LINEAR AND NONLINEAR FINITE ELEMENT ANALYSES OF

426 Pages·2004·3.56 MB·English

LINEAR AND NONLINEAR FINITE ELEMENT ANALYSES OF
ANCHORAGE ZONES IN POST-TENSIONED CONCRETE STRUCTURES
By
Songwut Hengprathanee
A DISSERTATION SUBMITTED TO THE FACULTY OF
VIRGINIA POLYTECHNIC INSTITUTE AND STATE UNIVERSITY
IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY
IN
CIVIL ENGINEERING
Carin L. Roberts-Wollmann, Chair
Thomas E. Cousins
Raymond H. Plaut
Gregor P. Wollmann
Donatus C. Ohanehi
September, 2004
Blacksburg, Virginia
Keywords: Prestressed concrete, Anchorage zones, Post-tensioned, Finite element analysis
Copyright 2004, Songwut Hengprathanee
L A N F E A O
INEAR ND ONLINEAR INITE LEMENT NALYSES F
A Z I P -T C S
NCHORAGE ONES N OST ENSIONED ONCRETE TRUCTURES
By
Songwut Hengprathanee
Committee Chair: Carin L. Roberts_Wollmann
Civil and Environmental Engineering
(ABSTRACT)
Linear and nonlinear finite element analyses are used for the investigation of rectangular
anchorage zones with the presence of a support reaction. The investigation is conducted
based on four load configurations consisting of concentric, inclined concentric, eccentric, and
inclined eccentric loads. The method of model construction is illustrated thoroughly. The
influence of several parameters, including anchorage ratio, inclination of prestressing load,
eccentricity, magnitude of the reaction force, bearing plate ratio, and the location of the
reaction force, is studied. Both graphical and numerical presentations of the results from
each load configuration are given. Improved equations, which are modified from the
equations presented in the AASHTO Standard Specifications (2002), are proposed. The
results from the equations are compared to those from the finite element method. Nonlinear
finite element analysis is used to verify the applicability of the equations and to study a new
bursting steel arrangement.
Linear and nonlinear finite element analyses are also used for the study of non-rectangular
anchorage zones. Four basic load configurations, including concentric, eccentric, inclined
concentric, and inclined eccentric loads, are investigated. The shell element is selected for
the construction of the finite element models. Several parameters, consisting of anchorage
ratio, inclination of prestressing load, eccentricity, web thickness, ratio of web thickness to
flange thickness, and flange width, are chosen for parametric studies. The results from the
studies are presented graphically and numerically. Equations to calculate the bursting force
and location of the force are developed from the Strut-and-Tie Model approach. The
verification of the formulations and the investigation of bursting steel arrangement are
conducted using nonlinear finite element analysis.
ACKNOWLEDGEMENTS
It is my deepest appreciation that I would like to express for the generosity, support, and
continuing guidance of my advisor, Dr. Carin L. Roberts-Wollmann, during the last four
years of my study at Virginia Tech. Her patience and encouragement have led me through
the hard time of my study, which will never be forgotten. I also would like to extend my
appreciation to Dr. Gregor P. Wollmann for his valuable advice and comments during the
course of my study. I want to sincerely thank all my other dissertation committee members,
Dr. Thomas E. Cousins, Dr. Raymond H. Plaut, and Dr. Donatus C. Ohanehi, for serving on
my Doctoral committee.
I am indebted and wish to express my gratitude to Dr. Pornsak Pudhaphongsiriporn, who
brought me to the educational world of structural engineering and also gave me the
opportunity to study for my Master’s and Doctoral degrees. Without his support, this present
dissertation would never exist.
I wish to express my great thankfulness to Mr. Prakasit Manirojana, whom I respect as my
brother, for his support and encouragement during my graduate study in the United States.
His suggestions have successfully brought me through the hard decisions that I have made. I
also wish to acknowledge my friends, Veerachai Kasuwan, Arichai Lalitkulanant,
Pattharawut Khamchoo, Yodmanee Tepanon, Dr. Surachet Kanprachar, and many others, for
their plentiful friendship.
Finally, I wish to express my forever gratefulness to my mother and father, who always
make me proud of being their son for every single breath of my life. Their unmeasured and
unquestionable love always gives me the courage to overcome obstacles. I also wish to
gratefully thank my older brother, Songchai, for his sacrifice that bought me a chance to
come to study in the United States, and my two younger brothers, Songphol and Songsak, for
helping me with everything else during the period of my study. I also would like to give my
thanks for all other members of my family for their love, support, and encouragement.
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T C
ABLE OF ONTENTS
L T xi
IST OF ABLES………………………………………………………………………...
L F xiv
IST OF IGURES……………………………………………………………………..
C 1 – I 1
HAPTER NTRODUCTION……………………………………………………….
1.1. Anchorage Zones in Prestressed Concrete Structures………………………………..1
1.2. Prestressed Concrete Structures………………………………………………………2
1.2.1. Development of the Technology………………………………………………2
1.2.2. Basic Concepts………………………………………………………………...3
1.3. Anchorage Zone Design……………………………………………………………...6
1.3.1. Previous Anchorage Zone Design…………………………………………….6
1.3.2. Current Anchorage Zone Design Presented in AASHTO…………………….8
1.3.2.1.Strut-And-Tie Model (STM)……………………………………………..11
1.3.2.2.Approximate Stress Analysis and Design………………………………..12
1.4. Literature Reviews…………………………………………………………………..15
1.4.1. Anchorage Zones…………………………………………………………….15
1.4.1.1.Morsch (1924) and Guyon (1953)……………………………………….15
1.4.1.2.Yettram and Robbins (1969, 1970, and 1971)…………………………...17
1.4.1.3.NCHRP Project 10-29 (1994)……………………………………………17
1.4.1.4.Roberts (1990)…………………………………………………………...18
1.4.1.5.Burdet (1990)…………………………………………………………….19
1.4.1.6.Sanders (1990)…………………………………………………………...22
1.4.1.7.Wollmann (1992)………………………………………………………...23
1.4.2. Nonlinear Finite Element Analysis of Reinforced Concrete Structures……..25
1.4.2.1.Ngo and Scordelis (1967)………………………………………………..25
1.4.2.2.Adeghe and Collins (1986)………………………………………………26
1.4.2.3.Al-Manaseer and Phillips (1987)………………………………………...26
1.4.2.4.Foster (1992)……………………………………………………………..29
1.4.2.5.Foster, Budiono, and Gilbert (1996)……………………………………..32
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1.4.2.6.Foster and Rogowsky (1996, 1997)……………………………………...34
1.4.3. Other Works Using DIANA………………………………………………….36
1.4.3.1.Johansson (2000)………………………………………………………...36
1.4.3.2.Tabatabai and Mosalam (2000)………………………………………….37
1.4.3.3.Lundgren and Magnusson (2001)………………………………………..37
1.4.3.4.Kwan and Billington (2001)……………………………………………..38
1.5. DIANA……………………………………………………………………………...38
1.5.1. Material Constitutive Models………………………………………………..39
1.5.1.1.Cracking andCrushing…………………………………………………...39
1.5.1.2.Yielding of Reinforcing Steel……………………………………………40
1.5.2. Element Types………………………………………………………………..40
1.5.2.1.Concrete Element………………………………………………………...41
1.5.2.2.Embedded Steel Element………………………………………………...41
1.5.2.3.Steel Bearing Plate Element……………………………………………...42
1.5.2.4.Spring Connector Element……………………………………………….42
1.6. Objectives and Scope of this Study…………………………………………………42
1.6.1. Objectives……………………………………………………………………42
1.6.2. Scope…………………………………………………………………………43
C 2 – P S U N FEA 44
HAPTER RELIMINARY TUDIES SING ONLINEAR ……...
2.1. Study Compared to Foster and Rogowsky’s Research……………………………...44
2.2. Study Compared to Sander’s Experimental Work…………………………………..48
C 3 – R S P S
HAPTER ECTANGULAR ECTIONS WITH RESENCE OF UPPORT
R 52
EACTIONS……………………………………………………………………………...
3.1. Introduction………………………………………………………………………….52
3.1.1. Objectives…………………………………………………………………….52
3.1.2. Scope…………………………………………………………………………53
3.2. Preparation of Work………………………………………………………………...54
3.2.1. Selection of the Model……………………………………………………….54
3.2.2. Convergence Test…………………………………………………………….55
3.2.3. Location of Vertical Boundary Support……………………………………...57
3.2.4. Location of Main Compressive Strut Line…………………………………...59
v
3.3. Parameters…………………………………………………………………………...64
3.3.1. Anchorage Ratio (a/h)………………………………………………………..64
3.3.2. Inclination Angle of Prestressing Force (α)………………………………….65
3.3.3. Eccentricity (e)……………………………………………………………….66
3.3.4. Magnitude of Reaction Force (R)…………………………………………….67
3.3.5. Bearing Plate Ratio (b/h)…………………………………………………….68
3.3.6. Location of Support Reaction (l)…………………………………………….68
3.3.7. Summary……………………………………………………………………..69
3.4. Load Configurations………………………………………………………………...69
3.4.1. Concentrically Loaded Anchor Configuration……………………………….70
3.4.1.1.Elastic Stress Distribution………………………………………………..70
3.4.1.2.Bursting Force……………………………………………………………74
3.4.1.3.Location of Bursting Force………………………………………………84
3.4.2. Inclined Concentrically Loaded Anchor Configuration……………………..93
3.4.2.1.Elastic Stress Distribution………………………………………………..93
3.4.2.2.Bursting Force……………………………………………………………98
3.4.2.3.Location of Bursting Force……………………………………………..114
3.4.3. Eccentrically Loaded Anchor Configuration……………………………….130
3.4.3.1.Elastic Stress Distribution………………………………………………132
3.4.3.2.Bursting Force…………………………………………………………..136
3.4.3.3.Location of Bursting Force……………………………………………..142
3.4.4. Inclined Eccentrically Loaded Anchor Configuration……………………...146
3.4.4.1.Elastic Stress Distribution………………………………………………147
3.4.4.2.Bursting Force…………………………………………………………..150
3.4.4.3.Location of Bursting Force……………………………………………..162
3.5. Examples Using Nonlinear Analysis………………………………………………170
3.5.1. Example Based on Wollmann’s Experimental Specimen………………….171
3.5.1.1.Problem Illustration…………………………………………………….171
3.5.1.2.Nonlinear Analysis Result……………………………………………...172
3.5.2. Example Based on Precast Beam with Multi-Strand Tendon in PTIManual……175
3.5.2.1.Problem Illustration…………………………………………………….175
3.5.2.2.Design of Bursting Reinforcement……………………………………..176
vi
3.5.2.2.1. Design Using Approximate Equations Addressed in the AASHTO…..176
3.5.2.2.2. Design Using Strut-and-Tie Model Method………………………..178
3.5.2.2.3. Design Using New Approximate Equations………………………..185
3.5.2.3.Nonlinear Analysis Result………………………………………………186
3.5.2.4.Nonlinear Analysis to Investigate the Reinforcement Arrangement…...189
3.5.3. Summary……………………………………………………………………191
3.6. Discussions And Recommendations……………………………………………….192
3.6.1. Design Recommendations………………………………………………….192
3.6.2. Detailing Recommendations………………………………………………..193
C 4 – N -R S 194
HAPTER ON ECTANGULAR ECTIONS…………………………….
4.1. Introduction………………………………………………………………………...194
4.1.1. Objectives…………………………………………………………………..195
4.1.2. Scope………………………………………………………………………..195
4.2. Preparation of Work……………………………………………………………….196
4.2.1. Selection of Non-Rectangular Sections…………………………………….196
4.2.2. Model Construction………………………………………………………....199
4.2.3. Comparison of the Models………………………………………………….201
4.3. Parameters………………………………………………………………………….206
4.3.1. Anchorage Ratio (a/h )……………………………………………………..206
w
4.3.2. Inclination Angle of Prestressing Force (α)………………………………..206
4.3.3. Eccentricity (e)…………………………………………………………….. 207
4.3.4. Web Thickness (t )…………………………………………………………207
w
4.3.5. Thickness Ratio of Flange and Web (t/t )………………………………….207
f w
4.3.6. Flange Width (b)……………………………………………………………208
f
4.3.7. Other Parameters……………………………………………………………208
4.3.8. Summary……………………………………………………………………208
4.4. Load Configurations……………………………………………………………….209
4.4.1. Concentrically Loaded Anchor Configuration…………………………….. 209
4.4.1.1.Finite Element Results………………………………………………….209
4.4.1.1.1. Elastic Stress Distribution……………………………………...209
4.4.1.1.2. Bursting Force………………………………………………….219
4.4.1.1.2.1.Symmetrical I-Section………………………………………219
vii
4.4.1.1.2.2.T-Section……………………………………………………227
4.4.1.1.2.3.Unsymmetrical I-Section……………………………………231
4.4.1.1.3. Location of Bursting Force……………………………………..234
4.4.1.1.3.1.Symmetrical I-Section………………………………………234
4.4.1.1.3.2.T-Section……………………………………………………242
4.4.1.1.3.3.Unsymmetrical I-Section……………………………………246
4.4.1.2.Formulations……………………………………………………………248
4.4.1.2.1. Symmetrical I-Section…………………………………………..251
4.4.1.2.2. T-Section………………………………………………………..264
4.4.1.2.3. Unsymmetrical I-Section………………………………………. 271
4.4.2. Eccentrically Loaded Anchor Configuration……………………………….276
4.4.2.1.Finite Element Results………………………………………………….276
4.4.2.1.1. Elastic Stress Distribution……………………………………...276
4.4.2.1.2. Bursting Force………………………………………………….282
4.4.2.1.2.1.Symmetrical I-Section……………………………………....282
4.4.2.1.2.2.T-Section……………………………………………………284
4.4.2.1.2.3.Unsymmetrical I-Section……………………………………286
4.4.2.1.3. Location of Bursting Force……………………………………..287
4.4.2.1.3.1.Symmetrical I-Section………………………………………287
4.4.2.1.3.2.T-Section……………………………………………………289
4.4.2.1.3.3.Unsymmetrical I-Section……………………………………291
4.4.2.2.Formulations……………………………………………………………292
4.4.3. Inclined And Inclined Eccentrically Loaded Anchor Configurations……...301
4.4.3.1.Finite Element Results………………………………………………….301
4.4.3.1.1. Elastic Stress Distribution……………………………………...301
4.4.3.1.2. Bursting Force………………………………………………….307
4.4.3.1.3. Location of Bursting Force……………………………………..310
4.4.3.2.Formulations……………………………………………………………312
4.5. Examples Using Nonlinear Analysis………………………………………………323
4.5.1. Example Based on Sanders’ Experimental Specimen………………………323
4.5.1.1.Problem Illustration……………………………………………………..323
4.5.1.2.Nonlinear Analysis Result………………………………………………327
viii
4.5.2. Example Based on Box Girder Bridge with Internal Tendons Presented in PTI
Manual………………………………………………………………………...335
4.5.2.1.Problem Illustration…………………………………………………….336
4.5.2.2.Design of Bursting Reinforcement……………………………………..336
4.5.2.3.Nonlinear Analysis Result………………………………………………347
4.5.3. Summary……………………………………………………………………357
4.6. Discussions and Recommendations………………………………………………..358
4.6.1. Design Recommendations………………………………………………….359
4.6.1.1.Design Using Strut-and-Tie Model Method……………………………359
4.6.1.2.Design Using Approximate Equations………………………………….362
4.6.2. Detailing Recommendations………………………………………………..362
C 5 – M R AASHTO 364
HAPTER ODIFIED ECOMMENDATIONS TO ……….
5.1. Design Recommendations for Rectangular Sections ……………………………...364
5.2. Design Recommendations for Non-Rectangular Sections ………………………...366
5.2.1. Design Recommendations of the Web…………………………………….. 367
5.2.2. Design Recommendations of the Flange…………………………………...369
5.2.3. Design Recommendations Using the Strut-and-Tie Model Method………. 370
C 6 – C 372
HAPTER ONCLUSIONS…………………………………………………….
6.1. General Conclusions……………………………………………………………….372
6.1.1. Design of Rectangular Anchorage Zones with the Presence of a Support
Reaction……………………………………………………………………….373
6.1.2. Design of Non-Rectangular Anchorage Zones……………………………..374
6.2. Recommendations for Further Research…………………………………………..375
6.2.1. Experimental Research for Rectangular Anchorage Zone with a Support
Reaction……………………………………………………………………….375
6.2.2. Non-Rectangular Anchorage Zones………………………………………...376
R 377
EFERENCES………………………………………………………………………….
A A – G E 382
PPENDIX ENERAL XPRESSIONS…………………………………….
A.1.Centroid of Compressive Stress Diagram………………………………………….382
ix
A.2.Kern of Non-Rectangular Sections……………………………………………….. 383
A.3.Centroid of the Resultant Force……………………………………………………385
A B – T R 387
PPENDIX ABLES OF ESULTS………………………………………….
B.1.Comparison ofT on Horizontal and Inclined Strut Line……………………… 387
burst
A C –T S W 390
PPENDIX ENSILE TRESSES IN EB………………………………….
C.1.Tensile Stresses in the Web of Symmetrical I-Sections …………………………..390
A D – D E N -R
PPENDIX ESIGN XAMPLES OF ON ECTANGULAR
A Z 391
NCHORAGE ONES……………………………………………………………….
D.1.Section with the Thickest Flange…………………………………………………. 391
D.2.Section with the Thinnest Web…………………………………………………… 394
D.3.Section with the Widest Flange……………………………………………………396
V 399
ITA……………………………………………………………………………………..
x