Comparison between Abaqus Analysis and AASHTO Refined Method

125 Pages·2017·2.2 MB·English

Simulation of the effect of deck cracking on the behavior of the prestressing
force in a single span prestressed concrete girder

A thesis

submitted in partial fulfillment of the requirements for the degree of

Master of Science in Civil Engineering

in the Department of Civil and Architectural Engineering and Construction Management

of the College of Engineering and Applied Sciences

at the University of Cincinnati

by

Soumya Vadlamani

Bachelor of Technology in Civil Engineering

Gitam University, India, August 2013

Committee Chair: Dr. Richard Miller, Ph.D.

Committee Members:

Dr. Gian Andrea Rassati, Ph.D.
Dr. Thomas M. Burns, Ph.D.
Abstract
The current AASHTO LRFD Bridge Design Specifications have a Refined Method for calculating
the time-dependent prestress losses, which estimates a gain in the prestressing force due to the
differential shrinkage between the girder and the deck. However, the method does not consider the
possibility of cracking in the deck. When the deck cracks, some stress is relieved from the girder
and some, but not all, of the gain in the prestress is lost. Not all state departments of transportation
allow the gain in prestressing force to be included in the prestress loss calculations as it is very
small, often 2-3%, and may be lost when the deck cracks. Some other state departments of
transportation believe that upon cracking, not all of the gain is lost and they allow some percentage
(often 50%) of the gain to be included. The Prestressed/Precast Concrete Institute Bridge Design
Manual recommends including the entire gain.
Three different length models were simulated using the ABAQUS finite element software. The
variables considered were the deck strength, deck shrinkage coefficient, girder type and the age of
the girder at the time of casting the slab. Simulations were done in two broad categories; one where
the cracking in the deck was most likely and the other where it was least likely. To see the effect
of deck cracking on the prestressing force, it was important to know whether the deck would
always crack or if there were circumstances where the deck would not crack.
It was observed that for all times of deck placement considered in this study, the deck always
cracked although the amount of cracking varied. Upon cracking, the deck continued to provide
some restraint to the girder. Post-cracking, all of the gain in the prestressing force was not lost and
nearly half of the gain was retained. It seems reasonable to use 50% of the gain due to differential
shrinkage, in the overall prestress loss calculations.

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Acknowledgements
I am extremely grateful and thankful for the active and constant support of Dr. Richard Miller,
my advisor, and Dr. Gian Rassati. They have been a constant source of inspiration, motivation
and guided me at every stage of this thesis work. I am also very grateful for the support rendered
by Dr. Thomas Burns.
I am very thankful to my family members for their continuous love and support throughout my
life.

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Table of Contents
Chapter 1. Introduction ................................................................................................................... 1
1.1 Concept of Precast Girder Bridge...................................................................................... 1
1.2 Construction sequence of a PC girder bridge .................................................................... 2
1.3 Differential Shrinkage and its Relevance .......................................................................... 3
1.4 Motivation for the research ............................................................................................... 3
Chapter 2. Background and Literature Review............................................................................... 5
2. 1 NCHRP Report 496 .......................................................................................................... 5
2.1.1 Factors Influencing Creep and Shrinkage .............................................................. 7
2.1.2 Prestress Loss Calculation Methods ...................................................................... 7
2.1.2.1 Time-Step Method ......................................................................................... 7
2.1.2.2 Refined Methods............................................................................................ 8
2.1.2.3 Lump-Sum Methods ...................................................................................... 8
2.1.3 Research Results .................................................................................................... 9
2.1.3.1 Proposed Shrinkage Formula ......................................................................... 9
2.1.3.2 Proposed Creep Formula ............................................................................... 9
2.1.3.3 Detailed Method .......................................................................................... 10
2.1.3.4 Approximate Method ................................................................................... 10
2.2 AASHTO-LRFD Bridge Design Specifications Code: Prestress loss methods (2010
Revised Edition) .................................................................................................................... 11
2.2.1 Approximate Estimate of Time-Dependent Losses Method ................................ 12
2.2.2 Refined Estimates of Time-Dependent Losses Method ....................................... 13
2.3 Previous Research done at UC ........................................................................................ 19
2.3.1 ‘Simulation of the Long-Term behavior of Precast/Prestressed Concrete Bridges’
Stephen (2006) .............................................................................................................. 19

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2.3.2 ‘Simulation of the effect of deck cracking due to creep and shrinkage in a single
span precast/prestressed concrete bridges’ Kasera (2014)............................................ 20
2.4 FHWA Study on High Performance Concrete in Washington State SR18/SR516
Overcrossing (Barr et al.2000) .............................................................................................. 23
Chapter 3: Finite Element Modeling............................................................................................. 24
3.1 Introduction ..................................................................................................................... 24
3.2 Units ................................................................................................................................ 25
3.3 Geometry ......................................................................................................................... 25
3.4 Part Partitioning ............................................................................................................... 25
3.5 Meshing ........................................................................................................................... 25
3.6 Material Properties .......................................................................................................... 29
3.6.1 Steel...................................................................................................................... 29
3.6.2 Concrete ............................................................................................................... 30
3.6.3 Concrete damaged Plasticity ................................................................................ 32
3.7 Assembly ......................................................................................................................... 35
3.8 Sections............................................................................................................................ 37
3.9 Defining Steps ................................................................................................................. 37
3.10 Loadings: ....................................................................................................................... 38
3.10.1 Prestress Load .................................................................................................... 38
3.10.2 Dead Load .......................................................................................................... 39
3.10.3 Creep and Shrinkage .......................................................................................... 39
3.10.3.1 ACI-209 Report (ACI Committee 209 – Creep and Shrinkage, 2008) ..... 40
3.11 Field Output Request ..................................................................................................... 42
3.12 Job.................................................................................................................................. 43
3.13 Visualization .................................................................................................................. 43
Chapter 4: Analysis Approach ...................................................................................................... 45

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4.1 Newton-Raphson Method (Abaqus 6.12 documentation) ............................................... 46
Chapter 5: Results and Discussion ................................................................................................ 50
5.1 Category 1: Deck cracking most likely ........................................................................... 52
5.1.1 Displacement plots for 85-ft, 95-ft and 120-ft girders for a girder age of 90-days
....................................................................................................................................... 52
5.1.2 Prestress plots for 85-ft, 95-ft and 120-ft girders for a girder age of 90-days ..... 54
5.1.3 Combined displacement and prestress plots for a girder age of 90-days ............. 56
5.1.4 Deck cracking pattern for a girder age of 90-days ............................................... 58
5.2 Category 2: Deck cracking least likely ............................................................................ 60
5.2.1 Displacement plots for 85-ft, 95-ft and 120-ft girders ........................................ 60
5.2.2 Prestress plots for 85-ft,95-ft and 120-ft girders for a girder age of 90-days ...... 63
5.2.3 Combined prestress and displacement plots for a girder age of 90-days ............. 65
5.2.4 Deck cracking pattern for 85-ft, 95-ft and 120-ft girders .................................... 67
5.3 Time of Deck Placement and Prestressing Force ............................................................ 69
5.3.1 Category 1: Deck Cracking most likely for 95-ft girder ...................................... 69
5.3.2 Category 2: Deck Cracking least likely for 95-ft girder ...................................... 73
5.3.3 Category 1: Deck cracking most likely for 120-ft girder ..................................... 74
5.3.4 Category 2: Deck cracking least likely for 120-ft girder ..................................... 77
5.3.5 Category 1: Deck cracking most likely for the 85-ft girder ................................. 80
5.3.6 Category 2: Deck cracking least likely for 85-ft girder ....................................... 83
5.3.7 Tabular summary of girder-age at which deck starts to crack and the time duration
between the slab casting and the start of cracking in the slab. ..................................... 86
5.4 Plot showing cambers of different girders ages for category 1 and 2 ............................. 89
Chapter 6: Conclusion and Future Research: ................................................................................ 94
6.1 Conclusion ....................................................................................................................... 94
6.2 Future Research: .............................................................................................................. 96

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References ..................................................................................................................................... 97
Appendix A: Results for Category 3 (Intermediate cases) ........................................................... 99
Appendix B: Comparison between Abaqus Analysis and AASHTO Refined Method .............. 104
Appendix C: CDP Parameters .................................................................................................... 106
C.1 Yield Surface ................................................................................................................ 106
C.2 Stress Invariants ............................................................................................................ 106
Appendix D : FORTRAN subroutine ......................................................................................... 108

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List of Figures
Figure 2 Elastic shortening………………………………………………………………………...2
Figure 2.1: Prestress Losses ............................................................................................................ 5
Figure 2.2 :Displacement of girder top flange at different times of deck cast (Kasera 2014) ...... 21
Figure 2.3: Variation of prestress with time for decks placed at different girder ages (Kasera 2014)
....................................................................................................................................................... 22
Figure 3.1: ABAQUS CAE main window (Abaqus documentation 6.13, Hibbitt et al) .............. 24
Figure 3.2: Mesh elements used in the model............................................................................... 26
Figure 3.3: 2D sketch of girder and deck (BT-63 girder) ............................................................. 27
Figure 3.4 3D view of BT-63 girder and deck .............................................................................. 28
Figure 3.5: Reinforcement/ Prestressing strand ............................................................................ 29
Figure 3.6: Concrete uniaxial tensile behavior (Hibbitt et. al 2012) ............................................ 33
Figure 3.7: Concrete uniaxial compressive behavior (Hibbitt et. al 2012) ................................... 34
Figure 3.8: Reinforcement in the slab and BT-63 girder .............................................................. 35
Figure 3.9: BT-63 girder and deck mesh ...................................................................................... 36
Figure 3.10: 3D view of girder and deck mesh ............................................................................. 36
Figure 5.2: Category 1 Prestress plots .......................................................................................... 55
Figure 5.3: Category 1 Prestress and displacement plots ............................................................. 57
Figure 5.4: Category 1 Cracking in the deck for 85-ft girder ....................................................... 58
Figure 5.5: Category 1 Cracking in the deck for 95-ft girder ....................................................... 59
Figure 5.6: Category 1 Cracking in the deck for 120-ft girder ..................................................... 59
Figure 5.7: Category 2 Displacement plots for 85-ft girder for girder ages of 90 and 120-days . 60
Figure 5.8 a : Category 2 Displacement plot, 95-ft girder ............................................................ 61
Figure 5.8 b: Category 2 Displacement plot, 120-ft girder ........................................................... 62
Figure 5.9: Category 2 Prestress plots .......................................................................................... 64
Figure 5.10: Category 2-Displacement and prestress plots .......................................................... 66
Figure 5.11: Category 2 -Deck cracking in 85-ft, 95-ft and 120-ft girder respectively ................ 68
Figure 5.13: Category 1- Deck cracking for 95-ft girder .............................................................. 70
Figure 5.14: Category 1- Displacement and prestress plot for 95-ft girder .................................. 71
Figure 5.15: Category 2-Variation of the prestress force with different girder ages at the time of
deck cast for 95-ft girder ............................................................................................................... 73

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