be used for design, and, while the ability to

117

make direct comparisons between DESCUS-I and the field measurements is somewhat limited

(due to constraints of specifying actual loading, etc. in DESCUS-I), it is felt that stresses

obtained from DESCUS-I are representative of what is seen in the field.

5. Fit-up stresses were measured in the crossframes, but they dissipated as construction

progressed, and they remained below 6 ksi.

6. There is evidence from the analysis results that the skew supports seem to have little effect on

the distribution of stresses in the crossframes of this bridge. The crossframes near the stiffer,

outer facia girder consistently have higher stresses from the analyses, regardless of their

relation to the skew. However, this data is insufficient to extrapolate this conclusion to other

steel curved girder bridges.

7. It is recommended that a minimum of 20 to 30 psf live loading for construction be included in

analyses to capture maximum stresses.

8. While not discussed in this report, it may be mentioned that the University of Minnesota

curved girder program accurately assesses the stability of curved girder bridge systems during

construction: this bridge was shown to have adequate strength and stiffness using second-

order inelastic analysis techniques [5].

Future research in this area should include further tests with increased live loading. The two

trucks placed on this structure induced only approximately 2 ksi in the measured members. If

additional trucks are placed on the structure, more substantial and reliable strain readings may be

made, which will provide firmer evidence of the service load behavior of these types of structures.

In addition, it may be possible to ascertain whether composite behavior diminishes over time.

118

REFERENCES

1. American Association of State Highway and Transportation Officials (1989). Standard

Specification for Highway Bridges, 14th Edition, AASHTO, Washington, DC.

2. Hall, D. H. (1994). "Curved Girders are Special," Structural Stability Research Council -- Link

Between Research and Practice, Proceedings of the 1994 SSRC 50th Anniversary Conference, 21-

22 June 1994, SSRC, Bethlehem, Pennsylvania, pp. 101-117.

3. Fu, C. C. (1992). "DESCUS-I, Design and Analysis of Curved Girder Bridge System," Revision

2, Production Software Inc., Engineering Computer Services, College Park, Maryland.

4. Pulver, B. E. (1996). "Measured Stresses in a Steel Curved Girder Bridge System," M.C.E.

Report, Department of Civil Engineering, University of Minnesota, Minneapolis, Minnesota.

5. Huang, W.-H. (1996). "Curved I-Girder Systems," Ph.D. dissertation, Department of Civil

Engineering, University of Minnesota, Minneapolis, Minnesota.

6. Stegmann, T. H. and Galambos, T. V. (1976). "Load Factor Design Criteria for Curved

Steel Bridges of Open Section," Report No. 43, Department of Civil Engineering, Washington

University, St. Louis, Missouri, April.

7. Zureick, A., Naqib, R., and Yadlosky, J. M. (1993). "Curved Steel Bridge Research Project

Interim Report I: Synthesis," Report No. FHWA-RD-93-129.

8. Dabrowski, R. (1968). Curved Thin-Walled Girders, Springer Verlag, Berlin, 1968 (in

German).

9. Heins, C. P. (1975). Bending and Torsional Design in Structural Members, Lexington

Books, New York.

10. Nakai, H. and Yoo, C. H. (1988). Analysis and Design of Curved Steel Bridges, McGraw-

Hill, New York.

11. Minnesota Department of Transportation Bridge Division (1994). Documentation of MN/DOT

Bridge No. 27998, Minnesota Department of Transportation, St. Paul, Minnesota.

12. Geokon Incorporated (1994). "Instruction Manual: VK-4100/4500 Vibrating Wire Strain

Gages," Lebanon, New Hampshire.

119

13. Mondkar, D. P. and Powell, G. H. (1974). "CURVBRG -- A Computer Program for Analysis of

Curved Open Girder Bridges," Internal Report, Division of Structural Engineering and Structural

Mechanics, University of California at Berkeley, Berkeley, California, 171 pp.

14. Hambly, E. C. (1976). Deck Behavior, Halsted Press, John Wiley & Son, Inc., New York.

15. Lavelle, F.H. and Davidson, M.J. (1970). "Proposed Lateral Flange Bending Method,"

Department of Civil Engineering, University of Rhode Island, Kingston, Rhode Island,

September.

16. Brennan, P.J. (1970). "Analysis of Horizontally Curved Girder Bridges Through Three-

Dimensional Mathematical Method and Small-Scale Structural Testing," Research Project

HPR 26111, Department of Civil Engineering, Syracuse University, Syracuse, New York,

November.

17. Shore, S., Ali, S.A., and Wilson, J.L. (1970). "Preliminary Design of Horizontally Curved

Girder Bridges by Equivalent Straight Beams," CURT Report T0170, Towne School Of Civil

and Mechanical Engineering, University of Pennsylvania.

18. Bell, L.C. and Heins, C.P. (1968). "The Solution of Curved Bridge Systems Using the Slope-

Deflection Fourier Series Method," Department of Civil Engineering, University of Maryland,

College Park, Maryland, June.

19. Vlasov, V.Z. (1961). "Thin-Walled Elastic Beams," Second Edition, National Science

Foundation, Washington, D.C..

20. McManus, P.F., Nasir, G.A., and Culver, C.G. (1969). "Horizontally Curved Girders - State

of the Art," Journal of the Structural Division, ASCE, Vol. 95, No. ST5, May.

21. Dabrowski, R. (1964). "Zur Berechnung von Gekrummten dunnvandigen Tragern mit

offenem Profil," Der Stahlbau, Vol. 33, No. 12, December.

22. United States Steel (1965). "Highway Structures Design Handbook, Volume I," Pittsburgh,

Pennsylvania.

23. Kuo, J.T.C. and Heins, C.P. (1970). "Torsional Properties of Composite Steel Bridge

Members," Report No. 37, Department of Civil Engineering, University of Maryland, College

Park, Maryland, June.

120

24. Kuo, J.T.C. and Heins, C.P. (1971). "Behavior of Composite Beams Subjected to Torsion,"

Report No. 39, Civil Engineering Department, University of Maryland, College Park,

Maryland, February.

121

APPENDIX A


A-1

APPENDIX A


This appendix presents the stresses due to construction of MN/DOT Bridge No. 27998, excluding the

stresses produced during pouring of the concrete deck, which are reported in the following appendix.

A-3

A-4

OBSERVATIONS OF GIRDER STRESSES

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Date and Time of Reading: July 19, 1995 at 11:00 p.m.

Temperature: 30 °C

Weather: Partly Cloudy

Loading Condition:

Objective of Reading:

General Observations:

The eight girders of span one, which runs from the southern abutment to themiddle pier, were in place when this readings was taken. The diagonaldiaphragms were in place and held with three to four bolts. The splicesbetween the girders were fully tightened. Shoring towers were present atapproximately the midspan of span one to enhance the stability of the girdersuntil the diaphragms could be fully tightened and the remaining girders couldbe placed.

This reading was taken to determine the stresses present with only the firstspan in place. These observations are for the actual magnitudes of the stressespresent.

There does not appear to be a consistent pattern in the stresses for this stage. Insome cases, a given flange registers a tensile stress present at one flange tip,and a compressive stress at the other flange tip. These erratic stresses couldresult from complex conditions present while the readings were taken. Theshoring towers were put into place before the diaphragms were completelyaligned. These towers were probably not perfectly level, so when they weretightened up to the bottom flange of the girder the alignment of the girdermight have been affected, thus distorting the strain readings somewhat. Alsowhen the diaphragms were placed, they were initially attached with three orfour bolts, depending the accuracy of the alignment. If the alignment betweenthe diaphragm bolt holes and the girder bolt holes was poor, then sometimesthe bolts had to be hammered into place to create the proper alignment for thecorrect fit-up between the individual members of the structure. This procedurecould have induced small, unpredictable stresses in the girders and diaphragms.

Notes on Specific Gages: Gage I IB was damaged during the placement of the girder.

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Date and Time of Reading: July 24, 1995 at 4:00 a.m.

Temperature: 21 °C

Weather: Clear

Loading Condition:



Girder 315C3, the second from the outside facia girder, was being erected onthe north span. This girder was held by the crane while the splice wastightened to girder 311D2. The outside facia girder, 316D3, was already inplace, and the splice was fully tightened. The all of the diagonal diaphragmsand end diaphragms in the south span were in place, and all of the bolts for allof the diaphragms were in place but not fully tightened.

This reading was taken to determine the stresses present during the erectionof a girder. These observations describe the changes in the stress due to thegiven loading stage.

Aside for the top inside flange tip of girders 1 and 4 and the top two flange tipsof girder 3, compressive stresses were experienced by the girders at themidspan gages. At the middle pier, the girder 4 stresses demonstratedequivalent behavior to that of the stresses of girder 4 at the midspan. Girder 3experienced compressive stress except for the outside bottom flange tip whichexperienced a minimal tensile stress. Girder 2 experienced compression in thebottom flange and minimal stresses in the top flange. This being the girder towhich girder 315C3 is being spliced, this behavior is fairly reasonable. Asidefor the inside top flange tip, girder 1 is reacting as expected. The bottom flangeexperienced an increase in compression, and the top flange experienced anincrease in tension. This is behavior typical of a girder over a middle piersupport, i.e. in a negative moment region. In regards to the other girders, thecorrelation of their behavior is not obvious. The same can be stated for thebehavior of the diaphragms. The erection of the girders in span 2 was difficultbecause of the small tolerance between the girders being hoisted into place, thesplice of the girders already in place, and the north abutment support. Duringthe maneuvering of the girder into alignment with the splice, the crane could beforcing the girder back against the erected portion of the structure, and thiscould be a possible explanation for the compressive stresses observed. At themidspan, the range of stresses were -0.34 to -4.40 ksi (compression) and 0.11 to1.76 ksi (tension). The largest change in compressive stress occurred at gage22A, and the largest change in tensile stress occurred at gage 17A. At themiddle pier, the ranges were -0.16 to -8.76 ksi and 0.06 to 5.64 ksi. Thegreatest change in stress occurred at gage 4B for compression and gage IB fortension. The range of stress for the diaphragms was -0.44 to -3.74 ksi (largestat gage IC) and 0.36 to 2.11 ksi (largest at gage 3C).

Notes on Specific Gages: Not applicable

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Date and Time of Reading: July 24, 1995 at 4:00 a.m.

Temperature: 21 °C

Weather. Clear

Loading Condition:



Girder 315C3, the second from the outside facia girder, was being erected onthe north span. This girder was held by the crane while the splice wastightened to girder 311D2. The outside facia girder, 316D3, was already inplace, and the splice was fully tightened. The all of the diagonal diaphragmsand end diaphragms in the south span were in place, and all of the bolts for allof the diaphragms were in place but not fully tightened.

This reading was taken to determine the stresses present during the erectionof a girder. These observations are for the actual magnitudes of the stressespresent.

For the observed stresses, there is no obvious correlation to the given loadingstage. The readings for the gages at the middle pier for girder 1 wereconsistent with the behavior of a girder supported by a middle pier with twoend supports under self weight. Warping across the flanges can also beobserved, although it is of a greater stress range than was predicted by thecomputer analysis. The largest tensile stress observed at the middle pier was7.90 ksi (at gage IB), and the largest compressive stress was -5.86 ksi, at gage4B. The largest tensile stress observed at the midspan was 3.27 ksi, at gage7A, and the largest compressive stress was -2.91 ksi, at gage 19A. In thediaphragms, the largest tensile stress was 2.13 ksi, at gage 1C, and the largestcompressive stress was -2.59 ksi, at gage 8C.

Notes on Specific Gages: Not applicable

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Temperature: 25 °C

Weather: Clear

Loading Condition:



All of the girders were in place. The splices were fully tightened for all of thegirders, and the diagonal diaphragms for span two were held in place withthree to four bolts. In some cases the diaphragms were slightly skewed. Thesealignment problems were present in both spans, and this problem was remediedonce all of the bolts were placed. Shoring towers were present at theapproximate midspan of span two for all of the girders. The towers were usedto increase the stability of the girders during the erection process. The bolts forall of the diagonals for span 1 had already been placed, and the whole structurewill be "rattled up" after all of the bolts for span 2 are placed.

This reading was taken to determine the stresses with all of the girders inplace before all of the diagonal diaphragms were fully tightened. Theseobservations describe the changes in the stress due to the given loading stage.

At the midspan, the bottom flanges experienced tensile stresses of - I to 2 ksi(with 2.11 ksi being the greatest magnitude), and the top flanges (except for theoutside tip of girder 4) experienced compressive stresses of- 0.6 to 4 ksi (-3.98ksi being the greatest magnitude). This behavior is expected in a positivemoment region with the present loading being the self weight of the girders. Atthe middle pier, girders 2,3, and 4 behaved (except for a few gages) as would beexpected for the girders in a negative moment region. This is an increase intension for the top flanges and compression for the bottom flanges. Girder Idisplayed the opposite behavior for the middle and outside flange locations forboth the top and bottom flanges. The range of stresses at the middle pier were0.83 to 3.25 ksi and -0.35 to -2.27 ksi. At the middle pier, the largest increasein tensile stress, 5.00 ksi, occurred at the outside bottom flange tip of girder 1,and the largest increase in compressive stress, -2.27 ksi, occurred at gage 15B.Except for gage 12C, the top two members of the diaphragms experiencedtension, ranging from 0.31 to 3.14 ksi, while the bottom two membersexperienced compression ranging from -0.13 to -2.12 ksi.

Notes on Specific Gages: Not Applicable

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Temperature: 25 °C

Weather: Clear

Loading Condition:



All of the girders were in place. The splices were fully tightened for all of thegirders, and the diagonal diaphragms for span two were held in place withthree to four bolts. In some cases the diaphragms were slightly skewed. Thesealignment problems were present in both spans, and this problem was remediedonce all of the bolts were placed. Shoring towers were present at theapproximate midspan of span two for all of the girders. The towers were usedto increase the stability of the girders during the erection process. The bolts forall of the diagonals for span 1 had already been placed, and the whole structurewill be "rattled up" after all of the bolts for span 2 are placed.

This reading was taken to determine the stresses with all of the girders inplace before all of the diagonal diaphragms were fully tightened. Theseobservations are for the actual magnitudes of the stresses present.

At the midspan except for gages 12A and 15A, the bottom flanges experiencetensile stresses. The magnitude of these stresses ranges from 0.30 to 3.17 ksi.The top flanges (except for gages 7A and 13A) experienced compressivestresses. Warping can be observed across the top flanges of girders 1,2, and 3.Warping occurs because of the curvature of the girders. The curvature causes,the magnitude of the stress at the right flange tip to decrease across the width ofthe flange to a lessor value at the left flange tip. The range of compressivestresses is -0.66 to -4.34 ksi with the greatest value occurring at gage 17A. Atthe middle pier, the top flanges are in tension, as expected, ranging from 0.76to 6.50 ksi. The largest magnitude of stress occurred at gage lB. Except forgage 22B. the bottom flanges are in compression, as expected, ranging from-0.04 to -3.34 ksi. The largest magnitude of stress occurred at the gage 15B.There was not an observable pattern to the stresses present in the diaphragms.The largest tensile stress was 5.28 ksi at gage IC and the largest compressivestress was -3.56 ksi at gage 4C.


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Temperature: 24 °C

Weather: Clear

Loading Condition:



All of the girders were in place. All of the diaphragms, end and diagonal, werein place and fully tightened.

This reading was taken to determine the stresses that occur after the diagonalswere placed and the bolts fully tightened. These observations describe thechanges in the stress due to the given loading stage.

At the midspan, it is observed that the bottom flanges experienced compressivestress, ranging from -0.01 to -0.47 ksi, while the top flanges (except for the topoutside flange tip of girder 4) experienced tensile stress ranging from 0.04 to1.15 ksi. This could be a result from the tightening of the diaphragms. Thesame behavior, tension in the top flanges and compression in the bottomflanges, was observed in the gages at the middle pier. Regarding thediaphragms, the top two members of diaphragms experienced compressivestress (-0.12 to -0.87 ksi) and the bottom two members experienced tensilestress (0.14 to 0.52 ksi).


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Loading Condition: All of the girders were in place. All of the diaphragms, end and diagonal, werein place and fully tightened.

Objective of Reading: This reading was taken to determine the stresses after all diaphragmswere placed and the bolts fully tightened. These observations are for the actualmagnitudes of the stresses present.

General Observations: The process of putting all of the diagonals into place and fully tightening thebolts is called "rattling up" the bridge.. This process involves, in many cases,hammering the bolts into place to properly align the diagonals. This mightintroduce residual stresses into the members. After each night of erectionduring the following day, the remaining bolts for the diaphragms erected wereplaced. After the all of the bolts were in place, the bolts for the entire structurewere tightened and considered "rattled up". The shoring towers were removed,and the structure was then ready for the placement of the formwork. Except forgages 7A and 13A, the top flanges at the midspan experienced compressivestress as expected. Except for gages 12A and 15A, the bottom flanges at themidspan experienced tensile stress as expected. At the middle pier, the girdersexperienced tensile stress in the top flanges and compressive stress in thebottom flanges. This behavior is consistent for girders in a negative momentregion. The top member and top diagonal, except for gage 9C, indicated thatthe change in stress was compressive, and the bottom two members, except forgage 3C, indicated the presence of a tensile force. At the midspan gages, thegreatest compressive stress was -3.78 ksi (at gage 17A), and the greatest tensilestress was 2.87 ksi (at gage 10A). At the middle pier gages, the greatestcompressive stress was -4.15 ksi (at gage 15B), and the greatest tensile stresswas 6.74 ksi (at gage IB). The greatest compressive and tensile stresses in thediaphragms were -3.04 ksi at gage 4C and 4.41 ksi at age IC respectively.


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Date and Time of Reading: August 7, 1995 at 7:00 a.m.

Temperature: 20 °C


Loading Condition:



The placement of the formwork was complete. All of the generators wereremoved from the deck. The shear connectors were attached.

This reading was taken to determine the stresses present with all of theformwork completed and the shear connectors present. These observationsdescribe the changes in the stress due to the given loading stage.

At the midspan gages, the top flanges for girders 2 and 4 experiencedcompression (-0.37 to -1.84 ksi) as expected, but the bottom flanges (except forgages 16A and 24A) also experienced compressive stress. This is not behaviorconsistent with girders in the positive moment region. Girders I and 3experienced a minmal stress change at the flange tips (0.02, 0.00, 0.02, and -0.08 ksi) The stresses for the gages located on the webs (intended to predict thestresses at the middle of the flange) ranges from -0.17 to -0.50 ksi. For thegages on girders 1 and 4 this stress could be occurring because of thecantilevered support for the formwork outside of the girders. These supportstransfer some portion of the load directly to the lower portion of the web. Thismaybe an explanation for the compressive stresses observed. The bottomflanges at the middle pier experienced compression (-0.44 to -0.85 ksi) asexpected. The top flanges experienced both tension and compression (exceptfor girder 4 which is in tension as expected) which does not seem to beexplainable. The only change in stress greater than I ksi occurred at gage 23B,the inside top flange tip, with a magnitude of 3.08 ksi. The members of thediaphragms responded in a similar manner which was tension for the topmembers and compression for the bottom three members. The stress ranges foreach of the bottom three members are similar. Starting with the top diagonaland proceeding to the bottom horizontal the ranges are as follows: -0.03 to -0.08, -0.22 to -0.33, and -0.80 to -0.87 ksi. This pattern of compression in thelower members once again could relate to the cantilevered formwork supports.

Notes on Specific Gages: During the placement of the formwork, gage IA was damaged. This gagealong with gage 1 IB was repaired, and the following readings are relativereadings compared to the state of stress recorded after the gages were attached.Note the gray shading for the stress readings of these gages. Gage 17B and12C did not register when the reading was taken.

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CO,M

TMLL

U,)N'


Temperature: 20 °C

Weather. Partly Cloudy

Loading Condition:



The placement of the formwork was complete. AU of the generators wereremoved from the deck. The shear connectors were attached.

This reading was taken to determine the stresses present with all of theformwork completed and the shear connectors present. These observations arefor the actual magnitudes of the stresses present.

At the midspan, the compressive stress ranged from -0.08 to -4.66 ksi with thegreatest value occurring at gage 19A.. The range of tensile stress was 0.07 to2.76 ksi, and the largest stress occurred at gage 3A. At the middle pier, therange of compressive stress was -0.79 to -4.69 ksi, with the largest stress beinglocated at 15B. and the range of tensile stress was 0.11 to 7.26 ksi, with thelargest stress being located at gage 23B. The largest tensile stress in thediaphragms was 5.59 ksi at gage IC, and the rangeof stress was 0.74 to 5.59ksi. The largest compressive stress was -3.90 ksi at gage 4C with the range ofstress being -0.01 to -3.90 ksi.

Notes on Specific Gages: During the placement of the formwork, gage IA was damaged. This gagealong with gage 1 IB was repaired, and the following readings are relativereadings compared to the state of stress recorded after the gages were attached.Note the gray shading for the stress readings of these gages. Gage 17B and12C did not register when the reading was taken.

A-24

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A-25

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Temperature: 20 °C

Weather: Overcast

Loading Condition:


General. Observations:

The loading for this set of readings consists of the self weight of the girders,the weight of the formwork, and the weight of all the reinforcement for theconcrete bridge deck. This was the state of the bridge before the pouring of theconcrete deck began.

This reading was taken to determine the stresses present with all of the deckreinforcement in place before the concrete deck was poured. These observationsdescribe the changes in the stress due to the given loading stage.

At the midspan, the bottom flanges experienced tension (0.11 to 0.55 ksi) as isexpected in the positive moment region. The top flanges experienced bothcompressive and tensile stresses which does not have an obvious explanation.Except for girder 1, the change in stresses for these top flanges are minimal(ranging from -0.09 to 0.29 ksi), so these values are fairly insignificant. Thetop flanges at the middle pier experienced tension as expected ranging from0.35 to 0.65 ksi. The bottom flanges experienced both compression and tension(-0.02 to -0.11 and 0.02 to 0.20 ksi). Except for gage 5C, all of the members ofthe diagonals experienced tensile stresses ranging from 0.01 to 0.63 ksi.

Notes on Specific Gages: Gage 12C and 17B did not register during this reading.

A-26


Temperature: 20 °C

Weather: Overcast

Loading Condition:



The loading for this set of readings consists of the self weight of the girders,the weight of the formwork, and the weight of all the reinforcement for theconcrete bridge deck. This was the state of the bridge before the pouring of theconcrete deck began.

This reading was taken to determine the stresses present with all of the deckreinforcement in place before the concrete deck was poured. Theseobservations are for the actual magnitudes of the stresses present.

At the midspan, the stress in the bottom flange gages increased in tension asexpected with the additional dead load from the reinforcement. The top flangegages did not respond uniformly though. Approximately half of the gagesshowed an increase in compression as expected, but the remaining gagesindicated a decrease. The range of compressive stress is -0.62 to -4.36 ksi (thelargest value at gage 19A), and the range of tensile stress is 0.25 to 3.18 ksi(the largest value at gage 16A). At the middle pier, the top flanges increased intensile stress, and a majority of the bottom flanges increased in compressivestress. The ranges of compressive and tensile stresses are -0.67 to -4.78 ksi and0.67 to 7.75 ksi respectively. The largest stresses occurred at 15B(compression) and 23B (tension). Except for gage 5C the diaphragm membersindicated an increase in tensile stress. The stress ranges for the diaphragms areas follows: -0.31 to -3.68 ksi and 0.22 to 5.60 ksi. Once again the largeststresses occur at IC and 4C with the top member experiencing tension and thebottom horizontal experiencing compression.

Notes on Specific Gages: Gage 12C did not register during this reading.

A-27

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Temperature: 23 °C

Weather: Clear

Loading Condition:



The self weight of the bridge was the loading condition present when thereading was taken. The self weight for this loading stage includes the weight ofthe girders, the weight of the formwork, and weight of the concrete deck. Thereinforcement for the side walls was being placed.

This reading was taken in order to examine the stresses present in the girdersafter the concrete deck had been poured and cured for five days. These stresseswill be compared with the readings taken for the loading stage involving thestresses due to the presence of the formwork reinforcement. These observationsdescribe the changes in the stress due to the given loading stage

At the midspan, the top flanges experienced an increase in compressive stressesranging from -1.83 to -6.22 ksi, and the bottom flanges experienced an increasein tensile stress ranging from 0.85 to 3.12 ksi. The largest change.in tensilestress occurred at gage 6A and the largest change in compressive stressoccurred at gage 5A. At the middle pier, the top flanges experienced tensilestress ranging from 4.05 to 6.00 ksi, and the bottom flanges experiencedcompressive stress ranging from -2.43 to -7.87 ksi. The largest change intensile stress occurred at gage 17B, and the greatest change in compressivestress occurred at gage 24B. The stresses observed for the girders is consistentwith the behavior that is expected for this loading stage. The range of stresschanges for the diaphragms is -0.02 to -5.45 ksi (the largest stress occurring atgage 4C) and 0.51 to 5.14 ksi (the largest stress occurring at gage IC).

Notes on Specific Gages: Gage 12C did not register.

A-30

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Temperature: 23 °C

Weather:. Clear

Loading Condition:



The self weight of the bridge was the loading condition present when thereading was taken. The self weight for this loading stage includes the weight ofthe girders, the weight of the formwork, and weight of the concrete deck. Thereinforcement for the side walls was being placed.

This reading was taken in order to examine the stresses present in the girdersafter the concrete deck had been poured and cured for five days. These stresseswill be compared with the readings taken for the loading stage involving thestresses due to the presence of the formwork reinforcement. These observationsare for the actual magnitudes of the stresses present.

The stresses observed in the midspan gages behaved as is expected in a positivemoment region. The top flanges are in compression (ranging from -2.43 to -9.65 ksi), and the bottom flanges are in tension (ranging from 0.43 to 5.95 ksi).The largest stresses occur at gage 5A (compression) and gage 10A (tension).At the middle pier, the gages behaved as expected fro a girder in a negativemoment region. The top flanges are in tension (ranging from 5.44 to 11.79ksi), and the bottom flanges are in compression (ranging from -4.42 to -11.72ksi). The largest stresses are at gage 23B (tension) and gage 24B(compression). The stresses in the diaphragms range from -1.26 to -9.13 ksi,with the largest stress occurring at gage 4C, in compression, and range from0.20 to 10.75 ksi, with the largest stress occurring at gag: IC, in tension.

Notes on Specific Gages: Gage 12C did not register during this reading.

A-32

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A-33

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C


Temperature: 30 °C

Weather. Cloudy and Overcast

Loading Condition:



The self weight of the bridge was the loading condition present when thereading was taken. The self weight for this loading stage includes the weight ofthe girders, the weight of the formwork, the weight of the concrete deck, andthe weight of the newly poured parapet walls. Composite action was presentbetween the slab and the girders.

This reading was taken in order to determine the effect that the side wallswould have on members of the bridge. These observations describe the changesin the stress due to the given loading stage

The stresses at the middle pier were as expected. The top flanges increasing intension and the bottom flanges increasing in compression. The range of tensilestress was 0.41 ksi to 2.21 ksi, the largest of which occurred at gage 5B. Therange of compressive stress was -0.29 to -2.34 ksi, the largest of which occurredat 2 lB. The bottom flanges at the midspan experienced an increase in tensionranging from 0.45 ksi to 1.82 ksi, the largest of which occurred at gage 3A.The top flange stresses were not as consistent. Girder I experienced anincrease in tension across the top flange. The other girders registered anincrease in both tension and compression stresses. This phenomonon does nothave an obviuos explanation. Except for gage 23A, the largest change in stressfor tension and compression is not greater than 0.35 ksi. This could be theobservation of the distribution of the stress across the width of the bridge. Thestresses observed in the members of the diaphragms were varied. The largestcompressive stress was at gage location 1 IC while the largest tensile stressoccurred at gage 10C, and the range of stresses were 0.54 to 1.08 ksi (tension)and -0.04 to -3.27 ksi (compression).

Notes on Specific Gages: Gage 12C did not register during this stage.

A-34

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<£ 5 S

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Temperature: 30 °C

Weather: Cloudy and Overcast

Loading Condition:



The self weight of the bridge was the loading condition present when thereading was taken. The self weight for this loading stage includes the weight ofthe girders, the weight of the formwork, the weight of the concrete deck, andthe weight of the newly poured parapet walls. Composite action was presentbetween the slab and the girders.

This reading was taken in order to determine the effect that the side wallswould have on members of the bridge. These observations are for the actualmagnitudes of the stresses present.

At the midspan, the behavior of the girders was as expected. The top flangeswere in compression, and the bottom flanges were in tension. The range ofcompressive stress was -2.32 to -7.99 ksi, and the range of tensile stress was1.15 to 6.88 ksi. The largest compressive stress occurred at gage 17A, and thelargest tensile stress occurred at gage 10A. The middle pier stresses were alsoas expected which is the top flanges in tension and the bottom flanges incompression. The tensile stress ranged from 6.37 to 13.26 ksi, and thecompressive stress ranged from -5.68 to -13.79 ksi. The location of the greatesttensile stress was gage 23B and the greatest compressive stress was 24B. Thestresses in the diaphragms did not have an identifiable pattern. The tensilestress ranged from 2.68 to 9.77 ksi, and the compressive stress ranged from -0.41 to -9.17 ksi. The greatest values of stress occurred once again at gage IC(tension) and 4C (compression).

Notes on Specific Gages: Gage 12C did not register during this stage.

A-36

c (0 P P.r- r-

C, V -.. N ,.

co CD

in h

CV? CV

00r0 C V) - C)

co ( : uCN Ln

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(NI t,^

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A-37

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C

C114

0.(n

CO(-LLHL0NCV)

Date and Time of Reading: October 7, 1995 at 11:30 p.m.

Temperature: 8 °C

Weather: Clear

Loading Condition: The loading condition for the bridge was the total dead load of the bridge whichincluded self weight, formwork, the reinforced concrete deck and parapet walls, andthe 2 inch overlay of low slump concrete. This was the final state of the bridgewhen it was opened to traffic.



This reading was taken to determine the final state of stress of the bridge beforebeing put into service. This reading was also used as the base line to determinethe live load stress induced by two 50 kip trucks in various loading positions.These observations describe the changes in the stress due to the given loadingstage

At the midspan, the top flanges continued to experience an increase incompression with the increased dead load. The change in stress for the bottomflange was not as uniform. There was both tensile and compressive stressexperienced by the bottom flanges, but the majority of the stress changes wereas expected for a positive moment region. The range of the increase incompression was -0.09 to -3.34 ksi with the largest change occurring at gage1A. The range of tensile stress was 0.07 to 1.20 ksi with the largest changeoccurring at gage 24A. At the middle pier, the top flanges, except for gage IB,were experiencing tension ranging from 0.01 to 1.08 ksi (the largest change atgage 11B). The bottom flanges were experiencing compression which rangedfrom -0.30 to -2.45 ksi (the largest change at gage 12B). Except for gages 6Cand IC, the diaphragms experienced compressive stress ranging from -0.02 to-4.03 ksi with the largest compressive stress occurring at gage 8C. The rangeof tensile stress was 0.09 to 0.80 ksi. The largest tensile stress occurred at gage6C.


A-38

H °

<-V co( D 7to m

r-

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A-39

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(1)

-0

-S2

*.0

-)

C§0.

p:


Temperature: 8 °C

Weather: Clear

Loading Condition: The loading condition for the bridge was the total dead load of the bridge whichincluded self weight, formwork, the reinforced concrete deck and parapet walls, andthe 2 inch overlay of low slump concrete. This was the final state of the bridgewhen it was opened to traffic.

Objective of Reading: This reading was taken to determine the final state of stress of the bridge beforebeing put into service. This reading was also used as the base line to determinethe live load stress induced by two 50 kip trucks in various loading positions.These observations are for the actual magnitudes of the stresses present.

General Observations: At the midspan the stresses are as expected for members in a positive momentregion. The top flange compressive stresses range from -4.13 to -11.10 ksi, andthe bottom flange tensile stresses range from 1.06 to 7.73 ksi. The largestcompressive stress occurred at gage 5A, and the largest tensile stress occurredat gage 3A. At the middle pier, the stress are as expected for members in anegative moment region. The top flange tensile stresses range from 6.89 to13.27 ksi, and the bottom flange compressive stresses range from -8.14 to -14.68 ksi. The largest tensile stress occurred at gage 23B, and the largestcompressive stress occurred at gage 24B. The final state of stress of thediaphragms once again did not have an obvious explanation. For diaphragm Ithe top member was in tension, and the lower three members were incompression. For diaphragm 2, the top two members were in tension, and thebottom two were in compression. For diaphragm 3, the top diagonal memberwas in tension, and the other three members were in compression. The rangeof tensile stress for the diaphragms was 2.02 to 9.87 ksi, and the range ofcompressive stress was -0.94 to -12.36 ksi. Once again the largest tensile stressoccurred at gage IC, and the largest compressive stress occurred at gage 4C.


A-40

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A-41

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L0C4mZ

APPENDIX B

STRESSES DUE TO POURING OF THE

CONCRETE DECK

B-1

APPENDIX B

STRESSES DUE TO POURING OF THE

CONCRETE DECK

This appendix presents the stresses due to pouring of the concrete deck on MN/I•OT Bridge No.

27998.

B-3

B-4

4

4

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B-6


B-7

Date and Time of Reading: August 11. 1995 at 4:45 a.m.

Temperature: 20 °C

Weather: Overcast

Loading Condition:



The pouring of the concrete deck began at the north abutment at 4:15 a.m.Deck locations will be referenced from the north abutment. For this reading,the concrete was located at the first quarter point. Additional loading wasprovided from the finishing machine. There were ten to fourteen workers alsopresent.

This reading was taken to determine the stresses present during the pouring of theconcrete bridge deck.

The three outside most girders, 306B 1, 307C 1, and 308D 1, experienced an increasein tension on the top flange and compression on the bottom flange at the midspan ofspan one. Girder 305A1, the inside facia girder, experienced the opposite change instress from the other three girders. This girder showed a maximum change in stressof only 0.06 ksi which is fairly negligible. The largest increase in stress, 1.08 ksi,occurred at gage 5A which is at the inside tip of the top flange of the outside faciagirder. At the middle pier, the top flanges experienced an increase in tensile stress.and the bottom flanges experienced an increase in compressive stress. The range ofstress changes at the middle pier were -0.25 to -0.83 ksi for compression and 0.39to 0.83 ksi. The largest stress increases occurred at gage locations 5B (tension) and24B (compression). The diaphragms showed ranges, in the change in the stresses,of -0.14 to -1.37 ksi and 0.23 to 0.79 ksi. The top two members experienced anincrease in compressive stress while the bottom two experienced an increase tensilestress. The greatest compressive stress of -1.37 ksi occurred at gage location I C,and the greatest tensile stress of 0.79 ksi occurred at gage 4C. All of the diagonalsexperienced a change in stress of approximately the same value. At the midspangages, the stresses are smallest on the inside facia girder and increases in eachgirder as the outside facia girder is approached with the largest stresses beingexperienced by the outside girder. This behavior is not manifest in the gages at themiddle pier. The behavior of the girders in span one is consistent with the what isexpected when the loading is applied in the second span.


B-9

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CD

Date and Time of Reading: August 11. 1995 at 5:15 a.m.

Temperature: 20 °C

Weather: Overcast

Loading Condition:



The pouring of the deck had progressed to the midspan of span two.

This reading was taken to determine the stresses present during the pouringof the concrete bridge deck.

The pattern of stress change observed for load stage I continued for this load stage.This pattern is compression in the top flange and tension in the bottom flange forgirder 4 with girders 1,2, and 3 experiencing tension in the top flanges andcompression in the bottom flanges. The stresses increased at the midspan, in mostcases. by 2 to 2.5 times the increase observed previously. At the middle pier gages,the greatest increase in the change in stress was approximately 2.8 times theprevious change in stress. The largest change in stress at the midspan, 2.64 ksi.occurred at gage location 5A. The greatest change in stress at the middle pier, 1.51ksi, occurred at gage location 5B. The change in the stresses in the diaphragms didnot increase appreciably. The largest compressive stress, -1.71 ksi. is still occurringat gage location 1C. and the greatest tensile stress is 1.25 ksi which occurs atlocation 4C. The inside diaphragm, 325CF13, is experiencing the least change instress with the outside most diaphragm experiencing the greatest stress change.The middle diaphragm, 324CF13, experiences a stress change in between these twodiaphragms. The top two members of the diaphragms experienced compressionwhile the bottom two experienced tension.


B-12

a)

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Temperature: 20 °C

Weather: Overcast

Loading Condition:



The pouring of the deck had progressed to the middle pier.


There was a slight increase in the top flange tensile stresses and a decrease in thebottom flange compressive stresses at the midspan gages. The greatest change,once again at 5A, was 0.65 ksi. At the middle pier gages, the behavior continued asbefore with the tensile stresses increasing on the top flanges while the compressivestresses increase in the bottom flanges. The range in tensile stress change was 0.14to 1.01 ksi. The range in compressive stress change was -0.19 to -0.78 ksi. Therewas not much change in the stresses in the diaphragms. Gage 9C was the only tophorizontal to experience an increase in tensile stress, and the top two membersexperienced an increase in compressive stress. The bottom two membersexperienced an increase in tensile stress. The range of stress change was -0.07 to-0.49 ksi and 0.02 to 0.67 ksi..


B-15

00 9

0)(96 9

< sg aCD o 9<r-

'a ) ~Ul)7 ov V7

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< ocu 09CL

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m)

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CDC

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B-16

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t

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CO)

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CL

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(NCIO

0U)CO


Temperature: 20 °C

Weather: Overcast

Loading Condition:



The pouring of the deck had progressed to the first quarter point in span one.


The gages at the midspan began to register the reversal of stress (compression inthe top flanges and tension in the bottom flanges) consistent with a positive momentregion as the concrete was poured in span one. The absolute value of the change instresses was minimal and ranged from 0.00 ksi to 0.59 ksi. Stress reversal alsooccurred in the diaphragms. The top two members, except for gage 9C,experienced tensile stresses with the bottom two experiencing compressive stresses.Except for girder 309A2 and gages 13B, the stresses at the middle pier experiencedan increase in tensile stresses on the top flanges and increase in compressivestresses on the bottom flanges. Aside for gage 23B on girder 309A2, the gagesregistered a tensile stress increase for all of the locations. A possible explanationfor this different behavior might result from the fact that these gages are locatedfurther away from the middle pier since gage line B is located along a diagonal lineabove the pier. Except for a compressive stress increase in gage 9C, the top twomembers of the diaphragms experienced an increase in tensile stress, and thebottom two members experienced an increase in compressive stress. This reactionresulting from the deck beginning to force the girders downwards as the deck ispoured. When the deck was being poured in span two, the opposite reaction wasobserved.


B-18

9 9 9 9.o co

< mC) C) C <0 d

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Temperature: 20 °C

Weather: Overcast

Loading Condition:



The pouring of the deck had progressed to the midspan of span one.


The gages continued to respond in a manner consistent with the loading beingpresent in the first span. At the midspan, the top flanges experienced anincrease in compressive stress ranging from -0.60 ksi to -3.12 ksi The bottomflanges experienced an increase in tensile stress ranging from 0.58 ksi to 1.31 ksi.The middle pier gages experienced an increase in compressive stress on the bottomflanges and tensile stress on the top flanges. The tensile stress changes ranged from0.58 ksi to 1.65 ksi, and the compressive stress changes ranged from -0.58 ksi to-1.52 ksi. The change in stresses at the middle pier are of approximately the samemagnitude. The stresses in the diaphragms increased in tension in the top twomembers and compression in the bottom two. The ranges of increase were 0.74 ksito -4.35 ksi and -0.55 ksi to -2.94 ksi.

Notes on Specific Gages: Gage 1C did not register in the for the 6:15 a.m. reading, so the value of stresschange for this stage was calculated by averaging the percentage of change of theother gages from the previous stage to this stage. The value used was 52%.

B-21

a g g

( o0 0

Cl)

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Temperature: 20 °C

Weather: Overcast

Loading Condition:



The pouring of the deck had progressed to the third quarter point of span one.


The girders and diaphragms continued to respond in the same manner as describedin the previous loading stage. The stress ranges at the midspan were -0.72 ksi to-6.05 ksi on the top flanges and 0.73 ksi to 2.80 ksi on the bottom flanges. At themiddle pier the ranges were 0.93 ksi to 1.28 ksi on the top flanges and -0.44 ksi to -1.30 ksi on the bottom flanges. The tensile forces in the top two members rangedfrom 0.16 ksi to --4.01 ksi with the compressive forces in the other bottom membersranging from 0.96 ksi to 3.73 ksi.

Notes on Specific Gages: Gage 12C did not register for this loading stage. The change in stress for gage1C was once again calculated for this stage.

B-24

0 ,, CM

<

4N r)el- -

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T- -C)

CL

V

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C1-(96

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a

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T301€0

CO

00

0)

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I


Temperature: 20 °C

Weather: Overcast

Loading Condition:



The pouring of the deck was completed when this reading was taken.


The readings for this stage were erratic in most of the members, but a majority ofthe stress increases were consistent with the expected behavior. The changes instress were minimal which could explain some of the discrepancies observed. Thisreading might be the perceiving some stress redistribution within the structure. Thetotal range of the stress change was -0.46 ksi to 0.29 ksi at the midspan and -0.06ksi to 0.12 ksi at the middle pier. The diaphragms experienced at change in stressthat ranged from -0.19 ksi to 0.18 ksi.

Notes on Specific Gages: Gage 12C did register during this loading stage.

B-27

D o N

<

C, N

ci0

mo9 d

a)9C0

Q 0i

d

Ie 8 as §

(.D

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g cm

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Cw, (

m (m

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CO,

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cr)

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i 0)

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(0

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B-29

Cl)C)Cl)C/,C)

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C)

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tot)

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(U

0)0

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LL


Temperature: 20 °C

Weather: Raining

Loading Condition:



This reading was taken twenty-five minutes after the deck was completed.

This reading was taken to determine if a change occurs in the stresses withinthirty minutes. This would help determine how long it takes for the compositeaction to begin.

There was not an appreciable change in the stresses after twenty-five minutes.Thegreatest change in either tensile or compressive stresses was -0.47 ksi which waslocated in the diaphragm at gage location 8C. This reading was taken to observe ifcomposite action began forming within 30 minutes of the completion of the pouringof the deck. Since there was a minimal change in the stresses, it appears that thecomposite action has yet to begin for this bridge.

Notes on Specific Gages: Gage 12C did not register during this loading stage.

B-30

o 0

I-ICY¾< 8

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r.)

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999o o-0

° 96

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O

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IiU60)Cy

CVO

Li0U')(NCf)

c.

C

Q-0

0

POURING OF THE CONCRETE DECK PLOTS

CHANGE IN STRESSES OBSERVED

B-33

B-34

tL)T-

(B-35) ssais

B-35

O-0C)

0)O0

0

c)00cu

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a

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B-37

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B-38

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B-39

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(isj)) ssaeis

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af)

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5-

S 0 0 0 0 0 0C 0 0 0 0 0

(•sm) sseJis

B-42

0

(I)

o0C00

c'O

cC,

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B-43

0 (

U)4)U)U)a)

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(!S>l) ssJaiS

B-44

00)

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CO,

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S0- d o o0 - T-

(Is>N) ssaJs

B-45

B-46

POURING OF THE CONCRETE DECK PLOTS

ACTUAL STRESSES OBSERVED

B-47

B-48

CM - 0co0 0

3+L..

C)

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0)

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0

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B-49

4

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o o 0 0 0 * 0 0 0 0 LL0 0 0 0 0 0 0 0 0

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(!Si) ssais

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C.)

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00

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APPENDIX C

STRESSES DUE TO TRUCK LIVE LOADING

C-1

APPENDIX C

STRESSES DUE TO TRUCK LIVE LOADING

This appendix presents the stresses due to truck live loading applied to MN/DOT Bridge 27998.

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Temperature: 8 °C


Loading Condition: Two 50 kip trucks were placed side by side at the first quarter point of span 1.

Objective of Reading: This reading was taken to observe the change in stress due to the loadingcondition mentioned above

General Observations: At the midspan gages except for girder 4, the top flanges experiencedcompression, and the bottom flanges experienced tension. This behavior is asexpected for loading in span 1 which results in a positive moment region beingformed at the midspan of the girders. It appears that the loading was notsignificant enough to cause the entire top flange of girder 4 to experiencecompressive forces. The range for stress increase was -0.03 to -0.15 ksi for thetop flanges and 0.31 to 0.53 ksi for the bottom flanges. The stresses in the topflanges did not increase appreciably which could be due to the composite actionin this region. At the middle pier gages, as expected for a negative momentregion, the top flanges experienced tension and the bottom flanges experiencedcompression. The range of stress increase was 0.01 to 0.06 ksi in the topflanges and -0.15 to -0.37 ksi in the bottom flanges. It appears that there issome composite action occurring at the top flanges and the concrete. There areno shear connectors in this region, so this might be resulting from frictionbetween the two materials. The loading appears to not have been significantenough to break the bond between the top of the girders and the concrete deck.The top two members in the diaphragms displayed an increase in tension, 0.09to 0.26 ksi, and the bottom two members displayed an increase in compression,-0.05 to -0.60 ksi.


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Temperature: 8 °C


Loading Condition:



Two 50 kip trucks were placed side by side at the midspan of span 1.

This reading was taken to observe the change in stress due to the loadingcondition mentioned above

As observed in the previous loading position, except for girder 4, the topflanges experienced compression, and the bottom flanges experienced tensionat the midspan gages. These stress changes ranged from -0.07 to -0.31 ksi inthe top flanges and 0.79 to 1.48 ksi in the bottom flanges. The behavior of thegirders at the middle pier was equivalent to the previous loading stage which isan increase in tension in the top flanges and compression in the bottom flanges.The range of the stress changes was 0.07 to 0.13 ksi for the top flanges and-0.38 to -0.72 ksi for the bottom flanges. The top two members of thediaphragms increased in tension while the bottom two members, except forgages 8C and 12C, increased in compression. The stress changes ranges were0.14 to 0.92 ksi and -0. 14 to -1.76 ksi.


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Date and Time of Reading: October 8, 1995 at 12:10 a.m.

Temperature: 8 °C


Loading Condition:



Two 50 kip trucks were placed side by side at the third quarter point of span 1.


The stresses at the midspan decreased from the previous loading conditionwhich is expected. Except for girder 4, the top flanges are still experiencingcompression while the bottom flanges are experiencing tension. These stressesrange from -0.03 to -0.25 ksi in the top flanges and 0.39 to 1.13 ksi in thebottom flanges. The bottom flanges at the middle pier continued to experiencecompressive stresses. For this loading condition, the bottom flange stresses ingirders 1,2, and 3 continued to increase in compression. The changes in thetop flange stresses were varied, but the flanges continued to experience tension.The range in the top flange stresses was 0.05 to 0.16 ksi, and the range for thebottom flanges was -0.44 to -0.70 ksi. The top two members in the diaphragmsexperienced tensile stress, ranging from 0.13 ksi to 0.54 ksi, and the bottomflanges experienced compressive stress, ranging from -0.04 ksi to -1.39 ksi.

Notes on Specific Gages:

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Temperature: 8 °C


Loading Condition:



October 8, 1995 at 12:35 a.m.

Two 50 kip trucks were placed side by side at the first quarter point of span 2.


The loading moved into span 2, and for most of the midspan gages a stressreversal could be observed. Therefore, the top flanges began to experiencetension while the bottom flanges began to experience compression. The totalrange of stress was -0.13 ksi to 0.06 ksi. These stresses are quite small whichcould explain the lack of uniform behavior across the girders. Except for gagesI B, 2B, and 7B, the middle pier stresses continued to experience tension in thetop flange and compression in the bottom flanges. The magnitude of thestresses experienced decreased as the loading crossed into the other span. Sincethe loading is now on the other side of the support, a majority of the load mustbe resisted by the support which then decreases the stress being observed by thegages. The range of stress observed was 0.00 to 0.11 ksi in the top flanges and-0.09 to -0.36 ksi in the bottom flanges. The largest stress for the bottomflanges was observed in girder four. There was not an explainable pattern inthe stress changes observed for the diaphragms, but a majority of the membersexperienced compressive stress. The total range of stress for the members was -0.24 ksi to 0.22 ksi.


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Temperature: 8 °C


Loading Condition:



Two 50 kip trucks were placed side by side at the midspan of span 2.


Except for gages 15A and 20A, the midspan gages behaved, as expected, whichis as girders in a negative moment region. This negative moment was createdby the truck loading located in the second span of the bridge. The top flangesexperienced tension, ranging from 0.01 to 0.07 ksi, and the bottom flangesexperienced compression, ranging from -0.05 to -0.28 ksi. The middle pierstresses increased to approximately the same magnitude experienced when thetrucks were located at the third quarter point of span 1. The top flangesexperienced tension, ranging from 0.05 to 0.16 ksi, and the bottom flangesexperienced compression, ranging from -0.34 ksi to -0.67 ksi. Except for gages3C, 4C, and 7C, the diaphragm members experienced compressive stress. Therange of stresses were -0.06 to -0.28 ksi for compression and 0.18 to 0.45 ksifor tension. Diaphragm 1 did display a reversal in stress with the top twomembers experiencing compression while the bottom two members experiencedtension.

Notes on Specific Gages:

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Temperature: 8 °C


Loading Condition:



Two 50 kip trucks were placed side by side at the third quarter point of span 2.


In general the stresses at the midspan continued to decrease as the loading waslocated further away from the gages. Except for gages 15A and 20A, the topflanges experienced tension, ranging from 0.00 to 0.07 ksi, and the bottomflanges experienced compression, ranging from -0.01 to -0.23 ksi. At themiddle pier except for girder 1, the stresses decreased in the girders as the loadwas location further away from the middle pier. The top flanges continued toexperience tension, ranging from 0.02 to 0.013 ksi, and the bottom flangescontinued to experience compression, ranging from -0.22 to -0.62 ksi. Thesame stress patterns continued to be observed in the diaphragms. Diaphragm 1experienced compression in the top two members with tension in the bottomtwo, diaphragm 2 experienced compression in its members except for gage 7C,and diaphragm 3 experienced compressive stress in all of its members. Thetotal range of stress for the diaphragms was -0.28 ksi to 0.38 ksi.


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Temperature: 8 °C


Loading Condition:



One 50 kip truck was placed at the first quarter point of span 1.


At the midspan gages, girder 1 was the only girder to behave as a girder in apositive moment region which is compression in the top flange and tension inthe bottom flange. Girders 2,3, and 4 experienced tensile stresses at theirinside and outside flange tips while the gage affixed to the web registeredcompressive stress. This behavior could result from the composite behaviorpresent at this location. The one truck does not appear to have a significantenough load to properly stress the three inside girders at the midspan. Thestresses observed in these top flanges were fairly insignificant and ranged from0.00 ksi to 0.08 ksi. The bottom flanges, which are in tension, experiencedstresses ranging from 0.07 to 0.45 ksi. The largest stresses occurred in girder1, so it appears that this being the stiffest girder means that it is carrying agreater portion of the load. There is not an observable pattern to the middlepier stresses. Gages IB, 5B, 11B, 13B, 17B, and 23B displayed an increase intension, which would be expected for these gage locations, and the remaininggages displayed an increase in compressive stress. Except for six gages thegirder is behaving as expected for a girder in a negative moment region. Therange of tensile stress was 0.01 to 0.07 ksi, and the range of compressive stresswas -0.04 to -0.25 ksi. Except for gage 10C, the members of the diaphragmsexperienced compression ranging from -0.01 to -0.55 ksi. The lone tensilestress was 0.21 ksi.


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Loading Condition: One 50 kip truck was placed at the midspan of span 1.


General Observations: Having the load located directly over the gages caused, except for the twoflange tips of girder 4, the girders to respond in the manner expected for a loadpresent in span 1. The top flange compressive stresses increased and rangedfrom -0.01 to -0. 18 ksi while the bottom flange tensile stress range increased to0.25 to 0.79 ksi. The gages affixed to the top of the web at the middle piercontinued to display compressive stress, but the flange tips experienced tensilestress ranging from 0.00 to 0.12 ksi. The bottom flanges experiencedcompression ranging from -0.21 to -0.43 ksi. The top members for diaphragms1 and 2 experienced tensile stress while the bottom two experiencedcompression. For diaphragm 3, the top member displayed compressive stress,the next member down displayed tension, the next member down displayedcompression, and the bottom member displayed tension. The stress ranges forthese members were -0.10 to -0.96 ksi and 0.01 to 0.31 ksi.


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Loading Condition:



One 50 kip truck was placed at the third quarter point of span 1.


Girders I and 2 at the midspan continued to respond in a manner consistentwith a girder in a positive moment region. The range of compressive stressexperienced by all of the midspan girders ranged from -0.01 to -0.14 ksi. Thetensile stress in the bottom flanges decreased as the loading moved beyond themidspan of span 1. These stresses ranged from 0.16 ksi to 0.66 ksi. The samebehavior described for the middle pier gages in the previous loading stagecontinued for the girders. The tensile stresses ranged from 0.01 to 0.12 ksi,and the compressive stress for the bottom flanges ranged from -0.24 to -0.44ksi. The stresses for the diaphragms ranged from -0.04 to -0.67 ksi and 0.08 to0.20 ksi.


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Loading Condition:



One 50 kip truck was placed at the first quarter point of span 2.


A partial stress reversal, tension in the top flanges and compression in thebottom flanges, can be observed in the midspan gages. The term partial wasused because there was not a uniform stress reversal across the cross section,.but there is the beginning of an observable trend in girders 2,3, and 4. Onceagain, it appears that there is not enough load to cause uniform behavior acrossthe girders at the midspan. The range of stress experienced was 0.00 to 0.17ksi in tension and -0.01 to -0.14 ksi in compression. Except for gages 11B,13B, 17B, 19B, and 23B, the gages at the middle pier displayed compressivestress. These stresses ranged from -0.03 to -0.29 ksi. The tensile stress rangedfrom 0.00 to 0.09 ksi. Except for gages 3C and 10C, the members of thediaphragms experienced compression ranging from -0.04 to -0.44 ksi. Thetensile stresses were 0.09 ksi and 0.23 ksi.


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One 50 kip truck was placed at the midspan of span 2.


The midspan gages are basically displaying stresses consistent with girders in anegative moment region. The range of tensile stress is 0.00 to 0.08 ksi, and therange of compressive stress is -0.02 to -0.17 ksi. The equivalent statement canbe made for the gages located at the middle pier. Theses stresses range from0.01 to 0.09 ksi in tension and -0.01 to -0.46 ksi in compression. The range ofstress for the diaphragms is 0.02 to 0.32 ksi in tension and -0.02 to -0.35 ksi incompression.


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Loading Condition:



One 50 kip truck was placed at the third quarter point of span 2.


The same behavior as described in the previous loading stage continued at themidspan. The stresses ranged from 0.00 to 0.09 ksi in tension and -0.01 to -0.14 ksi in compression. At the middle pier, the gages continued to displaystresses basically consistent with the behavior previously described. Thesestress ranges were 0.00 to 0.09 ksi in tension and -0.01 to -0.37 ksi incompression. The stress ranges observed in the diaphragms were 0.02 to 0.25ksi in tension and -0.03 to -0.32 ksi in compression.


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Loading Condition:



Two 50 kip trucks placed end to end at the midspan of span 1.


Except for the two flange tip gages on girder 4, the midspan gages registeredtension for the bottom flanges and compression for the top flanges. Beginningat girder 1 and progressing towards girder 4, warping can be observed acrossthe width of the bridge. At each gage location, except for gage 4A, the largeststress occurred in girder 1 and progressively decreased as girder 4 wasapproached. This warping could be one explanation for the tensile stressesobserved in the inside and outside flange tips of girder 4. The stresses rangedfrom 0.02 to 1.37 ksi in tension and -0.01 to -0.26 ksi in compression. At themiddle pier, tension was experienced in the top flanges, and compression wasexperienced in the bottom flanges (except for the compressive force at gage20A). The range of stresses were 0.05 to 0.21 ksi and -0.33 to -0.74 ksi.Diaphragm I experienced tension in the top two members and compression inthe bottom two members. This pattern did not continue in the other twodiaphragms. The stress range for the diaphragms was 0.03 to 0.82 ksi and-0.10 to -1.81 ksi.


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Loading Condition:



Two 50 kip trucks placed at the midspan of span 2.


The stresses observed at the midspan gages with the load in span 2 were fairlyinsignificant, but a basic trend of tension in the top flanges and compression inthe bottom flanges could be identified. The range of stresses was 0.00 to 0.10ksi and -0.03 to -0.23 ksi. At the middle pier, the top flanges, except for gage2B, experienced tensile stress, ranging from 0.00 to 0.15 ksi, and the bottomflanges experienced compression ranging from -0.27 to -0.56 ksi. DiaphragmI experienced tension in the bottom two members and compression in the toptwo members. This pattern did not continue in the other two diaphragms. Thestress range for the diaphragms was 0.01 to 0.46 ksi and -0.07 to -0.40 ksi.


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Loading Condition: One 50 kip truck was placed at the midspan of both spans simultaneously.


General Observations: At the midspan except for the inside and outside flange tips of girder 4, the topflanges experienced compression, and the bottom flanges experienced tension.These stresses ranged from -0.01 to -0.14 ksi in the top flanges and 0.17 to0.66 ksi in the bottom flanges. At the middle pier, the top flanges experiencedtensile stress, and the bottom flanges experienced compressive stress. Thesestresses ranged from 0.02 to 0.17 ksi in the top flanges and -0.38 to -0.75 ksi inthe bottom flanges. Diaphragm I experienced tension in the top two membersand compression in the bottom two members. This pattern did not continue inthe other two diaphragms. The stress range for the diaphragms was 0.03 to0.38 ksi and -0.03 to -0.79 ksi.


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APPENDIX D


D-1

APPENDIX D


Starting from the in-situ steel framing of the superstructure, this appendix describes the construction

sequence in four steps. First, assembly of the steel superstructure is introduced, including the method

of erection, the equipment used in the erection, and the erection sequence. Placement of formwork

plus reinforcing steel is then described, followed by the pouring of the concrete deck. Finally, the

construction of parapets and the overlay are outlined. As the construction proceeds, the proof loading

under construction will be summarized resulting from the correlation between the field measurement

and the structural analysis based on the grillage method.

D.1 STEEL ASSEMBLING

In order to avoid the inconvenience to drivers and to reduce the control volume of the traffic flow, the

third-shift hours from 11 p.m. to 7 a.m. were selected by the contractor for the erection of the steel

superstructure. A total four nights were spent erecting the steel, including two on the south span and

two on the north span.

Three cranes were used on the south span, while two were used on the north span. The erection gear

included two crawler cranes with lifting capacity of 100 tons (200 kips) and one 4-wheel crane with a

capacity of 50 tons (100 kips) for the south span erection. One crawler crane plus the 4-wheel crane

were used for erection of the north span erection, primarily since only one girder segment had to be

erected per girder on the north span, versus two on the south span. In addition, a Highlander lifter with

a capacity of several tons lifted workers and connection bolts into position, especially when assembling

the splices. An air pump driver was employed to tighten the bolts.

One temporary scaffolding-tower, 4 feet by 5 feet in cross-section, was used under each girder line to

support the erected girders at mid-span of each span when the girders were being into place and the

D-3

crossframes being bolted in. These temporary towers were moved from the south span to the north

span during the erection of the north span and then totally removed when all of the crossframes and

end diaphragms were rattled up.

The prefabricated girders and crossframes for the day were transported separately on the morning of

their erection from the fabrication site to the construction site. Preparation for erection, such as setting

handrails (for the workers) on the top of the girder, building temporary towers on the ground, building

falsework, were done in the afternoon, prior to erection during the early morning hours.

Day 1 on the south span: July 17-18, 1995

1. The girders on this span were erected from the innermost girder to the outermost girder. Girder

305A1 (see Figure 2.4) was first hoisted by both 50 ton crane (50T) using one lifting point on girder's

top flange and 100 ton crane (100T) using two lifting points through a 20 foot spreader beam (20-

footer).

2. After having moved girder 305A1 to let one end set on the south abutment under one or two

workers' guide, two cranes (50T+100T) remained holding girder 305A1. At the same time, another

100 ton crane (100TA) erected girder 306B1 using only two lifting points on girder's top flange,

through a 30 foot spreader beam (30-footer), plus a "come-along" (see Figure 3.1). The splice

between girders 305A1 and 306B1 was tightened by three workers (group 1) in the lifter.

3. After the bolts for the splice connecting girders 305A1 and 306B1 were tightened, girder 306B1

was aligned on the center pier by two workers (group 2). A temporary scaffolding tower was then

added near the midspan of the south span by two workers (group 3) to support the erected girders.

The two girders became one continuous girder on three vertical supports and overhung the center pier

approximately 38 feet into the north span. Crane 100T with a 20-footer and crane 50T were then

released to erect a third girder, while crane 100TA continued holding girder 306B1.

D-4

4. The 50T+100T cranes lifted girder 307C1 and moved it to let one end sit on the south abutment.

Crane 100T continued holding 307C1, while crane 50T released girder 307C1 and began lifting

crossframes.

5. Crane 50T lifted crossframes D1 and D4 (see Figure D.1 for nomenclature). D4 was put into place

first by group 2, and one bolt in each comer was tightened snug. Crossframe D1 was then loosely

fastened in place.

6. Crane 100TA released 306B1 and lifted 308D1 into place. Group 1 spliced 307C1 and 308D1

while group 2 worked on placing the girder on the center pier.

7. Crossframe D5 was in put into place and group 3 placed a scaffolding tower under girders 307C1

and 308D1 near midspan.

8. The 100T and 100TA cranes were used to lift the remainder of the south span crossframes into

place in the following sequence: D2, D9, D3, D6, D7, D8, D10, Dll, D12, and D13. These

crossframes were originally bolted in with just four bolts, one in each comer of the crossframe. All

bolts were tightened up during the daytime of the following day.

Day 2 on the south span: July 18-19, 1995

1. The 50T+100T cranes erected girder 309A2, placing one end on the south abutment. Crane 50T

then released girder 309A2 to pick up crossframes, while crane 100T remained holding girder 309A2.

2. Crane 50T lifted crossframes 2a and 5a, and group 2 bolted them into place.

3. Crane 100TA lifted girder 310B2. Group 1 spliced 309A2 and 310B2 while group 2 worked on

setting girder 310B2 on the center pier.

D-5

4. Crossframes were placed in the following sequence by group 2: 3a, 4a, 9a, 10a, and lla.

5. Group 3 set a tower under girders 309A2 and 310B2 near the midspan of the south span.

6. Crossframe 2b was erected before girder 311C2 was erected. This type of cantilever erection of a

crossframe occurred only once, apparently because of the difficulty of subsequent fitup.

7. The 50T+100T cranes lifted girder 311C2 and held it in place.

8. Crane 100TA lifted girder 312D2. Worker group 1 spliced girders 311C2 and 312D2 while group

2 worked on placing the girder on the center pier.

9. Another sequence of crossframes, including 5b, 3b, and 4b were put into place by group 2, as was

the temporary scaffolding tower for girders 311C2 and 312D2, set up by group 3.

10. The rest of the crossframes were put into place in the following approximate sequence: 9b, 10b,

lib, 6a, 7a, 12a, 13a, 8a, 13b, lib, 6b, 12b, 7b, and 8b. All bolts were tightened fully during the

following day.

Generally speaking, the steel assembling on the south span went smoothly, except that the holes in the

bottom plate of girders 305A1 and 307C1 at the southern support were too small. Consequently,

wood blocks were used for supporting the girders on bearing plates. This problem was fixed later after

the south span erection was nearly complete, except that the end diaphragms were still on the ground.

To fix this problem, the sole plates were first cut off the holes were drilled to fit the pintles, and the

sole plates were then welded back to the bottom flange and seated in the pintles. It was also found on

day 2 that the holes in sole plates to fit the pintles on center pier were drilled too big. The following

day, additional sets of bushings were then jammed into the holes to grip the pintles. The end

diaphragms were then erected in the order of El, E2 and E3, thus completing erection of the southern

span.

D-6

Day 3 on the north span: July 24-25, 1995

1. The girders on this span were erected from the outermost girder to the innermost girder. Girder

313A3 was first raised by the 100 ton crane (100T) using the 30-foot spreader beam and a "come-

along". To move girder 313A3 into place, crane 100T had to make a 90 degree turn with the girder

due to tight maneuvering room as the girder was wedged between the splice and the north abutment.

The splice of girder 313A3 was then tightened by group 1, followed by the girder being placed on the

north abutment.

2. Crane 100T released 313A3 and continued to erect girder 314B3, tightening its splice.

3. The 50 ton crane (50T) lifted a sequence of crossframes, put into place by group 2: D20, D19,

D18, D14, D15, D17, and D16. All bolts on the crossframes were tightened loosely, and were

tightened fully after the north span erection was finished.

4. During the daytime of July 25, the temporary scaffolding towers used in the south span were all

moved to support the girders at the midspan of the north span, and the workers began placing the

formwork on the south span.

Day 4 on the north span: July 25-26, 1995

1. Crane 100T erected girder 315C3 similarly to how girders 313A3 and 314B3 were done.

2. Crane 50T lifted crossframes 20a and 19a were then erected by crane 50T.

3. Crane 50T was moved to make room for crane 100T, and crane 100T released 315C3 in order to

erect 316D3 when one of the scaffolding towers was positioned to support girder 315C3.

D-7

4. The last tower was set up to support girder 316D3 once 316D3 was in place.

5. Crane 50T returned to lifting crossframes 20b and 19b.

6. Crane 100T released 316D3 and continued to erect crossframes 14a, 15a, 14b, and 15b.

7. The following few days, all bolts were rattled up.

8. The erection was smooth on the north span.

D.2 FORMWORK PLUS REINFORCING

Wooden formwork decking was set up predominantly from July 28 through August 3, starting at the

south abutment. Plywood forms of 3/4" thickness were supported by 2"x10" joists, which connect to

the upper part of curved girders by using steel hangers. Overhanging brackets connected to the

innermost and the outermost girders were added to support both the overhanging plywood forms and

their supporting joists in two directions, including 4"x4" joists in the longitudinal direction supported by

2"x6" joists in the transverse direction. Immediately after the formwork was in place, shear studs were

welded to the top flanges of the girders and the end diaphragms, starting from the south abutment to

the splice line of the south span and then from the north abutment to the splice line of the north span.

Reinforcing bars were then placed on the north span first, from the abutment to center pier, and then

extended to the south abutment of the south span. The 50T and 100T cranes were used in this step,

alternately. There were, in general, five to ten workers and two air compressors weighing 2,785 lbs

each on the bridge. To meet the scheduled date, August 11th, of pouring the concrete, working

overtime took place a couple of days before August 10th, and an additional five to ten workers were

on the deck during this time. All the preparation work for pouring the concrete was completed by

August 10th.

D-8"

D3 CONCRETE DECK POURING

The concrete pouring started from the north abutment at 4 a.m. and ended to the south abutment at 8

a.m. on August 11th. A total of 149 cubic yards of concrete were placed on the bridge. The ready mix

concrete was delivered by concrete trucks and was then distributed by a concrete mobile hose with an

air-pump conveyor. Ten to fourteen people using finishers and vibrators worked on casting, vibrating,

finishing, and sloping the casted concrete, but four of them started covering the casted deck when the

weather turned to a drizzle, when two thirds of the concrete slab was in place. A small motor to

generate power for the vibrators was also on the deck throughout the concrete pouring.

D.4 PARAPETS AND THE OVERLAY

The reinforcement needed for the parapets was placed from August 16-18. The slip former was used

here to cast the concrete in the parapets since the parapets of this bridge are uniformly shaped. On

August 22, the slip former was used to pour the innermost parapet, and the next day it was used on the

outermost parapet. The ready mix concrete was delivered by concrete trucks. Six to eight workers

were working with the slip formers. Great care was taking in finishing the concrete surface as the

former progressed.

The placement of the two inch thick overlay composed of low slump concrete on the top of concrete

was first placed on the east half width of the bridge. The remaining part of the overlay was placed on

September 13th, thus completing the construction of the bridge.

D-9

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D-10

APPENDIX E


E-1

APPENDIX E


This appendix provides the details of how the dead loads were computed for use in the UM program.

E.1 FORMWORK: 5 PSF

The weight of formwork is estimated as 5 psf based on the information obtained from the construction

site of MN/DOT bridge No. 27998. The specific gravity for plywood is assumed 0.55 which turns out

to be 35 pcf It follows that

1. Deck weight: 3/4" thick

35 x 3/4 x 1/12= 2.19 psf

2. Joist weight: 2x10 joist @ 2'-0" on center

35 x 2 x 10 x 1/144 x 1/2= 2.43 psf

There is no deduction of the area of beam flanges. This is compensated by the weight of shear studs

and that of clamps to connect the beam flanges and the wood joists. Total 4.62 psf is further round off

to 5 psf.

E.2 REINFORCEMENT: 10 PSF

A total of 86,985 lbs of reinforcing bar was placed on the plan area of 9940 ft2.

E.3 PIAIN CONCRETE: 80 PSF

E-3

The volume of wet concrete was estimated at 5,520 ft3 by the following calculation:

5,698 - (86,985/490) = 5,520 ft3 = 204 cubic yards

where the total volume of reinforced concrete is estimated at 5,698 ft3 and the density of reinforcing

bar is estimated to be 490 pcE The uniform floor load resulting from the concrete slab is then

determined by taking 144 pcf as its density.

144 x 5520 / 9940 = 79.97 psf

E-4

APPENDIX F


F-1

APPENDIX F


This appendix outlines the procedure by which vertical loads applied to the bridge were distributed to

the discrete joints of the finite element model.

F.1 RIGOROUS DISTRIBUTION

It is not unusual that the center of applied loads does not coincide with the center of rigidity of the

structure in a curved I-girder system with varying depth from girder to girder. As a result, the vertical

load transferred to each girder is due not only to the flexural deformation but also to torsional rotation.

In order to determine the vertical load distribution factors, it is appropriate to assume that the

crossframes provide rigid links to prevent the girders from being deformed differentially. Based on the

assumption of no differential deflections, the following equation may be used:

Vi VI, 2Xli

(F.1)

vi-?Vi = V

where Vi is the vertical load taken by Ii, the moment of inertia for each girder. V is the vertical load

being transferred and S means summation.

In Figure F.la, the center of the resultant forces also called the rigidity center is obtained as follows:

V2 d2 +V 3 d3 +V4d 4 = V*xo

(F.2)

12 d 2 + 13 d3 +I4d4XO =

I + 2 + I3 +14

F-3

where xo, d2, d3, and d4 are the distance to girder 1 from rigidity center girders 2, 3, and 4 respectively.

An additional torque Vx eo has to be considered when there exists an eccentricity eo between the

center of external loads and the rigidity center.

Based on the assumption of no differential rotations, the following equation can be written

K- = ui = ixi*li

(F.3)

Ti= -xiIi=i xiliK

where k is a proportional constant, q is a rotation angle, T1 is the shear force taken by each girder, ui is

the vertical deflection on each girder due to rotation, and xi is the arm length from each girder to the

rigidity center as shown in Figure F.lb. Furthermore, f and k are combined into one parameter q.

Setting the sum of Ti equal to zero, one obtains the location of the torsion center which is actually the

same point as the rigidity center defined in Eq. F.2. Also making the moment equilibrium yields the

following equation

Mz V*eoS Mz = Ve (F.4)

and substitution of q in Eq. F.3 leads to the following equation.

Ti = -xi ieo V (F.5)IxfI

Consequently, the vertical load Pi transferred to each girder is obtained from the combination of Eqs.

F.1 and F.5, i.e.,

P= xli eo) V (F.6)I/ liExf li

F-4

F.2 EXAMPLES

The following data are used to determine the vertical distribution factors:

1. On an average, the relative moments of inertia are as follows:

II= 0.595, 12= 0.751, 13= 1.130, and I4= 1.523

2. The distance from each girder to girder 1 is denoted as

di= 0, d2= d, ds= 2d, and d4= 3d

3. The distance from rigidity center to girder is computed from Eq. F.2, i.e.,

xo= 1.895 d

4. Values of eccentricity varied from case to case are described as follows:

a. For the case of uniform distributed loads

e0= (1.895-1.5) d

b. For the case of parapet loading

eo=(1.895-1.75) d, where the ratio of weight for the inner parapet to the outer one is 2.95/3.85

c. For the case of truck loads

eo= x, - 1.895 d, where x, is measured along the horizontal distance from truck gravity to girder

1 as shown in Fig. F.2a.

F.3 DISTRIBUTION FACTORS

The distribution factors of vertical loads are listed in Table 6.5 for the cases of 4a and 4b in the

previous section, while for case 4c, because of the variation of the truck gravity, a simple method is

presented herein. Figure F.2b shows the influenced panel between two crossframes which encloses the

truck gravity. Loading transfer in the longitudinal direction is achieved by simple support theory,

which is:

W(Ls- 11) WP 1P = ; P2 =-

Ls Ls

or (F.7)

Pi=r i W

in which W, li, and L. shown in Fig. F.2c are the weight of a truck, the horizontal arc distance from

truck gravity to the line of front wheels, and the arc length passing the truck gravity between two

F-5

crossframes of the influenced panel. It is noted that one of the crossframes is always underneath the

line of the front wheels.

Each load Pi is distributed to the panel point j by the method described above in section F.2. The

regenerated equation has the following form:

Fij = (fj + tj) Pi

or (F.8)

Fij = liW(f j + tj) W

where F, means the distribution of load Pi to the panel point j; 4= Ij/SIj and t;= eoAIj/Sxi2I are the

distribution factors due to flexural and torsional deformations respectively. Therefore the distribution

factor is defined as:

Dij = ri (f j+tj) (F.9)

F-6

Xo

center

V, V2 V3 V4

(a) Flexural distribution

V M.= V-eo

Xi

U2

X2 X3

Us U4

X4

(b) Torsional distribution

FigureF.1. Distribution of vertical dead loads

F-7

rI

I - -T - - -- ~

v%

X eo Sf c eRigiditycenter

(a) Eccentricity of truck loads

Panel front

diaphragms. Truck /

Girders Panel rearGirders

d J -d d

(b) Influenced panel and truck location

6O 60I l 1

O05 • 0-i---i-

(c) Longitudinal distribution

FigureF.2. Distribution of truck loads

F-8

b

APPENDIX G

BACKGROUND ON ANALYSIS OF STEEL CURVED

GIRDER BRIDGE SYSTEMS

G-1

APPENDIX G

BACKGROUND ON ANALYSIS OF STEEL CURVED

GIRDER BRIDGE SYSTEMS

This appendix contains excerpts from a paper by Stegmann and Galambos [6] so as to provide a

review of available computer capabilities for use by design agencies.

Edited Excerpts from STEGMANNAND GALAMBOS [61

Additional factors are encountered in the analysis of the curved as opposed to the straight girder

in that a load applied perpendicular to the plane of the bridge generates a torque as shown in

Figure G.1. This torque then is the cause of three types of stress in addition to the usual normal

and shear stress due to the flexural effects, namely St. Venant shear stress, warping shear stress,

and warping normal stress. A portion of a girder with these stresses acting on it is shown in

Figure G.2. For an open-section girder, the warping normal stresses can be very large (50+%)

relative to the bending normal stresses. Thus it is desirable that the structural analysis account for

warping normal stresses in a fairly accurate manner.

All analyses cannot and should not do all things. Where very precise and accurate results are

required, such as in stress analysis for fatigue strength determinations or for a structure of unusual

configuration, a more complex program is warranted. For the first preliminary design of sections

in an engineering office, such an involved program would be unnecessary and wasteful. This

would then indicate an arbitrary segregation of the methods of analysis into three distinct groups

or levels of sophistication.

Level I Analyses are the most sophisticated. They could be of the general finite element analysis

type that would take into account the entire girder system and slab (if composite) and would, at

any location, give the total stress resultant picture; or they could be general analytical solutions

G-3

that would take all factors, such as warping, cross-sectional distortion, etc., into account and give

dependable, accurate results. This total stress resultant could then be broken down into the

normal and shear stresses and the appropriate deformations. Use of such a complex program

would obviously be limited. Its main purposes would be in evaluation of research conducted in

such areas as box girder distortion effects, diaphragm spacing, precise stress analyses for details

with relation to fatigue, effective width studies of composite beams, and so on. The Level I

analysis would not be used for the final check analysis of a bridge, but it would serve to calibrate

the Level II analysis which would be used in this situation.

The Level II analyses are one step down in complexity from the Level I, but still retain the

sophistication necessary to give an accurate final check analysis of a bridge. As opposed to the

previous level of analysis, the Level II analysis would not take the entire bridge system into

account as a single entity, but would subdivide it into distinct elements such as slab, girder

(straight or curved), diaphragms, and braces. This is accomplished through the judicious

application of simplifying assumptions and idealizations. Again, the output would consist of the

stress resultants at any location of interest to the analyst, and could be broken into the normal and

shear stresses. Warping stress values should also be made available because of its relations to the

limit state calculations which will be discussed later. Availability of the Level II analysis programs

would be much greater in that they should be readily accessible to the state highway departments

and consulting design offices that would have need of them. Lastly, the Level II analysis

programs are used in calibration of the Level III analyses.

Level III Analyses are the basic tools that the designer would use for the initial formulation of the

bridge elements. The objective here is to give quick and approximate values for normal and shear

stresses so that member sizes may be selected and organized into a rational configuration. These

analyses are usually of the form of a simple design algorithm using stresses obtained from straight

girders and modifying these values to account for curvature and bracing spacing.

G-4

As of the present (1976) many programs and analyses have been developed. All levels of

sophistication are encountered. Following is a summary of some of the available programs.

G.1 THE GRID METHOD

The Grid Method was developed at Syracuse University. The main assumptions are [15]:

1. The structure behaves like a grid, i.e., any force or displacement vector acting at a point has

three components, one linear (perpendicular to the plane of the structure) and two angular

(about axes in the plane).

2. The principal axes of each member cross-section must lie in the plane of the structure.

3. Uniform torsion is assumed (St. Venant).

The stiffness matrix of a curved member was derived based on these assumptions and a computer

program was written utilizing this stiffness matrix to determine the relevant displacements at the

selected points. This method gives normal stress distribution in the girders with the same

variation as in straight girders; that is, normal stress is a function of the distance from the bending

axis, and is constant across the width of the section. Comparison of the stress distributions of this

analysis with experimental results and the studies of the influence of the St. Venant torsional

constant on the results of the analysis indicate the presence of a significant amount of non-uniform

or warping torsion which is not accounted for in this method. Because of this limitation the Grid

Method would be of the Level III type analysis, and should be recommended only for use in

preliminary design.

G.2 LATERAL FLANGE BENDING METHOD

The Lateral Flange Bending Method was developed at the University of Rhode Island [15]. It is

basically an extension of the previously discussed Grid Method, and hence utilizes the same basic

assumptions concerning the structure. One additional assumption is that the flange is assumed

free to warp at end diaphragms and is considered fixed at intermediate diaphragms. As noted, the

major shortcoming of the former analysis is in ignoring the warping stresses produced in the curve

G-5

member. The Lateral Flange Bending Method overcomes this by the inclusion of two additional

angular degrees of freedom, one at each flange about axes that are perpendicular to the plane of

the structure as shown in Figure G.3. A stiffness matrix is then derived for the five degrees of

freedom at each end of the member. Forces acting on the interface between each flange and the

web are ignored and the cross-section is assumed constant along the length of the member. By

imposing boundary conditions on the flange degrees of freedom that approximate the end

conditions for the flanges of a curved member of a curved girder bridge, the flange degrees of

freedom are forced out, and a stiffness matrix in terms of grid degrees of freedom results.

Although the flange degrees of freedom are eliminated the effects of flange bending are still

present in the stiffness matrix. Warping normal stresses, or rather a normal stress analogous to it,

can be computed by assuming the flange to be a beam acted upon by the lateral flange moments

producing a linearly varying normal bending stress across the flange which is demonstrated in

Figure G.4. These lateral flange moments are obtained through a simple step-by-step algorithm.

Comparisons of this analysis with tests and more sophisticated analyses show that the inclusion of

the lateral flange bending mode brings relatively close agreement with the actual states of stress.

This, therefore, would indicate that the Lateral Flange Bending Method would be of Level II

sophistication, and along with its straightforward input and output format would be a useful tool

for the bridge designer.

G.3 THE THREE-DIMENSIONAL METHOD

The Three Dimensional Method of analysis was developed at Syracuse University. This method

has been formulated into a computer program and a User's Manual is available [16]. The main

assumptions of the analysis are:

1. All members are assumed straight.

2. The girders, slabs, structural diaphragm members and lateral bracing members may act

independently satisfying continuity conditions, i.e., fully composite action may be assumed.

G-6

3. The principal axes of each member cross-section are assumed to lie in the plane of the

structure.

4. Static loading only.

5. Diaphragms and supports can be either radially positioned or skewed.

6. Girders can be arranged concentrically or non-concentrically (i.e., girder spacing may vary).

The bridge is divided into an arbitrary number of individual members and loads are considered to

be applied at the joints between these members. The axial forces, shears, bending and twisting

moments are then expressed in terms of the six components of deformation that are considered at

each joint: three rotations and three displacements as shown in Figure G.5. The geometry of the

bridge and applied joint loads are in the input to the program. Deformations are first expressed in

terms of a global coordinate system and then components of the deformations with respect to

local coordinate system of the member are determined. Next the equilibrium equations for each

joint are set up. Using appropriate boundary conditions this system of equations is solved for the

unknown joint deformations which are then in turn used to compute the shears and moments of

each joint Thus the output of this analysis program consists of the displacements and rotations of

all pre-selected nodes or joints, the axial forces, and the bending and twisting moments. Although

the analysis itself does include the effect of warping, the output consisting of forces and moments

does not lend itself to a simple computation of the warping stress, which is a drawback in relation

to the proposed design criteria. It should be noted that through idealization an order of

magnitude type analysis of warping stress could be obtained. The program's sophistication,

however, does qualify it as a Level II program which could be used as a final check in the design

process.

G.4 THE EQUIVALENT STRAIGHT BEAMS METHOD

The Equivalent Straight Beams method for the analysis of curved girder bridges was developed at

the University of Pennsylvania expressly as a simplified approach to be used for preliminary design

only [17]. Simply stated the method of analysis used is that an "equivalent" straight beam is

chosen to correspond to the curved girder being analyzed. An "equivalent" straight beam is

G-7

generally one that gives the same magnitude of a certain stress resultant at the same location as in

the curved beam. Through utilization of the analogies between curved and "equivalent" straight

beams, ip factors were determined that modify the stress resultants in a straight girder to

approximate the stress resultants in a curved girder.

Stress Resultant (curved beam) = p [ Stress Resultant (straight beam) ]

These stress resultants will give a determination of the reactions, bending moments, torsional

moments, shears, vertical deflections, and angles of twist. The basic assumptions of this

technique are:

1. All the assumptions of the elementary beam theory apply.

2. Only slender beams are considered.

3. Warping torsion is neglected.

4. Only the mid-length radius, R, is considered in computations.

5. All supports are idealized as fixed or pinned.

6. The girder must have a constant, circular curvature.

7. The range of flexural-to-torsional rigidity (EI/GJ) considered is from 1.0 to 100.0, where E, I,

G, and J refer to the modulus of elasticity, moment of inertia about the bending axis, shear

modulus of elasticity, and St. Venant torsional constant, respectively.

8. Concentrated or distributed loads are allowed.

What is available to the designer are computed charts giving the Vp factors for many various

geometric configurations. An equivalent straight beam is then chosen, the Vp factors applied, and

the resulting stress and displacement values are determined.

The same limitation applies to the Equivalent Straight Beam Method as to the Grid Method.

Warping torsion is ignored which can lead to underestimating the calculation of the flange normal

G-8

stresses. This would limit the Equivalent Straight Beam Method to being a Level III type

analysis, which is what the developers intended for it to be.

G.5 SLOPE-DEFLECTION FOURIER-SERIES METHOD

The Slope Deflection Fourier Series method was developed at the University of Maryland [18].

The basic method of analysis is to establish the general differential equations incorporating the

slope deflection equations. The solution to the differential equation for the deflection is assumed

as a Fourier Series. The plate forces, girder deflection and girder forces are similarly defined as a

Fourier Series. This was first done for a curved orthotropic plate as shown in Figure G.6. This

was next extended to a system of curved orthotropic plates continuous over curved girder

supports as shown in Figure G.7, evolving into a system of curved plate girders. The method will

consider any number of concentrated and/or uniformly distributed loads for a single or two-span

continuous case. Also included are the effects of diaphragms and non-uniform torsion.

This method is incorporated into a computer program, COBRA I. The input consists of the

bridge configuration, the girder stiffnesses, and the number of Fourier Series terms desired to be

used in determining, the solution. Output consists of slopes, deflections, shears, bending moments

and torsional moments.

As this analysis considers the curved girder as such and does include non-uniform torsion and its

effects, it would be relatively sophisticated and could be considered as a Level I analysis for the

cases of spans and geometry to which the program is limited.

G.6 DABROWSKIS ANALYSIS APPROACH

Outside of the CURT program many other methods or techniques have been developed to deal

with curved girder systems. One of the most rigorous solutions is that of Dabrowski. The first

closed form solution was formulated by Vlasov who derived the differential equations governing

the behavior of horizontally curved girders [19]. Dabrowski then took up the problem of torsion

and bending of curved thin-walled beams that were asymmetric in cross-section. In 1960 he re-

G-9

derived Vlasov's equations including several terms that had been neglected by Vlasov. Dabrowski

then in 1964 derived the governing differential equation for the warping or bimoment of a curved

girder of open thin-walled cross-section loaded normal to the plane of curvature. This equation

was then solved for deformations and the internal stresses due to the bimoment, the warping shear

stress and warping normal stress [20, 21]. The results of Dabrowski's work were four equations

which will give at any point along the span the bending moment, St. Venant torque, bimoment,

and total torque on the section. The basic assumptions of his method are:

1. No distortion of the cross-section

2. Elastic theory

3. Small deflections only

4. Mild curvature (a < 0.05 Radians)

5. Concentrated load and torque may be applied anywhere in the span or a distributed load and

distributed torque may be applied.

Although the equations appear involved, all variables, except the position along the girder, are

dependent on the cross-section geometry. Once the section properties are determined for the

girder the computational effort required to obtain the results is minimal.

Noting the deficiencies of some previously discussed analysis methods, Dabrowski's solution

would appear very good in that it takes into account the warping of the cross-section and also

gives the designer the ability to determine a value of the warping stress at any point along the

span. This method would then be of the Level II or possibly Level I type.

G.7 UNITED STATES STEEL METHODS

Several methods of analysis are given by United States Steel in their "USS Highway Bridge

Design Manual" [22]. They are summarized as follows:

G.7.1 Rigorous Analysis

G-10

This is a fundamental method of consistent deformation [22]. That is, the various components of

the structure must distort in such a way as to maintain geometric compatibility with each other,

and at the same time remain in a state of equilibrium. To do this is possible only with a unique set

of internal forces. The necessary internal forces can be determined by solving a series of

equations which are mathematical statements of equilibrium and geometric compatibility. In the

case of a two-girder bridge with intermediate diaphragms (cross-bracing, floor beams, etc.) when

the load is applied the girders will deflect and twist which apply torques and vertical shear forces

on the floor beams (diaphragms) which will be the redundants. This can be seen in Figure G.8.

This will result in "4n" redundants (each end of the floor beam will have two redundants). By

considering the equilibrium of the floor beam these can be reduced to "2n" redundants. Then

considering the differential deflection and rotation of the panel, two equations may be written for

each panel. So, for the entire bridge with N diaphragms or floor beams this results in 2N

equations in 2N unknowns. Once the redundants are solved for, the internal shear, torque and

moment of each girder can be computed.

G.7.2 Simplified Method

In the Simplified Method the curved girder is straightened out to its full length and the external

loads applied [22]. The moment diagram for this condition is then constructed by standard

procedures for continuous beams. This is referred to as the Primary Moment Diagram. Next, the

Primary Moment Diagram Radius is set equal to the Distributed Torque Diagram. This can be

explained as follows: Equivalent axial forces, M/d are computed in the flanges, where M is the

bending moment obtained from the Primary Moment Diagram and d is the distance between the

flange centroids. Next, consider a free body diagram of a differential element of the flange which

is illustrated in Figure G.9. This shows that there must be a radial force, w = M/Rd, acting in

order to produce static equilibrium. By straightening out the flange and considering it to be

laterally supported at each diaphragm line, and applying the radial load as a distributed load on

this continuous beam, a lateral bending moment diagram can be obtained. Using the section

properties of the flange considered as a beam bending in the horizontal plane, normal stresses

caused by this lateral bending can be computed and combined with the normal stresses produced

G-11

in accordance with the Primary Moment Diagram. Also, the torque at each particular cross-

section along the girder can be computed from this lateral force:

Torque = wd = d(M/Rd) = M/R = Distributed Torque

This torque then is transmitted to the cross or floor beams. The shears and moments in return

applied to the girders from the floor beams can be easily deduced considering the equilibrium of

each member. These shears from the floor beams are then applied to the girder as vertical loads

and from this a Secondary Moment Diagram is constructed. The Primary and Secondary

Diagrams are then added, and the entire process can be iterated until desired convergence is

achieved. From this final moment diagram and the Distributed Torque (which is not altered from

its initial state) the girders can then be designed. This is an approximate, Level III type analysis.

G.73 Approximate Analysis

The Approximate Analysis is a further simplification of the previously discussed Simplified

Method [22]. The same basic procedure is retained in that a Primary Moment Diagram is

constructed from the girders straightened to their full developed length and external loads applied,

the Distributed Torque Diagram is determined from the lateral forces applied to the flanges, and

finally the redundant shears and moments in the floor beams are determined as before. The

further simplifications referred to are with respect to distribution of moments and end fixity

approximations in the form of empirical factors. As with the Simplified Method this is a very

approximate method of obtaining stress resultant values and would be used for preliminary design

calculations only.

These previously presented methods are only a few of the many that have been proposed and are

currently available in print McManus et al. [20] include an extensive bibliography and summary

of the available analytical tools. From a study of this listing and the individual methods, the most

widely available, thorough, and easily employed method would be that of Dabrowski [21]. It is an

exact solution of the differential equations of the curved girder arranged in a format that can be

G-12

easily used, it incorporates warping torsion in the analysis and gives a direct calculation of the

bimoment. It is not, however, a computer program, and it does not readily permit the

consideration of the composite deck slab. The incorporation of the slab is possible through the

sophisticated Level I finite analysis programs (e.g., COBRA) or through the application of

simplified equivalent single composite girders in an analysis such as Dabrowski's or any other

method which permits the inclusion of unsymmetric curved girders. Considerable research has

concentrated on the development of equivalent simple composite sections, especially with

reference to their torsional properties [23, 24].

To the designer the most important methods are those which give good Level III results in

preliminary design and good Level II performance for the final check analysis. Several of these

have been described previously in this appendix. At present, it seems that the relative merits of

each must await reporting on the success of their use in the literature. It is not clear as to which

method, if any, can be singled out for preferred recommendation.

G-13

Fig G.1 Loading of curved girder

G-14

St. Venant Shear Stress

Warping Shear Stress

Warping Normal Stress

Fig. G.2 Additional effects due to torsion

G-15

Fig. G. 3 Additional flange angular degrees of freedom

I I

II iiI I I

II I !

J !-, J~ -^

Fig. G.4 Flange acting as laterally loaded beam

G-16

1Z

Fig. G.5 Three-dimensional method - six degrees of freedom

G-17

pport

Fig. G. 6 Single curved orthotropic plate

Flexible

Simple Support

a b

Fig. G.7 System of curved orthotropic plates

G-18

-- --

Fig. G. 8 Rigorous analysis - distortion of girders and beams

w

/R /

/

/

/

D

Mw = RD

R = radius

D = beam depth

Fig. G.9 Differential element of flange under assumed lateral loadG-19

APPENDIX H

SPECIFICATIONS OF THE

VIBRATING WIRE STRAIN GAGE

H-1

APPENDIX H

SPECIFICATIONS OF THE

VIBRATING WIRE STRAIN GAGE

This appendix presents the specifications of the Geokon VK-4100 vibrating wire strain gage used for

all strain measurements recorded in this research project. The following pages are reproduced from

Re£ [12].

H-3-

igeo!kon

^ " *^''c

Features* Spot weldable* Low profile* Small size* Waterproof* Stainless steel* Detachable plucking coil* Adjustable range9 High compliance* Epoxy bondable

The Model VK-4100 Vibrating Wire Strain Gage is de-signed to measure strains in steel structures, such asbridges, piles, tunnel linings, buildings etc. It can be in-stalled quickly and easily in the field by means of a spotwelder. (Alternatively, the gage may be epoxy-bondedto the surface of either steel or concrete). The VK-4100has a fully-sealed, all stainless steel construction, makingit waterproof and highly resistant to corrosion.The gage utilizes the vibrating wire principle: a length

of steel wire is tensioned between two end blocks whichare spot-welded (or epoxy-bonded) to the surface of thesteel member. The wire is plucked so that it vibrates atits natural resonant frequency. This frequency dependson the wire tension which will vary as strain in the steelmember varies. An electromagnetic coil is used to pluckthe wire and to measure the frequency of the vibrationso produced. The change in frequency is then display-ed as a strain change directly by the readout box.A dual coil auto-resonant circuit and driver is availablefor low frequency dynamic strain measurements (up to120Hz).

Advantages of the VK-4100 Vibrating Wire Strain Gage:*The vibrating wire principle gives maximum accuracy,sensitivity and long-term stability.*Installation is quick and simple, requiring the use of aportable spot welder only. Surface preparation is mini-mal. Installation can also be made by epoxy bondingthe gage to either steel or concrete.*The gage is of small size and the wire is in close prox-imity to the surface to which it is attached.*The wire is positively gripped in the end blocks by apatented swaging technique.*True O-ring seals provide complete waterproofing and

SPOT-WELDABLE TYPE

Vibrating WireStrain Gage

Gage

allow the protective tube to 'float' around the wire.This, coupled with a pretensioning of the wire, makesthe gage very compliant, or 'soft', in that strains in thesteel or concrete member do not have to stretch the pro-tective tube, as well as the wire, in order to alter wiretension. This places a minimum strain on the weldpoints and makes epoxy bonding possible.*An external spring holds the wire at an initial tensionwhich can be set to any desired level by a simple adjust-ment technique. Thus gages can be set to place theavailable range mostly in tension or mostly in compres-sion, as required.*The gage is constructed from carefully selected stain-less steel elements so that the corrosion resistance of thegage is maximized.*Temperature compensation is achieved by matching thecoefficient of expansion of the wire to that of the un-derlying steel. Temperatures can be measured by a ther-mistor encapsulated in the plucking coil housing.*The plucking coil housing is separate from the gage el-ement and can be carried around with the readout boxso that only the gage element is left behind on the struc-ture. If the gage is inaccessible the coil housing is at-tached permanently in place around the gage. Also,should the plucking coil or signal cable become damag-ed in any way they can easily be replaced without dis-turbing the gage element.*Lightning protection may be specified for gages in ex-posed locations.* Frequency signals can be transmitted over electricalcables many thousands of meters long without loss ofaccuracy. Cable resistance changes caused by tempera-ture or moisture effects are not a problem with vibrat-ing wire strain gages.

H-5

______ n __ ---- 2%" ---.235"

,--.---w--- -- .110" Gage length 2"

IT T"I3" I

GageCoil Housing

SPECIFICATIONS - Model VK-4100 Vibrating Wire Strain Gage

Gage ElementRangeSensitivityActive gage lengthWire height above surface

Thermal coefficient of expansion

Overall dimensions LxWxH

Temperature range

Materials

Coil HousingOverall dimensions LxWxH

Temperature rangeMaterials

CableMaterialSize

microstrainmicrostrain

in (mm)in (mm)

ppm/ F.(/°C)in (mm)

OF (oC)

in (mm)0 F (oC)

in (mm)

25000.5 to 12 (50.8)

,110 (2.79)

6.7 (12.0)2.5x0.5x0.24"

-40 to +250 (-40 to +120)Stainless steel, buna N

3x.88x.69 (76x22x17)-40 to +4175 (-40 to +80)

Waterproof copolymer epoxy

4 conductor-shielded 22 gage vinyl jacket.187 (4.7)

AccessoriesSetting tools (test strips,tension adjustment fixture).

Spot welding equipment.Epoxy kits.Vibrating Wire Readout Box.Thermistor Readout Box.Terminal boxes.

OptionsThermistors.Lightning protection.Autoresonant coil assembly.Ordering InformationSpecify: 1.Cable length.

2.Options required.3.Accessories required.

For further informatiao contact us..

H-6

eOIkoi48 SPENCER STREETLEBANON, NH 03766,TEL: 603/448-1562FAX: 603/448-3216TELEX: 4995473GEOK'

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DIMENSIONS

i

Vibrating WireReadoutFeatures:

3 User friendly.2 Multi-line LCD.3 Rugged and reliable.3 Temperature readout.3 Rechargeable battery.3 Cold weather operation.3 Internal real-time clock.3 Battery-backed memory.3 Easy-to-use control panel.3 RS-232 communications port.3 Two modes of data acquisition.

The GK-403 Vibrating Wire Readout is designed f(with all of Geokon's vibrating wire sensors in all Iweather. It incorporates all the features of the eai401 Readout plus it can read and display temrreadings, and can store all readings in memtransmit the values to a host computer.There are seven modes of-operation. Modes A I

are designed for use with specific Geokon gagereading is displayed directly in microstrain, frsquared or period. A convenient feature of the GIits ability to read the thermistors encapsulatedmost Geokon vibrating wire sensors, and to displatemperature reading.Storage of the readings is a simple one-bul

operation. Each stored reading is identified treference number, ranging from 1 to 256, plus thdate and temperature. Selection of the reference rmeans of a toggle switch or, if preferred, by autovery useful feature is the ability at the flip of a togithe previously stored readings taken from any seon-site evaluation of the readings and the early detMode G permits programming of gage factors,

engineering units and identifiers for up to 256 dinterent gages. A twodimensional storage matrix of rows and columns allows sets of readings from many instruments taken at aparticular time (rows) or sequential readings of any particular gage (columns) to be stared. An easy-to-usemenu lists options to transmit readings, clear stored readings, set the date and/or time, configure the autoincrement of the reference numbers and set gage parameters. Mode G also provides the ability to download afile from an IBM-compatible computer containing gage parameters (zero, gage factor, offset etc.) and the abilityto view previously stored data. The comma delineated output format allows easy importing into spreadsheets

and database programs such as Lotus 1.2.3, Microsoft Excel etc.The GK-403 includes a 15x8 column LCD matrix and automatic shutoff to conserve the life of the rechargeable12-volt lead acid gel-type battery. Waterproof seals are incorporated into the face plate, switches and inputconnectors.Included with the readout is a battery charger, a gage patchcord, an RS-232 interface cable, communications

,software and a manual. See specification overleaf.

t H-7

48 SPENCER STREET ge lkonL LEBANON. NH 03766 USA - I on1

TEL: 603/448-1562FAX: 603/448-3216TELEX: 4995473GEOKON

I -%- Iincorporated

GEOTECHNICALINSTRUMENTATION

-7r --~-------------· ----- ---- 1 slI

i

Vibrating Wire Readout:Excitation Range:Measurement resolution:Timebase accuracy:

Temperature Readout:Sensor type:Sensor accuracy:Measurement range:Measurement resolution:Measurement accuracy:

Memory:RAM:ROM:Reading storage:Array partition:

Real-time Clock:Features:Time format:Date storage format:Date display format:Oscillator:Accuracy:

Communications:Default parameters:Handshake:Transmission format:

Physical:Display:Dimensions:Weight:Temperature range:Battery:Operating time:

400Hz to 6000Hz, 5 volt square wave0.25ps/2550.01%

Thermistor, Dale #1C3001-B3 (YSI 44005)±0.50 C-500 C to +150 0 C0.1°C0.5-1.0% FSR

64K Static, 48K used32K EPROM, 16K used2000 arrays256 arrays for Modes A-F, remaining for Mode G

Full calendar with automatic leap year correction24 hour (hhmm)Julian daymonth/day/year (mm/dd/yy)32.768kHz±1 minute per month

9600 baud, 8 data bits, 1 stop bit, no parityXON/XOFFComma-delineated ASCII

15 column x 8 line backlit LCD19.1cm(7.5") x 13.3cm(5.25") x 23.5cm(9.25")3.2kg (71bs)-10°C to +500 C12volt, 2.6aHr (Yuasa NP2.6-12)Approximately 10 hours

Optional accessories:D SPLIT data formatting software.1 Y-cable (permits simultaneous RS-232

communication and gage measurement).:1 Vibrating wire load cell module.

For further information contact us ...H-8

geokon..i__ COrloraotec

48 SPENCER STREETLEBANON, NH 03766 USATEL: 603/448-1562FAX: 603/448-3216

SPECIFICATIONSModel GK-403 Vibrating Wire Readout

r

Documents

Stresses in Steel Girder Bridges - College of Engineering