135640720 FB MultiPier Help Manual

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Table of Contents

FB MultiPier 17

What’s New in FB-MultiPier? 17

Program Menus 19

View Menu ..................................................................................................... 19 Control Menu ................................................................................................. 20 Wizard Menu.................................................................................................. 20 Help Menu ..................................................................................................... 21

Model Data 21

Global Data Edit ............................................................................................ 21 New Project/Problem Tab ....................................................................... 21

General Pier Option.......................................................................... 23 Pile and Cap Option ......................................................................... 23 Single Pile Option ............................................................................. 24 High Mast Light/Sign Option............................................................. 25 Retaining Wall Option....................................................................... 26 Sound Wall Option............................................................................ 27 Stiffness Option ................................................................................ 28 Pile Bent Option................................................................................ 29 Column Analysis Option ................................................................... 30 Bridge (Multiple Piers) Option .......................................................... 31

Analysis Tab............................................................................................ 32 Analysis Tab ..................................................................................... 32 Pile/Pier Behavior ............................................................................. 34 Cap Behavior .................................................................................... 34 Section Properties ............................................................................ 35 Soil Behavior .................................................................................... 35 Iteration Control ................................................................................ 35 Interaction Diagram Phi Factor......................................................... 36 Analysis Type ................................................................................... 36 Design Options ................................................................................. 37 Print Control...................................................................................... 37

AASHTO Tab .......................................................................................... 38 AASHTO Tab.................................................................................... 38 AASHTO Load Factors Table........................................................... 39 Automated AASHTO Loads.............................................................. 40 AASHTO Load Manager................................................................... 41 Wind Load Generator ....................................................................... 42 AASHTO Load Combination Preview Table..................................... 43 Limit States to Check........................................................................ 44

Dynamics Tab ......................................................................................... 45 Dynamics Tab................................................................................... 45 Analysis Type Dynamic .................................................................... 47 Global Mass...................................................................................... 47 Global Damping................................................................................ 47 Time Stepping Parameters............................................................... 48 Rayleigh Damping Factors ............................................................... 48 Model Analysis Damping .................................................................. 49 Time Functions ................................................................................. 49

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Edit Load Functions.......................................................................... 49 Load Function Edit Table.................................................................. 51

Pushover Tab.......................................................................................... 52 Pushover Tab ................................................................................... 52

Pier Data Edit................................................................................................. 53 Pile and Cap Tab .................................................................................... 53

Pile and Cap Tab.............................................................................. 53 Pile Length Data ............................................................................... 54 Pile Cross Section Type ................................................................... 55 Pile/Shaft Type ................................................................................. 56 Pile to Cap Connection..................................................................... 56 Pile Cap Data ................................................................................... 57 Pile Cap Grid Geometry ................................................................... 57 Grid Spacing Table........................................................................... 58 Edit Cross Section ............................................................................ 59

Gross Section Pile Properties ............................................................................................................59 Gross Pile Properties .....................................................................................................................59 Pile/Shaft Segment List..................................................................................................................60 Pile Set Info....................................................................................................................................61 Database Section Selection ...........................................................................................................61 Section Type ..................................................................................................................................62 Segment Dimensions .....................................................................................................................63 Section Properties..........................................................................................................................63

Full Cross Section Pile Properties......................................................................................................64 Full Cross-Section Pile Properties..................................................................................................64 Detailed Cross Section...................................................................................................................65 Section Dimensions .......................................................................................................................66 Section Type ..................................................................................................................................67

Section Type ..............................................................................................................................67 Circular Section Properties ........................................................................................................67

Circular Section Properties.....................................................................................................67 Edit Bar Groups......................................................................................................................69 Group Data.............................................................................................................................70

Confined Concrete Option..................................................................................................71 Shear Reinforcement .............................................................................................................73 Miscellaneous ........................................................................................................................73 Confined Concrete Model ......................................................................................................73

Mander Models for Confined Concrete...............................................................................74 Unconfined Concrete .........................................................................................................82

Reinforcement......................................................................................... 83 Longitudinal Reinforcement................................................................................................84

Transverse Reinforcement...................................................................... 87 Steel Jacket............................................................................................. 87 Full-Scale Column without Steel Casing................................................. 88 Half Scale Column With Steel Retrofitting Jacket................................... 90 Conclusions............................................................................................. 91

Rectangular Section Properties .................................................................................................92 Rectangular Section Properties..............................................................................................92 Void Data ...............................................................................................................................94 H-Pile Properties ....................................................................................................................95

H-Pile Properties ................................................................................................................95 Section Dimensions ...........................................................................................................95 Section Orientation.............................................................................................................96

H-Pile Properties ........................................................................................................................96 Pipe Pile Properties....................................................................................................................96

Pipe Pile Properties................................................................................................................96 Material Properties .........................................................................................................................96

Material Properties .....................................................................................................................96 Default Stress/Strain Curves......................................................................................................96 Custom Stress/Strain .................................................................................................................97

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Section Stress-Strain Plot ..........................................................................................................98 Soil Tab ................................................................................................... 99

Soil Tab............................................................................................. 99 Soil Layer Data ............................................................................... 101 Elevations ....................................................................................... 102 Soil Table........................................................................................ 102 Soil Layer Models ........................................................................... 104

Soil Layer Models.............................................................................................................................104 Soil Dynamics Dialog .......................................................................................................................108 Soil Model Plot .................................................................................................................................108 Printable Soil Graph.........................................................................................................................110 Advanced Soil Data..........................................................................................................................112

Soil Strength Criteria ...................................................................... 113 Soil Strength Criteria ........................................................................................................................113 SPT Window ....................................................................................................................................114

Pier Tab................................................................................................. 115 Pier Tab .......................................................................................... 115 Taper Data...................................................................................... 116 Pier Geometry ................................................................................ 117

Pier Geometry..................................................................................................................................117 Pier Rotation Angle ..........................................................................................................................119 Bearing Locations ............................................................................................................................120 Bearing Angle ..................................................................................................................................121

Pier Cross Section Type................................................................. 122 Pier Cross Section Type ..................................................................................................................122 Gross Section Pier Properties..........................................................................................................122

Gross Pier Component Properties ...............................................................................................122 Pier Components .........................................................................................................................123 Database Section Selection .........................................................................................................124 Section Data.................................................................................................................................125 Section Properties........................................................................................................................126 Parabolic Taper Cantilever Properties .........................................................................................126

Full Cross Section Pier Properties ...................................................................................................127 Full Pier Component Properties ...................................................................................................127 Section Dimensions .....................................................................................................................128 Section Type ................................................................................................................................130

Section Type ............................................................................................................................130 Circular Section Properties ......................................................................................................130

H-Pile Properties ..................................................................................................................130 Rectangular Section Properties ...............................................................................................130

H-Pile Properties ..................................................................................................................130 H-Pile Properties ......................................................................................................................130 Bullet Section Properties..........................................................................................................130

Bullet Section Properties......................................................................................................130 Group Data...........................................................................................................................131 Void Data .............................................................................................................................132 Cross Section Orientation ....................................................................................................132

Material Properties .......................................................................................................................133 Bent Cap ............................................................................................... 133

2D Bridge View............................................................................... 133 Wall Structure........................................................................................ 133

Sound Wall Explanation ................................................................. 133 Extra Members Tab............................................................................... 134

X-Members Tab.............................................................................. 134 Extra Members List......................................................................... 135 Extra Member Sections .................................................................. 135 Nodes Attached .............................................................................. 136

Load Tab ............................................................................................... 136 Load Tab......................................................................................... 136

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Load Case ...................................................................................... 139 Buoyancy .............................................................................................. 140

Node Applied .................................................................................. 140 Loads .............................................................................................. 140

Bearing Location Loads ........................................................................ 141 Load Table...................................................................................... 142

Load Table .......................................................................................................................................142 Dynamic Loads ............................................................................................................................142

Table Format....................................................................................................................................144 Table Edit Options............................................................................................................................144 Load Case Options ..........................................................................................................................144

AASHTO Load Table...................................................................... 145 AASHTO Load Table .......................................................................................................................145 AASHTO Table Format ....................................................................................................................146 AASHTO Table Edit Options............................................................................................................146 AASHTO Load Case Options...........................................................................................................147

Spring Tab............................................................................................. 147 Spring Tab ...................................................................................... 147 Spring Stiffness .............................................................................. 148 Spring Nodes.................................................................................. 148

Discrete Mass/Damper Tab .................................................................. 149 Mass/Damper Tab .......................................................................... 149 Mass/Dampers in 3D View ............................................................. 149

Retaining Tab........................................................................................ 151 Retaining Tab ................................................................................. 151 Soil Layer........................................................................................ 152 Wall and Layer Geometry............................................................... 152 Retaining Wall Explanation............................................................. 153 Soil Layer Data ............................................................................... 154

Soil Layer Data ................................................................................................................................154 Retaining Wall Soil Layer Data ........................................................................................................155

Wall Load Data ............................................................................... 155 Wall Load Data ................................................................................................................................155 Surcharge ........................................................................................................................................155

Bridge Data Edit .......................................................................................... 156 Bridge Tab............................................................................................. 156

Bridge Tab ...................................................................................... 156 Edit Supports .................................................................................. 158 Edit Custom Bearings..................................................................... 159 Edit Span ........................................................................................ 160 Add Substructure............................................................................ 163 Span End Condition........................................................................ 164

Model View Windows 165

Soil Edit Window.......................................................................................... 165 Soil Edit Window ................................................................................... 165

Pile Edit Window.......................................................................................... 166 Pile Edit Window ................................................................................... 166

Zoom Feature Tutorial .................................................................... 168 Pile Data................................................................................................ 168 Edit Cap Thickness ............................................................................... 169 Custom Grid Spacing ............................................................................ 169

Bridge Plan View Window ........................................................................... 170 3D View Window ......................................................................................... 170

3D View Window................................................................................... 170 Element Data Dialog ............................................................................. 173

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Program Results 174

Pile Results.................................................................................................. 174 Pile Results ........................................................................................... 174 Pile Selection ........................................................................................ 174 Plot Display Control............................................................................... 175 Graphs .................................................................................................. 176 Printable Forces Dialog......................................................................... 177

Pier Results ................................................................................................. 179 Pier Results........................................................................................... 179 Pier Selection ........................................................................................ 179 Graphs .................................................................................................. 180 Printable Forces Dialog......................................................................... 180 Pier Cross Section Table ...................................................................... 182

Pile Interaction ............................................................................................. 185 Interaction Diagrams............................................................................. 185 Pile Selection ........................................................................................ 185 Pile Segment Selection......................................................................... 186 Pile Element Selection .......................................................................... 187 Interaction Diagram............................................................................... 188

Pier Interaction ............................................................................................ 189 Pier Selection ........................................................................................ 189 Pier Segment Selection ........................................................................ 190 Pier Element Selection.......................................................................... 191

3D Results ................................................................................................... 192 3D Results............................................................................................. 192 3D Results Window............................................................................... 193 3D Results Dynamic Options ................................................................ 196 Result Forces Dialog............................................................................. 197 3D Display Control ................................................................................ 198

3D Display Control.......................................................................... 198 Display Control ............................................................................... 200 Node Information ............................................................................ 202 Max Min Forces Dialog................................................................... 202

XML Report Generator ................................................................................ 203 XML Report Generator.......................................................................... 203

Results Viewer............................................................................................. 205 Results Viewer ...................................................................................... 205

General Modeling 206

Column Connection to the Pile Cap ............................................................ 206 Taper Modeling............................................................................................ 207 Bridge Span Overview................................................................................. 210 Node Numbering ......................................................................................... 213 Span Length Calculation ............................................................................. 214 Preliminary Soil Values................................................................................ 216

Bridge Span Modeling 216

Deck Modeling ............................................................................................. 216 Transfer Beam Properties ........................................................................... 219 Rigid Link Properties ................................................................................... 220 Bearing Pad Properties ............................................................................... 221 Bridge Span Dead Load .............................................................................. 224 Transfer Beam............................................................................................. 229 Wind Generator ........................................................................................... 232 Bridge Span Element Numbering................................................................ 234

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Setup Options 235

Expanding Memory...................................................................................... 235 The FB-MultiPier Engine can be adjusted to allow larger pile system solutions. If the problem is to large for the current settings the engine will generate a error message like: ........................................................................................................ 235 Not enough Memory.............................................................................. 235 You can correct this from the Program Settings Dialog in the control menu in the interface as mentioned above............................................................... 235

Program Settings......................................................................................... 235

FB-Pier License Installation 236

License File.................................................................................................. 236 FB-MultiPier operates using a license file to determine its status. All shipped versions run in Demo mode as the default. The program can be "unlocked" into various modes including full version and student version, networked or stand-alone. This unlocking can be done by hand, through phone contact with the Bridge Software Institute ( http://bsi-web.ce.ufl.edu ) or automatically through an internet connection to the BSI web server................................................................................ 237 The program requires a license file to be installed. This license file is linked to the computer on which it is installed. .......................................................... 237 The following describes the modes and processes required:............... 237 E-mail/Fax/Phone License Update ....................................................... 238

FB-MultiPier License Installation Help......................................................... 239 Update a License on a Stand Alone Workstation........................................ 240 Update/Install a License on a Network Server ............................................ 241

License Update Tutorial ........................................................................ 242 Set Client Path for a License File on a Network Server .............................. 242 Transfer License to a Different Computer ................................................... 244

Toolbar Icons 246

DESCRIPTION OF TOOLBAR ICONS ....................................................... 246 General Pier Wizard .................................................................................... 248

Batch Analysis 249

Batch Mode.................................................................................................. 249 Running FBPier_eng in Batch Mode ........................................................... 250

Soil-Pile Interaction 251

Axial Efficiency ...................................................................................... 255 Soil Resistance Due to Pile Rotation........................................................... 255

This option is used for the program to calculate and apply rotational springs to the pile nodes in the ground. These springs are based on the axial resistance of the piles (skin friction) as well as the rotation of the piles. It is particularly important in soil layers where the piles can develop large values of skin friction. ..................................................................................................................................256 Calculation of bending strains ..........................................................................................................256

Soil’s Lateral Resistance P(F/L) Form Bending Moments and Skin Friction........................................................................................................ 256 Moment Due to Side Shear, Ms ..................................................... 257

Soil Properties ............................................................................................. 258 Lateral Soil-Pile Interaction.......................................................................... 265 Figure B17: Reese et al (1975) Static P-Y Curve for Stiff Clay Located Below the Water Table .274

P-Y Resistance for Florida Limestone (McVay).................................... 275 Limestone (McVay no 2 - 3 Rotation) .................................................. 277 Sand (API)............................................................................................. 280 Clay (API) .............................................................................................. 281

Axial Soil-Pile Interaction............................................................................. 281

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Axial Soil-Pile Interaction ...................................................................... 281 Driven Pile Sand (API) .......................................................................... 282 Driven Pile Clay (API) ........................................................................... 282 Axial T-Z Curve for Side Friction........................................................... 283

Axial Skin Friction for Florida Limestone (McVay).......................... 284 Drilled and Cast Insitu Piles/Shafts ................................................ 288

Axial T-Z(Q-Z) Curve for Tip Resistance .............................................. 293 Driven Pile Sand (API)_QZ............................................................. 295 Driven Pile Clay (API)_QZ.............................................................. 295 Drilled and Cast Insitu Piles/Shafts ................................................ 296

Torsional Soil-Pile Interaction...................................................................... 301

Finite Element Theory 303

Finite Element.............................................................................................. 303 Membrane Element ..................................................................................... 304 Plate Element .............................................................................................. 304 Flat Shell Elements...................................................................................... 306 Mindlin Theory ............................................................................................. 307 Special Element for FB-MultiPier................................................................. 309 Mesh Correctness and Convergence.......................................................... 310

The difference in element stresses at a node is an important measure of model correctness. In general, we do not have the exact displacements in order to check our model. Hence, the stress check is necessary to verify convergence of our model. If the difference in stresses between elements is small the finite element mesh is good. ..................................................................................................... 311

Nonlinear Behavior 311

Nonlinear Behavior ...................................................................................... 311 Discrete Element Model .............................................................................. 311

Discrete Element Model ........................................................................ 311 Discrete element model is elaborated in the following sections (use the links): ...........................312

Element Deformation Relations ............................................................ 312 Integration of Stresses .......................................................................... 314 Element End Forces.............................................................................. 317 Element Stiffness .................................................................................. 317

Stress-Strain Curves ................................................................................... 319 Stress-Strain Curves ............................................................................. 319 Concrete................................................................................................ 319 Mild Steel .............................................................................................. 320 High Strength Prestressing Steels ........................................................ 321 Adjustment for Prestressing.................................................................. 322

When piles are prestressed prior to installation, there are stresses and strains existing at the time of installation cue to the prestressing. The program shifts the origin of the stress-strain curve for the steel by the amount of the prestressing stress in the steel and the corresponding steel strain. Also, the program shifts the origin of the concrete stress-strain curve by the amount of compression in the concrete and the corresponding concrete strain. It is assumed that the prestressing is symmetrically placed and thus only a constant compressive stress is developed in the concrete due to the prestressing. ....................................................................................................................................322

Confined Concrete Model............................................................................ 322 Bi-axial Interaction diagram ......................................................................... 322

Assumptions and Features for the Biaxial Interaction Diagram ..... 322 Failure (Demand/Capicity) Ratio for Cross Sections ............................ 326

Nonlinear Solution Strategies ...................................................................... 327 Nonlinear Solution Strategies ............................................................... 327

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Equivalent Stiffness Formulation 329

Equivalent Stiffness Generation .................................................................. 329 Converting FB-MultiPier Coordinates to a Standard Coordinate System ... 331

Engine Input Users Guide 335

Engine Input Overview ................................................................................ 335 Global Headers............................................................................................ 335

Header .................................................................................................. 335 Print Control .......................................................................................... 336 General Control..................................................................................... 337 Multiple Pier Substructure Information.................................................. 340 Superstructure Information ................................................................... 342 User Defined Bearing Connection ........................................................ 346 Self Weight and Buoyancy Load Factors.............................................. 348 Bridge Spring Toggle ............................................................................ 348

Case #1................................................................................................................................348 Case #2................................................................................................................................348 Case #3................................................................................................................................348 Case #n................................................................................................................................348

Pushover ............................................................................................... 349 Combination (AASHTO)........................................................................ 349

COMBINATION .............................................................................. 350 Modify Load Factors.............................................................................. 351 Dynamic Control Parameters................................................................ 353 Dynamic Step by Step Integration ........................................................ 356

T1,F1 T2,F2 T3,F3 T4,F4......................................................................................................357 Spectrum Analysis ................................................................................ 357 Span Concentrated Nodal Loads.......................................................... 360

Pier Specific Headers .................................................................................. 362 Pile Information ..................................................................................... 362

For Nonlinear Analysis of Oblong Piers, used with NLOPT=2 and KTYPE=4 NOTE: This type is ONLY available for pier elements NOT for piles. .....................................................................379 Multiple Pile Sets................................................................................... 386

PILESET......................................................................................... 386 PILESET......................................................................................... 386

Pile Batter Information .......................................................................... 387 Missing Pile Data .................................................................................. 388 Multiple Soil Sets................................................................................... 397

SOILSET......................................................................................... 398 SOILSET......................................................................................... 398

Structural Information............................................................................ 398 SOUND........................................................................................... 402 STRUCTURE ................................................................................. 417

Column Information............................................................................... 418 Concentrated Nodal Loads ................................................................... 419 Wind Load Generation .......................................................................... 422 Spring Properties .................................................................................. 425 Pile Cap Properties ............................................................................... 427 Removed Pile Cap Element.................................................................. 427 Removed Pier Cap Element ................................................................. 428 Bearing Connection............................................................................... 429 Point Mass ............................................................................................ 430

MASS.......................................................................................................................................430 NS,NF,NI M=MX,MY,MZ,MRX,MRY,MRZ ..............................................................................430 Point Dampers ...................................................................................... 431

DAMP.......................................................................................................................................431

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NS,NF,NI C=MX,MY,MZ,MRX,MRY,MRZ................................................................................431 Dynamic Load Function Application...................................................... 432

NF,NL,NI L=LCN F=L1,L2,L3,L4,L5,L6 M= MODEXF D=FUNC.............................................432

Post Processing Formats 433

POST PROCESSING FILE FORMATS ...................................................... 433 Multiple Pier Generation .............................................................................. 433 Pier to Superstructure Connectivity............................................................. 434 Geometry and Control Information .............................................................. 437

Npset ..................................................................................................... 437 Is the number of pile sets for the piles. ................................................. 437 Nseg1, nseg2, nseg3, ….. nsegN......................................................... 437 Name..................................................................................................... 438 NUMNP, nstr, kbent .............................................................................. 438 X, Y, Z ................................................................................................... 439 Idx, idy, idz, idrx, idry, idrz..................................................................... 439

Mtype, nume................................................................................... 440 DX, DY, DZ, RX, RY, RZ ...................................................................... 440 MINIMUMS............................................................................................ 441

Pile Data ...................................................................................................... 442 NUMPN, NUMLC .................................................................................. 443 NPX, NPY, nmpil, npil, kfix, nplnod....................................................... 443 TPL, GSE .............................................................................................. 444

Axial Forces for Beam Elements ................................................................. 445 Mtype, nume................................................................................... 445 Axial ................................................................................................ 446

Maximum Moments in Beam Elements....................................................... 446 Mtype, nume................................................................................... 446 Rmom ............................................................................................. 446

Stresses of Pile Cap .................................................................................... 447 Capacity Information.................................................................................... 447

Nxpile, nxstruc....................................................................................... 447 PTUV, YPC, ZPC.............................................................................................................................448

Shear and Moment Results ......................................................................... 449 W, V2I, V3I, V2J, V3J, XMI2, XMI3, XMJ2, XMJ3, XMMAX, XML, FRATI, FRATJ, AXLI, AXLJ............................................................................................ 450

Analysis Convergence Information.............................................................. 450 Mode Shape and Frequency Information (Response Spectrum Analysis) . 452 AASHTO Load Combination Results .......................................................... 454

References 455

References .................................................................................................. 455

Tutorials 458

Tutorial Index ............................................................................................... 458

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Segment Selection 460

Confined Concrete Model References 460

AASHTO Table 463

AASHTO Table 464

P-Y Multiplier Reduction for Shaft with Torsion 464

Barge Impact 466

BARGE ........................................................................................................ 466

3D Bridge View 467

Calculating Foundation Stiffness Using FB-MultiPier 468

Sound_Wall_Eplanation 470

3D 3D Display Control .................................................................... 470 3D 3D Results ....................................................................................... 470

3D Display Control.......................................................................... 470 3D Node Information ...................................................................... 471

3D Results Dynamic Options ................................................................ 471 3D Results Window............................................................................... 471

AASH AASHTO Load Factors Table.............................................. 471 AASH Automated AASHTO Loads................................................. 471 AASH Limit States to Check........................................................... 472

AASHTO Load Case Options...........................................................................................................472 AASHTO Load Combination Preview Table................................... 472

AASHTO Load Combination Results .......................................................... 472 AASHTO Load Manager................................................................. 472

AASHTO Load Table .......................................................................................................................473 AASHTO Table Edit Options............................................................................................................473 AASHTO Table Format ....................................................................................................................473

Add Substructure............................................................................ 473 Adjustment for Prestressing.................................................................. 473

Analysis Convergence Information.............................................................. 473 Analysis Type ................................................................................. 474

Angle of Internal Friction ....................................................................... 474 AP 1020 Pile Pier Behavior ............................................................ 474 AP 1033 Iteration Control ............................................................... 474 AP 1123 Print Control..................................................................... 474 AP 1211 Soil Behavior.................................................................... 475 AP 1258 Design Options ................................................................ 475 AP 1708 Interaction Diagram Phi Factor........................................ 475

Axial Forces for Beam Elements ................................................................. 475 Axial Skin Friction for Florida Limestone ........................................ 475

Axial Soil Pile Interaction ...................................................................... 476 Axial T Z Curve for Side Friction .................................................... 476 Axial T Z Q Z Curve for Tip Resistance.......................................... 476

Batch Mode.................................................................................................. 476 Bearing Connection............................................................................... 476 Bearing Location Loads ........................................................................ 477

Bearing Pad Properties ............................................................................... 477 Bearing Rotation ..............................................................................................................................477

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Bridge Multiple Piers Option........................................................... 477 Bridge Span Overview................................................................................. 477

Bridge Spring Toggle ............................................................................ 478 Bridge Tab ...................................................................................... 478 Cap Behavior .................................................................................. 478

CAP Edit Cap Thickness....................................................................... 478 Capacity Information.................................................................................... 478

CD Custom Stress Strain .........................................................................................................479 Clay API ................................................................................................ 479

ClayEnd ...........................................................................................................................................479 ClaySide...........................................................................................................................................479

Column Connection to the Pile Cap ............................................................ 479 Column Information............................................................................... 479 Combination AASHTO .......................................................................... 480 Concentrated Nodal Loads ................................................................... 480 Conclusions........................................................................................... 480 Concrete................................................................................................ 480

CONFINED CONCRETE MODEL....................................................................................480 Control Menu ............................................................................................... 481 Converting FB Pier Coordinates to a Standard Coordinate System ........... 481 Deck Modeling ............................................................................................. 481 DESCRIPTION OF TOOLBAR ICONS ....................................................... 481

Discrete Element Model ........................................................................ 481 DrilledEnd ........................................................................................................................................482 DrilledSide........................................................................................................................................482

Driven Pile Clay API.............................................................................. 482 Driven Pile Clay API QZ ................................................................ 482

Driven Pile Sand API............................................................................. 482 Driven Pile Sand API QZ............................................................... 483 DrivenEnd....................................................................................... 483 DrivenSide ...................................................................................... 483

Dynamic Control Parameters................................................................ 483 Dynamic Load Function Application...................................................... 483 Dynamic Step by Step Integration ........................................................ 483

Dynamics Tab................................................................................. 484 Edit Custom Bearings..................................................................... 484 Edit Load Functions........................................................................ 484 Edit Span ........................................................................................ 484 Edit Supports .................................................................................. 484

Element Deformation Relations ............................................................ 485 Element Dialog...................................................................................... 485 Element End Forces.............................................................................. 485 Element Stiffness .................................................................................. 485

Engine Input Overview ................................................................................ 485 Equivalent Stiffness Generation .................................................................. 486 Expanding Memory...................................................................................... 486

Failure Ratio for Cross Sections ........................................................... 486 FB PIER LICENSE INSTALLATION HELP ................................................. 486

FB Pier1 486

Figure B 2.............................................................................................. 487 Figure B 3.............................................................................................. 487

File Menu ..................................................................................................... 487 FINITE ELEMENT ....................................................................................... 487 Flat Shell Elements...................................................................................... 487

Full Scale Column without Steel Casing............................................... 488

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General Control..................................................................................... 488 General Pier Wizard .................................................................................... 488 Generalized Stress and Strain..................................................................... 488 Geometry and Control Information .............................................................. 488

GRID 2094 Grid Spacing Table...................................................... 489 GRID Custom Grid Spacing.................................................................. 489

Gross Pier Component Properties ...............................................................................................489 Gross Pile Properties ...................................................................................................................489

Group Interaction......................................................................................... 489 Half Scale Column With Steel Retrofitting Jacket................................. 490 Header .................................................................................................. 490

Help Menu ................................................................................................... 490 High Strength Prestressing Steels ........................................................ 490

HP H Pile Properties ........................................................................................................490 HP Section Dimensions....................................................................................................491 HP Section Orientation.....................................................................................................491

Hyperbolic Curve................................................................................... 491 ID Interaction Diagram .......................................................................... 491 ID Interaction Diagrams ........................................................................ 491 ID Pier Selection ................................................................................... 491 ID Pile Selection.................................................................................... 492 Integration of Stresses .......................................................................... 492 INTERACTION DIAGRAMS ................................................................. 492

Intermediate GeomaterialQZ............................................................................................................492 Intermediate GeomaterialTZ ............................................................................................................492

Lateral Soil Pile Interaction ................................................................... 493 LE Database Section Selection....................................................................................................493 LE Parabolic Taper Cantilever Properties ....................................................................................493 LE Pier Components ....................................................................................................................493 LE Section Data ...........................................................................................................................493 LE Section Properties ..................................................................................................................494

License File.................................................................................................. 494 Limestone McVay use 2 3 Rotation ...................................................... 494

Load Function Edit Table................................................................ 494 LOAD Load Case Options................................................................................................................494 LOAD Load Table ............................................................................................................................494 LOAD Table Edit Options.................................................................................................................495 LOAD Table Format .........................................................................................................................495

Longitudinal Reinforcement..............................................................................................495 LP Database Section Selection....................................................................................................495 LP Full Cross Section Pile Properties ..........................................................................................495

LP Load Case................................................................................. 496 LP Loads......................................................................................... 496 LP Node Applied............................................................................. 496

LP Pile Set Info ............................................................................................................................496 LP Pile Shaft Segment List ..........................................................................................................496 LP Section Properties ..................................................................................................................496 LP Section Type...........................................................................................................................497 LP Segment Dimensions..............................................................................................................497

Mander Models for Confined Concrete.............................................................................497 Mass Damper Tab .......................................................................... 497 Mass Dampers in 3D View ............................................................. 497

Matlock s Soft Clay Below Water Table................................................ 498 Max Min Forces Dialog................................................................... 498

Maximum Moments in Beam Elements....................................................... 498 MEM Extra Member Sections......................................................... 498 MEM Extra Members List ............................................................... 498 MEM Nodes Attached..................................................................... 499

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Membrane Element ..................................................................................... 499 Mesh Correctness and Convergence.......................................................... 499

Mild Steel .............................................................................................. 499 Mindlin Theory ............................................................................................. 499

Missing Pile Data .................................................................................. 500 MLE Section Type....................................................................................................................500

Mode Shape and Frequency Information Response Spectrum Analysisi ... 500 Modify Load Factors.............................................................................. 500

Multiple Pier Generation .............................................................................. 500 Multiple Pier Substructure Information.................................................. 501 Multiple Pile Sets................................................................................... 501 Multiple Soil Sets................................................................................... 501

NLE Full Pier Component Properties ...........................................................................................501 NLE Section Dimensions .............................................................................................................501

NLP Material Properties ...........................................................................................................501 NLP Section Dimensions .............................................................................................................502

NLP Section Type ....................................................................................................................502 NONLINEAR BEHAVIOR ............................................................................ 502

Nonlinear Solution Strategies ............................................................... 502 O Neill s Clay ........................................................................................ 502 O Neill s Sand ....................................................................................... 503

OP Bullet Section Properties................................................................................................503 OP Cross Section Orientation ..............................................................................................503 OP Group Data ....................................................................................................................503 OP Void Data .......................................................................................................................503

P Y Resistance for Florida Limestone................................................... 504 PAD Bearing Locations....................................................................................................................504

PI Pile Data ........................................................................................... 504 Pier Cross Section Table ...................................................................... 504 Pier Element Selection.......................................................................... 504

Pier Rotation Angle ..........................................................................................................................504 Pier Segment Selection ........................................................................ 505

Pier to Superstructure Connectivity............................................................. 505 Pile Batter Information .......................................................................... 505 Pile Cap Properties ............................................................................... 505

Pile Data ...................................................................................................... 505 Pile Element Selection .......................................................................... 506 Pile Information ..................................................................................... 506 Pile Segment Selection......................................................................... 506

Pipe Pile Properties..............................................................................................................506 Plate Element .............................................................................................. 506

Point Dampers ...................................................................................... 507 Point Mass ............................................................................................ 507 Poisson s Ratio ..................................................................................... 507

POST PROCESSING FILE FORMATS ...................................................... 507 PP 1044 Pile Cap Grid Geometry .................................................. 507 PP 1087 Pile Cross Section Type .................................................. 508 PP Pile Cap Data............................................................................ 508 PP Pile Length Data ....................................................................... 508 PP Pile Shaft Type ......................................................................... 508 PP Pile to Cap Connection ............................................................. 508

PR Graphs ............................................................................................ 508 PR Pile Results ..................................................................................... 509 PR Pile Selection .................................................................................. 509 PR Plot Display Control ........................................................................ 509 PR Printable Forces .............................................................................. 509 Print Control .......................................................................................... 509

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Printable Soil Graph.........................................................................................................................510 Program Settings......................................................................................... 510

PRP 1049 General Pier Option ...................................................... 510 PRP 1050 High Mast Light Sign Option ......................................... 510 PRP 1051 Retaining Wall Option ................................................... 510 PRP 1052 Sound Wall Option ........................................................ 511 PRP 1059 Pile and Cap Option...................................................... 511 PRP 1060 Single Pile Option.......................................................... 511 PRP 1061 Stiffness Option............................................................. 511 PRP 1062 Column Analysis Option................................................ 511 PRP 1063 Pile Bent Option ............................................................ 511

PRR Graphs.......................................................................................... 512 PRR Pier Results .................................................................................. 512 PRR Pier Selection ............................................................................... 512 PRR Printable Forces Dialog ................................................................ 512 Pushover ............................................................................................... 512

PYM Advanced Soil Data.................................................................................................................513 Reese and Welch s Stiff Clay Above Water Table ............................... 513 Reese s Stiff Clay Below Water Table .................................................. 513

References .................................................................................................. 513 Reinforcement....................................................................................... 513 Removed Pier Cap Element ................................................................. 514 Removed Pile Cap Element.................................................................. 514 Result Forces Dialog............................................................................. 514 Results Viewer ...................................................................................... 514

RET Retaining Wall Soil Layer Data ................................................................................................514 RET Soil Layer ............................................................................... 514

RET Soil Layer Data ........................................................................................................................515 RET Surcharge ................................................................................................................................515

RET Wall and Layer Geometry ...................................................... 515 RET Wall Load Data ........................................................................................................................515

Retaining Wall Explanation............................................................. 515 Rigid Link Properties ................................................................................... 516

RP Circular Section Properties.............................................................................................516 RP Confined Concrete Option..........................................................................................516

RP Edit Bar Groups..............................................................................................................516 RP Group Data.....................................................................................................................516 RP Miscellaneous ................................................................................................................516 RP Shear Reinforcement .....................................................................................................517

Running FBPier eng in Batch Mode ............................................................ 517 Sand API ............................................................................................... 517 Sand of Reese Cox and Koop .............................................................. 517

SandEnd ..........................................................................................................................................517 SandSide .........................................................................................................................................518

SECTION Detailed Cross Section................................................................................................518 Section Properties .......................................................................... 518

Self Weight and Buoyancy Load Factors.............................................. 518 Set Path for a License File on a Network Server ........................................ 518 Shear and Moment Results ......................................................................... 519

Shear Modulus ...................................................................................... 519 Soil Dynamics Dialog .......................................................................................................................519

Soil Information ..................................................................................... 519 SOIL PILE INTERACTION .......................................................................... 519

Soil Properties....................................................................................... 520 Soil Resistance Due to Pile Rotation........................................................... 520

Soil Table........................................................................................ 520 SOILPLOT Soil Model Plot...............................................................................................................520

Sound Wall Explanation ................................................................. 520

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SP Elevations ................................................................................. 520 SP Rectangular Section Properties......................................................................................521

SP Soil Layer Data ......................................................................... 521 SP Soil Layer Models.......................................................................................................................521 SP Soil Strength Criteria ..................................................................................................................521

SP Void Data........................................................................................................................521 Span Concentrated Nodal Loads.......................................................... 522

Span End Condition........................................................................ 522 Special Element for FB-PIER ...................................................................... 522

Spectrum Analysis ................................................................................ 522 SPR Spring Nodes ......................................................................... 522 SPR Spring Stiffness ...................................................................... 523

Spring Properties .................................................................................. 523 SPT Window ....................................................................................................................................523

SS Default Stress Strain Curves ..............................................................................................523 SSPLOT Section Stress Strain Plot .........................................................................................523 Steel Jacket........................................................................................... 523

STP Cross Section Type..................................................................................................................524 STP Pier Geometry..........................................................................................................................524

STP Taper Data.............................................................................. 524 Stress Strain Curves ............................................................................. 524

Stresses of Pile Cap .................................................................................... 524 Structural Information............................................................................ 525 Subgrade Modulus ................................................................................ 525 Superstructure Information ................................................................... 525

TAB 130 Soil Tab ........................................................................... 525 TAB 132 Pile and Cap Tab............................................................. 525 TAB 134 Pier Tab ........................................................................... 526 TAB 135 Load Tab ......................................................................... 526 TAB 136 Analysis Tab .................................................................... 526 TAB 137 Problem Tab.................................................................... 526 TAB 243 Spring Tab ....................................................................... 526 TAB 282 X Members Tab............................................................... 526 TAB 285 AASHTO Tab................................................................... 527 TAB 290 Retaining Tab .................................................................. 527 TAB 298 Pushover Tab .................................................................. 527

Taper Modeling............................................................................................ 527 Torsional Soil Pile Interaction ............................................................... 527

Transfer Beam Properties ........................................................................... 528 Transfer License to a Different Computer ................................................... 528

Transverse Reinforcement.................................................................... 528 Tutorials ....................................................................................................... 528

Unconfined Concrete .......................................................................................................528 Undrained Strength ............................................................................... 529

Update a License on a Network Server....................................................... 529 Update a License on a Stand Alone Workstation........................................ 529

User Defined Bearing Connection ........................................................ 529 User DefinedPY .................................................................................... 529

User DefinedQZ.............................................................................. 530 User DefinedTq ..................................................................................... 530

User DefinedTZ .............................................................................. 530 View Menu ................................................................................................... 530

Water Table........................................................................................... 530

What s New in Version 3 530

WIN 3D View Window........................................................................... 531 WIN Pile Edit Window ........................................................................... 531

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WIN Soil Edit Window ........................................................................... 531 Wind Load Generation .......................................................................... 531

Wind Load Generation Table.......................................................... 531 Wizard Menu................................................................................................ 532

XML Report Generator.......................................................................... 532 Young s Modulus .................................................................................. 532

17

FB MultiPier

What’s New in FB-MultiPier?

What's New in FB-MultiPier (FB-Pier v4)?

FB-MultiPier is the newest development of the FB-Pier program. FB-MultiPier is based on the

proven accuracy and reliability of FB-Pier with changes to the interface and features that make it

even more powerful. The name has changed to reflect the new capabilities and to keep the two

product lines separate.

Multiple Pier Modeling

Unique piers

Each pier can have an entire different set of properties, including: pier geometry, pile group size,

soil strata, loads, etc. Each pier can also have its own elevation. Up to 99 piers can be easily

generated to rapidly layout an entire bridge. The 2D Bridge window shows the bridge layout in

plan and the 3D Bridge window shows the 3D visualization of the bridge.

Pier rotation

Each pier can have a rotation about the vertical (z) axis. This is ideal for modeling skew bridges

and radial piers on curved alignments.

Bridge superstructure

The bridge superstructure is incorporated into the model using an equivalent beam that connects

the centerline of two piers. The bearing connections at the pier supports can be released,

constrained, or user-defined using a custom load-displacement curve.

Two rows of bearing locations

Two independent lines of bearings accommodate the transfer of load from the bridge

superstructure to the piers. Because the bearings are offset from the center of the pier cap, any pier

cap torque induced from unequal spans is automatically included.

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Wind Load Generation

Wind loads can be applied to the entire bridge at once. The resulting loads are transferred to the

bearings at each pier.

Dynamic Pier Analysis – Special Release Available

Time step integration

Time history load functions and ground acceleration records can be applied to the model. Different

time step integration methods are available as well as a variety of analysis control parameters.

Concentrated masses and dampers can be added to the model to simulate added mass and energy

dissipation effects.

Modal analysis

The modal analysis option performs a frequency analysis of the model. Both frequencies and

mode shapes are provided as output results.

Dynamic soil modeling

Soil gap modeling is available to model energy dissipation due to hysteretic damping. Cyclic

degradation parameters are also available to modify the lateral soil response during dynamic

loading.

Animated results

The 3D model displacement results can be animated for a time step integration analysis.

Animation results can be played and paused and a slider bar is provided for selectively viewing

individual time step results.

Time-Displacement plots

The displacement results for any model node can be plotted over time.

Seismic database

Ground acceleration records and response spectrums are provided for notable earthquakes.

19

Program Menus File Menu

The File menu handles the problem creation, file access, printing, and exiting the program.

Create a new problem

Open an existing problem

Close current problem

Save current problem

Prints the active window

Access the printer setup

Previously opened files

Exit the program

Figure A7: File Menu Options

View Menu

The View menu controls the appearance of the toolbar at the top of the screen and the status bar at the bottom of the

screen.

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Show/hide toolbar

Show/hide status bar Show/hide 3D control (zoom) bar

Figure A8: View Menu Options

Control Menu

The Control menu allows the user to access the output data from the program, log file options, program settings, access

to the license update wizard, and control the appearance of the fonts used in the dialogs, graphics, and plots.

Figure A9: Control Menu Options

The Program Settings option will open the Program Settings Dialog with options for pile nodes,

water tables and memory settings.

Wizard Menu

The Wizard menu provides access to General Pier Wizard. Following the steps provided by the wizard the user can

quickly create a customized general pier model.

21

Figure A11: Wizard Menu Options

Help Menu

The Help menu provides access to the online help manual. The Help About option is provided to list the version number

of the program and current system settings.

Figure A10: Help Menu Options

Help About Tutorial

Model Data

Global Data Edit

New Project/Problem Tab New Project/Problem Tab

Select a new problem type in the "Select a New Problem Type" window, or . . .

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Figure A13: New Problem Tab

Change an existing one in the "Model Data" window.

Choose from the following problem types to view a picture of each standard type (default

problems):

1. General Pier Option

2. Pile and Cap Option

3. Single Pile Option

4. High Mast Light/Sign Option

5. Retaining Wall Option

6. Sound Wall Option

7. Stiffness Option

8. Pile Bent Option

9. Column Analysis Option

10. Bridge (Multiple Piers) Option

Select the unit type (English or Metric) in the "Select a New Problem Type" window.

23

General Pier Option

Figure A14: General Pier Model

Select this option to begin a typical pier problem.

For complete a list of problem options go to the Problem Tab page.

Pile and Cap Option

24

Figure A15: Pile and Cap Model

Select this option to begin a typical pile and cap problem.


Single Pile Option

25

Figure A16: Single Pile Model

Select this option to begin a typical pile problem.


High Mast Light/Sign Option

26

Figure A17: High Mast, Light/Sign Model

Select this option to begin a typical high mast light/sign problem.


Retaining Wall Option

27

Figure A18: Retaining Wall Model

Select this option to begin a typical retaining wall problem.

Note: With this option, the Pier page becomes the Wall Structure page.


Sound Wall Option

28

Figure A19: Sound Wall Model

Select this option to begin a typical sound wall problem.

Note: With this option, the Pier page becomes the Wall Structure page.


Stiffness Option

29

Figure A20: Stiffness Model

Select this option to begin a typical stiffness problem.


Pile Bent Option

30

Figure A21: Pile Bent Model

Select this option to begin a typical pile bent problem.

Note: With this option, the Pier page becomes the Bent Cap page.


Column Analysis Option

31

Figure A22: Column Model

Select this option to begin a typical column problem.


Bridge (Multiple Piers) Option

32

Figure A23: Bridge Model

Select this option to begin a typical bridge (multiple piers) problem.


Analysis Tab

Analysis Tab

33

Pile/Pier Behavior allows linear or nonlinear material behavior.

Cap Behavior allows bearing capacity of cap to be included. The "Axial Bearing Effects" option is

used to model the soil reaction on the bottom of the pile cap. This is done by assigning vertical

soil springs to each of the nodes in the pile cap. The "Gap to Soil" parameter is used to specify an

initial gap between the bottom of the pile cap and the ground surface. If the loading is sufficient to

close this gap, then the analysis will consider the vertical soil reaction on the pile cap. Otherwise,

the vertical soil reaction will not be considered.

The Soil Behavior option "Include Soil in Analysis" is enabled by default and causes the program

to model soil in the analysis. Unchecking this option removes the soil and requires the user to

enter pile tip spring stiffness to restrain the model. Use very large springs since the stiffness is

only added on the diagonal.

Print control options determine what information is printed in the output file.

Figure A24: Analysis Tab

Choose options in the following categories:

1. 1. 1. 1. 1. 1. 1. 1. Pile/Pier Behavior

2. 2. 2. 2. 2. 2. 2. 2. Cap Behavior

3. 3. 3. 3. 3. 3. 3. 3. Section Properties

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4. 4. 4. 4. 4. 4. 4. 4. Soil Behavior

5. 5. 5. 5. 5. 5. 5. 5. Iteration Control

6. 6. 6. 6. 6. 6. 6. 6. Interaction Diagram Phi Factor

7. 7. 7. 7. 7. 7. 7. 7. Analysis Type

8. 8. 8. 8. 8. 8. 8. 8. Design Options

9. 9. 9. 9. 9. 9. 9. 9. Print Control

Pile/Pier Behavior

One may select either linear or nonlinear behavior of the pier and the piles.

Linear Behavior:

• Assumes the behavior is purely linear elastic.

• Deflections do not cause secondary moments; no P-delta moments (moments of the axial force

times the displacements of one end of element to another).

Nonlinear Behavior:

• Uses input or default stress strain curves which are integrated over the cross-section of the piles or

pier components. Full cross-section properties must be described for non-linear analysis to be

performed.

• Non-linear analysis accounts for second order effects (P-delta) as well as stiffness changes in the

structure, as when concrete cracks.

Return to the Analysis Tab page.

Cap Behavior

Check "Axial Bearing Effects" to consider the soil reaction on the bottom of the pile cap in the problem. The program will then use the input soil parameters to create vertical acting soil springs, which are automatically attached to the pile cap nodes.

35

If "Axial Bearing Effects" is checked, the user may also enter a "Gap to Soil" value, specifying the distance from the bottom of the Pile Cap to the ground surface.


Section Properties

When "Transformed Section" is checked, the program calculates the transformed section properties from

the input ‘Full Cross Section’ when the user specifies ‘Linear Analysis’.


Soil Behavior

Check "Include Soil in Analysis" to include soil in the problem.

If "Include Soil in Analysis" is unchecked, then enter the stiffness at the tip of the pile.

Use high spring values to model a rigid connection.


Iteration Control

Enter the maximum number of iterations that analysis will run before it determines that the solution will not converge.

36

Note: If a small value is entered, the solution may not converge, because it has not

been given the chance to finish the calculations. On the other hand, if a very large value

is entered, the analysis may take a long time.

A typical value for the number of iterations is 60.

Enter the tolerance between successive iterations that the analysis must reach before providing a

solution.

Note: This value is typically 1% of the loading.


Interaction Diagram Phi Factor

Check "User-defined phi" to enter a custom phi factor, or leave the option unchecked if you want

to use the default value.


Analysis Type

The Analysis tab offers two types of analysis:

1. 1. 1. 1. 1. 1. 1. 1. Static

2. 2. 2. 2. 2. 2. 2. 2. Dynamic


37

Design Options

Check "AASHTO Combinations" if you want to select various AASHTO load combinations to

use in the analysis.

The AASHTO tab will be enabled once this option is checked.

Load types need to be assigned to each load case when converting an existing model to an

AASHTO design model. Load type assignment is done on the Load tab.


Print Control

Select the type of output to be printed to an output file from the following:

1. 1. 1. 1. 1. 1. 1. 1. Pile Displacements

2. 2. 2. 2. 2. 2. 2. 2. Pile Element Forces

3. 3. 3. 3. 3. 3. 3. 3. Pile Properties

4. 4. 4. 4. 4. 4. 4. 4. Missing Pile Information

5. 5. 5. 5. 5. 5. 5. 5. Pier Displacements

6. 6. 6. 6. 6. 6. 6. 6. Pier Element Forces

7. 7. 7. 7. 7. 7. 7. 7. Pier Properties

8. 8. 8. 8. 8. 8. 8. 8. Soil Response Forces

9. 9. 9. 9. 9. 9. 9. 9. Soil Data per Layer

10. 10. 10. 10. 10. 10. 10. 10. Soil Data per Pile Node

11. 11. 11. 11. 11. 11. 11. 11. Soil Graph per Pile Node

38

12. 12. 12. 12. 12. 12. 12. 12. Unbalanced Forces

13. 13. 13. 13. 13. 13. 13. 13. Cap Stresses/Moments

14. 14. 14. 14. 14. 14. 14. 14. Stress-Strain Curves Data

15. 15. 15. 15. 15. 15. 15. 15. Bridge/Spring Forces

16. 16. 16. 16. 16. 16. 16. 16. Interaction Diagram Data

17. 17. 17. 17. 17. 17. 17. 17. Coordinates

18. 18. 18. 18. 18. 18. 18. 18. Bridge Span Displacement

19. 19. 19. 19. 19. 19. 19. 19. Bridge Span Forces

20. 20. 20. 20. 20. 20. 20. 20. Bridge Span Properties

21. 21. 21. 21. 21. 21. 21. 21. XML Data Printing – Creates XML

output file that can be used to extract FB-MultiPier data. See FB-MultiPier XML Specification

documentation.


AASHTO Tab

AASHTO Tab

Select the AASHTO combinations that will be used in the analysis using the following:

1. 1. 1. 1. 1. 1. 1. 1. AASHTO Load Factors Table

2. 2. 2. 2. 2. 2. 2. 2. Automated AASHTO Loads

3. 3. 3. 3. 3. 3. 3. 3. AASHTO Load Manager

4. 4. 4. 4. 4. 4. 4. 4. Wind Load Generation Table

5. 5. 5. 5. 5. 5. 5. 5. AASHTO Load Combination Preview Table

6. 6. 6. 6. 6. 6. 6. 6. Limit States to Check

Note: The AASHTO Combination option in the Design Options section of the Analysis Tab

must be selected for this tab to appear.

39

Figure A32: AASHTO Tab

AASHTO Load Factors Table

Edit the individual AASHTO load factors in the table, or reset the values to the default values.

40

Figure A33: AASHTO Load Factor Table

Return to the AASHTO Tab page.

Automated AASHTO Loads

Choose to include self weight and/or buoyancy cases.

For AASHTO LRFD, self weight is included in the "DC" case and buoyancy is included in the

"WA" case.

For AASHTO LFD, self weight is included in the "D" case and buoyancy is included in the "B"

case.


41

AASHTO Load Manager

The AASHTO Load Manager manages the type and number of load cases in your model. Changes made

with this manager apply to every pier.

Figure A34: AASHTO Load Manager Dialog

To add a new load case, select a load case from the "Available Types" list. Then click the "Add" ( << )

button. This will add the selected load case to the "Defined Load Cases" list.

To remove a defined load case, select a load case from the "Defined Load Cases" list. Then click the

"Remove" ( >> ) button.

To change the number of load cases for a particular load type, select a load case from the "Defined Load

Cases" list. Load case types which can vary in number will be followed by parenthesis and a number.

Example: Live Load (1). In the box below the "Defined Load Cases" list, change the value to the desired

number of load cases. This will change the number of load cases for that load type in the "Defined Load

Cases" list.

Note: certain load case types are grouped together. Example, "Wind on Structure" and "Wind on Live

Load". Changing the number of cases for one of these types will automatically change the number of

cases for the other type.

42

Wind Load Generator

Enter the wind load parameters.

Click ‘Generate Wind Load Cases’ to convert the wind load to loads at the bearing locations and

automatically create wind load cases. Depending on the problem type you will see one of the following

dialog boxes.

This dialog appears for the General Pier and Pile Bent Bridge problem type.

Figure A35-a: Wind Load Generation Dialog for Single Pier

This dialog appears for the Bridge problem type.

43

igure A35-b: Wind Load Generation Dialog for Multiple Piers

A wind angle of zero degrees applies all of the wind in the transverse direction. The equations used in the

wind load generation are found here.

AASHTO Load Combination Preview Table

Shows the load combination that will be run. Color changes indicate limit states.

44

Figure A36: AASHTO Load Combination Preview Table

Limit States to Check

Select the limit states to check in the analysis.

Note: The program does not display (or analyze) a load combination unless the load types

expected in that combination are defined. For example, the STRENGTH-III load combination will

not be considered until a dead load type (DC) and a wind load type (WS) are defined. Dead, live,

and wind load types are considered mandatory to generate load combinations. All other load types

are optional. Check the load combination preview in the AASHTO tab to confirm the generation

of specific load combinations.


45

Dynamics Tab

Dynamics Tab

The Dynamics Tab provides various options for controlling a dynamic analysis.

Figure A37: Dynamics Tab

Analysis Type

Two dynamic analysis types are available.

1. 1. 1. 1. 1. 1. 1. 1. Time Step Integration - Uses

implicit integration to solve for results at every time step.

2. 2. 2. 2. 2. 2. 2. 2. Modal Response Analysis –

Applies static loads and then performs a response spectrum analysis using the equilibrium

(deformed) position. Performs a CQC of the modal analysis results.

46

This analysis type requires the user to select the number of modes to use in

the analysis. Check the modal contribution factors in the printed output file to

ensure that at least 90% of the dynamic response is accounted for.

The reported analysis results do not include the effect of static loads (i.e. self

weight). Adding the static results and response spectrum results may not be

conservative and is left to engineering judgment.

Damping

Three types of damping input are available.

1. 1. 1. 1. 1. 1. 1. 1. Rayleigh damping. The damping is

proportional to the mass and stiffness. Factors can be entered for the pier, piles, and soil.

2. 2. 2. 2. 2. 2. 2. 2. Concentrated dampers. These

dampers are applied using the Mass/Damper tab.

3. 3. 3. 3. 3. 3. 3. 3. Hysteretic damping. This form of

damping is available when gap modeling is enabled for the lateral soil response as well as for

nonlinear pile and pier material behavior.

Mass

Two types of mass modeling are available.

1. 1. 1. 1. 1. 1. 1. 1. Consistent (distributed) mass.

2. 2. 2. 2. 2. 2. 2. 2. Lumped (concentrated) mass.

Time Stepping Parameters

Three types of time stepping options are available.

1. 1. 1. 1. 1. 1. 1. 1. Average acceleration (Newmark).

2. 2. 2. 2. 2. 2. 2. 2. Linear acceleration (Newmark).

3. 3. 3. 3. 3. 3. 3. 3. Wilson-Theta.

Enter a constant value for the time step to use in the analysis.

Enter the number of time steps to consider in the analysis.

For a Modal Response Spectrum analysis, enter the number of modes to consider and the damping

ratio used for the response spectrum.

Load Functions/Spectrums

47

Two types of load functions are available for a dynamic analysis.

1. Load (force vs. time)

2. Ground Acceleration (acceleration vs. time). The gravity factor is used in conjunction with the

acceleration record. If the acceleration is in terms of g’s, then the gravity factor would be either

386.4 in/sec2 or 9.81 m/sec2. If the acceleration is already in terms of an acceleration unit, then

the gravity factor should be entered as 1.0.

Ground Acceleration (acceleration vs. frequency). For response spectrum anaylsis.

Click the "Edit Load Functions " button to define one or more load functions to apply to the

model.

Analysis Type Dynamic

Time Step Integration

Modal Response

#Nodes

Global Mass

Consistent Mass

Lumped Mass

Global Damping

No Damping

48

Damping

Time Stepping Parameters

Average Acceleration

Linear Acceleration

Wilson Theta

Time Step Sec.

#Steps

Rayleigh Damping Factors

Mass Stiffness

Pier

Piles

Soil

49

Model Analysis Damping

Damping Ratio

Time Functions

Applied Load (Load vs Time)

Ground Acceleration

G= 366.2 in/sec^2

Scale Factor

Acceleration = Scale Factor *9* Time Function

Edit Load Functions

The Edit Load Functions dialog is used to define one or more load functions for a dynamic

analysis.

50

Figure A38: Edit Load Function Dialog

The "Load Function" combo box contains a list of all defined load functions. Select "Add Load

Function" in the combo box to create a new load function. When the ground acceleration option is

specified, only one load function can be defined and is automatically applied to the entire model.

For this case, select "Change Load Function" in the combo box to select a different function.

Click the "Read From File" button to retrieve an existing load function from a text file.

Predefined load functions have the following extensions:

".dlf" Load vs. Time

".acc" Acceleration (ground) vs. Time

".spt" Acceleration vs. Frequency (response spectrum)

The format of the text file should contain paired data (time, load), (time, acceleration), or (freq.,

acceleration). The file can have between one and four pairs per line (maximum 80 characters per

line).

Click the "Edit Function Values " button to display the "Load Function Edit Table", which is a

spreadsheet-style grid for customizing the data points.

51

Load Function Edit Table

The "Load Function Edit Table" displays the paired values used in the load function. Rows can be

inserted or deleted as needed. The "Update Table" button sorts the values according to increasing

time. You can drag and drop a range of data points from a spreadsheet directly into the table.

Figure A39: Load Function Edit Table Dialog

52

Pushover Tab

Pushover Tab

Click on the Run Pushover Analysis checkbox to activate the pushover analysis module.

There must be 2 load cases. The first load case is used to apply permanent loads that will not be

incremented (i.e. self weight). The second load case is used to specify the load that will be

incremented.

Enter the number of pushover steps and the load increment factor. The load increment factor

multiplies the loads in the second load case to create an accumulating load that is applied until

convergence cannot be achieved.

For example, a load increment factor of 1.0 would add 100% of the original load to each

incremental load case. If the original load increment was 10 kips, the second load increment would

be 20 kip load, the third increment 30 kips, and so forth for the number of load steps. The failure

load is printed to the output file when a load is reached that can not converge to a solution.

Figure A40: Pushover Tab

53

Pier Data Edit

Pile and Cap Tab

Pile and Cap Tab

Use the Pile/Shaft Drop down to select standard pile from the database.

You can add cross sections to the database in the edit mode.

Click the 'Edit Cross Section' button to customize the pile/shaft.

The number of piles in the X and Y-directions is used to create a grid for positioning the piles.

Piles not shown at a grid position are labeled as missing.

Enter data for the pile and cap in the following fields:

1. Pile Cap Grid Geometry

2. Pile Cross Section Type

3. Pile to Cap Connection

4. Pile Length Data

5. Pile/Shaft Type

6. Pile Cap Data

54

Figure A41: Pile and Cap Tab

Pile Length Data

Enter the elevation of the tip in the Tip Elevation text box.

Note: The tip elevation must be negative.

Enter the number of nodes in the pile free length above the soil.

55

Figure A42: Free Length of Pile Above Soil

Return to the Pile and Cap Tab page.

Pile Cross Section Type

A different edit window appears depending upon the type of cross section selected.

If "Linear Properties" is selected and the "Edit Cross Section" button is clicked, then the Linear

Pile Properties window will appear.

Otherwise, if "Full Cross Section" is selected, then the Full Cross-Section Pile Properties window

will appear.


56

Pile/Shaft Type

Choose the type of pile from the drop-down list.

Figure A43: Pile Database Options


Pile to Cap Connection

Choose to use either a "Pinned" of "Fixed" pile to cap connection.


57

Pile Cap Data

Enter the elevation of the pile cap in the "Head/Cap Elevation" text box.

Check the "Apply Overhang" box to enter the over hang of the pile cap.

Click the "Edit Pile Cap" button to enter the following properties for the pile cap:

1. Young’s Modulus

2. Poisson’s Ratio

3. Thickness

4. Unit Weight


Pile Cap Grid Geometry

Enter the number of grid points in the X and Y directions.

Then, select the pile spacing in the X and Y directions from the following pull-down menu:

Figure A44: Pile Spacing Drop Down Menu

58

Where d is the standard dimension of the cross section (the width of a square pile or the diameter

of a circular pile).

Note: With no over hang specified the program automatically places piles at all grid

points.

For the constant and variable spacing options see the Grid Spacing Table.


Grid Spacing Table

If constant spacing is selected from the pull-down menu in the Pile Cap Grid Geometry section on

the Pile and Cap Tab page, then only the "Constant Spacing" text box is editable.

Enter the custom spacing in both directions into the text box.

Note: Entering a constant spacing will also affect the overhang distance.

Otherwise, if variable spacing is selected, then the "Constant Spacing" text box is "grayed out" and the only individual spread sheet elements are editable.

Enter the custom spacing between each pile into the corresponding fields of the

spreadsheet.

59

Figure A45: Grid Spacing Table

Return to the Pile Cap Grid Geometry section.

Edit Cross Section

Gross Section Pile Properties

Gross Pile Properties

Modify the properties of a gross pile cross section in the following fields:

1. Pile/Shaft Segment List

2. Pile Set Info

3. Database Section Selection

4. Section Type

5. Section Properties

60

6. Segment Dimensions

Figure A46: Gross Pile Properties Dialog

Return to the Pile Cross Section Type page.

Pile/Shaft Segment List

61

Add and remove pile/shaft segments.

Return to the Linear Pile Properties or Full Cross-Section Pile Properties page.

Pile Set Info

Add and remove pile sets (types). This allows the user to use different pile types for each pile.


Pile Sets Tutorial

Database Section Selection

If the "Use Database Section" option is selected, the user can select from a predefined set of cross-

sections.

In the Linear Pile Properties page, there is only one option (Linear Pile) when you click on the

"Retrieve Section" button.

However, in the Full Cross-Section Pile Properties page, there are the following options:

62

Figure A47: Pile Database Options

If the "Modify Current Section" option is selected, the user can customize the current cross

section.

Furthermore, the user can also save custom cross sections by clicking the "Save Section" button.


Section Type

Select a cross section type from the following:

1. Circular Pile

63

2. Square Pile

3. H-Pile

Note: this option is only available if the "Modify Database Section" option is selected.

Return to the Linear Pile Properties page.

Segment Dimensions

Enter the following data for the dimensions of the segment:

1. Length

2. Area

3. Diameter—Only available for a circular pile

4. Width—Only available for a square pile

5. Depth—Only available for a square pile

6. [Unit] Weight



Section Properties


1. Inertia 2 Axis—The moment of inertia about the 2-axis


64

3. Torsional Inertia


5. Shear Modulus



Full Cross Section Pile Properties

Full Cross-Section Pile Properties

Modify all of the properties of a pile cross section in the following fields:

1. Pile/Shaft Segment List

2. Pile Set Info


4. Section Details

5. Section Type

6. Material Properties

7. Section Dimensions

65

Figure A48: Full Cross Section Properties Dialog

Return to the Pile Cross Section Type page.

Detailed Cross Section

By selecting Section Details on the Full Cross-Section Pile Properties page, one can edit the bar

groups and material properties of the cross section in a spreadsheet format.

66

Select a segment from the "Section List" and a pile set from the "Pile Set" list to edit.

Return to the Full Cross-Section Pile Properties or the Full Pier Component Properties page.

Section Dimensions

The fields in which one can enter data depend upon the type of cross section selected.

Circular Section:

1. Length

2. Diameter

3. Unit Weight

Rectangular Section:

1. Length

2. Width

3. Base

4. Unit Weight

H-Pile:

1. Length

2. Unit Weight

Pipe Pile:

1. Length

2. Diameter

3. Thickness

4. Unit Weight

Return to the Full Cross-Section Pile Properties page.

67

Section Type

Section Type


The "Edit Section Contents" button yields different windows depending upon the type of cross

section selected.

1. Circular Pile

2. Square Pile

3. H-Pile

4. Pipe Pile


Return to the Full Cross-Section Pile Properties page.

Circular Section Properties


Enter the data for a circular cross section in the following fields:

1. Edit Bar Groups

2. Group Data

3. Confined Concrete Option

4. Shear Reinforcement

5. Miscellaneous

68

Figure A49a: Circular Cross Section Properties Dialog - Custom Group Method

69

Figure A49b: Circular Cross Section Properties Dialog - Percentage Group Method

Percentage Steel Tutorial

Return to the Section Type page.

Edit Bar Groups

Add or remove rebar groups to or from the cross section.

Note: The properties of the bar group must be entered in the Group Data section.

Return to the Circular Section Properties, the Bullet Section Properties, or the Rectangular Section

Properties page.

70


Group Data

There are two methods for entering bar group data; Custom and Percentage.

Custom:

1. Enter the number of bars in the group in the "Number of Bars/Strands" text box.

2. Next, select the type of layout for the bars from the "Group Type" options—circular or

rectangular.

3. If the rectangular option is selected, choose the orientation of the group of bars from the

"Group Orientation" options—horizontal or vertical.

4. Then, enter the area of the bars and, depending upon the layout, the diameter of a circular

layout or the starting coordinates of a rectangular layout.

5. Click the Add button to add the bar group to the section.

6. Click the Apply button to update any changes made to the bar group.

7. Repeat steps 1-4 to add more groups of bars/strands.

8. Click OK when done to exit the dialog.

Percentage:

1. Enter a Reinforcement % (the % of the cross section area that is steel)

2. Enter the cover. Cover 2 is the distance between the cross section edge and the steel bars, in

the 2 direction. Cover 3 is the distance between the cross section edge and the steel bars, in the 3

direction.

3. Enter the Minimum Spacing (minimum distance between two bars).

4. Click the Update Bar List button to display the available bar options.

5. Select a bar type from the Bar Type list box.

6. Click the Apply button to apply the steel to the cross section, or double click the selected Bar

Type. Any existing bar data will be deleted.

7. Click OK when done to exit the dialog.


71

For both methods:

Choose between mild steel or prestress for the type of steel in the group.

If prestress is chosen, then enter the prestress after losses.

Return to the Circular Section Properties or the Rectangular Section Properties page.

Confined Concrete Option

Choose between "Shell & Spiral", "Spiral Only", and "None" to determine the type confinement

for the concrete.

72

Figure A50: Confined Concrete Options

Enter values for the yield stress, shear spacing, and bar diameter ( Note: Not available with the

"None" option).

73

Note: A shell thickness must be entered in the "Shell Thickness" text box in order to select Shell and Spiral.

Return to the Circular Section Properties page.

Shear Reinforcement

Select either spiral or tied for the type of shear reinforcement.


Miscellaneous

Enter data using the following fields:

Enter the shell thickness in inches in the "Shell Thickness" text box.

Enter the diameter of a void in the member in inches in the "Void Diameter" text box.

Click the "H-Pile Properties" button to edit the properties of an h-pile embedded in he circular

cross section.


Confined Concrete Model CONFINED CONCRETE MODEL

Introduction

74

Effective confinement has been shown to considerably enhance the compressive strength and ductility of concrete. The strength and ductility enhancement from confinement of the concrete will of course cause corresponding increases in the axial and flexural strength and ductility of reinforced concrete columns or piles. The confining effect of the column or pile may be accomplished by the used of circular hoops, spiral reinforcement, and an external steel jacket.

In the case of internal confinement i.e. spirals or circular hoops, the cover concrete will be

unconfined and will become ineffective after the maximum compressive strain of the concrete has

been attained, but the confined core will continue to carry stress at high strains. The compressive

stress-strain response used for the core and cover concrete are those obtained by the Mander

model (Mander and Priestly, 1988) for confined and unconfined concrete, respectively.

In the case of an external jacket, the jacket will provide confinement to the cover concrete and the

inner concrete will be doubly confined by the jacket and the internal confinement due to the

circular hoops or spirals. Although the steel area of the shell (casing) is not considered for direct

bending or axial strength the confining effects to the concrete are. The compressive stress-strain

response used for the core and cover concrete are those obtained by the modified Mander model.

The Mander model was modified for the confining effects of the external shell by Priestly et al

(1991).

Mander Models for Confined Concrete

Both the Mander and modified Mander models use the following equation for the longitudinal

compressive stress of confined concrete:

'

* *

1cc

rc

x rff

r x=

− +Eqn. d28

where

f ’cc is the compressive strength of the of confined concrete

x is given by:

'

c

cc

xεε

=Eqn. d29

The expression suggested for e’cc increases linearly with f ’cc and is given by:

75

'

' '

'1 5* 1cc

cocc

co

f

fε ε

= + −

Eqn. d30

where

f ’co is the unconfined compressive stress of the concrete

e’co is the unconfined concrete compressive strain, adopted as 0.002

The parameter r is given by:

sec

c

c

r EE E

=−

Eqn. d31

ε’co εsp ε’cc

f’co

f’cc

Confined Concrete

UnconfinedConcrete

εcu

Compressive Strain εc

Figure D8: Confining Effect on Compressive Response of Concrete (Priestly et al 1991)

Ec is the tangent modulus of elasticity for unconfined concrete and is given by:

'

60200c co

fE =Eqn. d32

76

Esec is the secant modulus for confined concrete, defined with respect to f ’cc and

e’cc and is given by:

'

'sec

cc

cc

fE

ε=Eqn. d33

For f ’cc, the confined concrete strength, Mander used the five-parameter failure criterion

proposed by William and Warnke and the tri-axial test data of Schickert and Winkler. In the case

of circular columns confined by circular hoops or spirals, the confined concrete compressive stress

has been shown to be:

' '

' '

' '2.254 1 7.94 2 1.254l l

CC co

co co

f ff f

f f

= + − −

Eqn. d34

where

f ’l is effective confining pressure, and may be obtained from the equilibrium of internal

forces acting on the dissected sections shown in Figure D9

For the cover concrete in columns, assuming uniform yield of the jacket, the equilibrium of forces

requires:

( )' 2

2

jyj

lj

j j

f tf

tD=

−Eqn. d35

where

f ’lj is the lateral confining pressure acting on the cover concrete

Dj is the outside diameter of the steel jacket

tj is the thickness of the steel jacket

fyj is the yield strength of the steel jacket

77

D j

Ja c k e t

fy j fy j

f ’ l h

d s

fy h fy h

H o o p

+

fy hfy h

f ’ l j

=

fy j fy j

C o m b i n e d Ja c k e t a n d H o o p

f ’ l j + f ’ lh

Figure D9: Confining Action of Steel Jacket and Internal Hoops [4]

78

The confining ratio for the steel jacket is defined as:

( )4

2

j

sj

j j

t

tDρ ≡

−Eqn. d36

Substituting into equation d35 we obtain

' 1

2lj sj yjf fρ=Eqn. d37

By using f ’l = f ’lj in equation d34, the compressive strength of the cover concrete confined by the

steel jacket can be determined.

Additional confinement is provided to the concrete core by the transverse reinforcement. The

additional lateral pressure, f ’lh, may also be determined from the equilibrium of forces.

Assuming uniform yield of the transverse steel yields the following equation:

'

2shyh

elhss

f Af k

d=Eqn. d38

where

ds is the diameter of the concrete core defined along the center line of the confining steel

s is the vertical spacing of the transverse steel

fyh is the yield strength of the transverse reinforcement

Ash is the cross-sectional area of the transverse steel

The confinement effectiveness coefficient, ke, is defined as:

e

e

cc

Ak

A≡Eqn. d39

79

where

Ae is the area of an effectively confined concrete core

( )1cc c ccA A ρ= −Eqn. d40

where

Ac is the core area of the section

rcc is the ratio of the area of longitudinal reinforcement to the confined area of the concrete

core of the section Ac, i.e.:

2

4 s

cc

s

Ad

ρπ

=Eqn. d41

where

A5 is the total longitudinal steel area .

By assuming an arching action between circular hoops in the form of a second -degree parabola

with an initial tangent slope of 45E, the confinement effectiveness ratio has been shown to be:

( )

2'

1

1 0.5

e

cc

s

s

dk

ρ=

−

−

Eqn. d42

where

s’ is the clear distance between the hoop.

Similarly, the confinement effectiveness coefficient for a circular spiral has been shown to be:

( )

'

1

1 0.5

e

cc

s

s

dk

ρ=

−

−

Eqn. d43

80

By introducing rs as the ratio of the volume of transverse confining steel to the volume of

confined concrete i.e.:

2

4

sh s

s

s

dA

sd

ππρ ≡Eqn. d44

81

A eD

d s

A s

E ffe c t iv e C o re

s s ’

A rc h in g A c t io n B e tw e e n H o o p s

Figure D10: Definition of Confinement Effectiveness Coefficient [4]

82

4 sh

sss

Ad

ρ =Eqn. d45

The lateral confining pressure due to transverse steel in equation d37 may be written as:

' 1

2 elh s yhf fk ρ=Eqn. d46

Thus using f ’l =f ’lj + f ’lh in equation d34 will allow the enhanced compressive strength of the

concrete core to be determined.

Scott et al (1989) proposed an expression for the ultimate compressive strain, ecu, which is given

by:

0.004 0.0207cu s yh

fρε = +Eqn. d47

where

rs is the volumetric ratio of steel to concrete core

fyh is the yield strength of the transverse steel

Unconfined Concrete

For the concrete outside the inner core when a steel shell is not used , the unconfined condition

may be simulated by setting the lateral confinement pressure equal to zero, i.e f’l = 0. The

following simplifications can be made to the prior equations:

' '

cc cof f=Eqn. d48

' '

cc coε ε=Eqn. d49

'

'sec

co

co

fE

ε=Eqn. d50

83

'

c

co

xεε

=Eqn. d51

It is assumed that the stress-strain curve for unconfined concrete follows equation d28 during the

earlier stages of loading up to 2e’co. For compressive strains larger than 2e’ co, the strains are

assumed to decrease linearly with strains up to the spalling strain esp. A value of 0.005 has been

adopted for esp. The longitudinal compressive stress for unconfined concrete may be written as:

For ec # 2e’co,

'

1co

rc

xrff

r x=

− +Eqn. d52

For 2e’co # ec # esp,

''

2 1

21

21 2 2

c co

c co

sp co

rf f

r

ε εε ε

− = −

− − +Eqn. d53

For ec > esp

0c

f =Eqn. d54

Reinforcement

To avoid congestion of reinforcement, earlier design practices tended to use large diameter bars,

up to #14 or #18, however, such practice may lead to potential bond problems in cases where the

column main reinforcement were lapped at insufficient length with starter bars in the plastic hinge

regions. Consequently, such columns are characterized by very rapid flexural strength degradation

under the design seismic loads. The current Caltrans (1981) approach has been to avoid lap

splicing of the main reinforcement in the potential plastic hinge region of bridge columns. The

analytical model developed here assumes full yield of the main reinforcement including strain

hardening.

84

Longitudinal Reinforcement

The monotonic uniaxial stress-strain curve of a typical reinforcing steel is shown by an elastic

region, a yield plateau, a strain hardening region, followed by a falling branch after peak stress up

to the strain at which fracture occurs. A typical stress-strain curve for the reinforcing steel is

shown in Figure D11.

The monotonic uniaxial stress strain curve for reinforcing steel is defined by the following

equations:

For the elastic range, i.e. es # ey

ss sf E ρ=Eqn. d55

Where

es is the axial strain in the reinforcing steel

fs is the stress in the reinforcing steel

Es is the modulus of elasticity of the reinforcing steel

For the yield plateau, i.e. ey < es # esh,

s yf f=Eqn. d56

where

esh is the axial strain at the on-set of strain hardening

fy is the yield stress of the reinforcing steel

85

Strain

εy

fy

εshεsu

Figure D11: Mild Steel Stress-Strain Curve [4]

For the strain-hardening range, i.e. esh # es # esu

( )( )

( )( )( )

2 60

60 2 2 130s sh s sh

s y

s sh s

m mf f

r

ε ε ε εε ε

− + − − = + − + +

Eqn. d57

where

esu is the ultimate strain in the reinforcing steel

fsu is the ultimate stress in the reinforcing steel and

86

( )2

2

1130 60

15

su

s

y

s

s

m

fr r

f

r

− − =

+Eqn. d58

su shsr ε ε= −Eqn. d59

It has been shown by Mizra and MacGregor (1979) that the ratio of ultimate to yield strength was

fsu/fy = 1.55. The steel model adopted for the program assumes a modulus of elasticity of 29000

ksi and a slightly lower ultimate to yield strength ratio of 1.50. The other mechanical properties

assumed for the stress strain model are:

For all grades of steel,

3218

y

sh y

yl

f

fε ε

= −

Eqn. d60

( )0.18 0.043 2y

sh shsu

yl

f

fε ε ε= + − +Eqn. d61

where

fyl is equal to 40 for ksi units. This would be converted to any other consistent set

of units

The above equations are non-dimensional, allowing the model to be used with any grade steel.

They were obtained by interpolating from the values given by Priestly for 40 and 60 ksi steel.

It should be noted that the tangent modulus at the onset of strain hardening may be obtained by

taking the derivative of Eqn. d57 with respect to steel strain, es, and operated at the strain-

hardening strain, esh:

( )2

2 120 60

42 130

sh y

m m

rs

fE

− −

= + +

Eqn. d62

87

Transverse Reinforcement

Closely spaced transverse reinforcement in regions of severe inelastic actions will maintain the

integrity of the concrete core and increase the rotational capacity of the column. Maintaining the

integrity of the core also allows higher shear forces to be resisted by the concrete. The potential

shear failure plane must intersect a large quantity of transverse reinforcement, which increases the

shear resistance. Lateral stability of the longitudinal reinforcement is improved by the presence of

the closely spaced hoop or spiral. The hoops or spiral acts as anti-buckling ties to allow full

compression yield of the mild steel to be developed. The integrity of the core and mild steel

ensures the vertical load carrying capacity of the column after a severe earthquake.

The effective use of the transverse reinforcement also requires careful detailing of spirals or

hoops. Current usage may entail welding at the lap splices of the spiral or hoop, or bending back

of these bars into the concrete core for anchorage in order to develop full yield capacity. Design

practice prefers the use of since fewer anchorages are required for spirals when compared to

hoops. The transverse reinforcement in earlier design practice, however was often anchored with

lap splices in the plastic hinge regions where serious spalling of the cover concrete is expected.

The loss of cover concrete may initiate unwinding of the spirals or hoops and renders the

transverse reinforcement ineffective. The model used here assumes full development of the

transverse steel strength at the ultimate condition.

Steel Jacket

The role of the steel jacket for a column is the same as that of the transverse reinforcement. The

jacket prevents the spalling of cover concrete and allows the development o large compressive

strains in the mild steel without buckling. The shear strength of the encased region is also

enhanced.

Although the commercially available structural steel for steel jackets has yield strengths ranging

from 36 ksi to 50 ksi or higher, the level of confining pressure required does not generally require

yield strength greater than 36 ksi. Suitable steel for the jacket is the A36 hot-rolled, which has

relatively low carbon content (from 0.25 to 0.29%). The low carbon content provides a good

welding property, which is important for on-site welding of the steel jacket.

Grout

88

It is assumed that the steel jacket is fully bonded to the reinforced concrete column to facilitate

composite action. It is further assumed that the strength of the grout is the same as that of the

concrete column.

Voids in members

While voids are allowed in the general analysis procedures used in FB-MultiPier, the reduction in

the beneficial effects of confinement due to voids in columns and piles are not considered in the

Mander and modified Mander models used FB-MultiPier.

Examples

Several example columns are analyzed and comparisons are made between the experimental

results, the results obtained from FB-MultiPier program with those produced by the COLRET

computer program.

In the analysis performed with FB-MultiPier, to achieve the large post yield displacements on the

flat portion of the P-D curves, a spring was placed at the tip of the column.

The force plotted is the force absorbed by the column attached to the spring. This is a technique

called displacement control.

Full-Scale Column without Steel Casing

The example used in the comparison was a full scale (60" diameter) flexure column tested by the

National Institute of Standards and Technology (Stone and Cheok, 1989). The column represents

the current ductile design for bridge columns. The design details for the column are described in

Table D1. The test column was subjected to an axial compression force of 1000 kips and a lateral

cyclic displacement of increasing amplitudes until failure of the column.

Table D1: Design details for Full-Scale Flexure Column

Diameter D 60"

Height L’ 30'

89

cover to main bar 4"

Concrete Strength f’co 5.2 ksi

Longitudinal Steel

Yield Strength fy

25 #14

68.9 ksi

Transverse Steel

Yield Strength fyh

#5 Spiral at 3.5"

71.5 ksi

Axial Force 1000 kips

0

50

100

150

200

250

300

350

Late

ral F

orc

e (

kip

s)

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14Lateral Deflection (in)

Experimental Values COLRET Values Flpier Values

Full-Scale Column

Figure D12: Force Deformation Curve for Full Scale Column

The force deformation curve for the full-scale column is given in Figure D12. As can be seen

from the figure, the data from FB-MultiPier program is generally close to both the COLRET

values and the experimental data. For the majority of the curve the FB-MultiPier values are less

than the COLRET values. Also, it is noted that the initial stiffness of the response is higher from

the CORLET than obtained from the FB-MultiPier Analysis and the measured response.

90

Half Scale Column With Steel Retrofitting Jacket

The second example analyzed for comparison purposes was a test column with a 24" diameter is

about half scale for most applications. It is retrofitted with a steel sleeve that has a length of 48

inches. The design details for the column are shown in Table D2.

Table D2: Design details for Column With Steel Jacket

Diameter D 24"

Height L’ 12'

Cover to Main Bar 4"

Concrete Strength f’co 5.2 ksi

Longitudinal Steel

Yield Strength fy

26 #6

45.7 ksi

Transverse Steel

Yield Strength fyh

#2 hoops at 5 in.

51.0 ksi

Length of Jacket 48"

Thickness of Jacket .188"

Yield strength of Jacket 47 ksi

Axial Force 400 kips

91

0

10

20

30

40

50

60

70 L

ate

ral F

orc

e (

kip

s)

0 1 2 3 4 5 6 7 Lateral Deflection (in)

Experimental Values COLRET Values FlPier Values

Column 4

Figure D13: Force Deformation Curve for Jacketed Column

The force-deformation curve for the jacketed column is given in Figure D13. Looking at the

results, we can see that FB-MultiPier provides a close estimation of the experimental and

COLRET curves until the post yield region of curve where we see a reduction in the lateral load

capacity predicted by FB-MultiPier in comparison to the experimental and COLRET values. It is

also noted that the CORLET program show slightly greater strengths than that for the test.

Conclusions

A model for the prediction of the non-linear response of circular concrete piles with confinement

has been presented. More details on the model are available in Stone and Cheok (1989) .

92

This model has been incorporated into the FB-MultiPier computer program that is used

specifically for analyzing bridge pier structures consisting of pier columns and cap supported on

piles or shafts. This allows the user of the program to model the behavior of concrete piles

confined by hoops, spirals and/or a steel jacket subjected to a broad variety of loadings.

In the comparative studies conducted, the FB-MultiPier results show generally less of an increase

in strength and ductility than those given by the COLRET program. This is due to the following

differences between the FB-MultiPier program and the CORLET program.

First, equation d47 is used to compute the maximum concrete strain, ecu gives less strain than the

procedure using COLRET. COLRET uses a more complex procedure that was only documented

for grade 40 and grade 60 steel. The FB-MultiPier program is written to handle a wide variety of

inputs and thus it used the more conservative equation d47 which is applicable for any grade of

steel.

Second, the COLRET program assumes the entire area contained within a diameter ds is confined

in integrating the stresses over the column area, whereas FB-MultiPier conservatively uses only

the effectively confined area of the core.

Finally, in the case of an external steel jacket, FB-MultiPier neglects the longitudinal stiffness of

the jacket, when using the confined model and the COLRET program takes this stiffness into

account.

These differences tend to give a somewhat conservative solution, which is probably best for a

general purpose program to be used for a wide variety of applications. The program can of course

be modified to accommodate more detailed models in the future.

Rectangular Section Properties


Enter the properties for a rectangular cross section in the following fields:

1. Edit Bar Groups

2. Group Data

3. Void Data

93

4. H-Pile Properties button

Figure A52a: Rectangular Cross Section Properties Dialog - Custom Group Method

94

Figure A52b: Rectangular Cross Section Properties Dialog - Percentage Group Method


Void Data

Enter the diameter for a circular void, or the length and width for a rectangular void.

Return to the Rectangular Section Properties page.

95

H-Pile Properties

H-Pile Properties

Enter the properties of the H-pile in the following fields:


2. Section Orientation

Figure A51: H-Pile Cross Section Properties Dialog

Return to the Section Type, the circular section properties Miscellaneous, or the Rectangular

Section Properties page.

Section Dimensions

Enter the depth, width, web thickness, and flange thickness of the H-pile in the text boxes.

96

Return to the H-Pile Properties page.

Section Orientation

Select the orientation of the H-pile (Web horizontal or web vertical).

Return to the H-Pile Properties page.

H-Pile Properties

Pipe Pile Properties

Pipe Pile Properties Enter a section length, diameter, shell thickness, and unit weight. Concrete is not included in this cross section. (f’c and Ec are set to zero.)

Material Properties

Material Properties

Choose between a Default Stress/Strain option and a Custom Stress Strain option.

Depending upon the stress-strain selection, the "Edit Properties" and "Plot Stress Strain" buttons

will yield different windows.

Return to the Full Cross-Section Pile Properties or the Full Pier Component Properties page.

Default Stress/Strain Curves

97

Depending upon the type of cross section chosen, the user can edit the individual material

properties, if the "Custom Stress Strain" option is selected, and the "Edit Properties" button is

clicked.

First choose a material type on the right, and then enter the properties for that material in the text

boxes.

Figure A53: Material Stress/Strain Properties Dialog

Return to the Material Properties page.

Custom Stress/Strain

98

The user can edit the stress-strain data of the materials present, if the "Custom Stress Strain"

option is selected, and the "Edit Properties" button is clicked.

First choose a material type on the right, and then enter the stress-strain data for that material in

the spreadsheet.

Figure A54: Custom Material Stress/Strain Properties Dialog

Return to the Material Properties page.

Section Stress-Strain Plot

If the "Plot Stress Strain" button in the Full Cross-Section Pile Properties window is clicked, or the

"Plot" button in the Custom Stress/Strain window is clicked, then a stress-strain plot will appear.

99

One can view the stress-strain plot for each material present in the problem, by selecting that

material from the options at the top.

Figure A55: Graph of Material Stress/Strain Properties

Return to the Full Cross-Section Pile Properties page or the Custom Stress/Strain page.

Soil Tab

Soil Tab

Choose soil set drop down to add a soil set.

Choose soil layer drop down to add a layer.

Choose soil model, then click 'Edit' to specify properties.

100

The 'Group' button specifies P-Y multipliers.

Edit the soil with the following options:

1. Soil Layer Data

2. Soil Layer Models

3. Soil Strength Criteria

4. Elevations

Figure A56: Soil Tab

The ‘Plot ’ button will activate the Printable Soil Graph dialog which allows the user to view and

print the various soil curves.

The ‘Table‘ button provides access to an alternate method for creating/modifying soil layers. This

feature allows the user to view/modify multiple soil sets and layers and the same time and quickly

enter properties for each.

101

The ‘Import’ button will retrieve all soil information (all soil sets, all soil layers, all soil

properties) from an existing input file, and replace the current soil data in the open model with this

data.

Water Table

The user has the option of specifying a water table for each soil layer. The latter may be used to model flowing water, perched water or continuous static water. Each soil layer must have a water table associated with it in order to compute effective stresses. In the case where the total stress is equal to the effective stress (i.e. no pore pressure), the user needs to place the water table for the layer at or below the layer’s bottom boundary, i.e. specify a water elevation at or below the bottom of the layer.

Self-weight of the piles is corrected when the pile is within the water table. The submerged

portion of the pile uses the buoyant unit weight.

Soil Layer Data

Create a new soil set or select an existing one from the "Soil Set" drop-down list.

Create a new soil layer or select an existing one from the "Soil Layer" drop-down list.

Select the type of soil from the following options in the "Soil Type" drop-down list:

1. Cohesionless

2. Cohesive

3. Rock

Select the layer models for each soil layer:

1. Lateral

2. Axial

3. Torsional

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The Tip Model selection only applies to the soil layer that contains the pile tip. It will be disabled for all other soil layers.

Enter the unit weight for the current soil layer in the "Unit Weight" text box.

Note: The unit weight is the total unit weight of the soil. The program will automatically

subtract the unit weight of water to get the effective unit weight

Return to the Soil Tab page.

Elevations

Enter the depth of the water table, the top of the layer, and the bottom of the pile.


Soil Table

All soil set and soil layer properties can be entered using the Soil Table. There are three main steps to complete this process.

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Figure A57: Soil Table (Global Data Tab)

1) Enter Soil Set data. From the Global tab, information is entered for each soil set used. Each soil set requires 4 properties need to be entered; number of soil layers, water table elevation, SPT ‘N’ values and number of cycles used.

2) Enter Soil Layer data. Under the Soil Set data on the Global tab, properties must be set for every layer in each set. Each layer requires; soil type, top and bottom elevations, unit weight, internal friction angle, and the Soil Model used for Lateral, Axial, Torsional and Tip. The option to set properties for both top and bottom of layer can be set here.

Note: The unit weight is the total unit weight of the soil. The program will automatically subtract the unit weight of water to get the effective unit weight.

3) Enter Soil Layer Properties. Move to each of the tabs (Lateral, Axial, Torsional, Tip) in turn and enter the requested properties. Each tab contains a table with a row for each soil layer and columns for all the possible properties that could be used by the available models. The selected model is displayed here and can be changed, which will update the global tab and will change the active table cells that are available to enter data.

Soil Table Tutorial

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Soil Layer Models

Soil Layer Models

Select options from the following drop-down lists to model the soil:

1. Lateral

a. Cohesionless

i. Sand (O'Neill)

ii. Sand (Reese)

iii. Sand (API)

iv. Custom P-Y

b. Cohesive

i. Clay (O'Neill)

ii. Soft Clay Below the Water Table

iii. Stiff Clay Below the Water Table

iv. Stiff Clay Above the Water Table

v. Clay (API)

vi. Custom P-Y

c. Rock

i. i. i. i. i. i. i. i. Limestone (McVay)

ii. Limestone (McVay) : NO 2-3 Rotation

iii. Sand (O'Neill)

iv. Sand (Reese)

v. v. v. v. v. v. v. v. Sand (API)

vi. Clay (O'Neill)

vii. Soft Clay Below the Water Table

vii. Stiff Clay Below the Water Table

ix. Stiff Clay Above the Water Table

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x. Clay (API)

xi. Custom P-Y

2. Axial

a. Driven Pile

b. b. b. b. b. b. b. b. Drilled Shaft Sand

c. c. c. c. c. c. c. c. Drilled Shaft Clay

d. d. d. d. d. d. d. d. Drilled Shaft IGM

e. e. e. e. e. e. e. e. Driven Pile Sand (API)

f. f. f. f. f. f. f. f. Driven Pile Clay (API)

g. g. g. g. g. g. g. g. Drilled Shaft Limestone (McVay)

h. h. h. h. h. h. h. h. Custom T-Z

3. Torsional

a. Hyperbolic

b. Custom T-?

4. Tip

a. a. a. a. a. a. a. a. Driven Pile

b. b. b. b. b. b. b. b. Drilled Shaft Sand

c. c. c. c. c. c. c. c. Driven Pile Sand (API)

d. d. d. d. d. d. d. d. Drilled Shaft Clay

e. e. e. e. e. e. e. e. Driven Pile Clay (API)

f. f. f. f. f. f. f. f. Drilled Shaft IGM

c. Custom Q-Z

One can edit the properties of the selected option by clicking the "Edit" button which opens the

Additional Soil Properties dialog below. One can also click the ‘Table ’ button to use the Soil

Table for entering soil properties.

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Figure A57: Additional Soil Properties Dialog

Clicking the "Dynamic Properties " button will open the Soil Dynamics Dialog which will allow

the user to input additional soil properties that pertain only to dynamic type analysis.

See Soil-Pile Interaction for details on the soil properties.

When using a custom soil curve, one can enter/edit the properties of the selected option by

clicking the "Edit" button which opens the dialog below.

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Figure A58: Custom Soil Properties Dialog

The Import Data button retrieves custom curves data from a text (.txt) file, and replaces the current curve

data in the table.

The Save to File button saves the custom curve data from the table to a text (.txt) file, in the format below.

Number of Curve Points in File

XValue YValue

XValue YValue

XValue YValue

XValue YValue

XValue YValue

XValue YValue

XValue YValue

The ‘Plot ’ button plots a "load" vs. deflection graph based upon the selected options.

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The Group button allows the user to specify advanced properties for the soil model.

The ‘Specify Top and Bottom Layer Props’ checkbox allows you to enter different soil properties

at the top and bottom of each layer. The values will be interpolated across the layer.


Soil Dynamics Dialog

Figure A59: Dynamic Soil Properties Dialog

The Dynamic Soil Properties dialog is used to input additional soil properties that pertain only to dynamic type analysis. It is available by clicking the "Dynamics Properties" button on the "Additional Soil Properties" dialog. These properties are for lateral behavior only.

Soil Model Plot

109

As of version 4.10 this topic has been renamed and moved. Please see ‘Printable Soil Graph for

the later help file entry.

Depending upon options selected in the Soil Layer Models section, different types of load vs.

deflection curves are plotted.

1. Lateral—Plots the lateral reaction per unit length vs. lateral deflection

2. Axial—Plots the axial stress vs. axial displacement

3. Torsional—Plots torsional stress vs. rotational displacement

4. Tip—Plots the tip force vs. tip displacement

Figure A60: Printable Soil Graph dialog

Return to the Soil Layer Models page.

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Soil Plot Tutorial

Printable Soil Graph

The ‘Plot’ button on the Soil page actives the Printable Soil Graph Dialog which allows users to plot the different types of load vs. deflection curves for multiple nodes of a pile. All plot types (P-Y, T-Z, T-0, Q-Z) may be viewed (one at a time) by changing the selected Plot Type radio button.

1. P-Y (Lateral) - Plots the lateral reaction per unit length vs. lateral deflection

2. T-Z (Axial) - Plots the axial stress vs. axial displacement

3. T-0 (Torsional) - Plots torsional stress vs. rotational displacement

4. Q-Z (Tip) - Plots the tip force vs. tip displacement

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Figure A60: Printable Soil Graph dialog

The properties of the selected Soil Layer are displayed on the right hand side for easy reference, and the exact plot values for the plot are displayed in a table below this. Each displayed plot and its corresponding data table may be printed or saved using the option buttons below each.

The Soil Set may be changed and will affect both the Soil Layers and Piles settings available. The only available Soil Layers will be those that exist in the selected Soil Set. Only Piles currently in the selected Soil Set will be available and will control the nodes (elevations) available for display.

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The elevations available are based on the selected Soil Layer and the location of nodes with in the selected pile. Elevations are listed from top down and will include the top of layer, all the nodes within the layer and then the bottom of layer. Each selection displays both the node number and elevation of the selection. Once these selections are completed press the ‘Update Plot’ button to show the new plot and table data.


Soil Plot Tutorial

Advanced Soil Data

Select the type of P-Y multipliers to use from the following:

1. User defined P-Y multipliers

2. All P-Y multipliers are one

3. Use the default P-Y multipliers by clicking "Default"

The user can choose to enter soil data for the top and the bottom of each layer.

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Figure A61: Advanced Soil Layer Properties Dialog


Soil Strength Criteria

Soil Strength Criteria

Enter the internal friction angle of the soil.

Enter the number of cycles for a cyclic loading.

Check the "Use SPT N Values" box and click the Edit SPT button to have the program calculate

the phi-angle.

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SPT Window

Enter the depth of the water table at the drilling location.

Enter the number of data points with N values for the calculation of the internal friction angle.

Enter the profile for the N values.

Choose to correct for overburden.

Figure A63: SPT Data Dialog

Return to the Soil Strength Criteria page.

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Pier Tab

Pier Tab

The 'Edit Cross Section' button allows selection of structure cross sections.

To specify bearing locations, check the bearing location box, then click the Bearing Locs button to

specify the bearing locations. Bearing locations must be specified before applying AASHTO

loads.

To specify tapered sections, check the taper box and specify the number of uniform sections.

This page is also the Wall Structure page for the Retaining Wall and Sound Wall options, and the

Bent Cap page for the Pile Bent option.

Edit the pier properties with the following options:

1. Pier Geometry

2. Pier Cross Section Type

3. Taper Data

116

Figure A63: Pier Tab

Taper Data

Choose to apply a taper to the pier column, pier cap beam, and the pier cap cantilever.

Also, select whether the cantilever taper is linear or parabolic.

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Figure A64: Pier Taper End Point Locations

For more detailed explanation, see the Taper Modeling page.

Return to the Pier Tab page.

Pier Geometry

Pier Geometry

Enter the height of the pier, the cantilever distance, the column spacing, the column offset, and the

number of pier columns.

118

Enter the number of column nodes, cantilever nodes, and beam nodes.

Choose to specify Bearing Locations for the pier.

Choose to have flooded pier columns.

Figure A65: Pier Node Spacing Diagram

119

Figure A66: Pier Cap Slope


Pier Rotation Angle

Pier Rotation Angle can be entered from the Bridge Page.

Figure: B2 Pier Rotation Angle

120

Bearing Locations

Select either uniform or variable bearing spacing. You will only be able to enter data into the

appropriate field for your selection.

If the current problem has a single pier then the Bearing Layout options will be visible. This

allows you to select one or two rows of bearing locations. If the problem has multiple piers then

this option will be located on the Bridge Tab. The interface will alter itself to only request the

needed data for the options selected.

Enter the number of Bearing Locations, the Column Offset of the starting location and the spacing

between locations. If more than one bearing row is present then the Bearing Offset must also be

entered.

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Figure A67: Bearing Location Dialog

Return to the Pier Geometry page

Bearing Angle

Bearing Angle can be entered from the Bridge Page.

Figure: B1 Bearing Angle

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Pier Cross Section Type

Pier Cross Section Type

A different edit window appears depending upon the type of cross section selected.

If "Gross Properties" is selected and the "Edit Cross Section" button is clicked, then the Gross Pier

Component Properties window will appear. If Gross Properties are selected only linear analysis is

possible.

Otherwise, if "Full Cross Section" is selected, then the Full Pier Component Properties window

will appear. When Full Pier component properties are input non-linear analysis is an option and

linear analysis also. (For linear analysis the program calculates linear elastic properties from the

Full Property description.)


Gross Section Pier Properties

Gross Pier Component Properties

Modify the properties of a linear pier cross section in the following fields:

1. Pier Components


3. Section Data

4. Section Properties

5. Parabolic Taper Cantilever Properties

123

Figure: G1 Gross Pier Properties

Return to the Pier Cross Section Type section.

Pier Components

Select the pier component to edit, or add and remove components.

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Figure A69: Component Taper End Point Locations

Return to the Linear Pier Component Properties or the Full Pier Component Properties page.

Database Section Selection

If the "Use Database Section" option is selected, the user can select from a predefined set of cross-

sections.

In the Linear Pier Component Properties page, there is only one option (Linear Pile) when you

click on the "Retrieve Section" button.

However, in the Full Pier Component Properties page, there are the following options:

125

Figure A70: Pier Cross Section Options

If the "Modify Current Section" option is selected, the user can customize the current cross

section.

Furthermore, the user can also save custom cross sections by clicking the "Save Section" button.


Section Data

Enter the area and the unit weight of the section

Return to the Linear Pier Component Properties page.

126

Section Properties




3. Torsional Inertia


5. Shear Modulus


Return to the Linear Pier Component Properties page.

Parabolic Taper Cantilever Properties

Enter the depths for a cantilever with a parabolic taper.

Figure A71: Cantilever Parabolic Taper Properties

127


Full Cross Section Pier Properties

Full Pier Component Properties

Modify all of the properties of a pier cross section in the following fields:

1. Pier Components


3. Section Type


5. Material Properties

6. Parabolic Taper Cantilever Properties

7. Section Details

128

Figure A72: Pier Full Cross Section Properties Dialog

Return to the Pier Cross Section Type section.

Section Dimensions

The fields in which one can enter data depend upon the type of cross section selected.

Circular Section:

129

1. Diameter

2. Unit Weight

Rectangular Section:

1. Width

2. Base

3. Unit Weight

H-Pile:

1. Unit Weight

Bullet:

1. Diameter

2. Width

3. Unit Weight

Figure A74: Bullet Cross Section Dimensions

Return to the Full Pier Component Properties page.

130

Section Type

Section Type


The "Edit Section Contents" button yields different windows depending upon the type of cross

section selected.

1. Circular Pile

2. Square Pile

3. H-Pile

4. Bullet


Return to the Full Pier Component Properties page.


H-Pile Properties


H-Pile Properties

H-Pile Properties

Bullet Section Properties

Bullet Section Properties

Edit the properties of a bullet section in the following fields:

1. Edit Bar Groups

131

2. Group Data

3. Void Data

4. Cross Section Orientation

Figure A64:


Group Data

132

Enter the data for the bars in an individual bar group in the following text boxes:

Enter the number of bars in the group in the "Number of Bars/Strands" text box.

If the rectangular option is selected, choose the orientation of the group of bars from the "Group

Orientation" options—parallel (linear bar groups) or circular end (semicircular regions at the ends

of the section).

Then, enter the area of the bars and, depending upon the layout, the diameter of a circular end

layout or the starting coordinates of a parallel layout.

Choose between mild steel or prestress for the type of steel in the group.

If prestress is chosen, then enter the prestress after losses.

Return to the Bullet Section Properties page.

Void Data

Enter the diameter for a bullet void, or the length and width for a rectangular void.


Cross Section Orientation

Select whether the cross section is oriented in the horizontal direction or the vertical direction.

133


Material Properties

Bent Cap

2D Bridge View

Wall Structure

Sound Wall Explanation

Figure: SW1 Sound Wall Explanation

134

Extra Members Tab

X-Members Tab

Additional members can be added to connect nodes in the pier.

Sections to be used for extra members can be selected from the "Extra Member Sections"

dropdown which contains sections used for the pier, pile and any sections created under the extra

member page. New sections can be created using the "Edit Cross Section" button.

The cross section type (Gross Properties or Full Cross Section) uses the same type selected for

the Pier cross sections and can only be changed by changing the selection on the Pier page.

To add an extra member, click on the first node (I-Node). Then, click on the second node (J-

Node). Click the 'Add' button to put the member in the list and choose an appropriate section

property.

To change the location of an extra member, select an extra member from the "Extra Member" list.

Then change the I-Node, J-Node, or both. This can be done by clicking nodes in the 3D Edit

Window, or by typing new values in the I-Node or J-Node boxes. Then click the "Update" button.

Create extra members using the following options:

1. 1. 1. 1. 1. 1. 1. 1. Extra Members List

2. Extra Member Sections

3. Nodes Attached

135

Figure A75: Extra Members Tab

Notes: Extra members cannot be used to replace sections along the length of a pile. Extra

members cannot cross the plane of the pile cap. For example, an extra member element cannot

connect a column node and a pile node. However, an extra member element can connect two

column nodes, or two pile nodes (but not along the same pile). Extra members are not available in

the following models: Pile and Cap Only, Stiffness, Single Pile, Column Analysis.

Extra Members List

Add and remove extra members to and from the project.

Return to the X-Members Tab page.

Extra Member Sections

136

Select the cross section type of the extra member from the drop down list.


Nodes Attached

Select the nodes to attach the member to.


Load Tab

Load Tab

To add a load, select a node with mouse in 3-D View window.

Then click the right 'Add' button to add the load to the node.

Enter load values for the 6 degrees of freedom.

Additional load cases can be added by clicking the left 'Add' button.

The 'Table' button shows a table of the loads for the selected load case.

The self-weight and buoyant load factors are used to set the contribution of self-weight and buoyancy for

each load case. These are used for non-AASHTO loads.

For AASHTO load cases, self weight is included by adding a dead load type case and buoyancy is

included by adding a buoyancy type case. See AASHTO tab to automatically include self weight and

buoyancy.

Edit the loads in the following areas:

137

1. Load Case

2. Node Applied

3. Loads

In static analysis mode, the Load tab looks as follows:

Figure A76-a: Load Tab

Check "Include Preload Case" to apply a pre-existing load to all load cases. Preload is typically used to

model construction loads.

Check "Applied Displacement" to apply a displacement (rather than a load) to a node. Loads and

Displacements can not be applied at the same node in the same load case.

In AASHTO load mode, the Load tab looks as follows:

138

Figure A76-b: Load Tab in AASHTO Mode

The ‘L’ and ‘R’ designations next to the bearing loads indicate a left and/or right bearing row,

respectively.

In dynamics analysis mode the Load tab looks as follows:

139

Figure A76-c: Load Tab in Dynamic Analysis Mode

Nodal loads are marked as either static (S), or dynamic (D). Clicking on the S or D letter toggles

the load type from static to dynamic, and vice versa. For dynamic load types, the directional

factors specify the direction of load application. The factors must be either 1 or 0, where 1

indicates load application in that direction, and 0 indicates no load application in that direction.

The load function is selected from the load function combo box. Each node can have a different

load function. Click on the "Acc. (all nodes)" placeholder in the node list to specify a direction

when the ground acceleration option is selected.

Click the "Table" button to edit both static and dynamic loads.

Load Case

Select a load case to view or modify. Add and remove new load cases.

Return to the Load Tab page.

140

Buoyancy

The buoyant force on the bridge substructure that is submerged, i.e., below the water table, is automatically computed if a buoyancy factor greater than 0 is selected in non-AASHTO mode and if buoyancy is activated (checked on) in AASHTO mode. The computation includes piles, pile cap, pier columns. Partial buoyancy for the pile cap is considered in the following manner: If the water table exists between 1/8 and 3/8 pile cap thickness measured from the bottom of the pile cap, then the half of the pile cap volume is used to calculate the buoyant force. If the water table exists above 3/8 of the pile cap thickness, then the entire pile cap volume is used to calculate the buoyant force. The user should select the water table elevation accordingly to include (or exclude) the buoyancy effect in the self-weight calculation of the pile cap. A convenient way to check buoyancy and self-weight calculations is to include only these loads, run the program, and then view the "Sum of Total Soil Spring Loads", Z direction in the output file.

Node Applied

Select the node to which a load is applied. Add and delete a nodal load.

Alternatively, click the Table button to edit the loads in a spreadsheet format.

If AASHTO load combinations are used, click the AASHTO Table button to edit the loads in a

spreadsheet format.

Designate AASHTO load cases by selecting the type of load (Nodal loads can be added in

addition to bearing loads).


Loads

141

Select whether or not pre-loading conditions (i.e. thermal stresses, construction loads, shoring,

etc.) are present. For the pre-loading situation, the equilibrium loads are found from the pre-

loading. Then, after equilibrium is established, the analysis uses the equilibrium conditions to

calculate the solution for the load cases

Enter point loads in the x, y, and z directions, and moments about the x, y, and z axes.

Also, enter factors for self-weight and buoyancy (for non-AASHTO loads).

Check ‘Applied Displacement’ to specify a displacement rather than a load for a node.


Bearing Location Loads

The following information is used by piers with bearings locations. The information under the LOADBP

header describes the concentrated loads applied to the bearing locations.

LOADBP

PADNUM L= LC F= FX, FY, FZ, MX, MY, MZ T=TYPE B=DIR (one line per nodal load)

Where

PADNUM is the bearing number

LC is the load case number

FX is the force in the global X-direction

FY is the force in the global Y-direction

FZ is the force in the global Z-direction

MX is the moment about the global X-axis

MY is the moment about the global Y-axis

MZ is the moment about the global Z-axis

142

TYPE is the load type specified in AASHTO (ignore for non-AASHTO loads)

DIR is the bearing row ("L" for left or "R" for right)

:

This section must end with a blank line.

Load Table

Load Table

Edit the loads in the spreadsheet by selecting a text field to edit.

Alter the spreadsheet with the following options:

1. Table Format

2. Table Edit Options

3. Load Case Options

The "Load Table" is used to define nodal loads in a spreadsheet-style format. Static and dynamic

loads are separated into two separate tables that can be toggled using the "Table Format" options.

Dynamic Loads

Enter the load case, node, direction factors (1 or 0), and the load function.

143

Figure A77-a: Load Table in Dynamic Analysis Mode

Static Loads

Enter the load case, node, and load values.

144

Figure A77-b: Load Table in Static Analysis Mode


Table Format

Select whether the table shows a "Single Load Case" or "All Load Cases".

Click the "Update and Sort" button to refresh the table.

Return to the Load Table page.

Table Edit Options

Insert and delete rows to and from the table.


Load Case Options

Add and delete load cases to and from the table.

Choose to duplicate an existing load case.


145

AASHTO Load Table

AASHTO Load Table



1. AASHTO Table Format

2. AASHTO Table Edit Options

3. AASHTO Load Case Options

146

Figure A78: AASHTO Load Table


AASHTO Table Format

The AASHTO load cases are shown in the load tree. Click on the ‘+’ sign to expand the case.

Bearing loads are shown first, followed by the nodal loads.

AASHTO Table Edit Options

147

With a load case expanded, right click the mouse on a nodal load to insert or delete loads. The

‘Add Load’ and ‘Remove Load’ buttons can also be used.

Bearing location nodes cannot be removed.

AASHTO Load Case Options

Load cases are added by selecting a load case from the load type list and then clicking the ‘Add

Case’ button. Only certain load types can have multiple cases. Select a load case from the load tree

and click the ‘Remove Case’ button to remove the load case.

Spring Tab

Spring Tab

To add a spring to the pier, select node with the mouse in 3-D View window.

Then click the 'Add' button.

Enter spring values for the 6 degrees of freedom.

Use the check boxes to apply the springs to each load case.

Edit the springs in the following areas:

1. Spring Stiffness

2. Spring Nodes

148

Figure A79: Spring Tab

Spring Stiffness

Enter the stiffness for each x, y, and z translation spring, and for each x, y, and z rotational spring.

Return to the Spring Tab page.

Spring Nodes

Click on a node in the 3-D view or select a node using the text box and click the "Add" button to

add a node to the "Spring Node List".

Select the load case to apply the springs to from the "Apply to Load Case" list.

149

Also, use the "Del" button to delete a node from the list.

Return to the Spring Tab page.

Discrete Mass/Damper Tab

Mass/Damper Tab

The Mass/Damper tab provides the capability of applying concentrated masses or dampers to any

pile cap or pier node. To apply a concentrated mass or damper, click on the node in the 3D View

window and then click the "Add" button to place the node in the node list. Concentrated mass

values can be entered without concentrated damper values, and vice versa. Concentrated damper

values can only be entered if "Damping" is enabled in the Dynamics tab.

Figure A80: Mass/Damper Tab

View Mass/Dampers in 3D Window

Mass/Dampers in 3D View

150

All concentrated masses and dampers are shown. Dampers are shown as a green dashpot. Masses

are shown as a purple cube.

Figure A81: Concentrated Mass and Damper in 3D View (Thin Element Mode)

151

Retaining Tab

Retaining Tab

Enter Retaining wall parameters for each layer.

Each layer will cause a pressure to be applied to the wall.

Each layer is divided into a number of sublayers.

A minimum of 10 sublayers is recommended for each layer.

The wall is modeled as a cantilever with its base located in the center of the pile cap.

(For the case where the wall is offset from the center of the Pile Cap use the remove feature in the

Pile edit window.

The weight of the retained soil must be included as load on the footing or by increasing the footing

concrete

self weight. Soil weight is not automatically accounted for)

Enter the data for the retaining wall in the following fields:

1. Soil Layer

2. Wall and Layer Geometry

3. Soil Layer Data

4. Wall Load Data

152

Figure A82: Retaining Tab

Soil Layer

Select a soil layer to edit from the drop down menu, or add and remove a soil layer.

Return to the Retaining Tab page.

Wall and Layer Geometry

Enter the incline of the wall.

Enter the incline of the top layer, the ground water height, and the unit weight of the water.

153

Enter the thickness, and the number of layers to divide the individual soil layers into.

Figure A83: Retaining Wall Geometry


Retaining Wall Explanation

154

Figure: A1 Retaining Wall Explanation

Soil Layer Data

Soil Layer Data

155

Choose between "Pressure at Rest" and the "Active Case" options, and then click the Layer Data

button to specify the data.


Retaining Wall Soil Layer Data

Enter the following properties off the retained soil layer:

1. Cohesion

2. Soil Angle of Friction

3. Soil-Wall Angle Friction

4. Unit Weight of Soil

5. Saturated Unit Weight of Soil

Return to the Soil Layer Data page.

Wall Load Data

Wall Load Data

Select the case number and click Surcharge.


Surcharge

156

Depending upon the type of surcharge selected, different parameters will be required.

1. No Surcharge

a. No parameters

2. Uniform Surcharge

a. The surcharge load

3. Line Load

a. Wall distance

b. Load intensity

4. Strip Load

a. Wall distance

b. Load width

c. Load intensity

Return to the Wall Load Data page.

Bridge Data Edit

Bridge Tab

Bridge Tab

The Bridge Tab is used generate and modify substructures (pier foundations) and superstructures

(bridge spans).

157

Figure A25: Bridge Tab

Substructure

Select a pier from the Substructure list or select "Add Pier " to add a new pier to the model. Click

the "Del" button to remove a selected pier.

The Model Type can be either a General Pier or Pile Bent model. Both models are capable of

having bearing locations, which are essential for connecting the piers using bridge spans.

The Global X Coord and Global Y Coord are used to layout each pier in the bridge model. By

default, the origin of the first pier in the multiple pier model is at the corner of the pile cap.

The Rotation Angle specifies a pier rotation about the vertical z-axis. The pier rotation is specified

as clockwise positive in the FB-MultiPier coordinate system and is typically used to model skew

or radial piers on a curved alignment.

Select the number of Bearing Rows and specify if the span should be continuous. Specific boundary conditions can be selected and customized by clicking the Edit Supports button.

158

Superstructure

Select a Span to edit from the span combo box. The "C/C Length" indicates the span length from

the center bearing line of one pier to the center bearing line of the next pier. Click the "Edit Span "

button to edit the span section properties.

Edit Supports

Custom bearing connections can be specified by selecting a boundary condition from the combo

box. Boundary conditions can be Released (free to move), Constrained (prevented from

movement), or Custom (user-defined load-displacement curve).

There are two versions of this dialog that are displayed based on the number of bearing rows

requested.

Single Row: Only a single option is available

159

Figure A26: Custom Bearing Connection Dialog for Single Row

Two Rows: Left and Right Rows are specified

Figure A27: Custom Bearing Connection Dialog for Two Rows

Click the "Edit Custom Bearings " button to define custom bearings using a load-displacement curve.

Edit Custom Bearings

Custom bearing behavior can be modeled using a load-displacement curve. This curve can be applied to any of the six degrees of freedom for a bearing connection. A maximum of 20 values can be used to define a custom bearing load-displacement relationship. Values should be entered from smallest to largest displacement. Click the "Add" button to add a new load-displacement curve. Click the "Del" button to remove an existing load displacement curve. Click the "Update Plot" button to refresh the load-displacement plot.

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Figure A28: Custom Bearing Data Dialog

Edit Span

Enter the cross-section description properties for the bridge superstructure. The program uses

these properties to model an equivalent beam that connects the centerline of two pier caps. The

Begin Height and End Height parameters are used to offset the beam from the center of gravity of

the pier cap to the center of gravity of the span.

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Figure A29: Bridge Span Properties Dialog

Section Area is the entire span area in the transverse direction, including girders, roadway, and parapets. Transverse Area is the span profile area for wind load on the structure application (usually computed as: [girder depth + roadway depth + parapet depth] x span length).

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Begin Height and End Height are measured from the c.g. of the pier cap to c.g. of the bridge span. Live Load Height is measured from the c.g. of the pier cap to the c.g. of the Live Load (i.e. at 6 ft above the roadway per AASHTO).

Span End Conditions are set independently for each side of the span. Different end conditions may exist based on the construction; FB-MultiPier can simulate these conditions by assigning various properties to the Transfer Beam.

• • • • • • • • Diaphragm – properties for a rigid element.

• • • • • • • • Non-Diaphragm - relaxed properties for a more flexible beam.

• • • • • • • •Custom – User assigned custom properties (Must be selected to enable Custom Properties Button)

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Figure A30: Variable Bridge Span Properties Dialog

The Variable Span Properties Table displays section properties for each element along the bridge section. Spans are divided into 10 elements of equal length. The 3D Bridge Window will show each element’s size in proportion to the inertia 3 axis entered.

Add Substructure

Figure A31: Add Substructure Dialog

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Choose a structure type for the newly added or changed pier. Then, in the "Select Model" combo, select

from a list of existing piers. This selected pier’s properties will be used for the newly created or changed

pier.

Span End Condition

This dialog is accessible when the "Custom" option is selected for either the Begin or End span end condition, on the Bridge Span Properties dialog.

Figure A32: Span End Condition Dialog

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Model View Windows

Soil Edit Window

Soil Edit Window

Right click in the soil edit window to bring up the view edit menu with the following options:

1. 2D Mouse Control--Hold the Control key and the left mouse button down to enable stretching

a. With the key and button pressed down move forward to stretch up

b. With the key and button pressed down move backward to stretch down

2. Pick Layer—Allows the user to pick a layer

3. Remove Layer—Delete the selected layer from the model

4. Add Layer—Add a new soil layer to the model

3. 5. 5. 5. 5. 5. 5. 5. Split Layer—Split the current layer in to two

layers

4. 6. 6. 6. 6. 6. 6. 6. Reset View

5. 7. 7. 7. 7. 7. 7. 7. Copy Layer—Replace properties of selected

layer with those of layer selected from submenu Note: Clicking the mouse scroll wheel button will

toggle between the Picking mode and the 2D Mouse Control.

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Figure A85: Soil Edit Window

The displayed pile shows the existing nodes currently in the pile. Nodes in the free length are

displayed in red, while nodes in the soil are displayed in blue. The blues nodes (only) are clickable

and selecting one will bring up the Printable Soil Graph dialog, showing the soil curve for the

selected node. Please see Printable Soil Graph for more details.

Pile Edit Window

Pile Edit Window

Right click in the pile edit window to bring up the view edit menu with the following options:

1. 1. 1. 1. 1. 1. 1. 1. 2D Mouse Control

a. Hold the left mouse button down and drag to pan the view

b. Hold the Control key and the left mouse button down to enable zooming

i. With the key and button pressed down move forward to zoom in

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ii. With the key and button pressed down move backward to zoom out

2. 2. 2. 2. 2. 2. 2. 2. Add/Remove Pile—Click on a grid

point/pile to add or remove a pile

3. 3. 3. 3. 3. 3. 3. 3. Add/Remove Cap—Click on a portion of the

pile cap to remove it

4. 4. 4. 4. 4. 4. 4. 4. Pile Data/Batter—Click on a pile to edit the

Pile Data

5. 5. 5. 5. 5. 5. 5. 5. Copy Pile Properties—Click on a pile to

copy properties from the highlighted pile

6. 6. 6. 6. 6. 6. 6. 6. Edit Cap Thickness—Click on a portion of

the pile cap to edit the Cap Thickness

7. 7. 7. 7. 7. 7. 7. 7. Edit Grid Spacing—Click on a spacing

"element" to edit the Spacing

8. 8. 8. 8. 8. 8. 8. 8. Assign Soil Sets—Click on a soil portion to

toggle through the soil sets

9. PY Multipliers—Allows the user to view the PY multipliers in the pile edit window (to view

go to the Soil Tab and click the Group button)

10. Numbering—Allows the user to view the pile numbers

11. Reset View—Returns the view back to the default

12. Help

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Figure A86: Pile Edit Window

Zoom Feature Tutorial

Pile Data

Adjust the arrangement of the piles using the following options:

Select the pile number to edit in the "Pile Number" scroll box.

Choose the cross section type from the list.

Enter the batter of individual piles as the horizontal distance over the vertical distance.

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Figure A87: Pile Batter

Select a pile and soil set to apply to the current pile.

Return to the Pile Edit Window page.

Edit Cap Thickness

Enter the "first" thickness of the cap (not the actual thickness), which allows the user to simulate different types of connections—very thin for a more pin-like connection, or thick for a more rigid connection.

Enter the "second" of the cap, which is the actual thickness to simulate the weight of the cap.


Custom Grid Spacing

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Enter the spacing of the row/column selected.

Alternatively, edit the grid spacing in a spreadsheet format by pressing the Spacing Table button.

Figure A88: Custom Pile Grid Spacing Dialog

Add a new row or column at the mid point of the column or row selected by pressing the "Split

Row/Column" button, or delete a row or column by pressing the "Delete Row/Column" button.


Bridge Plan View Window

3D View Window

3D View Window

Right click in the 3D view window to bring up the view edit menu with the following options:

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1. 3D Mouse Control

a. Hold the left mouse button down and drag to rotate the view

b. Hold the left mouse button and the shift key down and drag to pan the view

c. Hold the Control key and the left mouse button down to enable zooming



6. 3. 3. 3. 3. 3. 3. 3. Picking Node Mouse Control

7. 4. 4. 4. 4. 4. 4. 4. Picking Element Mouse Control—Allows

the user to select items in the view to edit in certain dialogs

a. Pick end nodes in the extra members dialog

b. Pick the loaded nodes in the load dialog

c. Pick the node to apply springs to in the spring dialog

d. View the coordinates of the node in most dialogs

3. Remove Pier Cap Element

a. Click on pier cap element to remove

4. Turn the following options on or off:

a. a. a. a. a. a. a. a. Piles

b. b. b. b. b. b. b. b. Caps

c. c. c. c. c. c. c. c. Nodes

1) 1) 1) 1) 1) 1) 1) 1) All Nodes

2) 2) 2) 2) 2) 2) 2) 2) Pier Nodes

3) 3) 3) 3) 3) 3) 3) 3) Span Nodes

4) 4) 4) 4) 4) 4) 4) 4) All Shell Nodes

5) 5) 5) 5) 5) 5) 5) 5) Bearing Locations

6) 6) 6) 6) 6) 6) 6) 6) Pile Cap Nodes

7) 7) 7) 7) 7) 7) 7) 7) Pile Nodes

8) 8) 8) 8) 8) 8) 8) 8) Column Nodes

9) 9) 9) 9) 9) 9) 9) 9) Cantilever Nodes

10) 10) 10) 10) 10) 10) 10) 10) Pier Cap Nodes

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d. d. d. d. d. d. d. d. Pier

e. e. e. e. e. e. e. e. Loads

f. f. f. f. f. f. f. f. Springs

g. g. g. g. g. g. g. g. Dampers

h. h. h. h. h. h. h. h. Masses

i. i. i. i. i. i. i. i. Soil

j. j. j. j. j. j. j. j. Numbering

k. k. k. k. k. k. k. k. Axes (Local)

l. l. l. l. l. l. l. l. Axes (Global)

m. m. m. m. m. m. m. m. Pier Data

n. n. n. n. n. n. n. n. Thin Elements

5. Views

a. a. a. a. a. a. a. a. XZ Plane—View the model from

the front

b. b. b. b. b. b. b. b. YZ Plane—View the model from

the side

c. c. c. c. c. c. c. c. Reset View—Return the view back

to the default setting

d. d. d. d. d. d. d. d. Help—Shows 3D View controls

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Figure A84: 3D View Window

Element Data Dialog

The 'Element Data Dialog' is a quick way to reference the properties of any pier element, pile

element or extra member element in the model. To launch the dialog, right-click in the 3D View

window. This will launch the window's popup menu. Make sure the window is in 'Thin

Elements' mode (this menu item should have a checkmark next to it). Then select the menu item

'Picking Element Mouse Control'. Then click an element in the model. The dialog will display,

showing the element's data, including element number, location in the model, dimensional data,

and material properties. To change the selected element, simply click another element.

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Fig. E1: Element Data Dialog

Program Results

Pile Results

Pile Results

Use the following windows to view the results of the analysis:

1. Pile Selection

2. Plot Display Control

3. Graphs

Pile Selection

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Select the piles to view in the Graphs.

Figure A92: Pile Selection Window

Return to the Pile Results page.


Plot Display Control

Choose the type of data to be displayed in the graphs:

Structure:

Shear 2

Shear 3

Moment 2

Moment 3

Axial

Demand/Capacity Ratio

Soil (Not Available for Piers):

Soil Axial

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Soil Lateral X

Soil Lateral Y

Soil Torsional

Displacement (Not Available for Piers):

Displacement 2

Displacement 3

Rotational About 2

Rotational About 3

Click "Select all Maximum And Minimum Values" to automatically select the members with the

maximum/minimum values across all load cases. The only curves that display in the plot windows

when this option is selected are the maximum and minimum values.

For AASHTO loads, select the limit state to see the maximum load combination for that limit

state.

For a time step analysis, select a member force combo box item to display the maximum member

force, location, and corresponding time step.

This window shows the depth and pile number of the maximum and minimum values of the

selected piles.

Click on one of the plot windows to display the maximum and minimum values.

Return to the Pile Results or the Pier Results page.

Graphs

Graphs are plotted corresponding to the colored piles on the Pile Selection view.

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Figure A93: Pile Results Graphs

Right click a selected graph and select the option ‘Printable Graph’ to open the printable graph

dialog.

Return to the Pile Results page.

Printable Forces Dialog

This dialog is reached by right clicking in any plot window that contains data on the Pile Results

Page.

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Figure A94 : Pile Printable Forces Dialog

This dialog displays the forces plots of each pile/column/pier cap that is selected on the Pile/Pier

Results Forces dialog, as well as a table listing of the forces in numeric form at each node along

the member.

Graph Options:

- Customize: customize the appearance of the graph, i.e. change the font size, curve colors, graph

range, etc.

- Save as Bitmap: save the graph (not the entire dialog) as a bitmap (.bmp) file

- Print: Print the graph. Clicking this option will open the graph as a bitmap in your computer's

picture viewer (for example, "Window Picture and Fax Viewer"). >From here, the graph can be

printed. This will allow the graph to be printed without the print dialog displaying over the

graph. (To print the entire dialog, click the 'Print' button at the bottom of this dialog).

Table Options:

Print: prints the graph and its contents. (To print the entire dialog, click the 'Print' button at the

bottom of this dialog).

Save Data: saves the table data to a text file.

*If more than one pile/column if graphed, the member with the maximum value will be displayed

in the graph title. For example, (max at Pile 1).

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**The colors used to plot the curves are the identical colors used on the Pile/Pier Forces Dialog.

Printable Forces Tutorial

Pier Results

Pier Results

Use the following windows to view the results of the analysis:

1. Pier Selection

2. Plot Display Control

3. Graphs

Pier Selection

Select the piers to view in the Graphs.

Figure A95: Pier Component Selection Window

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Return to the Pier Results page.


Graphs

Graphs are plotted corresponding to the colored piles on the Pier Selection view.

Figure A96: Pier Results Graphs

Right click a selected graph and select the option ‘Printable Graph’ to open the printable graph

dialog.

Return to the Pier Results page.

Printable Forces Dialog

This dialog is reached by right clicking in any plot window that contains data on the Pier Results

Page.

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Figure A97:Figure A97:Figure A97:Figure A97: Column Printable Forces Dialog This dialog displays the forces plots of each pile/column/pier cap that is selected on the Pile/Pier

Results Forces dialog, as well as a table listing of the forces in numeric form at each node along

the member.

Graph Options:

- Customize: customize the appearance of the graph, i.e. change the font size, curve colors, graph

range, etc.

- Save as Bitmap: save the graph (not the entire dialog) as a bitmap (.bmp) file

- Print: Print the graph. Clicking this option will open the graph as a bitmap in your computer's

picture viewer (for example, "Window Picture and Fax Viewer"). >From here, the graph can be

printed. This will allow the graph to be printed without the print dialog displaying over the

graph. (To print the entire dialog, click the 'Print' button at the bottom of this dialog).

Table Options:

Print: prints the graph and its contents. (To print the entire dialog, click the 'Print' button at the

bottom of this dialog).

Save Data: saves the table data to a text file.

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*If more than one pile/column if graphed, the member with the maximum value will be displayed

in the graph title. For example, (max at Pile 1).

**The colors used to plot the curves are the identical colors used on the Pile/Pier Forces Dialog.

Printable Forces Tutorial

Pier Cross Section Table

The Pier Cross Section Table allows the user to enter and view most pier cross section data in a

single table. This makes double checking the data very easy. Each table column represents one

cross section. The properties available in the table depend upon the cross section shape, behavior,

type of steel, etc. For example, a round cross section would only have the 'Diameter' dimension

enabled, and not the 'Width' and 'Depth' dimensions.

Tips for using the table:

1. For cross section orientation, click the 'Graphic' button in the 'Shape' field. This displays the

cross section shape (not drawn to scale), with the 2-3 axis as reference.

2. If 'Material Properties' fields are not enabled, this is most likely due to a lack of steel

reinforcement in the cross section. Steel must be present in order to enable these fields. To do

so, click the 'Edit Steel' button in the 'Reinforcement' field, and enter steel data as necessary. Then

return to the table and the necessary material property fields will be enabled.

3. To taper a cross section, check the appropriate 'Taper' checkbox. This will create another

column in the table, so that cross section data can be entered for each end of the pier component.

Example: column bottom, column top.

4. To create custom Stress/Strain Curves, select "Custom Stress/Strain" in the 'Material Properties'

field. Then click the 'Custom Curves' button in the 'Custom Curves' field.

5. For quick access to directions on using the table, click the "Help >>" button.

6. When printing the table, to make the table more easily fit on a single page, hide the 'Help'

section on the right side of the table, by clicking the 'Help' button, so that the arrows point to the

right (Help >>).

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Figure P1: Pier Cross Section Table Linear

184

Figure P2: Pier Cross Section Table NonLinear

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Pile Interaction

Interaction Diagrams

View interaction diagrams for the piles or the pier elements.

Choose the type of diagram to view from the drop-down list in the tool bar:

1. Biaxial moment interaction diagram

2. Interaction diagram (2 axis)

3. Interaction diagram (3 axis)

Select the members and segments to display on the interaction diagram from the following:

1. Pile or Pier Selection

2. Segment Selection

3. Interaction Diagram

Pile Selection

Select the pile to view its interaction diagram.

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Figure A98: Pie Selection Window

Return to the Interaction Diagrams page.


Pile Segment Selection

Select the pile member segment to view its interaction diagram.

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Figure A99: Pile Segment Selection Window

Piles with multiple cross sections differentiate between segments by displaying each segment with

a different color/pattern. The legend to the right will provide basic cross section information for

each segment.


Pile Element Selection

Select the pile element from the model to view its interaction diagram.

188

Figure A100: Pile Element Selection Window



Interaction Diagram

View the interaction diagram for the selected segment.

189

Figure A101: Interaction Diagram


Pier Interaction

Pier Selection

Select the pier element to view its interaction diagram.

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Figure A102: Pier Component Selection Window



Pier Segment Selection

Select the pier member segment to view its interaction diagram.

191

Figure A103: Pier Component Segment Selection Window


Pier Element Selection

Select the pier element from the model to view its interaction diagram.

192

Figure A104: Pier Component Element Selection Window



3D Results

3D Results

View the three-dimensional results of the analysis in the following windows:

193

1. 3D Display Control

2. 3D Results Window

3. Result Forces Dialog

3D Results Window

View the results of the analysis. Elements that have a demand/capacity ratio exceeding 1.0 are

shown with a red (highlight) marker.

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Figure A105: 3D Results Window (Bridge View)

Right click in the 3D view window to bring up the view edit menu with the following options:

1. 3D Mouse Control

a. Hold the left mouse button down and drag to rotate the view

b. Hold the left mouse button and the shift key down and drag to pan the view

c. Hold the Control key and the left mouse button down to enable zooming


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2. Picking Mouse Control – Allows the user to select items in the view to edit in certain dialogs

a. Pick end nodes in the extra members dialog

b. Pick the loaded nodes in the load dialog

c. Pick the node to apply springs to in the spring dialog

d. View the coordinates of the node in most dialogs

3. Picking Forces Control – Allows the user to view result forces for selected element.

4. Piles

5. Caps

6. Nodes

a. All Nodes

b. Pier Nodes

c. Pile Nodes

d. Pile Cap Nodes

e. Bearing Nodes

f. Transfer Beam Nodes

7. Pier

8. Loads

9. Node Numbering

10. Element Numbering

a. Connector Elements

b. Structure Elements

c. Pile Elements

11. Element Highlighting

a. Connector Elements

b. Bearing Connector Elements

c. Pile Elements

d. Column Elements

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e. Pile Cap Elements

f. Pier Cap / Bent Cap

12. Axes

13. Plastic Hinge Zones

14. Undisplaced Model

15. Bridge View – Display the full bridge structure

16. Reset View – Return the view back to the default setting

Return to the 3D Results page.

3D Results Dynamic Options

The 3D Display Control is a toolbar option that allows the user to animate a displaced shape plot.

Click the play button on the left to begin animation. Click the pause button on the right to stop the

animation. Use the slider to fine-tune the time step selection. The actual time is shown below the

time step value. This option is currently only available for 3D results mode.

Figure A106: Dynamic Results Animation Control Dialog

The Results Time Plot allows the user to see the variation of displacement with time for a selected

node.

This option is only available in the 3D results mode. Click the "Plot" button in the 3D Results

mode to show the graph.

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Figure A107: Results Time Plot Dialog

Result Forces Dialog

This option is accessed via the following:

-Right click in the 3D Results Window, and select "Picking Forces Control".

-Then click on any pile or pier element in the 3D Results Window. (Pile cap elements and bridge

span elements are not included in this feature).

-The selected element will become highlighted, and the dialog will launch, displaying all relevant

forces in the selected element.

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Figure A108: Result Forces Dialog showing Column forces

*Element # (in Column) is the 1-based index of the element within the column, beginning at the

column base.

**Element # (in Pile) is the 1-based index of the element within the pile, at the pile head.

***Element # (in Model) is the 1-based index of the element in the model. This element number

can be referenced in the .out file.

Element Forces Tutorial

3D Display Control

3D Display Control

Control and view the display data numerically in the following fields:

1. Display Control

2. Node Information

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Figure A109: 3D Display Control Window

The "Results Plotting" section handles the graphical display of dynamic results.

There are two types of results plots:

1. 1. 1. 1. 1. 1. 1. 1. Time vs. Displacement. This

includes graphs for X Translation, Y Translation, and Z Translation.

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2. 2. 2. 2. 2. 2. 2. 2. Time vs. Rotation. This includes X

Rotation, Y Rotation, and Z Rotation.

Select the node you want to plot the results for. Then use the "Results Plotting" combo box to

select the desired graph. Then click the "Plot Results" button.

Return to the 3D Results page.

Display Control

Select the output to view in the Display Window from the following:

1. Displaced Shape—Shows a displaced wire-frame model

2. Displacement Contour—Distinguishes high displacement areas

a. X Translation

b. Y Translation

c. Z Translation

d. X Rotation

e. Y Rotation

f. Z Rotation

3. Stress Contour—Distinguishes areas of high stress concentrations

a. M1

b. M2

c. M12

d. S13

e. S23

f. S1

g. S2

h. S12

4. Mode Shape—Eigenvectors used in modal analysis

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5. Pier Max and Min Forces —Highlights Max and Min locations of selected stress

a. Displacement X

b. Displacement Y

c. Displacement Z

d. Rotation About X

e. Rotation About Y

f. Shear 2

g. Shear 3

h. Moment 2

i. Moment 3

j. Axial

k. D/C Ratio

l. Allow Multiple Forces – see Max Min Forces Dialog

6. Pier Max and Min Forces —Highlights Max and Min locations of selected stress

a. Displacement X

b. Displacement Y

c. Displacement Z

d. Rotation About X

e. Rotation About Y

f. Shear 2

g. Shear 3

h. Moment 2

i. Moment 3

j. Axial

k. D/C Ratio

l. Soil Axial

m. Soil Torsional

n. Soil Lateral X

o. Soil Lateral Y

p. Allow Multiple Forces – see Max Min Forces Dialog

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Return to the 3D Display Control page.

Node Information

View the data for a node in the following areas:

1. Node Number—Select the node to view

2. DOF—Displays the number of degrees of freedom for the selected node

3. Translation—Displays the translation in the X, Y, Z directions of the selected node as a result

of the loading

4. Rotation—Displays the rotation about the X, Y, Z directions of the selected node as a result of

the loading

5. Nodal Coordinates—Displays X, Y, Z coordinates of the selected node prior to loading

Return to the 3D Display Control page.

Max Min Forces Dialog

This option is accessed via the following:

-Select the "Pier Max and Min Forces" or "Pile Max and Min Forces" on the 3D Results Dialog. >From

the menu that is displayed, select the desired force.

-If "Allow Multiple Forces" is selected, the Max and Min Forces dialog will display.

* if more than one force is selected, each element that contains a maximum or minimum force will be

highlighted in the 3D Results Window.

** if a single element contains both the max and the min force (common when all forces of a certain type

are 0.00), the text "MaxMin" will display next to that element.

*** if a single element contains more than one maximum force (or more than one minimum force), the

element's color will match the selected force that is closest to the bottom of the "Max and Min Forces"

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dialog. For example, an element contained the maximum Shear2 force, and the maximum Axial force,

the element would be colored to match the Axial force.

Figure A110A: Max and Min Forces Dialog for Piles (Left)

Figure A110B: Max and Min Forces Dialog for Piles (Right)

Max Min Tutorial

XML Report Generator


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The XML Report Generator is an Internet Explorer based interactive data retrieval system. Based on the XML output created by FB-Pier or FB-MultiPier the report generator presents the user with a menu of available data. The selected options are then presented in an expandable menu format (below left). The requested information is then displayed in a separate report window (below right).

Figure A111: XML Report Generator

The XML Report Generator can be run outside of the FB-MultiPier program. All of the report generation files are located in the ModelReport folder found inside the program directory. Double-clicking on FB-MultiPier-Report.htm file will launch the report generator (provided that Internet Explorer is registered as the default web browser). A dialog box will prompt the user for the name of the XML data file.

Javascripting must be enabled in order to display the data reports. Most browsers have Javascripting enabled, but it can be disabled under the browser security settings. Check the computer Internet Options for further details.

The report generator can create cross section drawings using SVG graphics. Viewing these images requires the Adobe SVG Viewer which is a free plug-in for Internet Explorer. If the viewer is not present the graphics option will not be include in the menu. The Adobe SVG Viewer can be downloaded from their website. http://www.adobe.com/svg/viewer/install/main.html

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Results Viewer

Results Viewer

To use the Results Viewer go to Control > View Analysis Data > Results Viewer. The Viewer will

bring up the .out file with the Header List on the left and the Output Results on the right. By

selecting a header from the Header List, the Output Results will scroll to that location in the output

file. If you have selected a header, which may have more than one location in the output such as

multiple pile, pier or load case information, you can scroll to the next header by clicking the

‘Next’ button. Once you have selected a header, the mouse scroll wheel will be active in the

Output Results window.

Toolbar Options

- ‘Available List’ will provide all available headers for the output file you are viewing.

- ‘Custom List’ allows you to select specific headers that you would like to view. After selecting

the headers you click the ‘Select Headers’ button to build your custom list.

- ‘Clear List’ will clear all selected headers in the ‘Custom List’.

- Copy, Cut and Paste are standard windows commands. To use the right click Copy, Cut and

Paste you must select your text and then right-click outside the Output Results window.

- ‘Find’ allows you to select any text and is case sensitive.

- ‘Find Next’ will find the next text entered in Find if available.

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Figure: VR1 Results Viewer

General Modeling

Column Connection to the Pile Cap

The loads are transferred from the pier column to the pile cap and then to the foundation. The normal

way would be that the load from the pier column is applied at the base node of the column where it

connects to the pile cap. This would cause stress concentrations at that area. It would be more realistic if

the load from the column to the pile cap is spread to several nodes. FB-MultiPier is currently spreading

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the load to the four adjacent nodes to the pier column base node (see Fig. H1). Therefore we avoid the

stress concentrations.

This process is done internally by the program, based on the coordinates of the column base node the

program finds the four nodes adjacent to that and it adds ‘’connector’’ elements between those and the

base node. This way the load is also transferred. The connector elements that are created are "rigid"

elements generated by the program by assigning to them very high values of material properties.

The stiffness in the connector elements is based on the properties of the columns and its and it is

defaulted to 1000 times that. The end conditions at the connectors are set so there is no moment transfer

at the ends of the connectors. Therefore the connectors give the moment effect of columns without the

localized moments at the ends of the connectors.

The elements that are created, or better say the nodes that the ‘’connector’’ elements frame into are

shown in the output file in the paragraph ‘’PIER MEMBER CONNECTIVITY’’. Depending on the

location of the column base node the ‘’adjacent nodes’’ may change.

Figure H1: Column Connection to Pile Cap

Taper Modeling

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FB-MultiPier allows for the modeling of tapered columns, pier caps and pier cantilever elements

(Figure H2). The taper can be either linear or parabolic. The user is required to enter the properties

at the ends of each element (column, pier cap, pier cap cantilever) and also the number of sections

in each element. The program then discretizes each element into the number of specified sections

and generates a series of elements each of which having varying cross section properties to define

the paper (Figure H3). The axis of the parent element (i.e. column etc) remains the same (Figure

H4). During the analysis, the analysis engine treats each of the sections as individual elements

with the specified material properties and the results are provided for each of them.

Figure H2: Solid View of Model

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Figure H3: Engine Model Discretization (Solid View) based on taper input data

210

Figure H4: Engine Model (Thin Element View) of Structure

Bridge Span Overview

The deck of the bridge and its connection to the supporting pier is modeled with a combination of elements shown in the figure H5 below. The superstructure (Span) element is modeled with a series of linear discrete elements. With either constant or varying (tapered) cross sections. These element properties are input by the user, and are intended to simulate the behavior of the bridge deck.

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Since the span element is located at a distance from the bearings and essentially the pier cap centerline, FB-MultiPier generates and uses a vertical rigid link element. This element is required to be rigid and therefore FB-MultiPier internally assigns its properties. These properties are calculated based on those of the span element to ensure the rigidity of the vertical rigid link.

Figure H5: Bridge Span Components

The transfer beam is the last element to complete the bridge span modeling. The transfer beam is used to connect the bearings together and it therefore dictates the load path from the span element to the supporting pier. The properties that are assigned to the transfer beam are such that they can simulate different span end conditions.

The bearing elements are used to simulate the response of the bearings on the pier cap and they have six degrees of freedom at each end. Each degree of freedom can either be ‘constrained’, ‘released’ or it can have ‘custom’ properties. The ‘constrained’ condition implies that the bearing will behave much like a rigid link in that direction. The ‘release’ condition simulates the case when the bearing provides no resistance in that particular

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direction. Finally, the response of the bearing in a particular direction can be determined by user defined load displacement curve.

Uplift Bearing – Future Development

The program recognizes the fact that when a bearing physically rests on the pier cap it cannot displace downwards independently from the pier cap. It is, however, possible (based on the actual construction) to move upwards with no restriction (i.e. the deck falls off the bearing). Since the program acknowledges the fact the ‘release’ support condition is not available in the Z direction (vertical) of the degrees of freedom. FB-MultiPier instead provides a ‘uplift’ bearing which can be used to simulate the case where the deck can lift from the bearing but it cannot ‘go though’ it.

Span End Conditions

Based on the construction the spans may have different end conditions; FB-MultiPier can simulate these conditions by assigning various properties to the Transfer Beam. The ‘Diaphragm’ condition assigns such properties that the Transfer Beam will behave as a rigid element. The ‘Non-Diaphragm’ condition relaxes the values of the properties to allow a more flexible beam. Finally, the user is able to assign custom properties for the Transfer Beam to simulate other conditions.

The span end conditions must be assigned at both sides of the span independently using the ‘Edit Span’ window.

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Node Numbering

Fig N-1 Node Numbering

214

Span Length Calculation

216

Fig S-1 Span Length Calculation

Preliminary Soil Values

Bridge Span Modeling

Deck Modeling

There are six components used when modeling the deck in FB-MultiPier:

1) The Pier Cap is modeled as an Discrete element at centerline.

2) The Offset Rigid Links are used to model the connection from the bearing to the Pier Cap in the case of two rows of bearings where the bearings are some distance from the centerline of the Pier Cap.

3) The Bearings are modeled as six springs to represent the response of the bearing in all degrees of freedom. The Bridge Spring Element properties are either based on custom user input or are generated by the program based on the Span end conditions.

4) The Transfer Beam transfers the deck load via the rigid vertical link to the bearings. The Transfer Beam properties are either based on custom user input or are generated by the program based on the Span end conditions.

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5) The Vertical Rigid Link transfers the load from the Span (Deck) to the Pier Cap. This element is used to account for the eccentricity of the centerline of the bridge deck from the centerline of the pier cap.

6) The Span (Deck) element is used to simulate the behavior of the bridge deck. This is modeled as a series of discrete elements (default = 9) with properties specified by the user.

Figure I1: Deck Modeling Components

The Span (Deck) properties represent the actual deck and are provided by the user.

Note: The deck is always linear.

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Properties of the Vertical Rigid Link match the axes between the Span (S) and the Vertical Rigid Link (VL). The properties of VL are based on those of the span and the goal is to give similar stiffness terms as the span.

Figure I2: Axis for Vertical Rigid Link and Span

3

3VL

VL

S

Eqn. i1 L

I 1000 I2L

= × ×

3VL

2VL

S

Eqn. i2 85 A L

IL

=

VLVL

S

Eqn. i3 4E L

J 1000 I2G L

= × ×

VLVL

3S

Eqn. i4 L

A 12000 I3L

= × ×

219

Transfer Beam Properties

The transfer beam is used to model the end conditions of the span and to transfer the load to the bearings. The transfer beam’s properties are dependant on the properties of the vertical rigid link.

Stiff Transfer Beam: Use properties of vertical rigid link

Soft Transfer Beam: Use properties of vertical rigid link divided by 1000

Custom: User defined properties

Figure I3: Axis for Transfer Beam and Vertical Rigid Beam

TBTB VL

3VL

Eqn. i5 12L

A I3L

=

220

3VL TB

TB

VL

Eqn. i6 A L

I312 L

=

3TB

TB VL

VL

Eqn. i7 L

I2 I2L

=

VL TBTB

VL

Eqn. i8 4E I2 L

J G L

= ×

Rigid Link Properties

The properties of the Rigid Link (RL) are based on those of the Pier Cap (PC). The rigid link should be rigid compared to the pile cap.

221

Figure I4: Axis for Offset Rigid Link and Transfer Beam

PC RLRL

3PC

Eqn. i9 2400 I2 L

AL

=× ×

3 RL

RL PC

PC

Eqn. i10 L

I3 2000 I3 L

= × ×

3PC RL

PC

PC

Eqn. i11 A L

I2 85 L

= ×

PC RLRL

PC

Eqn. i12 E I3 L

J 8000 G L

= ×

Bearing Pad Properties

The properties of the bearings will be calculated in three ways:

1) Based on properties of the Transfer Beam (TB)

2) Based on properties of the Rigid Links (RL)

3) Based on user defined custom curve

When there is fixity the program will use the larger of the first two options.

222

When there is no fixity (Release) then the program is using "EWEAKSPRING" which is defaulted to 1E-05.

The Spring element that is used has a 12x12 stiffness matrix.

Method 1 - Bearings based on transfer beam properties

Figure I5: Axis for Bearing and Transfer Beam

( )TB

TB

Eqn. i13 1,1A E

SL

=

( )TB

3TB

Eqn. i14 2,224E I2

SL

=

( )TB

3TB

Eqn. i15 3,324E I3

SL

=

( )TB

Eqn. i16 4,4JG

SL

=

223

( )TB

TB

Eqn. i17 5,58E I3

SL

=

( )TB

TB

Eqn. i18 6,68E I2

SL

=

Method 2 - Bearings based on rigid link properties

Figure I6: Axis for Bearing and Offset Rigid Link

( )RL

3RL

Eqn. i19 1,112E I2

SL

=

( )RL

RL

Eqn. i20 2,2A E

SL

=

( )RL

3RL

Eqn. i21 3,312E I3

SL

=

224

( )RL

RL

Eqn. i22 4,44E I3

SL

=

( )RL

RL

Eqn. i23 5,5J G

SL

=

( )RL

RL

Eqn. i24 6,64E I2

SL

=

Bridge Span Dead Load

This dialog shows the program-generated dead load from the Bridge Span self weight,

based upon tributary span lengths. Prior to version 4.12b of FB-Multipier, these

loads were not displayed in the interface, though they were used in the Analysis.

This dialog is only available for Bridge models. For single pier models, the program does

not generate span dead load. To display the Bridge Span Dead Load Dialog, click the

"Span Dead Load" button on the Load Table.

Backwards Compatibility

For input files created prior to version 4.12b, and existing bearing loads are added

to the new program-generated Dead Load. For example, if the user

225

had applied a 100 kip load to each bearing location, and the program-

generated bridge span dead load is 50 kips at each bearing, then the interface will now

display a load of 150 kips at each bearing. This load of 150 kips will be used in the

Analysis. If the intent of the user is to have a 100 kip load on each bearing, the user

should use the Load Page or Load Table to change the load at each bearing to 100 kips.

It is strongly recommended that the user visit the Load Page or Load Table to ensure the

loading has been transferred correctly.

226

Figure. BR-1: Bridge Span Dead Load Dialog Non AASTO

Non AASHTO

During the analysis, the self weight factor will be applied to the span dead load. Thus,

these loads as they are displayed on this dialog and throughout the interface, have not

yet been factored. The self weight factor applies only to the dead load portion of loading

227

at a bearing location. For example, suppose the program-generated span dead load is 50 kips on

each bearing, and the user changes this load to 60 kips. If the user has input a self weight

factor of 1.25, then the load used in the analysis would be (50 kips * 1.25) + 10 kips, or 72.5 kips.

This is the value displayed in the 'Analysis Force Z' column of this dialog.

Helpful Hints: If the user does not wish to have the program automatically generate the span

dead load, one option is to input a span unit weight of 0.0, on the Bridge Span Properties Dialog.

Another option is to input a self weight factor of 0.0, on the Load Page or Load Table. However,

this self weight factor is applied to all pier components (piles, columns, pier cap, bridge spans, etc).

228

Figure. BR-2: Bridge Span Dead Load Dialog AASTO

AASHTO

In Aashto mode, in LRFD, the span dead load is displayed in the load case

"Components and Attachments" (DC); in LFD, the span dead load is displayed in the load case

"Dead Load" (D). The Analysis will factor these loads using the given DC (or D) factors.

Thus, these loads as they are displayed in the interface, have not yet been

229

factored.

Transfer Beam

Details regarding the "Transfer Beam" which is used to connect the bridge superstructure (which is modeled using linear elastic beam elements) to the substructure via bearings.

The "Transfer Beam" is an elastic beam element that transfers superstructure loads to the bearings. Currently all loads from the superstructure are applied directly to the bearings on the transfer beam, and continuity effects due to a continuous superstructure are calculated as the analysis is conducted. The next version of this program will allow for loads to be applied directly to the superstructure.

It is imperative that neoprene bearings are modeled because their stiffness provides for the best and most realistic, distribution of forces between super and substructure. This is important for loads applied in both horizontal and vertical directions to the transfer beam. For example: in order to obtain an even distribution of Dead Load forces the vertical long term neoprene bearing stiffness should be included (use the custom bearing feature) otherwise the Dead Loads will "migrate" to the bearings that are closest to the stiffest parts of the pier cap (as a bearing located over a column). The custom bearing stiffnesses are very easy to input and typically require just 3 lines of data to describe the linear stiffness of these bearings.

A paper in the August 2000 Journal of Bridge Engineering, "Effect of Bearing Pads on Precast Prestressed Concrete Bridges" provides stiffness values for typical bridge neoprene pads. The publication "Construction and Design of Prestressed Concrete Segmental Bridges", by Jean Muller and Walter Podolny , page 245, provide an excellent reference for calculating neoprene bearing stiffness and also discusses the need to use the long term shear modulus for sustained loads.

Note in figure TR-1 that the node on the Transfer Beam and the corresponding node on the pier cap are, so to speak, "master and slave nodes" that share the same coordinates in space but are linked by 6 springs that control the movement between super and substructure.

230

The stiffness of the Transfer Beam can be input by the Engineer or for preliminary design the Engineer may elect to use the stiff or soft Transfer Beam option provided by the program.

A future option we plan to develop at BSI is a preload option that would allow one to apply DL or other "built in" loads to the structure before the transfer beam is engaged. These built in loads, as is often the case with Segmental Bridges, would thus exist in addition to any other loads being applied.

231

Figure TR-1: Transfer Beam

232

The node numbering system for superstructure nodes, including Transfer Beam nodes, is depicted above. The sequence is as follows per bridge span: node 1 is located at the base of the left elevation beam; node 2 is located at the top of the left elevation beam; the bridge deck is divided into 10 elements of equal length, with a node separating each element (nodes 3 through 11); node 12 is located at the top of the right elevation beam; node 13 is located at the base of the right elevation beam. The number and location of the remaining superstructure nodes depend on the number of bearing locations. Node 14 is the first bearing location on the left rigid transfer beam. There is one transfer beam node per bearing location (nodes 14 through 19 as depicted in figure TR-1). The right transfer beam nodes then follow (nodes 20 through 25 as depicted in figure TR-1).

Wind Generator

Details regarding the use of the Wind Generator with the Bridge option.

The Wind Generator, which is available on the AASHTO page provides a convenient and rapid generation of wind forces applied to the bridge superstructure and live load. These forces are displayed as vectors in the GUI and are applied to the bearing locations on the transfer beam. The values of the wind forces are best seen in the AASHTO load table, where they can also be modified. The wind forces generated are calculated based upon tributary superstructure areas and, as with self weight of superstructure, these forces are redistributed during the analysis if the superstructure is continuous.

The wind forces generated can be manipulated in a number of ways including modifying the basic wind pressures from the defaulted Code values found in the Generator.

Some wind forces are not generated and must be manually added to the Wind on Structure (WS) load cases. These are wind on substructure and the upward wind force on superstructure. The wind on substructure is applied by the Engineer by applying calculated un-factored loads directly to the substructure nodes. The upward wind on

233

superstructure should be applied as loads to the bearings. In previous versions of this program wind on substructure was also generated and applied at the bearings along with the wind on superstructure forces. Applying the wind directly to the substructure provides a more accurate solution that the previous methodology, where these forces were generated by the program and then concentrated at the bearing locations.

234

Bridge Span Element Numbering

235

Fig B-1 Bridge Span Element Numbering

Setup Options

Expanding Memory

The FB-MultiPier Engine can be adjusted to allow larger pile system solutions. If the problem is to large for the current settings the engine will generate a error message like:

STORAGE EXCEEDED BY ******** UNITS

Not enough memory is available for the analysis

To change the available memory settings goto

Control -> Program Settings -> Analysis Settings

You can correct this from the Program Settings Dialog in the Control menu in the interface. Set

the ‘Memory for Current Analysis’ to a larger value than is currently used, repeating until the error

message does not appear. Older computer may not have enough memory to analyze large

problems.

Previous version of the program (v4.08 and earlier) report the same problem with a error message

like:

Not enough Memory

You can correct this from the Program Settings Dialog in the control menu in the interface as mentioned above.

Program Settings

236

Figure A12: Program Settings Dialog

To clarify the two different Analysis Settings:

‘Memory for Current Analysis’ is the amount of memory used when the current input file is analyzed and this value will be saved with input data.

‘Memory for New Problem’ is the amount of memory used with each new problem created.

FB-Pier License Installation

License File

237

FB-MultiPier operates using a license file to determine its status. All shipped versions run in Demo mode as the default. The program can be "unlocked" into various modes including full version and student version, networked or stand-alone. This unlocking can be done by hand, through phone contact with the Bridge Software Institute ( http://bsi-web.ce.ufl.edu ) or automatically through an internet connection to the BSI web server.

The program requires a license file to be installed. This license file is linked to the computer on which it is installed.

NOTE: You must have administrator rights on Windows NT or Windows 2000 to install FB-

MultiPier or the license file on a server.

The following describes the modes and processes required:

Stand-Alone

A stand-alone or fixed license version is locked to run on a single machine and only that machine. The

license file is installed on the individual machine.

Network Version

A network version is a floating license version that allows a fixed number of machines to run the

program at any one time. For example, a three-seat installation allows three computers to run the

program at the same time. The program is actually installed on any number of machines. For example,

you can install the program on 20 computers in your network. However, only three of the 20 can use the

program at the same time.

This installation requires a network server that shares a directory with all the computers wishing to run

FB-MultiPier. The shared directory is where the license file is installed. All client machines must have

read and write permissions for the shared directory in order for the program to run.

There is a separate install program for installing the license file on the server.

238

If your network installation has multiple servers, you will need to purchase multiple server versions.

Updating the license

Any installed version can have its permissions changed by entering encrypted numbers into the license

file. This is done by choosing the Control->Update license option from the main menu. The update can

be done by hand or automatically through the Internet.

E-mail/Fax/Phone License Update

This option is for installations that do not have an Internet connection. To do this installation, call the

BSI support number (check the web for the phone number) and you will be stepped through the process.

Numbers from your computer need to be given to the BSI representative and we can Fax or E-mail the

encoded numbers you will need to type into the program.

Internet License Update

This option requires the computer on which you are installing the license file be connected to the

Internet. Then, all numbers are communicated through the Internet and the license updated

automatically. The computer can either be a stand-alone system or the network server for a multiple seat

license.

Transfer License

There is a built in function that allows you to transfer you license to another machine. This allows you to

move the license file from your current server or workstation to a new machine.

Troubleshooting

The license file (both for servers and individual workstations) is locked to a machine based on hardware

components contained in the machine. If you change or modify your hardware (drives, motherboards

etc) your installation may not function. To do this, you should first transfer the license, then modify your

hardware, and then re-install the license on the machine.

Novell systems: Be sure that the directory where the license file is saved is accessible to any user. The

user must have read, write, modify, erase and create rights for that directory.

239

License Update Tutorial

FB-MultiPier License Installation Help

Before updating the program license for the first time, the FB-MultiPier program will run in demo mode. While running in demo mode, the model size is limited to a 5x5 pile group and the program execution is limited to 30 days. After purchasing the program, these limitations can be removed by using the License Configuration Wizard.

To update the software license at any time, select Update Software License from the Control menu while viewing the intro Logo window. Doing so brings up the License Configuration Wizard.

The initial License Configuration Wizard screen shows four options for updating the software license. The options are shown below:

Figure G1


240

Update a License on a Stand Alone Workstation

This option is used for a single installation of the software that does not rely on network to run the program. A license of this type is individually purchased per machine. Click the Next button to continue. The next screen presents two methods for updating the software license. The first method allows the user to update the license by phone/fax. The second method is the preferred method, which allows the user to update the software license via an Internet connection. This method is preferred since it is completely automated, assuming that a user account has been established in advance and that the user can connect to the Bridge Software Institute (BSI) web server. The user account will be created when downloading the FB-MultiPier program.

Figure G2

FB-MultiPier utilizes a license file to determine the program configuration. This license file must be updated by one of the two methods. If neither option is feasible, please contact the BSI for assistance. License File Update by Phone/Fax This option requires a phone call to the BSI. To update a license by phone/fax, select Update by Phone/Fax and click the next button to continue. The next screen shows a series of edit boxes for entering license data. The Session Code and Machine ID need to be given to the BSI representative. After validating the user’s account information and status, the BSI representative will then supply the user with a series of numerical codes that will modify the configuration of the license file. If the numerical codes are entered correctly, the program will be unlocked and will run without any limitations. If any of the numerical codes are entered incorrectly, the wizard will prevent the user from advancing to the next screen. License Update Tutorial Click Next after entering the numerical codes.

241

Figure G3

The Update Complete screen will then be shown after successfully entering the numerical codes. In order to apply the changes to the program configuration, the FB-MultiPier program needs to be restarted. Clicking the Finish button will update and automatically close the program. The program will now run in an unlocked state. License Update Tutorial

Update/Install a License on a Network Server

This option is used for a single installation of the software on a network server. This license update is identical to stand alone workstation update, except that the license is configured on the network server. This option would be used to run the program directly on the server to take advantage of the server hardware configuration (i.e. more memory, hard disk space, etc.). A license of this type is individually purchases per machine. Select Update a License on a Network Server from the initial screen and follow the steps outline for Updating a License on a Stand Alone Workstation.

242

Figure G7


Set Client Path for a License File on a Network Server

This option is used by the network client computer after a server license file has been configured and successfully installed on the network server (see LicServe Wizard). When a floating network license is purchased, the limiting factor is the number of network seats. The FB-MultiPier program can be installed on any number of client machines, however, the number of clients that can run the program at one time is limited by the number of network seats purchased. In order for the client machine to run the program using this scenario the client must locate the license file that has already been installed on the network server. Once this path has been established it will be saved so that the client machine will automatically find the license file each time the program is run.

243

Figure G8

Click the Next button to continue. The next screen asks the user to browse to the license file path on the network server. The user can either type the path or preferably click the Browse button to locate the file. The license file is named "FB-MultiPier.lf". Click the Browse button, locate the license file on the network server, and click Open to continue. You must browse through the network to locate the license file. You can not use a mapped drive letter.

244

Figure G9

Click Next after locating the license file on the network server. The Update Complete page is now shown. In order to apply the changes to the program configuration, the FB-MultiPier program needs to be restarted. Clicking the Finish button will update and automatically close the program. The program will now run in an unlocked state.

Figure G10

Transfer License to a Different Computer

This option is used to transfer a valid software license to another computer if the user no longer wishes to have the license on the current computer. Please note that selecting this option will invalidate the license file on the current machine. Also, this option is only valid for a stand along workstation installation of FB-MultiPier. Floating network installations are not applicable since the license is stored on the network server. To proceed, select Transfer License to a Different Computer and click the Next button.

245

Figure G11

Because this process can not be reversed, the user must check the box to confirm the remove the license from the current computer before proceeding. Doing so will enable the Next button. Click the Next button to remove the license. License Update Tutorial

246

Figure G12

The next screen informs the user that the license has been successfully removed. A verification code is displayed on the screen (and written to the file "LicRemoval.txt" in the application directory). This code must be given to a BSI representative in order to complete the license transfer process and activate the license on another computer.

Figure G13

Click the Next button to continue. The Update Complete page is now shown. In order to apply the changes to the program configuration, the FB-MultiPier program needs to be restarted. Clicking the Finish button will update and automatically close the program. The program will now run in an unlocked state.

Toolbar Icons

DESCRIPTION OF TOOLBAR ICONS

The buttons in the toolbar at the top of the screen control the access to different modules within the program. Some of

the menu items can also be accessing using the buttons instead for convenience. The purpose of each button in the

toolbar is described below.

Figure A1: Toolbar Icons

247

Figure A2: File Option Icons

Figure A3: Model Data and Analysis Icons

Figure A4: Analysis Results Control Icons

Figure A5: Pier and Load Case Menus

248

Figure A6: 3D Control Bar Icons (if activated)

General Pier Wizard

The General Pier Wizard creates a general pier problem using detail specified information.

Figure A12: General Pier Wizard

249

By entering the information requested at each step the user can create a customized general pier model in a short time.

Batch Analysis

Batch Mode

A batch of input files can be analyzed interactively in Batch Mode.

Figure A91: Batch Mode Dialog

Check the "Include" box to analyze the input file.

Select the memory size for each input file. Most normal size models only require 8MB of

memory. Larger models may require more memory. The program will provide a notification if the

250

memory size is exceeded. At this time, FB-MultiPier does not automatically determine the

memory requirements in advance of the analysis.

The Completion Status indicates a successful or unsuccessful analysis for each model.

Retrieving input files:

Select "Open Existing Batch File" to retrieve an existing set of input files.

Select "Add Input File(s)" to add input files to a new or existing batch file. One or more files can

be added at a time by using the Ctrl key while selecting files in the Open file dialog.

Run mode:

Select "Run Without Interruption" to analyze all input files without pausing for modeling errors or

convergence failures.

Select "Pause on Analysis Failure" to have the program pause to display modeling errors or

convergence failures a particular model.

Running FBPier_eng in Batch Mode

The FB-MultiPier engine can be run in a batch mode. This allows a number of input files to be

run sequentially. The input files need to be created by the graphics program (FB-MultiPier) as

normal and saved. Then, the engine can be run using a batch file or any other scripting language.

If you wish to use a DOS type batch, you can do the following:

1) 1) 1) 1) 1) 1) 1) 1) Use Notepad to edit a file

2) 2) 2) 2) 2) 2) 2) 2) The lines of the batch file are:

251

"C:\program files\BSI\FBMultiPier\FBPier_eng.exe" I:\my documents\FB-MultiPier\test.in

O:\my documents\FB-MultiPier\test.out

There can be as many lines as required for the number of input files.

The format is as follows:

The first thing on the line is the location of the executable. This includes the full path to the .exe

file. In addition, if there are spaces in the path name, the entire executable must be enclosed in

quotes.

Second is the input file, designated by I: Again, the full path must be included. Quotes should not

be used around the input file path.

Third is the output file name designated by O: Again, the full path must be included. Quotes

should not be used around the output file path.

There can also be a memory allocation change on the line if more memory is required. The format

is m:xx, where xx is the number of megabytes (MB) to use in the analysis. (i.e. m:64) The default

value is 8MB.

3) 3) 3) 3) 3) 3) 3) 3) Save the file as run.bat (run is an arbitrary

name, the extension must be .BAT).

4) 4) 4) 4) 4) 4) 4) 4) Double click on the run.bat file to start

execution.

As an example, here is a batch file that will run the program for three input files.

"C:\program files\BSI\ FBMultiPier\FBPier_eng.exe" I:\my documents\FB-MultiPier\test1.in

O:\my documents\FB-MultiPier\test1.out





Soil-Pile Interaction Soil-Pile Interaction

252

Input line 17 characterizes both the axial and lateral soil-pile interaction. The axial soil-pile

interaction is modeled through hyperbolic T-Z curves. The lateral soil-pile interaction is modeled

with nonlinear p-y curves. The user has the option of picking from one of six different P-Y

models. Four of the p-y models are the same as those given in FHWA's COM624P manual (Wang

and Reese, 1993).

Axial Soil-Pile Interaction

Lateral Soil-Pile Interaction

Torsional Soil-Pile Interaction

Pile Group Interaction

Soil Properties


Group Interaction

When a group of piles are subject to a vertical or lateral load (i.e. wind, earthquake, etc.) their

vertical or lateral resistance is generally not equal to the sum of the individual pile resistance.

Generally the group resistance is less than the individual pile resistance and is a function of pile

location within the group, and pile spacing.

Consider lateral loading of the variable groups (3x3, 4x3, to 7x3) in dense sand shown below:

Experimental testing (centrifuge) on pile groups has resulted in the following shear distribution in

each of the individual rows:

Table B1: Average Pile Shear (kN) - Medium dense Sand (Dr = 55%)

Layout 3x3 4

x

3

5

x

3

6

x

3

7

x

3

Aver

age

Lead

Row

2

4

5

2

9

4

2

9

4

3

0

2

2

8

5

284

2nd 1 2 2 2 2 206

253

Row 7

8

0

5

2

2

0

5

2

2

3rd

Row

1

4

2

1

5

1

1

6

0

1

7

8

1

7

8

167

4th

Row

1

4

2

1

5

1

1

4

2

1

5

1

148

5th

Row

1

4

2

1

4

2

1

4

2

142

6th

Row

1

4

2

1

4

2

142

7th

Row

1

4

2

142

Group 1

6

6

4

2

3

7

5

2

9

0

9

3

3

3

6

3

7

9

0

(Measured)

Group 1

8

9

8

2

3

9

8

2

8

4

3

3

2

7

0

3

6

9

7

(Predic

ted)

Error

(%)

1

4

1 2.

3

2 2.

5

Note that the individual row contributions, with the exception of the trail row, appear to be only a

function of row position. Also, using the average for the row (with exception of trail row) does a

good job of predicting the measured group response. Consequently, the approach recommended

by Brown and Reese (1988) with P-Y multipliers has been implemented in the code.

254

The following P multipliers are recommended for lateral loading at 3D pile spacing:

0.8, 0.4, 0.3, 0.2, 0.2, …..0.3 where 0.8 is the lead row and 0.3 is the trail row value

For 5D pile spacing the following P multipliers are recommended:

1.0, 0.85, 0.7, 0.7, …, 0.7 where 1.0 is the lead row and 0.7 is the trail row value.

These multipliers generally represent group efficiencies of 70-75% for 3D spacings and 95% for

5D pile spaced groups. Also, the multipliers were found to be independent of soil density (sands).

NOTE: The program will apply the PY multipliers to the correct pile rows (lead to trail) based on

the direction the piles move. The PY multipliers are always given in trail to lead order. This does

NOT depend on the direction of the applied load.

In the case of battered piles (A frame) as shown below:

Applied Lateral Load

8

1

1

4

1.9 m (6.23 ft)

Cross-Sectional View

11.25 m (36.9 ft)

11.25 m (36.9 ft)

0.43 m (17 in)

3 D D = 0.43 m (17 in)

D = .43 m (17 in)

5 D 5 D

Plan View

3 D Spaced Group Layout

5 D Spaced Group Layout

0.44 m (17.3 in)

0.88 m (34.5 in)

Reverse Batter

3 D

Forward Batter

EI=72.1 MN-m 2 (2.51x10 10

lb-in 2 )

Figure B1

Centrifuge Tests were conducted on both 3D and 5D groups shown in loose and dense sands.

Presented is one of the comparisons of plumb vs. battered response:

255

0.0

0.4

0.8

1.2

1.6

2.0

0 20 40 60 80 100

Lateral Deflection (mm)

Late

ral L

oad

(M

N)

0

40

80

120

160

200

240

0 1 2 3

Lateral Deflection (in)

Late

ral L

oad

(to

ns)

Pile Spacing - 3D

Dr - 55%

Free Head Plumb

Fixed Head Plumb

Battered, 6 Forward - 3 Reverse

Battered, 3 Forward - 6 Reverse

Figure B2

Based on the centrifuge results the same multipliers are recommended for battered (A frame) as

plumb pile groups. Presently there is little, if any data on other batter layouts.

Axial Efficiency

The program also has an axial group efficiency factor. This is a factor that effects the force

displacement in the axial direction. The axial efficiency factor is found from the soil tab page,

under the group button. For more information, see Sayed (1992).

Soil Resistance Due to Pile Rotation

256

This option is used for the program to calculate and apply rotational springs to the pile nodes in the ground. These springs are based on the axial resistance of the piles (skin friction) as well as the rotation of the piles. It is particularly important in soil layers where the piles can develop large values of skin friction.

Calculation of bending strains

At each location along the length of the pile, the total strain consists of an axial and a bending component.

Of interest is the bending strain, εb at any given section of the shaft,

Eqn.b1

1 2b

2

ε − εε =

where: ε1 and ε2 are the values of the strain on the opposite sides of the shaft.

Figure B3 shows in detail how the bending strains are obtained from the measured strains.

Figure B3: Total, axial and bending strains on cross-section.

Soil’s Lateral Resistance P(F/L) Form Bending Moments and Skin Friction

The difference in the moment at two different elevations is caused by soil’s lateral (P force/length) and axial force (T

force/length) resistance at the soil-shaft interface. The contribution to moment in the case of the latter is a function of

shaft diameter, and the soil’s T-Z curve as well as the rotation of the shaft. Figure B4 shows the contribution of T to the

Moment Equilibrium for the resulting Shear, V at a cross-section,

Eqn.b2 V = dM/dz

Consequently, from lateral force equilibrium, Figure B4, the soil lateral P (force/length) is found as

Eqn.b3 P = dV/dz = d2 M/dz

2

257

If the side shear, T (Figure B4), is taken into account, then moment equilibrium results:

Eqn.b4 dM/dz = V + TD/∆z

or

Eqn.b5 dM/dz = V + Ms

Figure B4: Forces acting on a shaft element of length dz.

where: M = moment on the cross-section

Ms = moment per unit shaft length from the side shear force, T

Evoking horizontal force equilibrium,

Eqn. b6 P = dV/dz

Substituting Eqn. b5 into Eqn. b6, then the soil lateral resistance, P, is obtained:

Eqn.b7 P = d2M/dz

2 – d(Ms)/dz

Evident from Eqn.b7 vs. Eqn.b3, the side shear on the shaft will reduce the soil’s lateral resistance, P, calculation. The moment/unit length, Ms, of the side shear is obtained from the T-Z curve for the soil. The value of T requires the displacement, Z, at a point on the shaft.

Moment Due to Side Shear, Ms Lateral loading causes a rotation of the shaft at any given cross section. The shaft rotation is resisted through skin friction, T, and lateral soil resistance, P, acting on the sides of the shaft. In the case of the unit skin friction, a Moment/length resistance, Ms , may be computed at any cross-section. The value of Ms is a function of the unit skin friction at the periphery of the shaft, which varies around the shaft’s circumference. To estimate the moment due to side shear (Ms), the shaft cross section was divided into slices as shown in Figure B5. Ri is the distance from the center of shaft to the center of slice i. For example R1, is the distance from the center of the shaft to the middle of slice 1.

258

Figure B5: Shaft cross-section divided into slices to calculate Ms .

The value of shear stress, τi, is a function of vertical displace ment, Zi, which is a function of the rotation, θ, and the distance from the center of cross-section to the center of the slice, Ri. If Z1 is the average axial displacement of slice

1 and τ1 (obtained from T-Z curve knowing z1) and C1 the arc length of slice 1 then the side shear force/unit length, T1, acting on slice 1 is given by

Eqn.b8 T1 = τ1.C1

The moment per unit shaft length about O, Ms1, is found by multiplying T1 by the distance to the cross-section centroid,

R1, as

Eqn.b9 Ms1 = T1.R1 = τ1.C1.R1

The total moment per unit length may be found by summing the moments acting on all the slices:

Eqn.b10

n

s i i i

1

M C R= τ∑

where: n = number of slices

Soil Properties Soil Properties

Following are the important soil properties required as input parameters.

Young's Modulus

Poisson's Ratio

259

Shear Modulus

Angle of Internal Friction

Undrained Strength

Subgrade Modulus

Water Table

Young's Modulus

The following recommendation is given by Kulhawy and Mayne (1990) for Young's Modulus, E,

for sands:

Normally Consolidated Clean Sands:

E (psf) = 20,000 N60

Over Consolidated Clean Sands:

E (psf) = 30,000 N60

Sand with fines:

E (psf) = 10,000 N60

where N60 is the corrected SPT blow count.

Poisson's Ratio

The following typical values may be used for the Poisson's ratio ν for soils:

260

ν = 0.2 to 0.3 for sand

= 0.4 to 0.5 for clay

or a spatial average, for the values of ν over depth may be used for soils

consisting of both sand and clay.

Shear Modulus

The shear modulus, G of soils, is a function of soil type, past loading, and geological history. It is

recommended that G be obtained from insitu tests such as dilatometer, CPT and SPT.

G can be computed from Young's Modulus , E and Poisson's ratio , ν, from the following

correlation:

( )2 1

EG

ν=

+Eqn. b11

In the case of no insitu data is available the following guide is provided:

( )0.5* *

1

k zG

ν=

+Eqn. b12

for sand

( )50*

1

CuG

ν=

+Eqn. b13

for Clay

where

k = soil modulus (F/L3)

z = depth below ground surface (L)

Cu = undrained shear strength (F/L2)

or a spatial average, for the values of GM should be used for any

soil profile.

261


Angle of internal friction, φ', can be computed from SPT N values using the following empirical

correlation:

N’ 4 10 30 50

φ’ 25-30 27-32 30-35 35-40 38-43

'N

N C N=Eqn. b14

Where

CN = correction for overburden pressure

FHWA 96 uses the correction by Peck, et al. (1974):

10 10

20 1915.20.77 log 0.77 log

' ( ) ' ( )N

v v

Ctsf kPaσ σ

= =

Eqn. b15

valid only for σ’v ≥ 0.25 tsf (24 kPa) (Bowles, 1977)

Normalizing for atmospheric pressure (pa): (1 atm = 101.3 kPa = 1.06 tsf )

100.77 log 20'

N

v

paC

σ

=

Eqn. b16

Larger values should be used for granular material with 5% or less of fine sand and silt.

For numerical implementation, the average correlation can be expressed as

' ' a N bε = +Eqn. b17

262

where

N’ a b

0 - 10 0.50 27.5

10 - 30 0.25 30.0

30 - 50 0.15 33.0

50 - 0 40.5

Undrained Strength

Estimates of undrained shear strength, cu can be made using the correlations of qu with SPT N-

values (see the figure below).

2

uu

qc =Eqn. b18

qu = unconfined compressive strength

263

0

5

10

15

20

25

30

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

Unconfined Compressive Strength, qu (tsf)

SP

T B

low

Cou

nt,

N

Sower's:

Clay of low plasticity and

clayey silt

Terzaghi & Peck

Clay of high plasticity

Clay of medium plasticity

Figure B6: Correlations between SPT N-value and Unconfined Compressive Strength

Subgrade Modulus

Subgrade modulus, k (F/L3) of cohesionless soil can be estimated from empirical correlations. For

sand, use SPT N-value to find φ Figure B7 and Figure B8 to find k.

Figure B7

264

0

20

40

60

80

100

0 20 40 60 80 100

Dr (%)

R ELA TIVE

D EN S ITY

VER YLOOS E

LOOS E M ED IUM D EN S E VER Y

D EN S E

N UM B ER S ON C UR VES

IN D IC A TE EF F EC TIVE

OVER B UR D EN P R ES S UR E

φφφφ 28o 29o 45o41o

36o3 0o

0 psi

20 psi

40 psi

Figure B7: SPT Blow Count vs. Friction Angle and Relative Density

Figure B8

265

0

50

100

150

200

250

300

0 20 40 60 80 100

Dr (%)

k (

lb

/ in

ch

3 )

V ER Y

LOOS ELOOS E

M ED IU M

D EN S E

V ER YD EN S E

D EN S E

S A N D B ELOW

THE W A TER

TA B LE

S A N D A B OV E

THE W A TER

TA B LE

Figure B8: K vs. Relative Density

Lateral Soil-Pile Interaction Lateral Soil-Pile Interaction

For the lateral pile-soil interaction, the user has the option of picking from 1 of 6 different p-y

models which are selected through the SOIL parameter. Followings are the available P-Y models.

O'Neill's Sand

Sand of Reese, Cox, and Koop

O'Neill's Clay

Matlock's Soft Clay Below Water Table

Reese's Stiff Clay Below Water Table

Reese and Welch's Stiff Clay Above Water Table

Limestone (McVay)

266

User Defined

O'Neill's Sand

SOIL=1, is O'Neill (1984) recommended p-y curve for sands:

tanhu

u

kzp Ap y

A pη

η

=

Eqn. b19

where η = a factor used to describe pile shape;

= 1.0 for circular piles;

A = 0.9 for cyclic loading;

= 3-0.8 z/D 0.9 for static loading;

D = diameter of pile;

pu = ultimate soil resistance per unit of depth;

k = modulus of lateral soil reaction (lb/ft3 or N/m3).

The ultimate soil resistance pu in equation b19 is determined from the lesser value given by

equations b20 and b21.

( ) tan tanu p a p

p z D K K zKγ φ β = − + Eqn. b20

( )3 2

02 tan tanu p p a

p Dz K K K Kγ φ φ= + + −Eqn. b21

where z = depth in soil from ground surface;

γ = effective unit weight of soil;

Ka = Rankine active coefficient;

= (1 - sin φ )/(1 + sin φ );

267

Kp = Rankine passive coefficient;

= 1/ aK;

Ko = at-rest earth pressure coefficient;

= 1 - sin φ;

φ = angle of internal friction;

β = 45o + φ/2 .

The p-y relationship given in equation b19 depends on the soil parameters k (lb/in3 or N/m3) and

φ (deg), which may be obtained from insitu SPT data. For sand, use SPT to find φ (Figure B10)

and φ to find k (F/L) (Figure B11).

A comparison between O'Neill's p-y curve for sand and Reese et. al. (1974) curve (SOIL=2) is

shown in figure B9 for φ=35, k=150 lb/in3, and γbuoyant =52.6 lb/ft3 at a depth of 25 ft. Evident

from the figure, O'Neill's curve fits Reese's initially, but differs for Pu (generally the case).

P-Y Curves (at 25 ft)

0

2

4

6

8

10

12

14

0 0.5 1 1.5

Displacement (in)

P (

kip

s/in

)

O'Neill

Reese

Figure B9: Comparison of O’Neill’s and Reese, Cox, and Koop’s P-Y Curves

268

0

20

40

60

80

100

0 20 40 60 80 100

Dr (%)

R ELA TIVE

D EN S ITY

VER YLOOS E

LOOS E M ED IUM D EN S E VER Y

D EN S E

N UM B ER S ON C UR VES

IN D IC A TE EF F EC TIVE

OVER B UR D EN P R ES S UR E

φφφφ 28o 29o 45o41o

36o3 0o

0 psi

20 psi

40 psi

Figure B10: SPT Blow Count vs. Friction Angle and Relative Density

269

0

50

100

150

200

250

300

0 20 40 60 80 100

Dr (%)

k (

lb

/ in

ch

3 )

V ER Y

LOOS ELOOS E

M ED IU M

D EN S E

V ER YD EN S E

D EN S E

S A N D B ELOW

THE W A TER

TA B LE

S A N D A B OV E

THE W A TER

TA B LE

Figure B11: K vs. Relative Density

Sand of Reese, Cox, and Koop

SOIL=2, Reese, Cox, and Koop (1974) developed p-y curves for static and cyclic loading of sands

based on an extensive testing of pipe piles in Texas. The p-y curve is shown below and a

complete description of curve is available in FHWA's COM624P (1993) manual. User must

supply the soil's angle of internal friction , φ , subgrade modulus, K, and the sand's buoyant unit

weight, γ ' .

270

k

m

b/60 3b/80

x = 0

x = x1

x = x2

x = x3

x = x4

u

pk

yk

ym

yupm

pu

m

k s x

y

p

Figure B12: P-Y Curves for Static and Cyclic Loading of Sand (after Reese, et al, 1974)

O'Neill's Clay

SOIL=3, is O'Neill's P-Y method for static and cyclic loading of clays. Shown in the figures

below are both the static and cyclic curves. The user must supply the clay's undrained strength , c,

the strain (in/in) at 50% failure, ε50 and 100% of failure ε100 from an unconfined compression

test.

271

0.0

0.5

1.0

RATIO OF DEFLECTION,

RA

TIO

OF

SO

IL R

ES

IST

AN

CE

, P

/ P

U

101

PP C

XXU r

F==== 0 5.PP

YYU C

==== 0 5 0 387. ( ) .

Y

YC

PP U Cr

U

P FO R X X==== ≥≥≥≥0 5.

Figure B13: O'Neill's Integrated Method for Clay (b) Cyclic Loading Case

0.0

0.5

1.0

RATIO OF DEFLECTION,

RA

TIO

OF

SO

IL R

ES

IST

AN

CE

, P

/ P

U

201

PP

YYU C

==== 0 5 0 387. ( ) .

Y

YC

P P FOR X XU Cr==== ≥≥≥≥

PP S S

XXU Cr

F F==== ++++ −−−−( )1

6

Figure B14: O’Neill’s Integrated Method for Clay (b) Static Loading Case

Matlock's Soft Clay Below Water Table

272

SOIL=4 is Matlock's (1970) p-y representation of soft clays below the water table. The p-y

curves for both the static and cyclic response are shown below. The user must supply the soil's

unit weight, γ, undrained strength, c, and the strain, ε50 at 50% of the failure stress in an

unconfined compression test. A complete description of the curves are given in the FHWA's

COM624 manual, as well as recommended soil values.

0.0

0.5

1.0

PPU

y

y50

1.0 8.0

p

p0.5

y

yu 50

1 / 3

=

Figure B15-a: P-Y Curve for Soft Clay Below Water Surface (Static Loading)

0.0

0.5

1.0

15

0.72

1 3

0.72 XX r

PPU

y

y50

For x ≥xr, (depth where flow around

failure governs)

273

Figure B15-b: P-Y Curve for Soft Clay Below Water Surface (Cyclic Loading)

Reese's Stiff Clay Below Water Table

SOIL=5 is Reese et al. (1975) p-y model for stiff clays located below the water table.

The p-y curves for both the static and cyclic response are shown below. The user must

supply the soil's subgrade modulus, k, unit weight, γ, undrained strength, c, the strain, ε50 at 50%

of the failure stress in an

unconfined compression test, and the average undrained strength cavg for the whole clay

layer. A complete description of the curves are given in the FHWA's COM624 manual,

as well as recommended values if no triaxial tests are performed.

Deflection, y ( in )

Soil

Res

ista

nce

, p

( l

b /

in

)

0.45 yp 1.8 yp0.6 yp

Esi = kcx

Ac pc

CYCLIC

Escp

yc==== −−−− 0 085

50

.

y A yp c==== 4 1 5 0.

y b50 50==== εεεε

p A pc c

y y

y

p

p

==== −−−−−−−−

( ).

.

.

10 45

0 45

0 25

Figure B16: Reese et al (1975) Cyclic P-Y Curve for Stiff Clay Located Below the Water Level

274

Deflection, y (in.)

So

il R

esis

tan

ce,

p (

lb/i

n.)

18Asy506Asy50y50Asy50

Esi = ksx

0.5Pc

0

P Pcy

y==== 0 5

50

0 5. ( )

.

P poffset cy A y

A ys

s

==== −−−−0 055 50

50

1 25. ( ) .

STATIC

Essp

yc==== −−−−

0 0625

50

.

Figure B17: Reese et al (1975) Static P-Y Curve for Stiff Clay Located Below the Water Table

Reese and Welch's Stiff Clay Above Water Table

SOIL=6 is Reese and Welch's (1975) p-y model for stiff clays above the water table. The p-y

curves for both the static and cyclic response is shown below. The user must supply the soil's unit

weight, γ, undrained strength , c, the strain, ε50 at 50% of the failure stress in an unconfined

compression test, and the average undrained strength cavg for the whole clay layer. Since this

model is a function of the number of load cycles, the variable, KCYC on line 7 of the input is

used. A complete description of the curves is given in the FHWA's COM624 manual, as well as

recommended values if no triaxial tests are performed.

275

ys

p

pu

p

p

y

yu

s==== 0.550

14( )

16 y50

p = pu

Figure B18-a: Welch and Reese (1972) Static P-Y Curve for Stiff Clay Above Water Table

yc

p

pu

16 y50 16 y5016 y50

yc = ys + y50 . C . logN1



N 1N 2 N 3

9.6 (y50) logN1

+ + +

9.6 (y50) logN2 9.6 (y50) logN3

Figure B18-b: Welch and Reese (1972) Cyclic P-Y Curve for Stiff Clay Above Water Table

P-Y Resistance for Florida Limestone (McVay)

276

The data for the PY curves presented below is based on the report "Development of Modified T-Z curves for large diameter piles/drilled shafts in limestone for FBPIER"(McVay et. Al. (2004)). The data for the back computed curves were obtained from 12 lateral load tests performed in the centrifuge with diameters of 6 and 9 ft, embedment (L/D) of 2, 3, and 4 and rock strengths of 10 and 20 tsf. (The report recommends that full scale field tests be employed to validate the curves presented). Each lateral load test gave multiple P-Y curves, which were averaged to obtain a representative curve.

Presented in Figure B20 are back-adjusted P-Y curves for all twelve-centrifuge tests with side shear considerations; i.e., two shaft diameters (6’ and 9’), three embedment lengths (L/D = 2, 3, and 4) and two rock strengths (10 tsf and 20 tsf). Also shown in the figure are the predicted

P-Y curves for soft and stiff clay models.

Figure B20: P-Y curves from 12 lateral tests corrected for side shear.

Evident from the figure, even though the lateral resistance is normalized with rock strength and diameter, there is quite a bit of variability in the P-Y curves. Therefore the curves were normalized even further to be represented by a single trend-line. The P values are normalized with qu

0.15 D

0.85. Figure B21 shows the normalized P-Y curves for

Florida Limestone corrected for side friction. Note that the curves are valid for all the experimental results (i.e., 6’ and 9’ diameter shafts, different rock strengths, etc.). Note also that the P-Y curves are unit dependent. That is for the English system, the rock unconfined compressive strength (qu), the shaft diameter and rock’s lateral resistance, P must be in ksf, feet and kips/ft, respectively. For the Metric system, the rock unconfined compressive strength (qu), the shaft diameter and rock’s lateral resistance, P must be in KN/m

2, m and KN/m, respectively. The normalized

curves can be obtained by the following equations:

Eqn.b23

)( qu D.13750 0.150.85

D

yP =

004.00 ≤<D

y

277

Eqn.b24

+= 51)(1083 qu D 0.150.85

D

yP

1.0004.0 ≤≤D

y

where: D = Pile diameter

qu = Unconfined Compressive strength

y = Pile Displacement

Figure B21: Normalized P-Y curves corrected for side shear.

Limestone (McVay no 2 - 3 Rotation)

When a shaft that is embedded in rock strata is laterally loaded then the lateral response at any

elevation along the shaft length is a function of the lateral resistance of the rock and the side shear

(skin friction) that is developed at the shaft/rock interface. The commonly used back calculated P-

Y curves do not account for the contribution of the side shear explicitly. Rather the skin friction

contribution is implicitly accounted for in the method of back calculating the P-Y curves.

However as the diameter of the shaft becomes larger together with the high shear stress that is

developed at the shaft/rock interface this effect can become very significant and the explicit

determination of the side shear contribution may be justified. Such effort will involve the

inclusion of the side shear contribution to the lateral response mechanism of the soil and thus it

will reflect in the P-Y curves. Figure 1 shows a free body diagram of an element of the shaft of

278

length dz. Based on force equilibrium we can calculate the lateral response of the soil per shaft

unit length either neglecting or including the contribution the side shear forces. If the contribution

of side shear T, is included in the calculation then we see that there is a moment Ms due to the side

shear.

Ms = TD/dz

This will result in a lateral force dP which actually reduces the total lateral resistance.

dP = - d(Ms)/dz

The skin friction in the shaft interface causes the reduction. The latter suggests that for large

diameter drilled shaft field tests in stiff rock, the back computed P-Y curve which neglects the

effects of the side shear may be un-conservative.

Figure 1: Forces acting on a shaft element of length dz

FB-MultiPier can generate two types of P-Y curves for the Florida limestone to allow the user to

either include or exclude the effect of the side shear contribution during the analysis. This option

is activated when choosing "Soil Resistance due to Pile Rotation about 2 and 3 axes" from the soil

279

page, under Soil Layer Models Lateral. When the analysis is requested to include the side shear

contribution to the lateral response mechanism then the program calculates the additional term dP.

If on the other hand the option is not selected then the effect of side shear is not calculated. Based

on the discussion above the user should use this feature with the necessary caution and only where

the use is justified. That is when this option is chosen then care must be taken so that the

appropriate P-Y curve is used.

Limestone (McVay): No 2 – 3 Rotation is an option for Soil Layer Model Lateral.

Figure: M1 Limestone (McVay 2 – 3 Rotation

Soil Resistance due to Pile Rotation about 2 - 3 axes may be selected or deselected on this dialog.

280

Figure: M2 Limestone (McVay 2 – 3 Rotation) Soil Properties

User Defined

See the section labeled "User defined P-Y data" of soil information of the input file.

Sand (API)

281

API Sand Model (Refer to Section G.8.6 API RP2A LRFD)

• • • • • • • • γsoil, total unit weight of soil

• • • • • • • • k, subgrade modulus: a value can be chosen

from Figure G.8-2 API RP2A LRFD.

• • • • • • • • φ, angle of internal friction that is used to

compute C1, C2, and C3, coefficients. The graphs provided in Figure G.8-1 API RP2A LRFD are

curve-fitted as a function of φ.

Note: based on total unit weight of soil input, an effective unit weight of soil, i.e.,

γ'soil = γsoil - γwater. is computed and subsequently used to compute overburden pressure and ultimate lateral resistance.

Clay (API)

API Clay Model (Refer to Section G.8.2 API RP2A LRFD)

• • • • • • • • c, undrained shear strength of soil


• • • • • • • • εc, strain at one-half the max stress on

laboratory undrained compression tests of undisturbed soil samples.

Note:

(1) Effective unit weight is internally computed for Equation G.8-1 of API RP2A LRFD

(2) a dimensionless empirical constant ‘J’ used in Equation G.8-1 of API RP2A LRFD is set equal to a value of 0.5 , which is recommended for Gulf of Mexico clay soils.



282

Axial pile capacity is comprised of side friction and tip resistance. Respective component forces are obtained from the following curves:

Axial T-Z Curve for Side Friction

Axial T-Z(Q-Z) Curve for Tip Resistance

Driven Pile Sand (API)

API Sand Model (Refer to G.4.3 API RP2A LRFD)


• • • • • • • • φ, internal friction angle that is used to

approximate δ, friction angle between the soil and pipe wall, e.g., δ = φ − 5 deg.

• • • • • • • • K, dimensionless coefficient of lateral earth

pressure

• • • • • • • • f ult, ultimate (limiting) unit skin friction


γ'soil = γsoil - γwater, is calculated for effective overburden pressure, which is subsequently used to compute the skin friction using Equation G.4-5 of API RP2A LRFD.

Driven Pile Clay (API)

Axial Load Transfer (T-Z) Curves

API Clay Model (Refer to G.4.2 API RP2A LRFD)

• • • • • • • • c, undrained shear strength of soil


283


γ'soil = γsoil - γwater, is calculated for effective overburden pressure, which is subsequently used to compute a variable used in Equation G.4-3 of API RP2A LRFD.

Axial T-Z Curve for Side Friction Axial T-Z Curve for Side Friction

Axial T-Z curves for modeling the soil-pile interaction are categorized for the following cases:

Driven Piles

Drilled and Cast Insitu Piles/Shafts

Axial Skin Friction for Limestone (McVay)

User Defined

Driven Piles

The axial T-Z curves used in modeling the pile-soil interaction along the length of the driven pile

is shown in following figure (McVay, 1989) and given as

( )( )

( )( )( )

lnm m oo o

i o m o

r r rrZ

G r r r

β βτβ β β

− −= +

− − − Eqn. b25

where

ro= o

f

τβ

τEqn. b26

At a particular location on the pile/shaft, τ0 is the shear stress being transferred to the soil for a

given z displacement, where r0 is the radius of the pile/shaft and rm is the radius out from the

pile/shaft were axial loading effects on soil are negligible, assumed equal to pile length times (1-

284

soil's Poisson's ratio) times the ratio of the soil's shear modulus at the pile's center to the value at

its tip. The user must supply Gi, the initial shear modulus of soil, ν Poisson's ratio of soil, and τf,

the maximum shear stress between the pile and soil at the depth in question. Evident from the

equation above, the side springs are highly nonlinear.

Figure B22: Axial T-Z Curve for Pile/Shaft

Axial Skin Friction for Florida Limestone (McVay)

The following data is based on tests which were performed on 6’ diameter shafts embedded 18’ (L/D = 3) into the rock and are described in the report "Development of Modified T-Z curves for large diameter piles/drilled shafts in limestone for FBPIER"(McVay et. Al. (2004) ). All of the plots, Figures B23 – B25 show the load–dis place ment data which mobilize significant axial resistance with small displacements (i.e., 80% capacities at 0.5% of diameter). Axial load tests in lower strength 5 tsf rock, proved unattainable, because the rock mass fractured from the shaft to the boundaries of the bucket.

285

Figure B23: Axial load vs. displacement in 10 tsf strength rock

Figure B24: Axial load vs. displacement in 20 tsf strength rock.

Figure B25: Axial load vs. displacement in 40 tsf strength rock.

286

The load applied at the top of each shaft was subsequently converted into shear stress (skin friction, fs) on the shaft/rock interface by dividing by the shaft area. Styro-foam was placed at the shaft tip so the entire load was transferred to the rock through skin friction. Plots of fs vs. axial displacement (T-Z curves) for each strength rock are shown in Figure B26.

Figure B26: T-Z curves for 10, 20 and 40 tsf rocks.

From the T-Z curves, the ultimate unit skin frictions were established from the horizontal tangents. Ultimate unit skin friction of 53 psi, 92 psi and 160 psi, were found for rock strengths of 10 tsf, 20 tsf, and 40 tsf, respectively. Shown in Figure 5.5 are the normalized T-Z curves (Fig. B26): fs values were normalized with respect fsmax (ultimate unit skin friction) and vertical displacement, Z, was normalized with respect to D (diameter).

287

Figure B27: Normalized T-Z curves for synthetic rock.

The three normalized curves are quite similar and can be represented by a single curve (shown in bold line), with the following equations:

Eqn. b27

0.33s

smax

f0.96R

f=

0 = R = 0.5

Eqn. b28

0.16s

smax

f0.86R

f=

0.5 = R = 3

Eqn. b29

s

smax

f1

f=

3 = R

where: R = z/D*100.

fs = skin friction

fsmax = ultimate unit skin friction

Kim (2001) analyzed data from 33 axial load tests (Osterberg) from various bridge sites throughout

Florida and recommended the normalized T-Z curve for the natural Florida Limestone given in Figure

B28. A comparison of Kim’s normalized T-Z curve with the synthetic rock curve, Figure B27 is also

shown in Figure B28. Evident from the figure there is a very good agreement between the normalized T-

Z behavior of the natural limestone and the synthetic rock.

288

Figure B28: Comparison of normalized T-Z curves.

User Defined

See the section labeled "User defined T-Z data" of soil information of the input file.

Drilled and Cast Insitu Piles/Shafts Drilled and Cast Insitu Piles/Shafts

The T-Z curves used for drilled and cast insitu piles/shafts are based in the recommendations

found in Wang and Reese (1993). They are based in the trend lines and are computed for each

node. Trend lines of stress transfer for axial end bearing and side resistance are provided for the

following materials:

Sand

289

Clay

Intermediate Geomaterial

Sand

Valid for φ ≥ 30°

' 'tan 2.0 (191.5 )sz z z

f K tsf kPaσ φ β σ= = ≤Eqn. b30

1.5 0.135 ( )z ftβ = −Eqn. b31

0.25 1.2β≤ <Eqn. b32

valid for depths ranging from 5 to 87.5 ft (1.5 to 26.7 m)

The immediate settlements are computed using non-linear t-z springs, with the shape presented in

following Figure B29. The equations are provided but it should be referred that there is a

considerable scatter around the trend line.

Side friction mobilization (trendline)

/ max - 2.16* 4 6.34* 3- 7.36* 2 4.15*fs fs R R R R= + +Eqn. b33 for R ≤ 0.908333

/ max 0.978112fs fs =Eqn. b34 for R > 0.908333

where

3 *100y

RD

=Eqn. b35

290

Figure B29:: Trend Lines for Drilled Shaft Side Friction in Sand

Clay

2.75 (263 )sz z u

f c tsf kPaα= ≤Eqn. b36 unless tests prove otherwise

From ground surface to depth of 5 ft (1.5 m) α = 0

Bottom 1 diameter of drilled shaft or 1 stem diameter above top of bell α = 0

All other points along the sides of the drilled shaft α= 0.55

The immediate settlements are computed using non-linear t-z springs, with the shape presented in

following Figure B30. The equations are provided but it should be referred that there is a

considerable scatter around these trend lines.

291

Side friction mobilization (trendline)

fs/fsmax = 0.593157*R/0.12 for R ≤ 0.12

fs/fsmax = R/(0.095155+0.892937*R) for R ≤ 0.74

fs/fsmax = 0.978929-0.115817*(R-0.74) for R ≤ 2.0

fs/fsmax = 0.833 for R > 2.0

where

3 *100y

RD

=Eqn. b37

Figure B30: Trend Lines for Drilled Shaft Side Friction in Clay


The design of drilled shafts founded in intermediate Geomaterials is directly from FHWA's Load

Transfer for Drilled Shafts in Intermediate Geomaterials .

292

Intermediate Geomaterials are characterized as one of the following 3 Types:

1. (Type 1) Argillaceous geomaterials: Heavily overconsolidated clay, clay shale, saprolite and

mudstone.

2. (Type 2) Calcareous Rock: Limestone and Limerock

3. (Type 3) Very Dense Granular Geomaterials: residual, completely decomposed rock, and glacial

till.

• • • • • • • • Note:

Types 1 and 2 are considered to be cohesive materials with an undrained strength, qu in the range

of 0.5 to 5.0 Mpa.

Type 3 is primarily cohesionless and has Nspt from 50 to 100

Method 1 proposed by FHWA's Load Transfer for Drilled Shafts in Intermediate Geomaterials,

for Type 1 and 2 materials has been coded herein.

• • • • • • • • Valid for IGM Type 1 and 2; 0.5 < qu <

5.0 Mpa; Recovery > 50 %;

• • • • • • • • Appropriate for very short sockets (L/D <2)

or very long sockets (L/D>20);

• • • • • • • • Where there is strong layering in the

formation, or where part of the socket is artificially roughened and part is smooth

Required Data:

• • • • • • • • Number of Layers

• • • • • • • • Type of surface (rough or smooth)

• • • • • • • • qu (Mpa)

• • • • • • • • modulus ritio (Em/Ei)

• • • • • • • • γ, unit weight of soil

• • • • • • • • Mass Modulus - Em

• • • • • • • • Thickness

293

• • • • • • • • drilled shaft diameter

• • • • • • • • Young’s modulus of drilled shaft

• • • • • • • • unit weight of concrete in drilled shaft

• • • • • • • • pumping rate of concrete placement

• • • • • • • • slump of concrete in drilled shaft

Ei is the Young’s modulus for the impact sample.

Em can be taken as 115 qu for Type 2 IGM’s and 250 qu for Type 1 IGM’s for design purposes if

modulus measurements are not made, provided that soft seams and open fractures are not present.

– Load Transfer for Drilled Shafts in Intermediate Geomaterials, pp. 80

A range of typical Em values for limestone is 50,000 psi to 300,000 psi.

Table B2: Estimation of Em/Ei based on RQD

RQD

(percent)

Em/Ei

(closed joints)

Em/Ei

(open joints)

100 1.00 0.60

70 0.70 0.10

50 0.15 0.10

20 0.05 0.05

Note: Values of Em/Ei for RQD values between those shown can be estimated by linear

interpolation on RQD.

Axial T-Z(Q-Z) Curve for Tip Resistance Axial T-Z (Q-Z) Curve for Tip Resistance

Axial Q-Z curves for tip resistance are categorized for the following cases:

Driven Piles

Drilled and Cast Insitu Piles/Shafts

294

User Defined

Driven Piles

The nonlinear pile/shaft's tip spring, i.e. Q-Z curve for driven pile is shown in the following figure and given as (McVay 1989):

( )2

0

1

4 1

b

bi

f

Qz

Qr G

Q

ν−=

−

Eqn. b38

where Qf is the ultimate tip resistance (force), Gi and ν are the initial shear modulus and Poisson's

ratio of the soil at the pile tip. R0 is again the radius of the pile/shaft, and Qb is the mobilized tip

resistance.

Figure B31: Axial T-Z (Q-Z) Curve for Driven Pile

User Defined

295

See the section labeled "User defined Q-Z data" of soil information of the input file.

Driven Pile Sand (API)_QZ

API Sand Model (Refer to Section G.7.3 API RP2A LRFD)

• • • • • • • • Pile end condition :

Plugged – a gross sectional area is used to compute ultimate end bearing capacity

Unplugged – a cross sectional area is used to compute ultimate end bearing capacity


• • • • • • • • φ, angle of internal friction that is used to

compute Nq, dimensionless bearing capacity factor, using an equation from Section G.13.3 API RP2A

LRFD

b ult, ultimate (limiting) unit end bearing

Driven Pile Clay (API)_QZ

API Clay Model (Refer to Section G.7.3 API RP2A LRFD)

• • • • • • • • Pile end condition :

Plugged – a gross sectional area is used to compute ultimate end bearing capacity

Unplugged – a cross sectional area is used to compute ultimate end bearing capacity


c, undrained shear strength of soil

296

Drilled and Cast Insitu Piles/Shafts Drilled and Cast Insitu Piles/Shafts

The Q-Z curves used for drilled and cast insitu piles/shafts are based in the recommendations

found in Wang and Reese (1993). They are based in the trend lines and are computed for each

node. Trend lines of stress transfer for axial end bearing and side resistance are provided for the

following materials:

Sand

Clay


Sand

Valid for NSPT > 10

if Bb > 50 in (1.27 m):

50 1.27

( ) ( )br b b

b b

q q qB in B m

= =Eqn.b39

The immediate settlements are computed using non-linear Q-z springs, with the shape presented in

Figure B32 shown below. The equation is provided but is should be referred that there is a

considerable scatter around the trend line.

297

End bearing mobilization (trendline)

/ max - 0.0001079* 4 0.0035584* 3- 0.045115* 2 0.34861*qb qb R R R R= + +Eqn.b40

Figure B32: Trend Lines for Drilled Shaft End Bearings in Sand

Clay

40 (3.83 )b c ub

q N c tsf MPa unless tests prove otherwise= ≤Eqn. b41

6 1 0.2 9c

b

LN

B

= + ≤

Eqn. b42

where cu = average undrained shear strength of the clay (computed 1 to 2 diameters below the

shaft)

for Bb > 75 in (1.90 m)

298

br r bq F q=Eqn. b43

2.51.0

( ) 2.5r

b

Fa B in b

= ≤ +

Eqn. b44

015.00021.00071.0 ≤

+=

bB

La

)(45.0 ksfcb u=

5.15.0 ≤≤ b

Immediate Settlements (trendline)

The reference curve is presented in the following Figure. The marks represent the values proposed

by Wang and Reese (1993) and the solid line is the adopted curve. It should be observed that a

considerable scatter is present around the curve.

Reference curve (trendline)

/ max 1.1823 - 4* 5 - 3.7091 -3* 4 4.4944 - 2* 3- 0.26537* 2 0.78436*qb qb E R E R E R R R= + +Eqn. b45

for R ≤ 6.5

/ max 0.98qb qb =Eqn. b46

for R > 6.5

299

Figure B33: Trend Lines for Drilled Shaft End Bearings in Clay


The design of drilled shafts founded in intermediate Geomaterials is directly from FHWA's Load

Transfer for Drilled Shafts in Intermediate Geomaterials.

Intermediate Geomaterials are characterized as one of the following 3 Types:

1. (Type 1) Argillaceous geomaterials: Heavily overconsolidated clay, clay shale, saprolite

and mudstone.

2. (Type 2) Calcareous Rock: Limestone and Limerock

3. (Type 3) Very Dense Granular Geomaterials: residual, completely decomposed rock, and

glacial till.

• • • • • • • • Note:

Types 1 and 2 are considered to be cohesive materials with an undrained strength, qu in the range of

0.5 to 5.0 Mpa.

300

Type 3 is primarily cohesionless and has Nspt from 50 to 100

Method 1 proposed by FHWA's Load Transfer for Drilled Shafts in Intermediate Geomaterials,

for Type 1 and 2 materials has been coded herein.

• • • • • • • • Valid for IGM Type 1 and 2; 0.5 < qu <

5.0 Mpa; Recovery > 50 %;

• • • • • • • • Appropriate for very short sockets (L/D <2)

or very long sockets (L/D>20);

• • • • • • • • Where there is strong layering in the

formation, or where part of the socket is artificially roughened and part is smooth

Required Data:

• • • • • • • • Number of Layers

• • • • • • • • Type of surface (rough or smooth)

• • • • • • • • qu (Mpa)

• • • • • • • • modulus ritio (Em/Ei)

• • • • • • • • γ, unit weight of soil

• • • • • • • • Mass Modulus - Em

• • • • • • • • Thickness

• • • • • • • • drilled shaft diameter

• • • • • • • • Young’s modulus of drilled shaft

• • • • • • • • unit weight of concrete in drilled shaft

• • • • • • • • pumping rate of concrete placement

• • • • • • • • slump of concrete in drilled shaft

Ei is the Young’s modulus for the impact sample.

Em can be taken as 115 qu for Type 2 IGM’s and 250 qu for Type 1 IGM’s for design purposes if

modulus measurements are not made, provided that soft seams and open fractures are not present.

– Load Transfer for Drilled Shafts in Intermediate Geomaterials, pp. 80

A range of typical Em values for limestone is 50,000 psi to 300,000 psi.

301

Table B3: Estimation of Em/Ei based on RQD

RQD

(percent)

Em/Ei

(closed joints)

Em/Ei

(open joints)

100 1.00 0.60

70 0.70 0.10

50 0.15 0.10

20 0.05 0.05

Note: Values of Em/Ei for RQD values between those shown can be estimated by linear

interpolation on RQD.

Torsional Soil-Pile Interaction Torsional Soil-Pile Interaction

The torsional stiffness of a pile embedded in soil is modeled using T-θ springs, where T is the torque applied to the pile

and θ is the angle of twist, in radians. The springs are located at the nodal points. T-θ springs can be represented by

any of the following ways:

Hyperbolic Curve

User Defined

Hyperbolic Curve

The non-linear T-θ behavior of the soil is modeled using an hyperbolic curve, with initial slope as

a function of the shear modulus G. The ultimate value is based on the ultimate shear stress at the

contact pile/soil.

302

θ (rad)

T (F*L)

Tult

Figure B34: Hyperbolic representation of T-θ curve

For a length of pile ∆L, the torque is given by

2

0 02T r Lπ τ∆ = ∆Eqn. b47

where:

ro = radius of the pile

τo = shear stress along ∆L

For a long rigid pile embedded in a soil with shear modulus G, Randolph (1981) deduced the

expression for the torque per unit length

2

04T

G rL

π∆

=∆

Eqn. b48

This expression does not consider the pile tip stiffness. For a long pile the tip contribution may be

considered negligible.

Using an hyperbolic curve defined by

303

Ta b

θθ

=+

Eqn. b49

where the coefficients a and b are given by

2

0

14

i

i

dTinitial slope r G L

a dπ

θ = = = ∆

Eqn. b50

2

0

12

ult ultT r L

bπ τ= = ∆Eqn. b51

The ultimate shear stress can be obtained with the same procedures as for axial skin friction. As

for the initial shear modulus, it should be determined from in-situ tests.

User Defined

See the section labeled "User defined T-θ data" of soil information of the input file.

Finite Element Theory

Finite Element

Following types of elements are available in FB-MULTIPIER:

Membrane Element

Plate Element

Flat Shell Element

Special Element for FB-MULTIPIER

304

Membrane Element

The membrane element is a flat, constant thickness element. It can be triangular, rectangular or

have curved sides. The element can have configurations of three, four, six, eight or nine nodes.

Whatever the shape or number of nodes, the element has two translational DOF per node. These

DOF must lie in the plane of the element. The results from the element consist of two normal

stresses and a shear stress in the plane of the element, (see Figure C1 below). The stress results

are given at each corner node in the element in FB-MultiPier.

S1 2

X

Z Y

S1

S2

Units: S1, S2, S1 2, S2 1 – Force/Area

Pier Global System

3 2

1

Local System

S2 1

Figure C1: Membrane Stress Results

The difference between element behavior is dictated by the choice of the number of nodes and

hence the number of DOF for the element. The three node triangle has linear shape functions and

hence constant strain and stress. This element is referred to as the constant strain triangle. The

four node element has slightly better response than the three node element. The six node triangle

has quadratic shape functions and linear stress and strain. The eight and nine node element has

better response than the six node element. FB-MultiPier uses a nine node version for the

membrane (in-plane) stresses.

Plate Element

True plate elements do not include in-plane effects. In-plane effects are handled by membrane

elements. Similarly in a beam element the bending and axial effects are un-coupled. This is the

same in two dimensions. These two elements are commonly merged to get a complete in and out-

305

of plane element referred to as a Flat Shell Element. We will discuss a true plate element before

discussing the flat shell elements used in FB-MultiPier. To do this we must cover a small amount

of theory.

There are two common versions of plate theory used in finite elements: Kirchoff and Mindlin.

Kirchoff plate bending theory is derived in a similar fashion to beam bending but includes bending

in both directions. The derivation assumes that the normal displacement, vertical displacement w,

controls. In Kirchoff theory the rotation, Θ, in the plate is the derivative of w. This is the same as

beam theory. This means that shear deformations are ignored. In Mindlin theory, shear is

included and the rotation is the sum of the derivative of w and the shear angle. FB-MultiPier uses

a Mindlin formulation.

The results from all plate elements consist of moments. Some plate elements also give the

transverse shear, Q, as a result. It is important to note that the moments and shear results are per

unit length of plate. The following figure (Figure C2) gives the sign convention for moment and

shear results.

Figure C2: Definition of Positive Plate Results

Note: M1 causes stress in the 1 direction following standard plate theory

M2 causes stress in the 2 direction following standard plate theory

Flat Plate elements can be found in three to nine node versions, just like the membrane elements

(see Figure C3 below). The same concepts of shape function order are true for the plates as well

as for the membrane. Three node triangular plates model constant moments exactly. Nine node

elements model linear moments with some second order effects. It is important to note that in

plates, moments are equivalent to stress and curvature is equivalent to strain, in terms of

modeling. In other words, we need more elements in a high moment gradient area for plates.

306

Triangular

(Constant Moment)

Nine Node

(Linear Moment)

Common Flat Plate Configurations

Figure C3: Common Flat Plate Configurations

Flat Shell Elements

Shell elements combine the effects of plate bending and in-plane (membrane) effects. There exist

formulations for both flat and curved shell elements. The curved element formulation is a much

more complicated derivation. The flat shell however can be considered to be merely the addition

of the membrane and flat plate elements (see Figure C4 below). This is the most common form of

shell element found.

Combine

ΘY

Z

Y

X

Plate

Membrane

Shell

Y

X

ΘX

X

Pier Global System

Z Y

ΘY

ΘX Z

Figure C4: Flat Shell Element as a Combination of Membrane and Plate Element

307

The flat shell element can be used to model structures where both bending and stretching effects

need to be considered. Many small flat shell elements can be used to form curved surfaces. The

modeling of bridge decks, wide flange beams and curved shell structures are three such structures

where flat shell elements are commonly used.

Bridge Deck

Curved Shell

Wide Flange Beam

Figure C5: Common Applications of Flat Shell Elements

FB-MULTIPIER, uses a nine node, Mindlin flat shell element for the pier cap.

Mindlin Theory

Mindlin theory includes shear deformations. As a result, the normal to the surface does not

remain normal. Likewise, the derivative of the shape function for the normal displacement w(x,y)

is not equal to the slope. In Mindlin theory the slope of the surface is the sum of the derivative of

w(x,y) and the shear angle change. Figure C6 below shows the relationship between the

displacement w(x,y), shear angle γ and the derivative of the displacement.

308

δw/δx

w

γ (shear)

Shear Included - Sum of Derivative and Shear

Mindlin Plate Theory

Figure C6: Mindlin Plate Theory

This sum of angles to get the total rotation implies that different shape functions can be used for

the displacement w and the rotations (ΘΘΘΘx , ΘΘΘΘy). This is the most common formulation found in

flat plate and shell elements used in current computer programs. This means there will not be

rotational continuity across elements boundaries (since shear exists). Hence the elements are

considered to be C0 elements. The following figure (C7) shows this lack of continuity across

elements.

Lack of Rotational Continuity for Mindlin

Different Rotations

Figure C7: Lack of Rotational Continuity for Mindlin Plate Theory

In either case, the pure plate bending element has three DOF per node; the normal displacement w

and the out of plane rotations (ΘΘΘΘx , ΘΘΘΘy). These are shown in Figure C8 below.

Y

Θ x

W

X

Z

Y X

Θ y

Plate Degrees of Freedom

309

Figure C8: Plate Degrees of Freedom

Generalized Stress and Strain

In plate theory, most derivations refer to the equations for generalized stress and strain. This is

because the equations for plate behavior can be converted to the form:

2 *

0

12 ( , ) * ( )

ult ultT r LM x y E curvature

bπ τ= = ∆ = ΨEqn. c1

Where E* is a modified constitutive matrix. Notice that this is just like the equation for stress and

strain except we have moments and curvature. In plates, the displacement unknowns are the

normal displacement and the two rotations. Following the analogy of generalized stress, moments

are equivalent to stress and curvature is equivalent to strain. This means when using these

elements in modeling, we treat the moment gradient like we would stress to determine the level of

shape function and number of elements required for an accurate analysis. In addition, the

difference in moment at a common node between two elements indicates the adequateness of the

mesh.

Special Element for FB-MultiPier

Neither the membrane or plate element offer normal rotational stiffness. This means that pile

torsion would not be transmitted to the pile cap using a standard element formulation. To account

for this torsional force transfer, special normal rotational stiffness terms have been added to the

shell element. The stiffness is calculated on an equivalent beam formulation using the tributary

area of the pier cap over each pile. This is an approximate method offering good transfer for thick

pile caps.

The second enhancement is the use of an eight point gauss integration scheme for the element.

The eight point scheme is a reduced integration scheme offering good shear integration while

avoiding locking problems. The eight point scheme is tuned for the pile problem so that zero

energy modes are removed while still retaining good element flexibility.

310

Mesh Correctness and Convergence

The accuracy of a finite element solution depends on the number of elements and the order of the

shape functions. As the number of elements increase, the piece-wise displacement approximation

approaches any true displacement field. Recall that two linear elements provided a better response

than a single linear element. Also, a single quadratic element performs even better.

The stress results also follow the same pattern. More elements provide better stress results.

However, since we only guarantee the continuity of the displacements, the stresses are

discontinuous. This means that at a node where two elements meet, the stresses do not match.

However, as the number of elements increase, the stresses between elements get closer. As an

example, below is a plot of the stress along the top of the cantilever beam. The results are plotted

for the four - four node membranes, the two nine node membranes and the 40 - four node

membranes.

4 - 4 node

2 - 9 node

40 - 4 node

5

10

15

20 Stress Plot for Cantilever Beam

Figure C9: Stress Plot for Cantilever Beam

Notice that for the four - four node elements, the difference between the elements is 28%. This

large percentage error indicates a poor mesh (or not enough elements). Looking at the two - nine

node model we see a closer difference. Here the error is 14.0%. This indicates that the mesh is

marginal but probably sufficient. Finally we look at the 40 element model. Here the error is much

better and only 3%. The 40 element model is very good.

311

The difference in element stresses at a node is an important measure of model correctness. In general, we do not have the exact displacements in order to check our model. Hence, the stress check is necessary to verify convergence of our model. If the difference in stresses between elements is small the finite element mesh is good.

Nonlinear Behavior

Nonlinear Behavior

Discrete element is used to model the nonlinear behavior of the piles in FB-MULTIPIER. The

discrete element models the nonlinear material and geometric behavior of the piles. The nonlinear

material behavior is modeled by using input or default stress strain curves which are integrated

over the cross-section of the piles. The nonlinear geometric behavior is modeled using the P-delta

moments (moments of the axial force times the displacements of one end of element to another) on

the discrete element. And since the user subdivides the pile into a number of sub-elements, the P-y

moments (moments of axial force times internal displacements within members due to bending)

are also modeled.

Discrete Element Model


The discrete element model (Mitchell 1973 and Andrade 1994) can be represented as a mechanical

model as shown in Figure D1. The center bar can both twist and extend but is otherwise rigid. The

center bar is connected by two universal joints to two rigid end blocks. The universal joints permit

bending at the quarter points about the y and z axes. Discrete deformational angle changes Ψ1,

Ψ2, Ψ3, Ψ4 occur corresponding to the bending moments M2, M1, M4, M3, respectively. A

discrete axial shortening corresponds to the axial thrust T and the torsional angle Ψ5 corresponds

to the torsional moment in the center bar M5.

312

Figure D1: Discrete Element Model

Discrete element model is elaborated in the following sections (use the links):

Element Deformation Relations

Integration of Stresses

Element End Forces

Element Stiffness


In Figure D1, w1 - w3 and w7 - w9 represent displacements in the x, y and z directions at the left

and right ends respectively, w4 and w10 represent axial twists (twists about the x -axis) at the left

and right ends, respectively, and w5-w6 and w11- w12 represent the angles at the left and right

end blocks about the x and z axes, respectively. Based on a small displacement geometric analysis:

( )

( )

3 9 5 11

8 2 6 12

Eqn. d1

Eqn. d2

2

2

hn w w w w

hs w w w w

= − − +

= − − +

313

The elongation of the center section of the element is calculated as follows:

7 1Eqn. d3 w wδ = −

The angle changes for the center section about the z and y-axes are then defined below:

( )

( )

6 128 21

5 113 92

Eqn. d4

Eqn. d5

2

2

w ww ws

h h

w ww wn

h h

θ

θ

+−= = −

+−= = −

The discretized vertical and horizontal angle changes at the two universal joints are then:

1 1 6 2 5 2

3 12 1 4 2 11

Eqn. d6

Eqn. d7

;

;

w w

w w

θ θ

θ θ

Ψ = − Ψ = −

Ψ = − Ψ = −

and the twist in the center part of the element is defined as:

5 10 4w wΨ = −Eqn. d8

Thus, the internal deformations of the discrete element model are uniquely defined for any

combination of element end displacements.

The curvature for small displacements at the left and right universal joints about the y and the z

axes are defined as follow:

At the left joint,

1 21 2;

h h

Ψ ΨΦ = Φ =Eqn. d9

At the right joint,

3 43 4;

h h

Ψ ΨΦ = Φ =Eqn. d10

314

The axial strain at the center of the section is given by:

2c

h

δε =Eqn. d11


Consider a beam subjected to both bending and axial loads. It is assumed that the strains vary

linearly over the area of the cross-section. This assumption enables the strain components due to

bending about the z and y-axes, and the axial strain, to be separated or combined using

superposition. Examples of these three components are represented separately in Figures D2-(a-c)

and combined in Figure D2-d. Also shown in Figure D2-d is a differential force, dFi, acting on a

differential area, dAi. Finally Figure D2-e represents the stress-strain relationship for the material.

a) Strain due to

z-axis bending

b) Strain due to

y-axis bending

c) Strain due to

axial thrust

�

�

�

�

�

�i

i

1

2

x

y

z

dF

dA

i

i

e) Stress-strain relationship

d) Combined strains

Figure D2: Linear Strain Distribution over Square Cross-Section

315

Then

i i idF dAσ= ⋅Eqn. d12

And, to satisfy equilibrium:

Z i i i iA A

Y i i i iA A

i iA A

M dF Y Y dA

M dF Z Z dA

T dF d A

σ

σ

σ

= ⋅ = ⋅ ⋅

= ⋅ = ⋅ ⋅

= = ⋅

∫∫ ∫∫

∫∫ ∫∫

∫∫ ∫∫

Eqn. d13

Eqn. d14

Eqn. d15

The relationship for strain at any point in the cross-section is:

1 2cY Zε ε= − Φ ⋅ − Φ ⋅Eqn. d16

The stress at any location in the section is found using the appropriate material stress-strain curve

described subsequently.

Numerical integration of equations is done using Gaussian Quadrature. To use the method of

Gaussian Quadrature, the function being integrated must be evaluated at those points specified by

the position factors. These values are then multiplied by the appropriate weighting factors and the

products accumulated. Figure D3-a shows a square section with 25 integration points (a 5x5

mesh). The number of defaults integration points for square pile is set at 49 (a 7 by 7 mesh). Users

may change this to a NPTS x NPTS mesh by inserting a value for NPTS as the last input item in

data line 6A.. For circular sections, the section is divided into circular sections (12 radial divisions

and 5 circumferential divisions as shown in Figure D3-b). The sections are integrated at the

centroid of each sector using weighting factors of 1.0. The stress in all steel bars is evaluated at the

centroid and a weighting factor of 1 is used for each bar.

316

Figure D3-a: Section Integration Divisions - Cross Section of square pile showing integration

points

Figure D3-b: Section Integration Divisions - Circular pile cross section showing steel rebars

317

When a circular void is encountered in a square section, the force is first computed on the un-

voided section and then the force that would be acting on the voided circular area is computed and

subtracted from the force computed for the non-void section. Circular sections with voids are

divided into sectors omitting the voided portion.

Even for nonlinear material analysis, the torsional moment M5 is assumed to be a linear function

of the angle of twist, ψ5, and the torsional stiffness GJ, where J is the torsional constant and G is

the shear modulus as shown next

55

2M G J

h

Ψ= ⋅ ⋅Eqn. d17

Element End Forces

From equilibrium of the center bar (see Figure D1 ):

4 21 1

1 32 2

M MV T

h

M MV T

h

θ

θ

−= − ⋅

−= − ⋅

Eqn. d18

Eqn. d19

And from equilibrium of the end bars:

1 2 1 3 2 4 5

5 1 2 5 6 2 1 6

7 8 1 9 2 10 5

11 3 2 11 12 4 1 12

; ; ;

;2 2 2 2

; ; ;

;2 2 2 2

f T f V f V f M

h h h hf M V T w f M V T w

f T f V f V f M

h h h hf M V T w f M V T w

= − = = − = −

= + ⋅ + ⋅ ⋅ = − + ⋅ + ⋅ ⋅

= = − = =

= − + ⋅ + ⋅ ⋅ = + ⋅ + ⋅ ⋅

Eqn. d20

Eqn. d21

Eqn. d22

Eqn. d23

where f1- f3 and f7 - f9 are the acting end forces, and f4 - f6 and f10 - f 12 are the end moments.

Element Stiffness

318

Using the standard definition, the stiffness of an element having n degrees of freedom (d.o.f.) is a

square matrix [K] of order n in which Kij is the force necessary in the i-th d.o.f. to produce a unit

deflection of the j-th d.o.f. The secant stiffness computed is the stiffness that the members would

have if each of the integration points had the secant stiffness defined by dividing the present stress

by the present strain as shown in the following figure (D4).

σi

Ei+1

εi

Figure D4: Secant Stiffness for Nonlinear Stress-Strain

During the iteration process the element stiffness matrix is reevaluated in each new deformed

position. For each iteration, initially the secant stiffness is stored at all integration points within an

element. Then on 12 subsequent passes a unit displacement is applied to each element degree of

freedom in turn keeping all other displacements as zero and the forces corresponding to that unit

displacement are calculated by integrating the stresses over the cross-section of the element as

described earlier. The previously stored secant moduli at each of the Gaussian integration points

are used in this integration of stresses. The element end forces thus computed would be the nth

column of the stiffness matrix corresponding to a case where the nth degree of freedom has a unit

displacement imposed, all other displacements being held to zero.

319

Stress-Strain Curves

Stress-Strain Curves

The user may define their own stress strain curves for concrete and steel or use the default values

described below (use the links).

Concrete

Mild Steel

High Strength Prestressing Steels

Adjustment for Prestressing

Concrete

The figure below shows the default value of stress-strain curve supplied by the program and is a

function of f'c and Ec input by the user. The compression portion of the concrete curve is highly

non-linear and is defined by the Modified Hogenstead parabola and straight line as shown in the

figure. For the tension portion the curve is assumed linear up to a stress of fr and then has a

tension softening portion as shown. The tension softening portion attempts to account for the

uncracked sections between cracks where the concrete still carries some stress. The value of fr is

based on the fixed value of er shown in Figure D5 and the modulus of elasticity Ec input by the

user. For English units this will give a value of fr of 7.5√f' c.

320

0.5f r

ε 0 2

= ′ ′ f

E c c

Straight

εεεε r = (7.5/57000) = 0.000131578

0.002

f f c c o o

= ′ ′

−

2

2 ε ε

ε ε

εεεε stf = 0.0003

f c

εεεε r εεεε

stf

E c

1

εεεε u = 0.0038

εεεε u

f r

εεεε c

′ ′ = ′ f c 0.85 f c

0.85 f c ′ ′

Figure D5: Default Stress-Strain Curve for Concrete

Mild Steel

For mild steel reinforcement the stress-strain relationship is assumed to be elastic-plastic and

similar in both tension and compression. A yield strain ey is computed based on the yield stress, fy

and the modulus of elasticity input Es,

y

y

s

f

Eε =Eqn. d24

The default relations for the mild steel stress-strain curve are given by,

321

Z i i i iA A

Y i i i iA A

i iA A

M dF Y Y d A

M dF Z Z d A

T dF d A

σ

σ

σ

= ⋅ = ⋅ ⋅

= ⋅ = ⋅ ⋅

= = ⋅

∫∫ ∫∫

∫∫ ∫∫

∫∫ ∫∫

Eqn. d25

Eqn. d26

Eqn. d27

The default stress -strain curve generated for steel with f'y=60 ksi and Ec=29600 ksi is shown in

the figure (D6) below.

Figure D6: Mild Steel Stress-Strain Curve for Fy = 60 ksi.


The figure in mild steel shows reinforcing as rebars. However, the user may select high strength

reinforcing strands as well as rebars. The stress-strain curves for prestressing steels generally do

not have a definite yield point as illustrated by the curve for fsu = 270 ksi in the figure below. The

most common values of fsu used in prestressing practice are fsu = 250 ksi and 270 ksi. For these

two input values when using standard (English) Units, the curves defined by the PCI design

handbook (PCI 1992) will be used. For other strengths or when using nonstandard units, the

default curves will be obtained by using non-dimensional equations based on curve fitting the two

cited curves. These curves are not recommended for use for values of fsu much different than the

standard values.

322

Figure D7: Prestressing Steel Stress-strain Curve for fsu = 270 ksi.


When piles are prestressed prior to installation, there are stresses and strains existing at the time of installation cue to the prestressing. The program shifts the origin of the stress-strain curve for the steel by the amount of the prestressing stress in the steel and the corresponding steel strain. Also, the program shifts the origin of the concrete stress-strain curve by the amount of compression in the concrete and the corresponding concrete strain. It is assumed that the prestressing is symmetrically placed and thus only a constant compressive stress is developed in the concrete due to the prestressing.

Confined Concrete Model

Bi-axial Interaction diagram Interaction Diagrams

Assumptions and Features for the Biaxial Interaction Diagram

The strength routines compute section strength under axial force and internal bending moments

about the two principle axes for a prestressed or non-prestressed reinforced concrete and steel

cross sections which can be used for both columns or piles. The analysis routine computes the

323

section moments, Mnz and Mny, and axial force, Pn and multiplies these by the appropriate

strength reduction (φ) factors which are discussed later for steel and concrete.

It is assumed that the user inputs the appropriate factored loads (service-level loads times load

factors). The analysis routines then compute the factored moments, Muz and Muy , and axial

force, Pu, acting at each section. The strength routines indicate whether the section is adequate or

not adequate. This information can be displayed graphically on an interaction diagram of

moments for a given level of axial force or found in the output as a single factor, called a Failure

Ratio, FR. The details of how the FR is calculated will be discussed later. If the FR is less than or

equal to one, this indicates the section is safe for the applied factored moments and axial force.

The interaction diagram routines do not consider any long column or stability effects that are

important for slender members. However, if the nonlinear analysis option is selected for the piles

and the structure, then the slenderness effects through the P∆ and Py moments are considered in

the computation of the factored axial force and moments as discussed earlier. Thus the direct use

of the interaction diagrams using the linear analysis option for the piles and structure could be very

unsafe for slender members. The option to use the interaction diagrams and linear analysis of the

piles and structure is provided for preliminary design phases and must not be used for a final

design.

Also it should be noted that the nonlinear analysis procedures while very thorough may not reflect

all of the criteria required for design of slender structures in appropriate codes. A list of factors

that may affect the final design that are not considered in the analysis are as follow:

1) Creep in concrete.

2) Initial imperfections or out of straightness of members.

3) Residual stresses.

4) A separate analysis phi factor to account for the possibility of undersized members.

All of the factors could potentially increase the defections and thus the P∆ and Py moments above

those given by the nonlinear analysis routines and should be accounted for by the designer as

appropriate.

The routine operates by computing numerous horizontal slices of the Pn, Mnx, Mny (nominal

strength) interaction surface. The result is a series of Mnx, Mny interaction curves for various

magnitudes of axial load, Pn. Next, each interaction curve is represented in the form.

1nynz

oz oy

MM

M M

βα

+ = Eqn. d63

324

The moments M0z and M0y represent the nominal moment strength at axial load, Pn, for uni-axial

bending about the z and y axes respectively. The exponents, α and β are computed in by the least

squares method. They enable the above expression to fit the computed interaction curve, and vary

with axial load. The actual FR is computed, by interpolation for the axial force Pu/φ using the

stored values of axial force and exponents, α and β. The program then computes the parameter,

FR, as; the ratio of the length of the vector for the actual forces (in 3-d space – Mux, Muy and P)

divided by the length of the vector with the same direction as the actual results but with that vector

touching the 3-D failure surface. This has the effect of assuming that the moments and axial load

will increase proportionally until failure.

Note that the routines handle square, rectangular or circular sections with prestressed or non-

prestressed steel and H-piles that themselves may be encased in concrete. The capabilities and

limitations of sections were discussed in detail earlier in the User Guide. The interaction diagrams

for all sections that contain concrete are handled in a similar manner and will be discussed next.

Then the case of the H-pile section without concrete will be discussed last.

Sections with reinforced or prestressed concrete.

The routine assumes a planar strain distribution across the section. The criterion for section failure

is that the concrete reaches the crushing strain εcu. (εcu = -0.003 in/in) at one corner of the

section. This conservatively ignores any effect of the ties or spiral reinforcement on the

compressive strength or crushing strain of the concrete.

All tensile stresses in the concrete are neglected. This includes both tension in uncracked regions

and tension stiffening in cracked regions.

Neither ACI 318 nor AASHTO permit the design of a perfectly axially loaded column. A certain

minimum eccentricity of load must always be included. This is accomplished by limiting the

applied factored axial force, Pu, to a factor times P0, where P0 is the nominal capacity of the

section in an axially loaded column. For a tied column, this maximum load is 0.8φP0, while for a

column with spiral reinforcement the maximum load is 0.85φ P0. When a factored load, Pu, larger

than these limits is input to the routine, the routine responds that the section is inadequate.

The routine also includes a maximum axial tension for a section based on all the mild steel bars

attaining the yield stress fy for mild steel and all the prestressing strands attaining the ultimate

stress fsu. Because of the difficulty in obtaining convergence for extremely high axial tension

force, no solutions are attempeted for axial forces greater than 95% of the maximum axial tension

force. If the factored Pu exceeds this maximum tension force the routine responds that the section

is inadequate.

Solutions for α and β for about 30 points between the maxiumn compressive and tensile forces

are attempted. The values of axial force are obtained for strains in the extreme bar farthest away

325

from the corner of the section with a strain of ecu varying form about 0.05 (mild steel) or 0.03

(prestressed steel) in tension to nearly εcu (compression)

The strength reduction factor, φ, is determined according to the unified requirements for

prestressed and nonprestressed concrete of AASHTO - LRFD. In these requirements, the

magnitude of φ is based on the net tensile strain occurring in the most heavily strained steel bar or

strand when the nominal strength of the section is attained (when the concrete crushes). The net

tensile strain is that portion of the steel strain associated with the development of tensile strain in

the concrete adjacent to the steel bar or strand. For nonprestressed steel, the net tensile strain is

exactly the total strain in the steel. For prestressed steel, the net tensile strain is the total strain in

the steel minus the sum of the effective prestress strain in the steel and the effective prestress

strain in the concrete adjacent to the steel. The last term can be thought of as the decompression

strain.

For load cases for which the maximum net tensile strain in the reinforcement is greater than 0.005,

load cases with very low compressive axial load or net axial tension, the routine uses φ=0.9. This

represents the most desireable ductile failure. For load cases for which the maximum net tensile strain

in the reinforcement is less than the compression control limit εcc, the routine uses φ=0.70 for tied

columns and φ=0.75 for spirally reinforced columns. For maximum net tensile strains between εcc

and 0.005, f is assumed to vary linearly with maximum net tensile strain. The compression control

limit εcc is taken as the yield strain for mild steel and at .002 for prestressing steel which is

approximately the yield strain for grade 60 steel.

H-piles embedded in concrete are treated as if fully bonded to the concrete and are thus treated just

as if they were an equivalent group of a large number of small rectangulear reinforcing bars.

H-piles without Concrete

H-Piles not embedded in concrete have their interaction diagrams computed in a similar manner to

the sections with concrete except that steel does not have a small limiting compression strain due

to its ductility. Thus the 30 points defining the range of axial forces are obtained by locating the

the neutral axis in sucessive positions across the depth of the section and the steel is assume fully

yielded on both sides of the neutral axis. Solutions are attempted for α and β to represent the

ineraction curves for 30 Points with varying axial load from a peak in tension to compression.

The phi factors specified by AAASHTO LRFD specification are used (1.00 for bending, 0.95 for

axial forces in tension and 0.90 for axial forces in compression). These factors are multiplied by

the nominal moments and axial force found by the analysis routine.

Steel Only Sections

Strength interaction diagrams for steel only H-Pile and Pipe pile sections are based upon

developing yield strain (stress/Young’s Modulus) in the outer fibers. Steel Code requirements

must be met for complete design.

326

Failure (Demand/Capicity) Ratio for Cross Sections

FB-MultiPier calculates the failure (demand/capicity) ratio for each cross section used in the

analysis. The failure ratio as well as the interaction diagram are only calculated when full cross

sections are specified (either linear with full cross section or nonlinear). The failure ratio is an

estimate of the percentage of the cross sections' capacity that has been reached for that particular

loading state. The failure ratio is calculated as the length of the vector for the current load state

divided by the length of the vector when it pierces the failure surface.

My

Mx

P

Mxo

Myo

Pactual

Failure Ratio = Surface Piercing Vector Length

Actual Result Vector

Length

Force Result Vector (P,Mx,My)

Figure D13: Biaxial-Moment Interaction Diagram caluclations for Failure Ratio

The actual result vector is the current set of forces that the cross section is experiencing due to the

applied load. The surface piercing vector length assumes that the applied loads will be increased

proportionally until the cross section fails. This assumption implies that the result state

(P,Mx,My) will also increase proportionally until the cross section fails. As a result, the surface

piercing point is found by extending the length of the result vector along its known direction until

it pierces the failure surface.

327

Typically, a cross section failure ratio is calculated by taking the Mx-My diagram for a constant

axial load P. This is equivalent to the shaded slice of the 3-D failure surface. Then the failure

ratio is calculated as the (Mx,My) vector length divided by the point at which the extended vector

will touch the failure curve. This assumes that the axial load will remain constant. While

conservative, it is not very realistic. In indeterminate structures, all forces interact and in order for

the moments to increase, the axial load must also increase. For pile groups, this is caused by the

frame action of the group which changes the axial load in the piles due to a changed lateral load.

Nonlinear Solution Strategies


A program such as FB-MULTIPIER that considers the nonlinear response of the soil and piles can be used to provide some very good models of physical behavior. However, the use of nonlinear analysis programs implies that the user understand the nonlinear models very thoroughly. The nonlinear models are described in the program documentation and it is assumed that the user is familiar with these. However, the user should also understand that the use of the nonlinear characteristics of the program may cause the program to be unable to converge on a solution for a particular loading and that in some cases described later, nonlinear programs may converge on a mathematical solution that isn’t physically reasonable.

A novice user may then be tempted to say that one should stick to linear programs and avoid such

difficulty. However, the counter argument can be made that a linear analysis will almost always

find a solution even if the user puts in a totally unreasonable loading.

For the sake of discussion, assume that a relatively simple structure is being modeled by FB-

MULTIPIER, perhaps even a single pile cap with one or two piles with some vertical load applied

which is held constant and then a lateral load is applied gradually. Several different scenarios of

lateral load versus lateral displacement are possible as shown in Figure D14.

328

Force/Load

Displacement

a

bc

d

Figure D14: Different Types of Load Displacement Response

The most desirable nonlinear response of the structure is shown as case 1. The load displacement

response starts to soften at about point a or b, reaches a peak load at c and has an essentially flat

top that show very good ductility. This is typical of a failure due is primarily due to yielding of the

structure at several locations in the piles possibly combined with similar action in some of the

supporting soil layers. However, if the user should put in a load above that corresponding to point

c, it is obvious that a solution will not be found. Likewise if a load near c is tried, it is possible that

the solution will be very slow to converge and may fail if a large number of iterations are not

allowed.

This failure to converge can be avoided by doing a preliminary linear pile analysis and then

checking the strength ratios of the pile to see if they are all less than 1. However, the capacities of

the soils springs should be considered as well. It should also be noted that solutions may be found

where the pile strength ratios are greater than 1.0. This is primarily because the analysis program

does not use capacity reduction factors as are used in generating the strength ratios.

The response indicated by case 2 is not as good as shown in case 1. The difference is that some

element in the soil or the pile has a very limited ductility and causes the collapse of the structure

before sufficient ductility is obtained. As examples, a section of the pile could be a way under

reinforced and fail when cracking or a section could be very over reinforced and fail when the

concrete fails in compression without adequate yielding of the steel. Numerous other causes are

possible such as premature shear failure and the designer must insure that these failure modes do

not prevent adequate ductile response, since they are not considered in the analysis. As in the type

329

1 response the user may encounter difficulties when trying to apply loads near the level of the

capacity.

Suppose the designer wants to demonstrate that the behavior is indeed type 1 versus type 2. A

push over analysis could be done and this requires a displacement-controlled solution. A large

spring would be placed at the node where the lateral load is applied and then a series of large loads

would be applied. The spring would take the larger amount of the load but by properly choosing

the spring stiffness and load, the displacements could be controlled and the load absorbed by the

structure could be found and the pushover results plotted.

In rare instances the response of a structure may be like that shown as case 3. Here at a load near d

the curve flattens and may even decrease. However, for increasingly large displacements the load

may start to rise again. It will be very difficult to obtain converged solutions for loads near d.

However, if a much larger load is applied a solution may be found on the curve well above d. This

type of behavior generally occurs when some type of local failure occurs. If the structure has

sufficient ductility it may then be able to find a new path to distribute the forces and carry some

additional load, albeit with a considerable reduction in stiffness. An example of this type of

behavior is when the gravity loading is small and because of a large lateral load a pull out occurs

on one of the piles. The question then arises, should the design based on the post pull out behavior

be used?

Clearly the use of nonlinear analysis program does not remove the responsibility of the designer to

monitor the local responses of the structure. Fortunately the program outputs detailed information

about the behavior of the soil and pile that can and must be reviewed before a structure can be said

to be adequate.

Finally, case 4 in which the structure appears to move against the loads must be considered. For

very slender structures with very large gravity loading, the stiffness of the structure will go

negative when the elastic buckling loading of the structure is exceeded. Again this is a rare case

and would almost never happen for a designer evaluating a real structure. However, someone

trying the program out with arbitrary dimensions and loads might create such a condition and then

be disturbed that the program is giving obvious unreasonable results. A linear analysis program

would of course produce even more possibly dangerous results; it would indicate a positive

displacement, which would then not give any indication that something was wrong with the

structure.

Equivalent Stiffness Formulation

Equivalent Stiffness Generation

FB-MultiPier can be used to calculate the foundation stiffness of a pile and cap system. The

purpose is to calculate the stiffness of the foundation structure including the piles, the pile cap the

soil etc. The stiffness is reported at a single point and therefore it is a 6x6 matrix. The point at

330

which the stiffness is reported is the pile head if it is a single pile or the center of the pile cap if it

is a pile and cap problem. The point (node) at which the stiffness is reported is internally generated

by the program.

The stiffness of the foundation is calculated as follows:

1. 1. 1. 1. 1. 1. 1. 1. The foundation (pile cap, piles,

soil) is analyzed based on the applied load. The load can only be applied at the additional node

that the program internally generates (see Figure E5).

2. 2. 2. 2. 2. 2. 2. 2. Once the solution is obtained for

the applied load, the program calculates the flexibility matrix of the structure at the particular

equilibrium state following general principles. To do that the program internally applies unit

forces (actually 0.01 load and then scales the results) at the additional point that is internally

created by the program. The forces are applied successively in all six possible directions (Fx, Fy,

Fz, Mx, My, Mz).

3. 3. 3. 3. 3. 3. 3. 3. The displacements from each

solution at the additional node comprise the columns of the flexibility matrix ie the displacements

from the solution under the application of the Fx load comprise the first column of the flexibility

matrix.

4. 4. 4. 4. 4. 4. 4. 4. Once the flexibility matrix is

obtained the program calculates the inverse of that which is the stiffness.

5. 5. 5. 5. 5. 5. 5. 5. In the output data file the program

reports both of the matrices.

The calculated stiffness (or flexibility) matrix is calculated after the equilibrium state of the

structure is obtained. This is necessary since the foundation is usually comprised from nonlinear

elements (including the soil springs). Therefore the snapshot in time (equilibrium state) that the

stiffness is calculated is very important.

If the program was not following the particular sequence ie not obtaining the equilibrium solution

first, then the calculation of the stiffness would be incorrect since it would be obtained using

information for a state of the structure other than the equilibrium.

The stiffness can be thought of as being the tangent stiffness (instead of secant) for the simple

reason that it is calculated for a particular instance in time.

The program makes the decision that the loading on the pile cap is applied at the center. The

reason for that is because the stiffness is reported at the particular point. Therefore to be consistent

with the theory the load could not be applied at any other place. It is therefore imperative for the

engineer to make sure that the resultant of the loads from the superstructure (bridge pier) passes

through the particular point.

331

Additional node created by the program in Orange

Figure E1: Stiffness model in thin mode showing additional node in orange

Converting FB-MultiPier Coordinates to a Standard Coordinate System

The following explanation shows how to convert a 6x6 stiffness matrix from the FB-MultiPier global coordinate system to a standard coordinate system defined below.

x

y

z

X

Y

Z

Figure E2: FB-MultiPier Coordinate System Figure E3: Standard Coordinate System

332

A 3x3 transformation matrix (T) is first defined to show how the two coordinate systems are related.

−

=

Z

Y

X

z

y

x

010

100

001

Which can be stated as [d] = [T][D]

This shows that x maps to X, y maps to Z, and z maps to –Y.

The same transformation matrix [T] is then used to transform the stiffness matrix from the FB-MultiPier coordinate system to the standard 3D coordinate system as follows.

[ ] [ ]STANDARD FB-MULTIPIER

TK T K T=Eqn. e1

[ ] [ ]STANDARD FB-MULTIPIER6 6 6 6

1 0 0 0 0 0 1 0 0 0 0 0

0 0 1 0 0 0 0 0 1 0 0 0

0 1 0 0 0 0 0 1 0 0 0 0

0 0 0 1 0 0 0 0 0 1 0 0

0 0 0 0 0 1 0 0 0 0 0 1

0 0 0 0 1 0 0 0 0 0 1 0

x xK K

− −

= −

−

This requires 2 matrix multiplications to obtain the transformed stiffness matrix. This can be easily done

using either Excel or MathCad.

As a result, to convert the FB-MultiPier stiffness to a standard coordinate system, use the following.

333

[ ]FB-MULTIPIER

11 12 13 14 15 16

21 22 23 24 25 26

31 32 33 34 35 36

41 42 43 44 45 46

51 52 53 54 55 56

61 62 63 64 65 66

K K K K K K

K K K K K K

K K K K K KK

K K K K K K

K K K K K K

K K K K K K

=

[ ]STANDARD

11 13 12 14 16 15

31 33 32 34 36 35

21 23 22 24 26 25

41 43 42 44 46 45

61 63 62 64 66 65

51 53 52 54 56 55

K K K K K K

K K K K K K

K K K K K KK

K K K K K K

K K K K K K

K K K K K K

− − − − − − − −

= − −

− − − −

− −

Note: Both the locations and signs change for some of the stiffness terms.

Example

The FB-MultiPier stiffness matrix is given by

[ ]FB-MULTIPIER

19.66 0 0 0 6489 0

0 19.66 0 6489 0 0

0 0 26110 0 0 0

0 6489 0 1.07 08 0 0

6489 0 0 0 1.07 08 0

0 0 0 0 0 1

KE

E

−

= − +

+

Then the stiffness matrix in the standard coordinate system would be.

334

[ ]STANDARD

19.66 0 0 0 0 6489

0 26110 0 0 0 0

0 0 19.66 6489 0 0

0 0 6489 1.07 08 0 0

0 0 0 0 1 0

6489 0 0 0 0 1.07 08

KE

E

−

= − +

+ To transform the 6x6 stiffness matrix generated by FB-MultiPier from the 2D x-z coordinates system to a standard 2D X-Y coordinate system.

x

z

X

Y

Figure E4: FB-MultiPier Coordinate System Figure E5: Standard Coordinate System

The following transformation is used to transform the stiffness matrix from the FB-MultiPier coordinate system to the standard 2D coordinate system as follows.

[ ] [ ]tan

T

S dard FB PierK T K T−=Eqn. e2

[ ] [ ]

36

66

63

33

000

100

000

010

000

001

010000

000100

000001

x

xPIERFB

x

xSTANDARD KK

−

−= −

As a result, to convert the FB-MultiPier stiffness to a standard coordinate system, use the following.

[ ]FB-MULTIPIER

11 12 13 14 15 16

21 22 23 24 25 26

31 32 33 34 35 36

41 42 43 44 45 46

51 52 53 54 55 56

61 62 63 64 65 66

K K K K K K

K K K K K K

K K K K K KK

K K K K K K

K K K K K K

K K K K K K

=

335

[ ]STANDARD

11 13 15

31 33 35

51 53 55

K K K

K K K K

K K K

− = − − −

Engine Input Users Guide

Engine Input Overview

The engine input parameters are divided into two categories. The Global headers category describes control data for the entire model. The Pier Specific headers category describes data that is specific to a particular pier in the model.

Pier specific data is separated in the input file by a special pier header as follows:

__PIER#x

Where

x Pier number

Global Headers

Header

PROBLEM

336

Problem Title

Units

Client

Project Name

Project Manager

Date

Completed By

Description

The first two lines* are reserved for user information - TITLE, DATE, JOB NUMBER, .... etc.

For instance, the second line usually serves as a reminder to the user of the units that were used to

create the input file. The above lines are always required.

*Note: a comment line can be added anywhere in the input file by simply placing a C in column

1 of the line.

Print Control

The following two lines specify the data to be printed to the output file. These lines are always

required.

PRINT

L=L1 M=M1 D=D1 O=O1 S=S1 P=P1 T=T1 F=F1 C=C1 B=B1 I=I1 R=R1 N=N1 X=X1

Z=Z1 Q=Q1

Any of the values: L1,M1,D1... etc. can be either 0 or 1. Setting a value to 1 enables its printing.

Setting the value to 0 turns off the printing of that data block. The default is =0 (NO print). Only

the options desired (=1) are required. A SUMMARY OUTPUT TABLE WILL ALWAYS BE

PRINTED.

Where

337

L1 is the flag for printing of the Pile and Structural coordinates.

M1 is the flag for printing the pier material properties.

D1 is the flag for printing the pile displacement.

O1 is the flag for the out of balance forces.

S1 is the flag for the soil response forces.

P1 is the flag for the pile element forces.

T1 is the flag for the pier columns and pier cap displacement.

F1 is the flag for the pier columns and pier cap force output.

C1 is the flag for the pile cap stress/moment output.

B1 is the flag for the bridge simulation spring force output.

I1 is the flag for printing the output of the interaction diagram.

R1 is the flag for printing section stress-strain data.

N1 is the flag for printing missing pile information.

X1 is the flag for XML data printing. This is used in conjunction with the Model Data Report

Generator for data extraction.

Z1 is the dynamics printing option.

0 = print displacement, velocity, and acceleration results to a binary file

1 = print displacement, velocity, and acceleration results to an ASCII file

Q1 is the flag for the printing span properties.

General Control

The following lines specify the control parameters for the FB-MULTIPIER program. There are four lines

of input for the general control section. These lines are always required.

CONTROL line 1

NUMLC U=U1 S=S1 V=VER N=NPLNOD P=PRELOAD R=NPUSH S=STIFF K=NSTIF F=PROT line 2

338

Where

NUMLC is the number of load cases (INTEGER)

U1 = 0 is for English units (kips and inches)

= 1 is for SI units (kilonewtons and meters)

= 2 is for metric (kilonewtons and milimeters)

S1 = 0 for no stiffness creation

= 1 for stiffness creation

VER =Version for English Units (Used For next release)

=0 is for current version - Means English units are Kip & Inches (Or consistent). English

units are a mixed set of Kip, Feet and Inches (V=1 and greater)

NPLNOD = number of nodes per pile

PRELOAD is the preload option

=0 for no preload

=1 for preload

NPUSH is the pushover option

=0 for normal analysis

=1 for pushover analysis

STIFF is the stiffness creation option

=0 no stiffness creation

=1 stiffness creation - one column, or (foundation stiffness option and modal analysis)

=2 stiffness creation - with multiple columns (modal analysis)

NSTIF is the type of stiffness.

= 0 secant stiffness (default).

= 1 tangent stiffness. (required for preload and time step dynamics, optional for a static

analysis)

PROT is the soil resistance due to pile rotation about the 2 and 3 axis

= 0 do not include soil resistance

= 1 include soil resistance (default)

339

NUMLC is the number of different load cases for analysis within a single input file. Each load case is a

separate analysis of the same structure with a different set of loads. It is intended to reduce the number of

input files that need to be created in order to analyze a bridge pier structure. An input of 0 will execute the

data check mode. This halts the execution of FB-MultiPier after all the structure data has been generated

and writes to the plot database files for viewing with post processor. The latter is useful for data checking.

U1 identifies the standard FDOT English or metric pile sections.

S1 identifies that the analysis is to create an equivalent foundation stiffness. There can be no structure,

only a cap. All six loads must be given (three forces and three moments). These will be applied at the

center of the pile cap.

S=IFLEX T=ITIP, TSTIF P=NLOPT F=Phi line 3

Where

IFLEX controls how the soil is to be modeled (INTEGER)

IFLEX=0 user supplied PY multipliers must be given

IFLEX=1 all user supplied P-Y multipliers are set to 1 internally in FB-MULTIPIER

IFLEX=2 pile restraint only occurs through tip springs (i.e. no soil); soil information may be supplied, but is ignored.

ITIP is for the linear tip spring option (IFLEX=2) (INTEGER)

ITIP =0 for no linear tip springs on piles

ITIP =1 for axial tip springs on piles of stiffness TSTIF

ITIP =2 all d.o.f. at tip have springs with stiffness TSTIF

TSTIF is the stiffness of linear tips springs (REAL)

Phi is the user defined Phi factor over-ride used for creating the interaction

diagrams. (REAL)

NLOPT chooses linear or nonlinear piles

NLOPT=1 for linear piles

NLOPT=2 for nonlinear piles (cracked concrete, steel yielding and P-∆).

NLOPT=3 for linear piles where interaction diagrams are generated

340

The no soil model (IFLEX=2) can be useful in testing the model and comparing its results to other

solutions. In this case, the user must make sure the structure is stable through the proper use of tip

springs (ITIP) and pile cap fixity (KFIX). The tip spring model allows the user to add either

linear springs to the axial (ITIP=1) or to all (ITIP=2) degrees of freedom at the bottom of each

pile. In the case of IFLEX=0 or 1, ITIP or TSTIF are still active in addition to any soil tip

properties specified through the use of soil tip modeling.

I=MAXITER T=TOLER M=MEM X=TRANS V=VER line 4

Where

MAXITER is the maximum # of iterations for the nonlinear soil analysis (INTEGER)

TOLER is the tolerance on the maximum out-of-balance force for any node in the system in the nonlinear analysis (REAL)

MEM is the amount of memory used during analysis, always in Megabytes (MB)

TRANS is the option to use the transformed section properties

= 0 do not use the transformed section

= 1 do use the transformed section

VER Version number used to generate input file

The out- of- balance forces are obtained in the following manner. The stiffness matrix is

multiplied times the current set of displacements to obtain a force vector. This force vector is then

compared with the applied forces on the structure. If the structure is in static equilibrium then the

two force vectors would be identical. The difference between the two sets of forces are the out-

of- balance forces.

The following default values are be used for the maximum # of iterations for nonlinear analysis

(MAXITER) and the tolerance on the out-of balance forces (TOLER) for convergence:

MAXITER = 50

TOLER = 1.0

FB-MULTIPIER offers the option to use linear or nonlinear piles and piers. Linear piles will

converge more quickly and should be used for preliminary design and when nonlinear sections are

not significant. NLOPT (on previous line) chooses which type of pile behavior will be used.

Multiple Pier Substructure Information

341

The following information is used by with multiple pier generation. The information under the

SUBSTR header describes the pier to pier geometry.

SUBSTR

NPIERS

PIERNUM X= XDIST Y= YDIST R= ZROT A= LBROT B= RBROT

Where

NPIERS is the number of piers (or pile bents)

XDIST is the x-distance from the global origin (located at the first pier)

YDIST is the y-distance from the global origin

ZROT is the pier rotation angle about the global z-axis (used for curved alignments)

LBROT is the left bearing row rotation angle about the global z-axis (used for curved alignments)

RBROT is the right bearing row rotation angle about the global z-axis (used for curved

alignments)


The pier rotation option allows each pier to be rotated about the global z-axis (clockwise positive) to accommodate skew and curved bridge alignments. The rotation is performed as follows based on the bottom left corner of the pile cap

Figure F4:

342

Superstructure Information

The following information is used by with multiple pier generation. The information under the SUPPROP header describes the superstructure properties. These properties are used in establishing the pier to pier connectivity.

SUPPROP

A=AREA, AREASUP I=I3, I2 J= TOR E=EMOD G=GMOD S=WEIGHT F=BEGIN X=AREA, I3,

I2, TOR, EMOD, GMOD B=END Y=AREA, I3, I2, TOR, EMOD, GMOD H=H1, H2 L=LH

V=VARSP

(One line for each span)

If variable span properties are present, each property line that follows applies to an element along the

span. There are a total of 10 elements per span. The above line contains the properties for Element #1.

A=AREA I=I3, I2 J= TOR E=EMOD G=GMOD (One line for each span element for

variable span properties)

Where

AREA is the transverse cross-sectional area of the superstructure

AREASUP is the span profile area used for wind load generation

I3 is the moment of inertia of the superstructure (girder strong axis bending)

I2 is the moment of inertia of the superstructure (girder weak axis bending)

TOR is the torsional moment of inertia of the superstructure

EMOD is the elastic modulus of the superstructure

GMOD is the shear modulus of the superstructure

WEIGHT is the unit weight of the superstructure

BEGIN is the flag for the begin (left) span end condition

0 = Diaphragm

1 = No Diaphragm

2 = Custom

END is the flag for the end (right) span end condition

343

0 = Diaphragm

1 = No Diaphragm

2 = Custom

X Property list for begin (left) span end condition

Y Property list for end (right) span end condition

H1 is the vertical distance from the center of the pier cap to the center of gravity of the

superstructure (beginning of span)

H2 is the vertical distance from the center of the pier cap to the center of gravity of the

superstructure (end of span)

LH is the live load height from the center of the pier cap to the center of the live load

VARSP indicates whether variable span properties are present (0;no, 1;yes).

:


Each span of the superstructure is modeling with a single beam (divided into sub-elements) that spans

from the center of the back span pier to the center of the forward span pier. The superstructure beam is

connected to rigid beams at the back span and forward span, which distribute the load to the bearing

locations.

344

Figure F1: Superstructure Beam

345

Figure F2: Superstructure Beam with Continuity Link

346

Figure F3: Continuity Rigid Link

User Defined Bearing Connection

The following information is used by with multiple pier generation. The information under the PADPROP

header describes the load-displacement behavior for the bearing locations. This information is only

provided for user-defined substructure to superstructure connectivity.

PADPROP

NPROP Z=UPLIFT

X1,X2,X3,…,X20

347

F1,F2,F3,…,F20

Where

NPROP is the number of custom load-displacement curve definitions

UPLIFT is the flag for the bearing condition 'Uplift'. This condition is only applicable in the Z

direction. If at least 1 bearing has 'Uplift' as its condition, this flag will be set to 1.

Otherwise, the flag will be set to 0.

F1…F20 are the load values in the load-displacement relationship (20 points max.)

X1…X20 are the displacement values in the load-displacement relationship (20 points max.)

(Repeat curve pair values for each user-defined curve definition)

:


A maximum of 20 points can be used to describe the load-displacement relationship for the bearing. Load

values should be entered for both positive and negative displacements. Zero force values can be entered

intentionally. For example, to model no vertical reaction due to girder uplift, enter a load-displacement

curve for the vertical displacement with positive load and displacement values (for loads acting

downward) and zero force values for negative displacement (loads acting upward). Displacement values

must be entered in order from the largest negative displacement to the largest positive displacement.

Examples:

Figure F4: Example Load-Displacement Curve for Vertical Displacement

348

Self Weight and Buoyancy Load Factors

Self weight and Buoyancy loading is handled automatically in the program by entering a unit

weight for each type of element (Pile, Pile cap and pier elements). Since self-weight and

Buoyancy have different load factors, these load factors can be input per load case. The following

data is input for the load factors for self-weight and buoyancy:

SWFACT

LC F=FSW, FBUO (one line per load case)

Where

LC is the load case in which to apply the load factors

FSW is the load factor for the self-weight in load case LC.

FBUO is the load factory for buoyancy in load case LC

Bridge Spring Toggle

Bridge spring toggle info,

BRSPR

Case #1

Case #2

Case #3

Case #n

349

Where Integer #n is the load case number for which the bridge springs are turned OFF. If pre-load is used and bridge springs are present, a –1 value should appear in this list to indicate that springs are turned off for the pre-load case. If pre-load is used and no bridge springs are present, the BRSPR header is not required.

Pushover

For static pushover analysis,

PUSH

N=NPSTEP I=PINCR

Where

NPSTEP is the number of load steps

PINCR is load increment (e.g. 1.0 = increase initial load by 100% for each load step)

2 load cases are required

Use load case #1 for permanently applied loads

Use load case #2 for initial load to be incremented

Under the CONTROL header,

R=NPUSH

Where

NPUSH = 0 for normal analysis

= 1 for pushover analysis

Combination (AASHTO)

350

AASHTO limit states can be turned on or off as needed. In the input file after the COMBINATION

header,

COMBINATION

D= CODE

K= L1, L2, L3, L4, L5, L6, L7, L8, L9, L10, L11

N= NREVER M= MAXMIN

Where

CODE = 0 for LRFD

= 1 for LFD

(LRFD)

L1 = 1 for STRENGTH-I ( 0 otherwise)

L2 = 1 for STRENGTH-II ( 0 otherwise)

L3 = 1 for STRENGTH-III ( 0 otherwise)

L4 = 1 for STRENGTH-IV ( 0 otherwise)

L5 = 1 for STRENGTH-V ( 0 otherwise)

L6 = 1 for EXTREME-I ( 0 otherwise)

L7 = 1 for EXTREME-II ( 0 otherwise)

L8 = 1 for SERVICE-I ( 0 otherwise)

L9 = 1 for SERVICE-II ( 0 otherwise)

L10 = 1 for SERICE-III ( 0 otherwise)

L11 = 1 for FATIGUE ( 0 otherwise)

(LFD)

L1 = 1 for GROUP-I ( 0 otherwise)

L2 = 1 for GROUP-IA ( 0 otherwise)

L3 = 1 for GROUP-II ( 0 otherwise)

351

L4 = 1 for GROUP-III ( 0 otherwise)

L5 = 1 for GROUP-IV ( 0 otherwise)

L6 = 1 for GROUP-V ( 0 otherwise)

L7 = 1 for GROUP-VI ( 0 otherwise)

L8 = 1 for GROUP-VII ( 0 otherwise)

L9 = 1 for GROUP-VIII ( 0 otherwise)

L10 = 1 for GROUP-IX ( 0 otherwise)

L11 = 1 for GROUP-VESSEL ( 0 otherwise)

NREVER = 1 for reversible loads ( 0 otherwise)

Reversible Loads: WS, WL, BR, FR, TU, TG (LFRD)

W, WL, LF, R, S, T (LFD)

MAXMIN = 1 to consider max and min factors for LFRD permanent loads (DC, DD, DW)

( 0 otherwise)

Modify Load Factors

Any of the AASHTO load combination factors can also be modified as follows. In the input file after the

COEFF header,

COEFF

COEFF S=LIMST T=TYPE

Where

COEFF is the new load factor

LIMST is the limit state to be modified (LRFD)

= 1 for STRENGTH I

= 2 for STRENGTH II

352

= 3 for STRENGTH III

= 4 for STRENGTH IV

= 5 for STRENGTH V

= 6 for EXTREME I

= 7 for EXTREME II

= 8 for SERVICE I

= 9 for SERVICE II

= 10 for SERICE III

= 11 for FATIGUE

LIMST is the load group to be modified (LFD)

= 1 for GROUP I

= 2 for GROUP I-A

= 3 for GROUP II

= 4 for GROUP III

= 5 for GROUP IV

= 6 for GROUP V

= 7 for GROUP VI

= 8 for GROUP VII

= 9 for GROUP VIII

= 10 for GROUP IX

TYPE is the load type specified in AASHTO

Use one line per load factor.

Example:

COEFF

1.60 S= 1 T= DC

1.45 S= 3 T= WS

:

353

Dynamic Control Parameters

The following lines specify the dynamic control parameters for the FB-MULTIPIER program.

DYN

Y=NDYNS C=NDAMP F=ALPHA1,BETA1,ALPHA2,BETA2 S=NPMAX J=DMP K=DMS

O=NPRT M=SMASS H=NSHM L=NBMM N=NDYSOL U=NMSE E=EPP R=NCMOD

T=NSTEEL P=D1,D2,D3,D4,D5,D6,D7 Z=NFREQ Q=CFRQ A=NSCS

W=JPIL(1),JPIL(2),JPIL(3) (all on one line)

Where

NDYNS is the type of dynamics solution.

= 0 Step by step integration (default).

= 1 Spectrum analysis (for the structure only).

NDAMP is the damping option.

= 0 no damping (default).

= 1 damping.

ALPHA1,BETA1 coefficients for Rayleigh damping for the structure (C=ALPHA*M+BETA*K).

ALPHA2,BETA2 coefficients for Rayleigh damping for the piles.

ALPHA3,BETA3 coefficients for Rayleigh damping for the soil.

NPMAX is the maximum number of time steps for the analysis.

DMP is the mass density for the piles. This a default global value used if a weight density if not

given for a pile cross-section.

DMS is the mass density for the pier (excluding pile cap). This a default global value used if a

weight density if not given for a pier cross-section.

NPRT is the output option for time step analysis.

= 0 maximum displacements and maximum forces caused by the maximum

displacements (default).

354

= 1 all displacements and maximum forces.

= 2 maximum displacements and all forces.

= 3 all displacements and all forces.

Note that NPRT = 2 or 3 options only allow the program to compute the element forces for the options above (because

this may take some time for a large structure), to print them out, you still have to use these in addition to the print out

option. For example, if you want the pile forces for every time step use O=4 and set P=1 under the PRINT label. If you

want only the structure forces use T=1. The maximum forces are the forces caused by the maximum displacements,

note that these can be smaller than the maximum forces for the structure. For options 2 and 3 a summary of the

maximum forces and the time step when it occurred will be printed out at the end.

SMASS is the concentrated mass adopted for the soil. This mass is applied to all the translational

DOF X, Y and Z to represent the attached soil mass.

NSHM is the option for the mass matrix for the cap.

= 0 consistent mass matrix (default).

= 1 lumped mass matrix.

NBMM is the option for the mass matrix for the structure and piles.

= 0 consistent mass matrix (default).

= 1 lumped mass matrix.

NDYSOL is the option for the type of numerical solution. This option is only valid for step by step

solution (NDYNS=0)

= 0 Newmark's method - average acceleration (default).

= 1 Newmark's method - linear acceleration. This method is conditionally stable and is

not guaranteed to converge unless dt/T < 0.551 for all vibration modes.

= 2 Wilson-Theta method.

NMSE is the option for multiple support excitation.

= 0 standard analysis.

= 1 multiple support excitation.

EPP is the strain rate for concrete (default = 1e-5)

NCMOD is the option for the concrete model in nonlinear analysis.

= 0 rational model 1.

= 1 rational model 1 with crushing and cracking option ON.

= 2 rational model 2.

355

= 3 rational model 2 with crushing and cracking option ON.

= 4 bilinear model.

NSTEEL is the steel model

= 0 elastic/plastic

= 1 include Baushinger Effect

D1...D7 this is an option if the user wants to save a specific NODE displacement to a file for

possible later plotting or checking.

D1 - is the number of NODES that will me saved (maximum = 6).

D2...D7 - is the number of the NODE to be saved. For example:

P=6,1,2,3,4,5,6

D1 = 6 - six NODES will be saved to the file.

1...6 - NODES 1 to 6 will be saved to the file. They do not have to be in any specific

order.

Note that the displacements will be saved in a text file with the name: 'inputname'.DSn, the velocities in

'inputname'.VSn, and the accelerations in 'inputname'.ASn, where n is the file number for the chosen node. In the

example above if the input file is called test.in, the displacements for node 1 are saved in test.DS1, for node 2 in

test.DS2 and so on.

NFREQ is the option for computing the period.

= 0 (default) - initial period for the structure will not be computed.

= 1- computes the initial periods for the structure.

CFRQ is the frequency of loading (used for cyclic degradation, in Hz)

NSCS is the option for subtracting the stress in the concrete at the level of the steel bar for

dynamic analysis.

= 0 (default) - does not subtract.

= 1 - subtracts.

JPIL is the option to track the forces in a specific pile element.

JPIL(1) = pile number

JPIL(2) = element number, must be between 1 and 16. 1 is top element, 16 is bottom

element. If not specified is set to 1.

JPIL(3) = element node, must be 1 or 2. 1 is bottom element node, 2 is top element node.

If not specified is set to 1.

This information is saved to the file ‘INPUT.DFO’, where INPUT is the input file name.

356

This section MUST end with a blank line.

Options shown with a strikethrough font will be implemented in the future.

Dynamic Step by Step Integration

Any structure may be analyzed using the step by step integration method of dynamic analysis.

This method uses the Newmark method and Raleigh damping to solve for dynamic response

resulting from time varying loading. The time varying loading can be applied as a single load

function applied at many nodes or different time functions applied at specific DOF. The STEP

program will perform this analysis. The distributed and concentrated loads applied to the structure

will be applied as a CONSTANT load throughout the analysis. The applied load function can be a

force or a ground acceleration.

TRANSIENT

T=T1 L=L1 P=P1 Q=Q1 G=GF A=A0 B=A1

Where

T1 is the time step increment for integration, default is 0.01s.

L1 is the number of time varying load functions to be specified. The functions are applied at the specified nodes and DOF.

P1 is the maximum number of time points specified for any load function. If three functions

are specified, P1 is the maximum number of points used to specify any of the three

functions.

Q1 is the flag for the type of load function applied. If Q1=0 then the load is a force. If

Q1=1, then the load applied is a ground acceleration.

GF is the gravity factor to multiply times the acceleration or load record input below. If the

acceleration record is given in g’s, then the gravity factor would be 386.4 in/sec2 or 9.81

m/sec2. Use GF=1.0 if the acceleration is not normalized by g.

A0, A1 are global damping factors, implying that only one damping factor will be applied to

structure, piles and soil.

Note: you must choose one damping factor, either here or under the DYN header, only for the soil. Both

can not be chosen.

357

Z= LFN

Where

LFN is the name of the load function. This can be up to 20 characters in length.

LOADING FUNCTION DEFINITIONS (L1 Sets of lines)

If you choose the multiple support excitation option, you have to create one set of loading

functions for each pile node. Including the first line.

The next lines specify the loading function values. The lines MUST contain FOUR pairs of

numbers each. The number of lines is dictated by the maximum number of points used to specify

the function (P1). The points do NOT need to be at even spacing.

T1,F1 T2,F2 T3,F3 T4,F4

Where

Ti,Fi are the time and force (or acceleration) values for the point being specified.


Spectrum Analysis

The results of an EIGEN solution can be used to perform a spectrum analysis. This procedure uses the mode superposition method to combine the individual eigen vectors into a single response, based on the excitation given by a response spectrum. Response spectrums are usually given for earthquake loading. This procedure combines the individual modes response for a spectrum acting in each of the three global directions, X,Y, and Z. The modal responses are combined using the Complete Quadratic

358

Combination (CQC) procedure, the directions are combined using Square Root Sum of the Squares (SRSS). SPECT allows only a single input response spectrum with different scale factors for that spectrum in each of the three directions (X, Y, and Z). The program will allow either an input spectrum or an input acceleration record and generate the spectrum values internally.

SPECTRUM

For input Spectrum use the following lines:

S=SP D=DX,DY,DZ N=NV F=FF E= EF H=CM L=SM

Where

SP is the number of spectrum points used to define the response spectrum curve. The points

are given in pairs (Circular frequency (rad/ sec), Value) and are assumed linear between

values.

X is the scale factor to apply to the input spectrum for use in the X direction. The response

spectrum values are scaled by this factor when used for the X direction.

DY is the scale factor to apply to the input spectrum for use in the Y direction. The response

spectrum values are scaled by this factor when used for the Y direction.

DZ is the scale factor to apply to the input spectrum for use in the Z direction. The response

spectrum values are scaled by this factor when used for the Z direction.

NV is the number of eigenvectors to use for the responses. The default is the total number of

vectors solved for from EIGEN.

FF is the flag for the file format of the modal response spectrum function file. 1 is

for new format, 0 is

for old format.

EF is the eigenvector analysis stop flag. 1 means analysis will stop after eigenvector

calculations are complete. 0 means analysis will run through to normal completion.

CM is the global mass flag for the cap. 0 means consistent, 1 means lumped.

SM is the global mass flag for the structure. 0 means consistent, 1 means lumped.

A spectrum analysis also needs damping ratios for each mode used in the analysis. The damping

ratio is the percentage of damping for the mode in question. These values must be specified if a

spectrum analysis is to be performed. The next line specifies the damping ratios to use.

359

NF,NL,NI S=S1

Where

NF is the first mode in a generation sequence for which the damping ratio is used.

NL is the last mode in a generation sequence for which the damping ratio is used.

NI is the increment for generating mode for which the damping ratio is used. Modes

between NF and NL will also use the specified ratio.

NL and NI can be left blank if no generation is desired.

S1 is the damping ratio value to be used (as a decimal).

Z= LFN

Where

LFN is the name of the load function. This can be up to 20 characters in length.

SPECTRUM DEFINITION LINES (Repeat for as many lines as necessary)

The next lines specify the spectrum function values. The lines MUST contain FOUR pairs of

numbers each. The number of lines is dictated by the number of points used to specify the

function (SP). The points do NOT need to be at even spacing.

F1,A1 F2,A2 F3,A3 F4,A4

Where

Fi,Ai are the frequency (rad/sec) and acceleration (length/sec^2) values for the point being

specified.

The acceleration values should represent the maximum absolute acceleration (spectral

acceleration), not the relative acceleration (between the structure and moving support).

360


Span Concentrated Nodal Loads

NODE L=LC F=FX, FY, FZ, MX, MY, MZ T=TYPE S=SPAN

These are automatically generate load input lines. As many lines as needed can be used. One line must be supplied for each loaded node and each load condition The load is the self weight of the bridge span dispersed onto it's left and right rows of bearings. There is a net load of 0.

Note: Users should not hand edit this data.

SPANLOAD

NODE L=LC F=FX, FY, FZ, MX, MY, MZ T=TYPE S=SPAN (one line per nodal load)

Where

NODE Span node number









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LRFD Loads:

TYPE =

DC Dead load of components

DD Downdrag

DW Dead load of wearing surfaces and utilities

EH Horizontal earth pressure load

EV Vertical earth pressure load

ES Earth surcharge load

LL Live load

IM Impact

CE Vehicular centrifugal force

BR Vehicular braking force

PL Pedestrian live load

LS Live load surcharge

WA Water load and stream pressure

WS Wind load on structure

WL Wind load on live load

FR Friction

TU Uniform temperature

CR Creep

SH Shrinkage

TG Temperature gradient

SE Settlement

EQ Earthquake

IC Ice load

CT Vehicular collision force

CV Vessel collision force

LFD Loads:

TYPE =

362

D Dead load

LL Live load (AASHTO Type "L")

IM Impact (AASHTO Type "I")

E Earth pressure

B Buoyancy

WS Wind load on structure (ASSHTO Type "W")


LF Longitudinal force from live load

CF Centrifugal force

R Rib shortening

S Shrinkage

T Temperature

EQ Earthquake

SF Stream flow pressure

ICE Ice pressure

SPAN Span number (starting at left pier)

Pier Specific Headers

Pile Information

The following input lines define the pile properties such as type of cross section, pile dimensions,

quantity and location of reinforcement and prestressing strands, and linear or non-linear material

properties. There are many parameters and input variations.

There are three allowable pile section types, circular, square/rectangular and H-pile. The H-pile

section can be embedded within the circular or square section. If the H-pile is embedded it is

considered a square/rectangular or circular pile. Also note that a pile can have varying cross

sections along its length.

363

The pile shape (KTYPE) sets the cross sectional shape of the pile. For square linear piles, the

effective diameter (for lateral soil interaction) is calculated automatically by FB-MULTIPIER.

For nonlinear piles, KTYPE determines the cross section for steel layout and behavior.

PILE line 1

NSET= NPSET N=NPLNOD S= SLUMP M=γγγγc NSEG= NPSEG1, NPSEG2, NPSEG3... line 2

Where

N1 specifies how many pile cross sections will be given along the length of the pile.

NSET is the number of pile sets

NPLNOD is the number of nodes in the pile

NPSEGi is the number of segments in pile set i (must specify for each pile set)

PARFIX is the reduction factor for the capacity for the TOP sub-segment of the pile (attached to

the pile cap). This feature is not available in FB-MultiPier, but was used with the

previous Florida Pier program.

γc is the concrete unit weight (used only for axial soil model type 4)

SLUMP is the concrete slump (used only for axial soil model type 4)

Cross Sections: The piles may be modeled as varying cross sections along the length. For

example we could have a drilled shaft where the casing only goes partially through the depth.

364

40'

30'

Steel Casing

No Steel Casing

Steel Casing

Concrete

Rebar

Figure F5: Varying Pile Cross sections

For each cross section, the pile properties must be specified. If any cross section is nonlinear, you

must specify:

1) The material by default (one line) or user defined stress strain curves (one control line and two

additional lines for each stress strain curve used.)

2) The pile shape - by default (one line) or multiple lines to define the shape and steel placement.

Finally, for both linear and nonlinear piles, six additional lines are needed to define the pile

geometry.

365

Linear Pile Properties

For circular linear piles (NLOPT=1, KTYPE=1)

K=KTYPE L=XPL E=E G=G I=RINER2, RINER3 J=J A=AREA D=DIA S=SW

line 3

For square/rectangular linear piles and/or linear h-piles (NLOPT=1, KTYPE=2 or 3)

K=KTYPE L=XPL E=E G=G I=RINER2, RINER3 J=J W=WIDTH D=DEPTH

A=AREA S=SW line 3

Where

KTYPE specifies the cross sectional shape of the pile

KTYPE=1 for a round pile.

KTYPE=2 for a square pile.

KTYPE=3 for an H-pile.

XP L is the pile length for this segment for plumb and battered piles (REAL)

E is Young’s Modulus of the pile (REAL)

G is the shear modulus of pile, default = E/2.4

RINER2 is the moment of inertia of the pile about the 2-axis (REAL)

RINER3 is the moment of inertia of the pile about the 3-axis (REAL)

J is the torsional moment of inertia (REAL)

AREA is the cross-sectional area of the pile (REAL)

DIA is the diameter for round piles (REAL)

WIDTH is the width for square piles (REAL)

DEPTH is the depth for rectangular piles (REAL) (if depth is not given the section is

assumed square)

SW is the unit weight of the pile, used for self-weight calculations.

If SW>0, self-weight is included in the analysis.

Nonlinear Property Lines

366

For nonlinear piles or linear piles with interaction diagrams (NLOPT=2 or 3)

The following lines are required for nonlinear piles, or when interaction diagrams are requested by

the user (NLOPT=2 or 3). For the non-linear pile properties, the user can specify the defaulted

stress strain curves or can generate the desired stress strain curves for the steel and the concrete.

For the default stress strain curves (MATOPT=1)

L=XPL M=MATOPT C=FPC, EC S=FY(1), FSU(2), FY(3), FY(4), ES(1), ES(2), ES(3),

ES(4) K=KTYPE

or

For user specified stress strain curves (MATOPT=2) plus up to 5 sets of stress strain points for

user defined curve

L=XPL M=MATOPT S=KSTEEL(1), KSTEEL(2), KSTEEL(3), KSTEEL(4) K=KTYPE

Where

XPL is the pile length for this segment for plumb and battered piles (REAL)

MATOPT is the material input option (INTEGER)

MATOPT=1 means input FPC, FY or FSU,ES,EC and KSTEEL on this line and default

stress strain curves will be generated.

MATOPT=2 means describe stress strain curves for steel and concrete in INPUT #6B

and #6C

No FPC,(FY or FSU),ES and EC values to be entered for MATOPT=2.

FPC is the compression stress, f'c, for concrete (REAL)

FPC = 0 for tubular steel sections

EC is the modulus of elasticity of concrete (REAL)

FY(1) is the yield stress, Fy , for mild steel (REAL)

FSU(2) is the ultimate stress for prestressed strands (REAL)

FY(3) is the yield stress for H-pile section (REAL)

FY(4) is the yield stress for tubular steel section (REAL)

(only for circular pile)

ES(1) is the modulus of elasticity of mild steel (REAL)

367

ES(2) is the modulus of elasticity of prestressing strand (REAL)

ES(3) is the modulus of elasticity of H-pile section (REAL)

ES(4) is the modulus of elasticity of tubular steel section (REAL)

KSTEEL(I) is the steel type option (INTEGER)

KSTEEL(I) = 1 includes steel type

KSTEEL(I) = 0 does not include steel type

KSTEEL(1) for mild steel reinforcement

KSTEEL(2) for prestressing steel strands

KSTEEL(3) for H-pile section

KSTEEL(4) for tubular steel section (only for circular piles)

KTYPE specifies the cross sectional shape of the pile

KTYPE=1 for a round pile.

KTYPE=2 for a square pile.

KTYPE=3 for an H-pile

Tubular and H-pile steel sections can be input by negating concrete as described above or in the

non-linear user defined stress strain curves and inputting the section properties described in the

sections for the input of circular piles and H-piles.

Stress-Strain Curve for Concrete, used with NLOPT=2 or 3 and MATOPT=2

NC=NPCC, SIGC(1), SIGC(2),,, line 1

EPSC(1), EPSC(2),,, line 2

where

NPCC is the number of points on concrete curve (INTEGER)

NPCC=0 for round tubular section or H-pile section (no concrete)

No SIGC or EPSC values to be entered for NPCC=0

SIGC(1) is the first stress point on concrete curve (REAL)

SIGC(2) is the second stress point on concrete curve (REAL)

EPSC(1) is the first strain point on concrete curve (REAL)

368

EPSC(2) is the second strain point on concrete curve (REAL)

Tubular and H-pile steel sections can be input by negating concrete as described above and

inputting the section properties described in the sections for the input of circular piles and H-piles.

Stress-Strain Curve for Mild Steel, used with NLOPT=2 or 3 and MATOPT=2 and KSTEEL(1) = 1

S1=NPSC, SIGS(1), SIGS(2),,, line 1

EPSS(1), EPSS(2),,, y=εεεεγ line 2

where

NPSC is the number of points on the mild steel curve (INTEGER)

SIGS(1) is the first stress point on the mild steel curve (REAL)

SIGS(2) is the second stress point on the mild steel curve (REAL)

EPSS(1) is the first strain point on the mild steel curve (REAL)

EPSS(2) is the second strain point on the mild steel curve (REAL)

εγ is the steel yield strain

Stress-Strain Curve for Prestressing Steel, used with NLOPT=2 and MATOPT=2 and KSTEEL(2) = 1


EPSS(1), EPSS(2),,, line 2

where

NPSC is the number of points on the prestressed steel curve (INTEGER)

SIGS(1) is the first stress point on the prestressed steel curve (REAL)

SIGS(2) is the second stress point on the prestressed steel curve (REAL)

EPSS(1) is the first strain point on the prestressed steel curve (REAL)

EPSS(2) is the second strain point on the prestressed steel curve (REAL)

Stress-Strain Curve for H-pile Steel, used with NLOPT=2 or 3 and MATOPT=2 and KSTEEL(3) = 1

369


EPSS(1), EPSS(2),,, y=εεεεy line 2

Where

NPSC is the number of points on the H-pile steel curve (INTEGER)

SIGS(1) is the first stress point on the H-pile steel curve (REAL)

SIGS(2) is the second stress point on the H-pile steel curve (REAL)

EPSS(1) is the first strain point on the H-pile steel curve (REAL)

EPSS(2) is the second strain point on the H-pile steel curve (REAL)

εy is the steel yield strain

Stress-Strain Curve for Tubular Steel, used with NLOPT=2 and MATOPT=2 and KSTEEL(4) = 1



where

NPSC is the number of points on the tubular steel curve (INTEGER)

SIGS(1) is the first stress point on the tubular steel curve (REAL)

SIGS(2) is the second stress point on the tubular steel curve (REAL)

EPSS(1) is the first strain point on the tubular steel curve (REAL)

EPSS(2) is the second strain point on the tubular steel curve (REAL)

εy is the steel yield strain

For Nonlinear Analysis of Square/Rectangular Piles, used with NLOPT=2 or 3 and KTYPE=2

W=WIDTH D=DEPTH V=DV B=BV P=PREST N=ISTNOPT

where

370

WIDTH is the width of square pile parallel to the local Z axis (REAL)

DEPTH is the depth of rectangular pile parallel to the local Y axis (REAL)

DV is the diameter of the void (DV=0 for no void) (REAL) (It can also be the width of a

rectangular void IF BV>0)

BV is the depth of a rectangular void. If BV>0, then the void is rectangular and the DV value

is used for the width of the void.

PREST is the prestressing stresses after release & all losses for standard sections only(AASHTO

9.15.1, 9.16.2) (REAL)

PREST=0 for non-prestressed (i.e. reinforced concrete)

ISTNOPT is the standard section option (INTEGER)

ISTNOPT=1 means use FDOT standard reinforcement for input width as shown below

(INTEGER)

Note: WIDTH MUST BE one of the values from a) through f) from Figures F6-a or F6-b

ISTNOPT=2 means describe the reinforcement in the section for the nonlinear analysis of

nonstandard rectangular piles. (Use next lines)

SW is the unit weight of the pile, used for self-weight calculations. If SW>0, self-weight is

included in the analysis.

(b) 14"x14"As=0.167sq in (8)d'=3.5"

(c) 18"x18"As=0.153sq ind'=3.5"

(d) 20"x20"As=0.153sq ind'=3.5"

(e) 24"x24"As= 0.167sq ind'=3.5"

(f) 30"x30"As=0.167sq in (28)d'=3.5"

1. All strands are equally spaced.

2. d' is cover distance to center

d'

d'

(a)As=0.115sq ind'=3.5"

NOTES

f’c = 6 ksi, Ec = 4415 ksi, Es = 29000 ksi

Prestress after losses = 145ksi

ultimate strand stress = 270 ksi

Prestressing stress after release and all

losses (PREST) = 145 ksi

Figure F6-a: Standard FDOT Prestressed Concrete Pile Sections (English)

371

(b) .355 m x .355 mAs= .00010774 sq m (8)d’=.089 m

(c) .455 m x .455 mAs=.00009871sq m (16)d'=.089 m

(d) .510 m x.510 mAs=.00009871 sq m(20) d'=.089 m

(e).610 m x .610 mAs= .0001077 sq m(24) d'=.089 m

(f) .760 m x .760 mAs=.00010774 sq m(28) d'=.089 m

1. All strands are equally spaced.

2. d' is cover distance to center of strands.

d'

d'

(a).305 m x .305 mAs=.0000742 sq m(8)d'=.089 m

NOTES

f’c = 41e3 kPa, Ec = 30.42e6 kPa, Es = 200e6 kPa

Presstress after losses = 1.0e6 kPa

ultimate strand stress = 1.86e6 kPa


losses (PREST) = 1.0e6 kPa

Figure F6-b: Standard FDOT Prestressed Concrete Pile Sections ( meters, kN)

f’c = 4.13e-02 kN/mm2, Ec = 30.4 kN/mm2,

Es = 200 kN/mm2

Prestress after losses = 1.0 kN/mm2

ultimate strand stress = 1.86 kN/mm2


losses (PREST) = 1.0 kN/mm2

(b) 355 mm x 355 mmAs=107.74 sq mm(8)d'=89 mm

(c) 455 mm x 455 mmAs=98.71sq mm (16)d'=89 mm

(d) 510 mm x 510 mmAs=98.71sq mm (20) d'=89 mm

(e) 610mm x 610mmAs= 107.7 sq mm (24)d'=89 mm

(f) 760mm x 760mmAs=107.74sq mm (28)d'=89 mm

1. All strands are equally spaced.2. d' is cover distance to center of strands.

d'

d'

(a) 305 mm x 305 mmAs=74.2 sq mm (8)d'=89 mm

NOTES

372

Figure F6-c: Standard FDOT Prestressed Concrete Pile Sections (millimeters, kN)

For nonlinear Analysis of Nonstandard Square/Rectangular Piles, used with NLOPT=2,

KTYPE=2, and ISTNOPT= 2

NG=NGRPS HPI= IHPILE M=BMETH X=MINSPACE Z=TYPE

AS, Y, Z, PREST N=N1 D=D1 repeat NGRPS times

Where

NGRPS is the # of groups of bars/strands(INTEGER)

IHPILE is the H-pile option.

IHPILE = 1 for H-pile embedded in the concrete,

else IHPILE = 0

BMETH 0=Custom

1=Percentage

MINSPACE Minumum spacing between two bars

TYPE Bar Type Number

AS is the bar or strand areas (REAL)

Y is the local Y coordinate for bar or strand (REAL)

Z is the local Z coordinate for bar or strand (REAL)

PREST is the prestressing stress in the strands after all losses (REAL)

N=N1 D=D1 is code to generate multiple bars in (INTEGER)

N=N1 D=2 means generate N1 bars/strands in the local Y direction as follows:

first bar is at coordinates Y,Z

if N1 = 2, second bar is at coordinate -Y,Z

if N1 > 2, then second bar is at coordinate -Y,Z

and remaining N1-2 bars/strand are equally spaced

between first two bars/strands

N=N1 D=3 means generate N1 bars/strands in the local Z direction as follows:


if N1 = 2, second bar is at coordinate Y,-Z

373

if N1 > 2, then second bar is at coordinate Y,-Z


between first two bars/strand

Concrete, Mild Steel, Prestessed Steel and Void

Concrete, Mild Steel, H-pile and Void

Figure 3. Permissable Nonstandard Rectangular Piles

Figure F7: Permissible Nonstandard Rectangular Piles

EXAMPLE INPUT

5 @ 3" = 15"

XS

YS

Z(3)

Y(2)

Figure F8: Example Rectangular Pile for Input

374

Rectangular Pile (WIDTH=20" and DEPTH = 15") with 12 strands As=0.08 each spaced as shown

and prestressed to 175 ksi.

W=20 D=15 V=0 N=2

NG=4 HPI=0

0.08, 4.5, 6.0, 175 N=4 D=2

0.08, 4.5, -6.0, 175 N=4 D=2

0.08, -4.5, 2.0, 175 N=2 D=3

0.08, 4.5, 2.0, 175 N=2 D=3

For Piles the orientation of the local Y-Z axis to that of the global XS, YS axes are shown in figure

above.

For Nonlinear Analysis of Round Piles, used with NLOPT=2 and KTYPE=1

NL=NLAY D=DP TH=DS V=DV HPI=IHPILE T=TR IC=ICONF

[PREST, NBS, D=DSI, A=ASI] S=SW repeat NLAY times

where

NLAY is the number of circumferential steel layers

DP is the outer diameter of pile (REAL)

DS is the thickness of the outer steel shell (REAL)

DV is the diameter of the void (REAL)

DV = 0 for no void and tubular steel sections

IHPILE is the h-pile option.

IHPILE = 1 for h-pile embedded in the concrete, else IHPILE = 0

TR TR=1 for spiral reinforcement with a φ? factor of 0.75 (REAL)

TR=2 for tied reinforcement with a φ factor of 0.70 (REAL)

ICONF is the confined concrete option.

ICONF=0 for none.

375

ICONF=1 for spiral only.

ICONF=2 for shell and spiral conferment.

NBS is the number of bars in the layer (INTEGER)

PREST is the effective prestressing stress in the strands for the layer (REAL)

PREST=0 for no prestressing

NBS is the numbers of bars/strands in the layer (INTEGER)

DSI is the diameter of the centerline of the steel layer (REAL)

ASI is the area of each steel bar/strand in the layer (REAL)

SW is the unit weight of the pile, used for self-weight calculations. If SW>0, self-weight is

included in the analysis.

376

Concrete, Mild Steel, Prestessed Steel and Void

Concrete,Mild Steel, H-pile , and Void

Concrete , Mild Steel, Steel Shell and Void

Steel Shell

Figure 2d. Permissable Circular Piles

Figure F9: Permissible Circular Piles

If the pile is prestressed, then neither tubular steel nor H-pile sections are allowed. If mild steel is

present along with prestressing strands, the prestressing stress on the concrete is reduced due to

the area of mild steel, and the strain in the concrete due to the prestressing is assumed to be shared

with the mild steel.

EXAMPLE INPUT

377

1"

22"

3"

2"

Figure F10: Sample Circular Pile for Input

22" diameter circular pile. 1" thick outer steel shell, 2 layers of reinforcing steel with 8 #7 bars in

each layer.

NL=2 D=22.0 V=0.0 TH=1.0 HPI=0

8 N=7 C=3

8 N=7 C=5.875

For steel H-piles used with KTYPE=3 or HP=1 in either circular or square sections

Two lines are required:

OR=ORIENT line 1

[D=DEPTH U=WEIGHT] line 2, for standard H-pile

sections

or

[D=DEPTH TW=WEB B=WIDTH TF=FLANGE] line 2, for user defined sections

Where

ORIENT is the orientation of the H-pile.

378

ORIENT=2 for web parallel to the Local Y axis, or 3 for web parallel to the

local Z-axis. (INTEGER)

DEPTH is the depth of the H-pile in inches (REAL). (Use the nominal depth for standard

sections)

WEIGHT is the standard unit weight of the H-pile in lb/ft3 (REAL)

WEB is the web thickness in inches (REAL)

WIDTH is the flange width in inches (REAL)

FLANGE is the flange thickness in inches (REAL)

Note: For metric examples H-pile dimensions will be soft converted to metric units.

After the cross section data is input, SIX additional lines defining the pile system are required

B

D

D

B

YS

XS, Y(2)

YS

XS, Y(2)

OR=2 OR=3

Figure 2e. Allowable H-pile Orientaions

Z(3) Z(3)

Figure F11: Allowable H-Pile Orientations

EXAMPLE INPUT

379

3" 6 @ 4" = 24" 3"

XSY(2)

Z(3)

YS

30”

Figure F12: Sample Mild Steel and H-pile Layout

Square Pile with 14 mild steel bars As=1

each spaced as shown with an embedded

14 x 117 H-pile.

W=30 V=0 N=2

NG=2 HPI=1

1.0 12 12 0 N=7 D=2

1.0 12 -12 0 N=7 D=2

OR=2

D=14 U=117

For Nonlinear Analysis of Oblong Piers, used with NLOPT=2 and KTYPE=4 NOTE: This type is ONLY available for pier elements NOT for piles.

R= OR RW=RWIDTH D=DIAM T=VT V=DV B=WV S=WDEN

where

OR is 2 or 3 and defines orientation, see Figure 1.8 (INTEGER)

RWIDTH is the width of rectangular portion (REAL)

DIAM is the diameter of semi-circular ends (REAL)

380

VT is void type, 1 or 2, see Figure 1.8. VT may be 1 or 2 for OR = 2 or 3

(INTEGER)

DV is the diameter of the void for VT=1 (DV=0 for no void)

DV is the depth of the void parallel to DIAM for VT=2

(DV=0 for no void)(REAL)

WV is the width of the void parallel to RWIDTH for VT=2

(WV= 0 for no void)(REAL)

WDEN is the self weight of the concrete

Reinforcement specification (Rectangular middle is similar to steel generation for rectangular

sections)

NG=NGRPS


Where

NGRPS is the # of groups of bars/strands (INTEGER)

AS is the bar or strand areas (REAL)

Y is the local Y coordinate for bar or strand (REAL)

Z is the local Z coordinate for bar or strand (REAL)

PREST is the prestressing stress in the strands after all losses (REAL)

N=N1 D=D1 is code to generate multiple bars in (INTEGER)

N=N1 D=2 means generate N1 bars/strands in the local Y direction as follows:


if N1 = 2, second bar is at coordinate -Y,Z

if N1 > 2, then second bar is at coordinate -Y,Z


between first two bars/strands

Reinforcement specification: (Semi-circular ends are similar to steel generation for circular sections.)

381

NL=NLAY

PREST, NBS, D=DSL, A=ASI repeat NLAY times

where

NLAY is the number of circumferential steel layers (INTEGER)

NBS is the number of bars in the layer (INTEGER)

PREST is the effective prestressing stress in the strands for the layer

PREST=0 for no prestressing (REAL)

NBS is the numbers of bars/strands in the layer (total for both semicircular ends.

DSL is the diameter of the centerline of the steel layer (REAL)

ASI is the area of each steel bar/strand in the layer (REAL)

Note: If mild steel is present along with prestressing strands, the prestressing stress on the

concrete is reduced due to the area of mild steel, and the strain in the concrete due to the

prestressing is assumed to be shared with the mild steel.

RWIDTH

DIA

M

OR = 2, VT = 1

DV

Z(3)

XS, Y(2)

YS

Figure F13: Allowable Horizontal Oblong Orientation

382

RW

IDT

H

WV

DIAM

DV

OR = 3, VT = 2

Z(3)

XS, Y(2)

YS

Figure F14: Allowable Vertical Oblong Orientation

Required for all types: Input for free length, number of sub-elements, axial efficiency and pile

head fixity

F=FLNG H=KFIX S=NSUB A=AXEFF G=GAP C=KBCAP pile configuration

line 1

or

E=ECAP H=KFIX S=NSUB A=AXEFF G=GAP C=KBCAP

Where

383

FLNG is the length of pile between the pile cap and the ground surface, the free length. It can

be zero. If < 0, the cap is analyzed as a buried cap.

ECAP is the elevation of the pile cap. This is assumed at the top of the pile heads, which is the

same as the centroid of the pile cap. Since the pile cap is modeled using a shell element,

the pier column base, the pile heads and the neutral axis of the pile cap all meet in the

same location. This modeling does NOT account for the thickness of he pile cap in the

geometry of the system (it is included in the behavior).

KFIX is for the pile head fixity into the cap (INTEGER)

KFIX=0 for pinned pile head

KFIX=1 for fixed pile head

NSUB is the number of sub-elements the length of pile between the pile cap and the ground

surface, Z, is to be divided into for the non-linear analysis only. (INTEGER). Typical

values for NSUB vary between 10 to 15 (NSUB ensures adequate cracking and failure

analysis over the large Z [free length] distances)

KBCAP is the option for soil-springs on the pile cap

KBCAP=0 for no springs

KBCAP=1 for 4 vertical springs under each cap element and 3 horizontal springs on the

sides in contact with the soil

KBCAP=2 for 9 vertical springs under each cap element and 3 horizontal springs on the

sides in contact with the soil

AXEFF is the axial efficiency. This is a reduction or increase of the axial force that the soil can

support. (MUST be > 0)

GAP is the gap between the bottom of the pile cap and the ground surface. Must be positive, a

zero or negative gap is ignored. Used in conjunction with the KBCAP parameter.

Input for the number of piles in the X and Y directions

NPX, NPY pile configuration line 2

Where

NPX is the # of piles in X direction (INTEGER)

NPY is the # of piles in Y direction (INTEGER)

The piles are generated in the order given in Figure F15:

384

1 2 3

4 5 6

7 8 9 X

Y

DX1 DX2

DY1

DY2

X spacing values

Y spacing values

Figure F15: Pile Numbering and Spacing

For Pile Spacing in the X-direction

The pile system may have even or uneven spacing in the X direction. If only ONE value is given

(DX1), then the spacing is uniform. Otherwise, values MUST be given for each distance between

every row of piles. There must be NPX-1 values given for uneven spacing.

DX1, DX2,... pile configuration line 3

Where

DX1 is the spacing between the first and second row of piles in the X direction. (REAL)

DX2 is the spacing between the second and third row of piles in the X direction. (REAL)

Pile Spacing in the Y-direction

The pile system may have even or uneven spacing in the Y direction. If only one value is given

(DY1), then the spacing is uniform. Otherwise, values MUST be given for each spacing value

between every row of piles. There must be NPY-1 values given for uneven spacing.

DY1, DY2,... pile configuration line 4

Where

385

DY1 is the spacing between the first and second row of piles in the Y direction. (REAL)

DY2 is the spacing between the second and third row of piles in the Y direction. (REAL)

Input for P-Y multipliers in the X-direction

P-Y multipliers used for the x direction given in order from trail to lead row of piles (Figure F16).

Multipliers have to be specified for existing rows only. The program assigns the values in the

correct order depending upon the resultant loads in the x direction.

PYMX1, PYMX2, ... pile configuration line 5

Where

PYMX1 is the multiplier for the trail row (REAL)

PYMX2 is the multiplier for the second row (REAL)

Lead Pile Trail Pile

PYM1 PYM2

PYM3 PYM4

Direction of load

Figure F16: PY multiplier definition

Input for P-Y multiplies in the Y-direction

P-Y multipliers used for the y direction given in order from trail to lead row of piles. Multipliers

have to be specified for existing rows only. The program assigns the values in the correct order

depending upon the resultant loads in the x direction.

386

PYMY1, PYMY2,... pile configuration line 6

Where

PYMY1 is the multiplier for the trail row (REAL)

PYMY2 is the multiplier for the second row (REAL)

Multiple Pile Sets

This section allows for the definition of multiple pile cross sections to be defined. This allows for

different pile cross sections in a group. Each cross section is referred to as a set. A set of cross

sections can be assigned to any pile in the group. The following data tells which pile cross section

set to use for each pile. Only sets greater that 1 (the default set to use) need to be specified.

PILESET

The next line can be repeated for as many pile as need to be specified.

PILEx PSETx (repeat for each pile of set greater than 1)

Where

PILE is the pile number to which the cross section set is applied.

PSET is the pile cross section set number to apply to this pile.

Example:

PILESET

1 2 (pile # 1 of pile set #2)


387



Pile Batter Information

This input specifies the batter of the piles. There can be as many lines as required. Each line can use the Ni

or Pi method of applying the batter for multiple piles but not both. This section can be skipped if there are

no battered piles. NOTE: the self-weight of the pile is corrected for a battered pile.

BATTER

N1, N2, N3, X=XB, Y=YB

or

P=P1, P2, P3,...PN X=XB Y=YB

Where

N1 is the battered pile number ( zero for no more battered piles) for generation, it is the

first pile number in series (INTEGER)

N2 is the last pile number in series. (defaults to N1) (INTEGER)

N3 is the pile number increment in the series (defaults to 1) (INTEGER)

Pi is a list of the piles to which the current batter is specified.(INTEGER)

XB is the battering in x-direction specified as a slope (Figure 8, example 0.33 in./in.) (REAL)

YB is the battering in the y-direction. (REAL)

Battered piles can be defined in one of several ways. The simplest approach is to list each pile that is

battered with its corresponding batter angle. This is of the form "N1 X=XB Y=YB". To decrease the

number of input lines, the pile numbers can be generated as in a FORTRAN do loop. The format

"N1,N2,N3 X=XB" applies the given batter to the piles starting at N1 and going to N2 with the increment

of N3. Thus "5,14,3 X=0.25" applies an X batter of H=3/L=12 (Figure 8) to the piles 5,8,11,14. Another

method of applying batter to multiple piles is to list all the pile numbers at which the batter is applied in the

form "P=P1,P2,P3,... X=0.25". To apply the same batter as before we could write "P=5,8,11,14 X=0.25".

388

L

H

Pile

Slope = H/L

Figure F17: Battered Pile with Slope Defined

Missing Pile Data

This data is used to specify any removed piles. If none are removed, skip this section.

MISSING

NMPIL

Where

NMPIL is the number of missing piles from the pile group (INTEGER). This value may be zero.

Specify missing piles by x-row, y-row pile coordinate system. The coordinate system of the pile rows is

shown in Figure 6. One line is used for each missing pile. Repeat the following lines NMPIL times.

IXORD, IYORD repeat NMPIL times

Where

IXORD is the x row location of missing pile (INTEGER)

IYORD is the y row location of missing pile (INTEGER)

389

X

Y

X-Row 1 X-Row 2 X-Row 3

Y-Row 3

Y-Row 2

Y-Row 1

Missing Pile

(3,2)

Figure F18: Missing Pile Coordinate System Definition

Soil Information

This section is used to specify the soil properties.

SOIL

NSET=SOILSETS, L=NLAYERS, R=NLAYER1, NLAYER2, … C=KCYC, S=NNSPT, W=WT, O=OBURDEN, W=WFREQ, P=NDYFLG, B=TB, X=LS1, LS2,… (all on

one line)

Where

SOILSETS is the number of soilsets.

NLAYERS is the total number of soil layers to be given (INTEGER).

NLAYER1,… is the number of layers in each soilset.

KCYC is for the cyclic response of soil (INTEGER).

KCYC=0 for a static soil response.

KCYC=N modifies P-Y curves to account for cyclic application of loads with N number

of events.

NNSPT is the number of points in the SPT sounding.

WT is the water table elevation used in conjunction with the SPT boring log table (in

graphical interface).

OBURDEN is the overburden option used in conjunction with the SPT boring log table (in graphical

interface).

390

0: Don’t include overburden.

1: Include overburden.

WFREQ is the frequency of loading (rad/sec) (Used to create pseudo dynamic p-y curves from

static curves for static loads only)

NDYFLG = 0 nonreversible p-y multipliers

= 1 reversible p-y multipliers

= 2 sets p-y multipliers to 1.0 after first peak

TB is the flag for user input at top and bottom soil layers

= 0 uniform properties specified for layer

= 1 properties specified for top and bottom of layer

LS1 is the flag to indicate the lateral model Limestone (McVay) is present in the soil set and

has at least one soil layer, of any type, beneath it. This is written once per soil set. The

‘1’ in LS1 indicates this flag belongs to soil set 1, and so on.

= 0 no layers exist beneath Limestone (McVay), or no layer of Limestone (McVay)

exists.

= 1 at least one layer, of any soil type, exists beneath a layer of Limestone (McVay)

Soil property input lines (repeat NLAYER times)

This input specifies the soil properties. When using the default curves, soil layers are defined with a pair

of lines. The first line of the pair provides the soil properties at the top of the layer, the soil type, and

depth of the layer. The second line of each pair provides the soil properties at the bottom of the layer.

Properties inside the layer are found by linear interpolation between the top and bottom of the layer. A

total of 2*NLAYER lines are required. When using user defined curves, six lines are required per layer.

Zero values must be given if that property is not used by the soil model chosen.

φφφφ, RK, γγγγ, Cu, εεεε50 or qu(Limestone), εεεε100 or Cavg ,or K, G, νννν, ττττf , or Fsmax, THICKNESS,

LSM, ASM, TSM, SURFACE TYPE, qu(IGM) or fsmax, CORE RECOVERY, Em, Em/Ei, qt,

E=ETOP, EBOT, B=PBOT, T=PTOP N=N50 L=SLR V=SWVS F=SFDF M=NSMOD J=RSDAMP

line one

φφφφ, RK, γγγγ, Cu, e50 or qu(Limestone), e100 or Cavg, or K, G, νννν, ττττf S=Stype, A=TANDB

or Fsmax line two

Where

φ is the angle of internal friction (REAL)

391

RK is the soil modulus k (REAL)

γ is the total unit weight of the soil (REAL)

Cu is the undrained shear strength (REAL)

ε50 is the major principal strain @ 50% maximum deviator stress in a UU triaxial

compression test (REAL)

or

qu(Limestone) is the unconfined compressive strength of limestone

ε100 is the major principal strain @ failure in a UU triaxial compression test (SOIL=3)

(REAL)

or

Cavg is the average undrained shear strength for the soil layer (REAL) (SOIL=5 & 6)

Or

K K is the Dimensionless Coefficient of Lateral Earth Pressure (REAL) (SOIL=10)

G is the shear Modulus of the soil (REAL)

ν is Poisson's ratio of the soil (REAL)

τf is the vertical failure shear stress on pile-soil interface (REAL)

or

Fsmax Fsmax is the Ultimate Side Friction (REAL) (SOIL=10)

THICKNESS is the thickness of the soil layer (REAL)

LSM is the Lateral Soil Model. It selects one of seven different lateral P-Y curves (INTEGER)

1 = Sand (O'Neill, 1984) requires φ, RK, γ

2 = Sand (Reese,Cox,Koop, 1974) requires φ, RK, γ

3 = Clay (O'Neill) requires Cu, ε50, ε100, γ

4 = Clay - Soft clay below water table; (Matlock, 1970) requires γ, Cu, ε50

5 = Clay - Stiff clay below water table; (Reese, 1975) requires RK, γ, Cu, ε50 , Cavg

6 = Clay - Stiff clay above water table; (Reese, 1975) requires γ, Cu, ε50 , Cavg

7 = user defined P-Y curve for lateral soil response. Requires four additional lines of

input (2 for top and 2 for bottom of layer).

8 = Limestone (McVay)

9 = Limestone (McVay) No 2-3 Rotation

10 = Sand (API)

392

11 = Clay (API)

ASM is the axial soil model. There are 5 allowable axial soil models.

1 = Driven Pile (McVay et al, 1989) requires G, ν, τf

2 = Drilled Shaft on Sand (O’Neill et al, 1996) requires γ

3 = Drilled Shaft on Clay (O’Neill et al, 1996) requires Cu

4 = Drilled Shaft on Intermediate Geo Material IGM (O'Neil) requires Surface Type, qu,

Core Recovery, Em, Em/Ei

5 = user defined T-Z curve. Requires four additional lines of input (2 for top and 2 for

bottom of layer)

6 = Driven Pile Sand (API)

7 = Driven Pile Clay (API)

TSM is the torsional soil model.

1 = Hyperbolic Model requires Gi, τf

2 = user defined T-θ curve. Requires four additional lines of input (2 for top and 2 for

bottom of layer)

Surface Type is the bore hole surface type ASM

type 4

1 = Rough surface

2 = Smooth surface

qu(IGM) is the unconfined compressive strength for intermediate geomaterial ASM

type 4

or

fsmax is the ultimate unit skin friction

Core Recovery is the IGM core recovery in percentage ASM

type 4

Em is the IGM mass modulus ASM type 4

Em/Ei is the ratio of IGM mass modulus to intact material modulus ASM

type 4

qt is the split tensile strength (used only rough surface and Florida Limestone) ASM

type 4

ETOP is the elevation at the top of this soil layer

EBOT is the elevation at the bottom of this soil layer

PTOP is the elevation of the piezometric head at the top of the layer

PBOT is the elevation of the piezometric head at the bottom of the layer

393

Stype is the soil layer type (used for graphical interface only)

0 = Cohesionless

1 = Cohesive

2 = Rock

N50 is the number of cycles necessary to degrade the soil by 50%.

SLR is the rate of loading for slow cyclic loading.

SWVSi is the shear wave velocity for each soil layer.

SFDF is the fully degraded soil factor.

NSMOD 0 = (default) - no soil gap, soil loads and unloads on the same curve.

1 = gap model, soil forms a gap when unloading parallel to initial stiffness in either

tension or compression.

RSDAMP is the force proportional soil damping factor (lateral only)

(e.g. 0.01 applies 1% of the lateral soil force as a damping force)

TANDB specify both Top and Bottom soil layer properties for the select layer.

0 = Use one set of properties per layer

1 = Specify top and bottom properties

User defined P-Y data - ONLY FOR LSM=7

User defined soils require FOUR additional lines of input.

(Two lines define the P-Y curve for the top of the layer and two lines for the bottom of the layer. )

Y1, Y2, Y3, Y4, Y5, Y6, Y7, Y8, Y9, Y10

P1, P2, P3, P4, P5, P6, P7, P8, P9, P10

Where

Yi is the ith Y value on the user specified P-Y curve.

Pi is the ith P value on the user specified P-Y curve.

394

The user defined curves are specified by a set of TEN points. The above two lines need to be repeated

once for the top of the layer, and a second time for the bottom of the layer (linear interpolation in

between)

User defined T-Z data - ONLY FOR ASM=5

User defined axial soil model requires FOUR additional lines of input.

(Two lines define the T-Z curve for the top of the layer and two lines for the bottom of the layer. )

Z1, Z2, Z3, Z4, Z5, Z6, Z7, Z8, Z9, Z10

T1, T2, T3, T4, T5, T6, T7, T8, T9, T10

Where

Zi is the ith Z value on the user specified T-Z curve.

Ti is the ith T (axial stress) value on the user specified T-Z curve.



between)

User defined T-θθθθ data - ONLY FOR TSM=2

User defined torsional soil model requires FOUR additional lines of input.

(Two lines define the T-θθθθ curve for the top of the layer and two lines for the bottom of the layer. )

θθθθ1, θθθθ2, θθθθ3, θθθθ4, θθθθ5, θθθθ6, θθθθ7, θθθθ8, θθθθ9, θθθθ10

T1,T2, T3, T4, T5, T6, T7, T8, T9, T10

Where

θI is the ith θ value on the user specified T-θ curve.

Ti is the ith T (torque) value on the user specified T-θ curve.

395



between)

Pile Tip Soil Data

After all layer data is supplied, the soil tip data is input

Gi , νννν, Qult, 1

or

NSPT, 0, 0, 2

or

Cub, 0, 0, 3

or

Emtip, 0, 0, 4

or

phi, EndCond, Eb, 6

or

Cub, EndCond, 0, 7

Where

Gi is the shear modulus of the soil (TipSM =1)

NSPT is the uncorrected SPT value at the tip elevation

(TipSM=2)

Cub is the undrained shear strength at the tip elevation

(TipSM=3)

Emtip is the IGM mass modulus at the tip elevation (TipSM=4)

ν is the Poisson’s Ratio at tip elevation (TipSM=1)

Qult is the axial bearing failure load (force) acting on the pile tip

(T.S.M.=1)

phi is the angle of internal friction (REAL)

EndCond is the pile end condition (pipe piles only)

396

0 = not plugged (pipe piles only)

1 = plugged (pipe piles only)

Eb is the ultimate unit end bearing

Tip Soil Model: 1 = Driven Pile (Mcvay et al, 1989) requires Gi, ν, Qult

2 = Drilled Shaft on Sand (O'Neil et al, 1996) requires

NSPT

3 = Drilled Shaft on Clay (O'Neil et al, 1996) requires Cub

4 = Drilled Shaft on Intermediate Geo Material

(O'Neil) requires Emtip

5 = user defined Q-Z curve. Requires two additional

lines of input

6 = Driven Pile Sand (API), requires phi, EndCond (for pipe piles), and Eb

7 = Driven Pile Clay (API), requires Cub, EndCond (for pipe piles)

User defined Q-Z data - ONLY FOR TIP SOIL MODEL=5

The user defined tip soil model requires TWO additional lines of input.

Z1, Z2, Z3, Z4, Z5, Z6, Z7, Z8, Z9, Z10

Q1, Q2, Q3, Q4, Q5, Q6, Q7, Q8, Q9, Q10

Where

Zi is the ith Z value on the user specified Q-Z curve.

Qi is the ith Q value on the user specified Q-Z curve.

The user defined curves are specified by a set of TEN points.

SPT data is defined as follows…

ELEV, NSPT (one per line)

397

Where

ELEV is the elevation where the blow count was recorded

NSPT is the blow count

SPT values are used by the graphical interface to the compute internal friction (φ) angles for sand

soil layers. The SPT values are currently not used by the engine.

Multiple Soil Sets

Multiple soil sets are used to define unique soil profiles for a particular pile (or piles) in a pile

group. In the input file after the SOIL header,

SOIL

NSET= NSSET L= NLAYER C= KCYC S= NNSPT R= NSSEG1, NSSEG2, NSSEG3...

Where

NSSET is the number of soil sets

NLAYER is the total number of soil layers

KCYC is for cyclic response of soil

KCYC=0 for a static soil response

KCYC=N modifies P-Y curves to account for cyclic application of loads with N number

of events

NNSPT is the number of points in the SPT sounding

NSSEGx is the number of layers in soil set x (must specify for each soil set)

(Soil properties for each soil layer)

398

SOILSET

PILEx SSETx (repeat for each pile of soil set greater than 1)

Where

PILEx is the pile number to apply soil set x

SSETx is the soil set number (x)

Example:

SOILSET

1 2 (pile # 1 of soil set # 2)



The following assumptions are made concerning the use of multiple soil sets:

Buoyancy calculations for the pile cap are based on the water table elevation for the first soil set.

Bearing capacity calculations for buried pile caps or pile caps in contact with the top soil layer are

based on the soil properties for the first soil set.

Structural Information

INPUT FOR VARIOUS TYPES OF STRUCTURES

The following lines are for the differing types of structures available for analysis. This section can

be skipped if no structure is used. There are four different allowable types of structures. These

are indicated by the following headers: STRUCTURE, MAST, SOUND, RETAIN. The user can

only select one type of structure.

The STRUCTURE header is for the standard pier structure

399

STRUCTURE

N=N1 S=S1, S2, S3… H=H1 O=O1 C=C1 B=B1, B2 W=W1 \ A=NUMLM, NUMPR J=NLOPT

T=TC, CANT [V=NPAD(L), POFF(L), PSPC1(L), PSPC2(L)… PSPCn(L), NPAD(R), POFF(R),

PSPC1(R), PSPC2(R)… PSPCn, NROW

or

P=NPAD(L), PUNF(L), POFF(L), NPAD(R), PUNF(R), POFF(R), NROW ] \

R=RH1, RH2, RH3 F=KFLOOD E=SPELEV D=CONT (all one line)

1 2

3

2

1

3

O= 7

5

S= 10

0

W= 5

0

H= 15

0

C= 3

B = 2,1

X

Y

Extra Beams

Cantilever Pier Pier Cap

NUMLM=2

(local pier cap axis)

(local column axis)

Figure F19: Structure Geometry

400

Figure F20: Pier Cap Superelevation

When using the STRUCTURE header, a minimum of three material property lines are required.

The first is for the column, the second is the pier cap and the third is for the center section of the

pier cap. After the three material lines, any additional properties (NUMPR) and then additional

members (NUMLM) should be given.

Superelevation is modeled by specifying a slope for the pier cap. When applying superelevation,

the leftmost column height remains the same while all other column heights are automatically

adjusted by the program.

The BENT header is for the pile bent structure

BENT

B=B1, B2 W=W1 J=NLOPT T=TC, CANT [V=NPAD(L), POFF(L), PSPC1(L), PSPC2(L)… ,

NPAD(R), POFF(R), PSPC1(R), PSPC2(R)… PSPCn, NROW

or

P=NPAD(L), PUNF(L), POFF(L), NPAD(R), PUNF(R), POFF(R) NROW ] (all one line)

401

Figure F21: Pile Bent Geometry

When using the BENT header, a minimum of two material property lines are required. The first is

for the pier cap and the second is for the center section of the pier cap.

The MAST heading is used for high mast lighting/sign type structures.

MAST

N=N1 H=H1 C=C1 B=B1, B2 W=W1 A=NUMLM, NUMPR T=TC, CANT J=NLOPT

F=KFLOOD

402

W= 5

0

H= 15 C= 3

X

Y

Cantilever Pier Single Column

Always Centered

Figure F22: Mast Geometry

When using the MAST header, a minimum of two material property lines are required. The first is

for the column, the second is for the mast/sign portion. Next comes any additional properties

(NUMPR) and then additional members (NUMLM).

The SOUND header is for use when sound walls are required.

SOUND

S=S1 H=H1 A=NUMLM, NUMPR J=NLOPT F=KFLOOD

403

X

Y

Width

Wind Pressure

Real System

Figure F23: Sound Wall Geometry

The sound wall is modeled as a single cantilever in the center of the pile cap. The properties

represent a given width (S1) of the wall. One material property line is required when using the

SOUND header. The properties represent the single column. Following this line should be any

additional properties (NUMPR) and then any additional members (NUMLM).

This header is needed if retaining walls are used. The retaining wall is modeled by a cantilever

representing a section of the wall. The soil layers behind the wall must also be defined. The soil

layers are used to apply load to the structure.

RETAIN

S=S1 H=H1 J=NLOPT

404

X

Y

Width

layer 3

layer 2

layer 1 THICK

line load

Figure F24: Retaining Wall Geometry

The following line defines the soil layers behind the wall

O=IOPTI S=ISURG L=NLAYE line 1

Where

IOPTI is equal to 1 for pressure at rest

is equal to 2 for active case computed with Coulomb expression

ISURG is 0 for no surcharge

is 1 for uniform surcharge

is 2 for line load

is 3 for strip load

NLAYE is the number of layers

This line defines the basic soil geometry

405

A=THETA S=BETA H= HWATE G=GWATE Q=Q1, Q2, Q3 line 2

Where

THETA is the inclination of the back of wall measured clockwise from horizontal plane (degrees)

BETA is the inclination of ground slope behind wall measured counterclockwise from the

horizontal plane (degrees)

HWATE is the Z coordinate of ground water level (reference is top of pile cap)

GWATE is the unit weight of water

Q1, Q2, Q3 are parameters for surcharge definition

If ISURG = 0 Q1, Q2, Q3 are not used

If ISURG = 1 Q1 = uniform surcharge

If ISURG = 2 Q1 = line load intensity

Q2 = Horizontal distance of line load from back of wall

If ISURG = 3 Q1 = Intensity of load

Q2 = Horizontal distance of load from back of wall

Q3 = Width of strip load

Soil Layer Property Lines (one line for each layer, NLAY)

T=THICK S=NSLAY P=COHES, PHI, DELTA G=GAMMA, GASAT

(one line per layer, the bottom layer being layer #1)

Where

THICK is the layer thickness

NSLAY is the number of sub-layers in which the layer will be divided

COHES is the cohesion of the soil

PHI is the friction angle of soil (degrees)

DELTA is the angle of friction soil/wall (degrees)

GAMMA is the unit weight of the soil

GASAT is the saturated unit weight of the soil

406

One material property line is required when using the RETAIN header. Then any additional

properties and extra members.

The definition of the parameters for all structures are given below.

Where

N1 is # of columns of the bridge bent supported on the pile group (INTEGER)

S1, S2, S3… is spacing of the pier columns. For retaining walls and sound walls, S1 is the wall width.

(REAL)

H1 is height of the pier columns (REAL,)

O1 is offset of the pile cap from the column (REAL)

C1 is # of column nodes (INTEGER)

B1 is # of pier cap nodes (Figure F21) (INTEGER)

B2 is # of pier cap cantilever nodes (Figure F21) (INTEGER)

NPAD(L) is the number of bearing locations (left row of bearings)

POFF(L) is the offset from the first bearing location (left row of bearings)

PSPCx(L) is the bearing location spacing value (left row of bearings)

NPAD(R) is the number of bearing locations (right row of bearings)

POFF(R) is the offset from the first bearing location (right row of bearings)

PSPCx(R) is the bearing location spacing value (right row of bearings)

PUNF(L) is the uniform bearing location spacing (left row of bearings)

PUNF(R) is the uniform bearing location spacing (right row of bearings)

PUNF is uniform spacing between bearing locations, same for all locations (REAL)

For a single row of bearing locations, the left and right row parameters should be the

same.

W1 is cantilever length of top of bent (REAL)

NUMLM is number of extra beam elements (Figure F21) (INTEGER)

NUMPR is number of extra beam properties (INTEGER)

TC is # of segments for tapered column (INTEGER), equal to zero for no tapered columns.

This overrides C1

407

TCANT is # of segments for tapered cantilevers (INTEGER), equal to zero for no tapered

cantilevers. This overrides B2

NLOPT selects the non-linear option for the pier structure analysis

NLOPT=1 for linear material

NLOPT=2 for nonlinear material

NLOPT=3 for linear material where interaction diagram are generated

RH1 is the depth of the pier cap at the cantilever base

RH2 is the depth of the pier cap at the center of the pier cap

RH3 is the depth of the pier cap at the cantilever tip

KFLOOD is the flag to tell if the column (if under the water table) is flooded or not. If flooded, the

buoyancy will use the net area. If not flooded, it will use the gross area (net=area-void).

SPELEV is the pier cap superelevation slope (+ or -) beginning at leftmost pier column. Expressed

as a decimal (not a percent).

CONT is the bridge span continuity option (over the pier)

0 for discontinous spans (does not transfer moment)(default)

1 for continous spans (transfers moment)

NROW is the number of bearing rows on the pier cap

1 for a single bearing row

2 for two rows of bearings (default)

Specify the number of tapered sections with CANT. If the RH1, RH2, and RH3 properties are

missing (zero by default) then a linear taper will be used.

The bearing locations are specified based on the following figure.

408

Figure F25: Positioning Two Rows of Bearings

MATERIAL PROPERTY LINES

The next lines specify the cross-sectional properties of the pier column and pier cap. A total of 1,2

or 3 + NUMPR properties (extra beam members) are required. The material properties are input

beginning with material # 2 (Figure F25) onward: pier columns, pier cap, center pier cap (Figure

F25), and extra beams, respectively for a general pier structure. The extra beam (Figure F25)

properties have the same format and may be given individually or lumped together. To simulate

no connection between piers, use very small values for I, E, G, J, and A for the center pier cap

material (Figure F25). For linear properties, use the following single lines for each property.

Linear Property Line

I=I3,I2 J=J1 A=A1 E=E1 G=G1 L=LEN W=WIDTH K=SHAPE

Where

I3 is the Moment of Inertia for axis 3 of the frame element (REAL)

I2 is the Moment of Inertia for axis 2 of the frame element (REAL)

J1 is Torsional Moment of Inertia of the frame element (REAL)

409

A1 is Area of c/s of the frame element (REAL)

G1 is Shear Modulus of the frame element (REAL)

LEN is the component length. Not currently used in the analysis. Reserved for future program

expansion.

WIDTH is the section width. Not currently used in the analysis. Reserved for future program

expansion.

SHAPE is the cross-section shape.

1: Circular

2: Rectangular

3: H-Pile

4: Oblong

Nonlinear property lines (Same as for Piles)

For nonlinear structures with interaction diagrams (NLOPT=2 or 3)

These lines are almost identical to the input for the piles. See pile input for definitions of terms.

For the default stress strain curves (MATOPT=1)

M=MATOPT C=FPC, EC S=FY(1), FSU(2), FY(3), FY(4), ES(1), ES(2), ES(3), ES(4)

K=KTYPE

or

For user specified stress strain curves (MATOPT=2)

M=MATOPT S=KSTEEL(1), KSTEEL(2), KSTEEL(3), KSTEEL(4) K=KTYPE

Stress-Strain Curve for Concrete, used with NLOPT=2 or 3 and MATOPT=2

NC=NPCC, SIGC(1), SIGC(2),,, line 1

EPSC(1), EPSC(2),,, line 2

Stress-Strain Curve for Mild Steel, used with NLOPT=2 and MATOPT=2 and KSTEEL(1) = 1


410


Stress-Strain Curve for Prestressing Steel, used with NLOPT=2 and MATOPT=2 and

KSTEEL(2) = 1


EPSS(1), EPSS(2),,, line 2

Stress-Strain Curve for H-pile Steel, used with NLOPT=2 and MATOPT=2 and

KSTEEL(3) = 1



Stress-Strain Curve for Tubular Steel, used with NLOPT=2 and MATOPT=2 and

KSTEEL(4) = 1



For Nonlinear Analysis of Square/Rectangular Piers, used with NLOPT=2 or 3 and KTYPE=2

W=WIDTH D=DEPTH V=DV P=PREST N=ISTNOPT

For nonlinear Analysis of Nonstandard Square/Rectangular Piers used with NLOPT=2,

KTYPE=2, and ISTNOPT= 2

NG=NGRPS HPI= IHPILE M=BMETH X=MINSPACE Z=TYPE


411

For Nonlinear Analysis of Round Piles, used with NLOPT=2 and KTYPE=1

NL=NLAY D=DP TH=DS V=DV HPI=IHPILE IC=ICON, T=TR

[PREST, NBS, D=DSI, A=ASI] repeat NLAY times

One of the next four lines is necessary for ICON ? 1(hoop or spiral steel is present)

FYH=FYHOOP HS=HOOPS N=NHOOP

or

FYH=FYHOOP HS=HOOPS D=DHOOP

or

FYS=FYSPI SP=SPIRS N=NSPI

or

FYS=FYSPI SP=SPIRS D=DSPI

For steel H-piles used with KTYPE=3 or HP=1 in either circular or square sections

Two lines are required:

OR=ORIENT line 1

[D=DEPTH U=WEIGHT] line 2, for standard H-pile

sections

or

[D=DEPTH TW=WEB B=WIDTH TF=FLANGE] line 2, for user defined

sections

412

Pier Columns

Material # 2

Extra Beams

Material #4 (for all, or

5,6,7 .... etc.)

Pier Cap and Cantilever Material # 3

Piles or Shafts

Center Pier Cap Material # 1

Figure F26-a: Material Property Identification

Prop. 2

Prop. 3

Prop. 4 Prop. 5 (Center)

Figure F26-b: Tapered column only - material numbers

413

Prop. 2


Prop. 5

Prop. 6

Figure F26-c: Tapered cantilever only - material numbers

Prop. 2

Prop. 3


Prop. 6

Prop. 7

Figure F26-d: Tapered column and cantilever material numbers

EXTRA MEMBER LINES ( Only Required if NUMLM 0 )

The next set of lines define any extra beams used in the superstructure. NUMLM lines are

required to define node numbers and material numbers for each extra beam. The nodes connecting

the extra beams must be in the pile cap or in the Pier. The material number must correspond to

one defined in material properties. The user has the option of using any previously defined

material property (ex. # 3, Pier Cap properties) for the extra beams or defining new ones (material

# 5, 6, etc.) in increasing sequential order.

INODE, JNODE M=MATNUM

414

Where

INODE is the first node of the extra beam

JNODE is the end node of the extra beam

MATNUM is the material number to use for the element

TAPERED COLUMN AND CANTILEVER SECTIONS

Columns and Cantilever Pier Cap sections can be set to tapered (non-prismatic) by setting TC

and/or TCANT to values greater than 0. When material properties, linear or non-linear, are set

for tapered sections, 2 sets of properties [base and top (tip)] are required instead of the one set

required for prismatic sections. Figures F26 and F27 and sample inputs, below, illustrate the

addition of tapered column and cantilever properties to the input file.

ColumnTop Cross-SectionProperties(prop. b)

ColumnBaseCross-SectionProperties(prop. a)

ColumnTaperSections[TC = 3]

Pile Cap

Cantilever Pier Cap

a

b

Figure F27: Addition of tapered Column properties

415

When tapered column properties are set, the Column Base properties are set on Material Property

Line #1, and the Column Top properties are set on Material Property Line #2. All subsequent

structure properties are set on one line # higher than as specified in MATERIAL PROPERTY

LINES.

A sample input for a structure with linear properties and tapered columns is given below. The

structure also has two extra members, with one extra member property. For reference purposes,

the material property lines are numbered and labeled in italics.

STRUCTURE

N= 2 S= 72.0 H= 120.0 O=90.0 C= 4 B= 1,2 W= 60.0 A= 2,1 J= 1 T= 3,2

1 I= 1000.0,1000.0 J= 5000.0 A= 500.0 E= 4400.0 G= 1830.0 (prop. a)

2 I= 900.0,900.0 J= 4000.0 A= 400.0 E= 4400.0 G= 1830.0 (prop. b)

3 I= 700.0,700.0 J= 3000.0 A= 350.0 E= 4400.0 G= 1830.0

4 I= 700.0,700.0 J= 3000.0 A= 350.0 E= 4400.0 G= 1830.0

5 I= 100.0,100.0 J= 500.0 A= 50.0 E= 4400.0 G= 1830.0

Material Property Lines (MPL’s) 1 and 2 list properties for the Column base and top, respectively.

MPL 3 lists properties for the Pier Cap, and MPL 4 lists properties for the Center Pier Cap

(defaulted to the same values as Pier Cap properties). MPL 5 lists the extra members’ properties.

416

Cantilever Base Cross-Section Properties (prop. c)Cantilever Tip Cross-

Section Properties(prop. d)

X

ZPile Cap

CantileverTaperSections[TCANT = 2]

Pier CapColumn

cd

Figure F28: Addition of tapered Cantilever properties

If the Cantilevers are prismatic [TCANT = 0], Cantilever properties default to the Pier Cap

Material properties. For a tapered Cantilever Pier Cap, the Cantilever Base properties are set on

Material Property Line #4, and the Cantilever Tip properties are set on Material Property Line #5,

unless tapered column sections have also been set (see example below), in which case the

properties are set on Material Property Lines #’s 5 and 6, respectively. Any extra member

properties are set on two line #’s higher (or three line #’s higher, if columns are tapered as well)

than as specified in MATERIAL PROPERTY LINES.

A sample input for a structure with linear properties and tapered cantilevers is given below. The

structure also has two extra members, with one extra member property. For reference purposes,

the material property lines are numbered and labeled in italics.

STRUCTURE

N= 2 S= 72.0 H= 120.0 O=90.0 C= 4 B= 1,2 W= 60.0 A= 2,1 J= 1 T= 3,2

1 I= 1000.0,1000.0 J= 5000.0 A= 500.0 E= 4400.0 G= 1830.0

2 I= 700.0,700.0 J= 3000.0 A= 350.0 E= 4400.0 G= 1830.0

3 I= 700.0,700.0 J= 3000.0 A= 350.0 E= 4400.0 G= 1830.0

417

4 I= 400.0,400.0 J= 1200.0 A= 100.0 E= 4400.0 G= 1830.0 (prop. c)

5 I= 300.0,300.0 J= 1000.0 A= 90.0 E= 4400.0 G= 1830.0 (prop. d)

6 I= 100.0,100.0 J= 500.0 A= 50.0 E= 4400.0 G= 1830.0

Material Property Line (MPL) 1 lists properties for the Column. MPL 2 lists properties for the

Pier Cap, and MPL 3 lists properties for the Center Pier Cap (defaulted to the same values as Pier

Cap properties). MPL’s 4 and 5 list the Cantilever Pier Cap base and tip properties, respectively.

MPL 6 lists the extra members’ properties.

For the output, the material properties are listed starting with property #2. Property #2 is for the

column. If the column is tapered, the base is property #2 plus as many of the next ones required to

get one property for each section in the column (TC). Next comes the beam property, then the

center beam. If the cantilever is tapered, then TCANT properties will be next. Finally only

additional (extra members) properties will be last.

Hammerhead Piers with Parabolic Tapered Pier Caps

Under the STRUCTURE header.

STRUCTURE

N=N1 S=S1 H=H1 O=O1 C=C1 B=B1, B2 W=W1 A=NUMLM, NUMPR J=NLOPT T=TC,

CANT [V=NPAD, POFF, PSPC1, PSPC2, …. or P= NPAD, PUNF, POFF]

R=H1, H2, H3 (all one line)

Where

H1 is the depth of the pier cap at the cantilever base

H2 is the depth of the pier cap at the center of the pier cap

H3 is the depth of the pier cap at the cantilever tip

Specify the number of tapered sections with CANT. If the H1, H2, and H3 properties are missing

(zero by default) then a linear taper will be used.

418

Figure F29: Parabolic Cantilever Taper

Column Information

This section allows the user to perform a biaxial bending analysis for a single column. This is

done internally by taking a single pile and treating it as a single column. The single column has

the ability to put springs at the top and bottom of the column. It also allows loads at the top and

bottom. The column properties are input as normal pile properties. No load or structure inputs are

used.

A total of five lines are required in addition to the pile property data.

COLUMN

S = S1, S2, S3, S4, S5, S6 top of column

S = S1, S2, S3, S4, S5, S6 bottom of column

L = LF, LL, LI F = FX, FY, FZ, MX, MY, MZ top of column

L = LF, LL, LI F = FX, FY, FZ, MX, MY, MZ bottom of column

Where

419

S1 is the tip spring resistance in the global X direction

S2 is the tip spring resistance in the global Y direction

S3 is the tip spring resistance in the global Z direction

S4 is the rotational spring resistance about the global X-axis

S5 is the rotational spring resistance about the global Y-axis

S6 is the rotational spring resistance about the global Z-axis

LF is the first load case number in the generation sequence that the load will be applied in.

LL is the last load case number in the generation sequence that the load will be applied in.

LI is the increment for the generation sequence between load cases LI and LL.

FX is the magnitude of the load in X direction

FY is the magnitude of the load in Y direction

FZ is the magnitude of the load in Z direction

MX is the magnitude of the moment about X axis

MY is the magnitude of the moment about Y axis

MZ is the magnitude of the moment about Z axis

The first S= line is for the top of the column. The second S= line is for the bottom of the column.

The first F= line is for the top of the column. The second F= is for the bottom of the column.

Concentrated Nodal Loads

These are load input lines. As many lines as needed can be used. One line must be supplied for each loaded joint and each load condition. This can be skipped if no concentrated nodal loads are applied. This can happen in the case of mast or sound walls where wind load is applied or in retaining walls where soil pressure is applied.

Note, torsion in the pile cap can only be applied where piles are located.

In the input file after the LOAD header,

420

LOAD

NF, NL, NI L=LC F=FX, FY, FZ, MX, MY, MZ T=TYPE (one line per nodal load)

Where

NF is the starting node number

NL is the ending node number

NI is the node numbering increment









LRFD Loads:

TYPE =

DC Dead load of components

DD Downdrag

DW Dead load of wearing surfaces and utilities

EH Horizontal earth pressure load

EV Vertical earth pressure load

ES Earth surcharge load

LL Live load

IM Impact

CE Vehicular centrifugal force

BR Vehicular braking force

PL Pedestrian live load

LS Live load surcharge

421

WA Water load and stream pressure

WS Wind load on structure


FR Friction

TU Uniform temperature

CR Creep

SH Shrinkage

TG Temperature gradient

SE Settlement

EQ Earthquake

IC Ice load

CT Vehicular collision force

CV Vessel collision force

LFD Loads:

TYPE =

D Dead load

LL Live load (AASHTO Type "L")

IM Impact (AASHTO Type "I")

E Earth pressure

B Buoyancy

WS Wind load on structure (ASSHTO Type "W")


LF Longitudinal force from live load

CF Centrifugal force

R Rib shortening

S Shrinkage

T Temperature

EQ Earthquake

SF Stream flow pressure

422

ICE Ice pressure


The following information is used by the wind load generator in the graphical interface:

WIND

N=NMWIND A=ANGLE1, ANGLE2, ANGLE3, ANGLE4, ANGLE5

S=SSAREA, SSWIND, SSWARM C= CPARET, CPAREL, CPWIND

P=CLARET, CLAREL, CLWIND, CLWARM (Wind load on structure--All on one line)

And

V=LTLENG, LTWIND, LTFARM (Wind load on live load)

SSWINDT SSWINDL PIERWINDT PIERWINDL LTWIND LLWIND (for 0 degrees)






Where

NMWIND is the number of wind load cases (WSx and WLx count together as one case)

A maximum of 5 wind load cases can be generated automatically.

ANGLEx is the skew angle of the wind in degrees measured from the transverse axis.

(angles can vary between 0 and 75°, in increments of 15 degrees)

423

SSAREA is the transverse area of superstructure

SSWIND is the transverse wind intensity on superstructure (not currently used)

SSWARM is the transverse wind force moment arm from the center of the pier cap to the

center of gravity of the superstructure

CPARET is the transverse area of the pier cap

CPAREL is the longitudinal area of the pier cap

CPWIND is the transverse wind intensity at the level of the pier cap (not currently used)

CLARET is the transverse area of the columns

CLAREL is the longitudinal area of the columns

CLWIND is the transverse wind intensity at the level of the columns (not currently used)

CLWARM is the transverse wind force moment arm from the base of the columns to the

center of gravity of the columns. This parameter is computed by the program for

Pile Bent models (using the water table or ground surface elevation).

LTLENG is the transverse length of the live load

LTWIND is the transverse wind intensity on the live load (not currently used)

LTFARM is the transverse wind force moment arm from the center of the pier cap to the

center of gravity of the live load

SSWINDT is the transverse wind pressure on the superstructure (at each angle)

SSWINDL is the longitudinal wind pressure on the superstructure (at each angle)

PIERWINDT is the transverse wind pressure on the pier (at each angle)

PIERWINDL is the longitudinal wind pressure on the pier (at each angle)

LTWIND is the transverse wind line load on the live load (at each angle)

LLWIND is the longitudinal wind line load on the live load (at each angle)

Parameters with a strikethrough font are not currently used. These parameters were used by

the previous wind load generator (based on the AASHTO-LRFD 1997 Interim Revisions).

424

Note: This section must end with a blank line.

The wind load generator calculations are as follows:

Wind Load on Structure (WS)

• • • • • • • • Transverse load (per bearing

location), Ftrans

locationsbearingofnumber

colheightclwarmpierwindtclaretpierwindtcparetsswindtssareaFtrans

÷⋅⋅+⋅+⋅=

• • • • • • • • Longitudinal load (per bearing

location), Flong


colheightclwarmpierwindlclarelpierwindlcparelsswindlssareaFlong

÷⋅⋅+⋅+⋅=

• • • • • • • • Vertical loads at the bearing

locations are determined using a rigid beam and spring model

• • • • • • • • Moment about the global x axis

(per bearing location), Mx

padsbearingofnumber

sswarmsswindlssareaM x

⋅⋅=

Note: Since the wind load on the column is applied at the centroid (and not the pier cap), ratio of

clwarm/colheight is used to reduce the wind load in order to apply it at the level of the pier cap.

425

Wind Load on Live Load (WL)

• • • • • • • • Transverse load (per bearing

location), Ftrans


ltwindltlengFtrans

⋅=

• • • • • • • • Longitudinal load (per bearing

location), Flong


llwindltlengFlong

⋅=

• • • • • • • • Vertical loads at the bearing

locations are determined using a rigid beam and spring model

• • • • • • • • Moment about the global x axis

(per bearing location), Mx

padsbearingofnumber

ltfarmllwindltlengM x

⋅⋅=

Spring Properties

This set of lines specifies springs, which may be placed on the piers, pier cap or pile/shaft cap.

They are generally used to simulate the bridge superstructure. These lines may be skipped if there

are no springs.

426

SPRING

NS

Where

NS is the number of spring elements (INTEGER) (zero identifies no springs)

A total of NS lines, one for each spring is required to define the spring stiffness.

If NS=0, no stiffness lines necessary.

NN S =KX, KY, KZ, KXX, KYY, KZZ

Where

NN is the node the spring element is connected to(INTEGER)

KX is the stiffness of the spring in X direction (REAL)

KY is the stiffness of the spring in Y direction (REAL)

KZ is the stiffness of the spring in Z direction (REAL)

KXX is the stiffness of the spring for rotation about X axis (REAL)

KYY is the stiffness of the spring for rotation about Y axis (REAL)

KZZ is the stiffness of the spring for rotation about Z axis (REAL)

LC, SFlag 1 line is used for each load case

Where

LC is the specified Load Case

SFlag is the flag to include Spring values with specified Load Case

0 = do not include springs

1 = include springs

427

Pile Cap Properties

These two lines specify the properties for the pile cap which is identified as material # 1 in Figure F26-a.

CAP

E=E1 U=U1 T=T1

Where

E1 is Young's modulus of the Pile Cap elements (REAL)

U1 is Poisson's ratio of the Pile Cap elements (REAL)

T1 is Thickness of the Pile Cap elements (REAL)

Specify thickened cap elements:

Additional lines can be input directly after the cap property line to specify that a particular element have a different thickness than the one specified above. This can be done using the following line (repeated as many times as necessary):

ROW, COL T=THICK, SELTHK

Where

ROW is the row number of the pile cap element

COL is the column number of the pile cap element.

THICK is the thickness to use for the stiffness calculations for this element

SELTHK is the thickness to use for the self-weight calculations.

Removed Pile Cap Element

428

Pile cap elements can be removed (similar to pier cap elements). The elements can be removed to

create separate pile cap structures. The following data is required:

REMOVE

XLOC, YLOC

Where

XLOC is the element index in the X direction to be removed

YLOC is the element index in the Y direction to be removed

Removed Pier Cap Element

Pier cap elements can be removed (similar to pile cap elements). The elements can be removed to

create separate pier structures. The following data is required:

RMBEAM

NSPAN, NELEM

Where

NSPAN is the span number in which the element is to be removed

NELEM is the element number in the span to remove

429

Bearing Connection

The following information is used by with multiple pier generation. The information under the PADBC

header describes the bearing location to superstructure connectivity. This information is provided per pier.

PADBC

L=LEFTPAD S= FX, FY, FZ, FRX, FRY, FRZ O=OFFSET

Or

R=RIGHTPAD S= FX, FY, FZ, FRX, FRY, FRZ O=OFFSET

Where

LEFTPAD is the bearing location index number in left row of bearing locations

RIGHTPAD is the bearing location index number in right row of bearing locations

FX is the fixity for the local x-direction

FY is the fixity for the local y-direction

FZ is the fixity for the local z-direction

FRX is the fixity for rotation about the local x-axis

FRY is the fixity for rotation about the local y-axis

FRZ is the fixity for rotation about the local z-axis

For all six directions: 0 for released (free), 1 for constrained

Values greater than 1 indicate the custom connection material property number. This

custom connection is described by a load-displacement relationship. See PADPROP

header.

OFFSET is the bearing offset (measured from the centerline of the pier cap to the center of the

bearing). This value must be greater than zero when two rows of bearings are used.

:


For a single row, the left and right bearing parameters should be the same.

430

Figure F30: Bearing Connection Layout for One and Two Rows

Point Mass

This section allows the addition of point masses to a structure.

MASS

The next line specifies the mass to be added to a node for each of the six global directions. There is one

header per pier.

NS,NF,NI M=MX,MY,MZ,MRX,MRY,MRZ

Where

NS is the starting node to add the mass to.

NF is the final node to add the mass to.

NI is the increment to generate additional node numbers at between NS and NF at which to

add mass.

MX \

MY |

431

MZ } are the mass values for the translational and rotational X,Y,Z directions

MRX |

MRY |

MRZ /


Point Dampers

This section allows the addition of point dampers to a structure. Point dampers are not allowed for

modal analysis.

DAMP

The next line specifies the dampers to be added to a node for each of the six global directions. There is

one header per pier.

NS,NF,NI C=MX,MY,MZ,MRX,MRY,MRZ

Where

NS is the starting node to add the dampers to.

NF is the final node to add the dampers to.

NI is the increment to generate additional node numbers at between NS and NF at which to

add dampers.

MX \

MY |

MZ } are the dampers values for the translational and rotational X,Y,Z directions

MRX |

MRY |

432

MRZ /

You can NOT add concentrated masses or dampers to the pile nodes.


Dynamic Load Function Application

LOADYN

The next lines specify the load function and its point of application. There is one header per pier.

There can be as many of these lines as required to specify all loaded nodes and DOF for this load

function. If the F= portion is NOT specified, ALL active DOF will be loaded.

NF,NL,NI L=LCN F=L1,L2,L3,L4,L5,L6 M= MODEXF D=FUNC

Where

NF is the first node in a generation sequence for which the DOF specification is used.

NL is the last node in a generation sequence for which the DOF specification is used.

NI is the increment for generating node numbers between NF and NL for which the DOF

specification is used. NL and NI can be left blank if no generation is desired.

LCN is the load case number

Li is the state at which the ith DOF can have, either loaded or NO load. Therefore Li can

have ONLY the two following values;

Fi = L is for loaded.

Fi = N is for NO load.

MODEXT is the flag for modifying the external force (0-no, 1-yes). The flag works in conjunction

with a user-defined subroutine in the program that modifies the external forcing function

at each time step in response to an outside excitation (currently a barge).

433

FUNC is the load function number to apply (default is 1)

Post Processing Formats

POST PROCESSING FILE FORMATS

FB-MULTIPIER writes many results files that are used by the post processing plotting program to

display the results. The following is a list of the files and their contents. NOTE: Each list

constitutes a sequential record in the file. Unless otherwise noted, the FORTRAN convention of

variables I-N are four byte integers, (A-H,O-Z) are four byte reals. Numbers appended to the file

extensions indicate the pier numbers (i.e. PLF2 is the Geometry and Control Information for Pier

#2).

*.MPR Multiple Pier Generation

*.PLS Pier to Superstructure Connectivity

*.PLF Geometry and Control Information

*.PIL Pile Data

*.AXL Axial Forces for Beam Element

*.MOM Maximum Moments in Beam Element

*.STR Stresses of Pile Cap

*.SLI Capacity Information

*.VMD Shear and Moment Results

*.NCV Analysis Convergence Information

*.EIG Mode Shape and Frequency Information

*.ASH AASHTO Load Combination Results

Multiple Pier Generation

434

File: name.MPR

This file contains information for generating multiple piers and bridge spans.

numPiers

Where

numPiers is the number of bridge piers

pierCoordX, pierCoordY, pierRot

Where

pierCoordX is the nodal x-coordinate for the pile cap origin (for that pier)

pierCoordY is the nodal y-coordinate for the pile cap origin (for that pier)

pierRot is the rotation angle about global z-axis (for that pier)

Pier to Superstructure Connectivity

File: name.PLS

This file contains information for the bearing row to bridge span connectivity (per pier).

nodesLeft, nodesRight, spanNodeLeft, spanNodeRight, spanNodeLeftHeight,

spanNodeRightHeight

Where

435

nodesLeft is the number of connection nodes for the left bearing row

nodesRight is the number of connection nodes for the right bearing row

spanNodeLeft is the connector node number for the begin of bridge span

spanNodeRight is the connector node number for the end of bridge span

spanNodeLeftHeight is the elevation above the pier cap (c.g.) for the begin of bridge span

spanNodeRightHeight is the elevation above the pier cap (c.g.) for the end of bridge span

(If there is a left row of bearings – i.e. nodesLeft > 0)

(nodesLeft number of lines)

padLeftCoordX, padLeftCoordY, padLeftCoordZ

Where

padLeftCoordX is the nodal x-coordinate for the bearing connection node

padLeftCoordY is the nodal y-coordinate for the bearing connection node

padLeftCoordZ is the nodal z-coordinate for the bearing connection node

(If there is a right row of bearings – i.e. nodesRight > 0)

(nodesRight number of lines)

padRightCoordX, padRightCoordY, padRightCoordZ

Where

padRightCoordX is the nodal x-coordinate for the bearing connection node

padRightCoordY is the nodal y-coordinate for the bearing connection node

padRightCoordZ is the nodal z-coordinate for the bearing connection node


(one line per connector element)

nElem, padLeftConnI, padLeftConnJ

Where

436

nElem is the connector element number

padLeftConnI is node number at the I-end of the connector element

padLeftConnJ is node number at the J-end of the connector element


(one line per connector element)

nElem, padRightConnI, padRightConnJ

Where

nElem is the connector element number

padRightConnI is node number at the I-end of the connector element

padRightConnJ is node number at the J-end of the connector element

Nodal displacement information (per load case)

Nodal modeshape information (per eigenvector). Response Spectrum Analysis only.


(nodesLeft number of lines)

PHIX_L, PHIY_L, PHIZ_L, PHIRX_L, PHIRY_L, PHIRZ_L

Where

PHIX_L is the connector node displacement in the x-direction

PHIY_L is the connector node displacement in the y-direction

PHIZ_L is the connector node displacement in the z-direction

PHIRX_L is the connector node rotation about the x-axis

PHIRY_L is the connector node rotation about the y-axis

PHIRZ_L is the connector node rotation about the z-axis


437

(nodesRight number of lines)

PHIX_R, PHIY_R, PHIZ_R, PHIRX_R, PHIRY_R, PHIRZ_R

Where

PHIX_R is the connector node displacement in the x-direction

PHIY_R is the connector node displacement in the y-direction

PHIZ_R is the connector node displacement in the z-direction

PHIRX_R is the connector node rotation about the x-axis

PHIRY_R is the connector node rotation about the y-axis

PHIRZ_R is the connector node rotation about the z-axis

Geometry and Control Information

File: name.PLF

This is the main structure geometry and control information file. The contents are as follows:

Npset

Is the number of pile sets for the piles.

Nseg1, nseg2, nseg3, ….. nsegN

Where

nsegi is the number of cross section properties per pile set. There are npset numbers written.

ktype, dia, width, depth

438

There is one record for each segment. (nseg records)

Ktype is the shape of the section (1=round, 2=square/rectangular, 3=Hpile)

Dia is the effective diameter of the cross section

Width is the width of the section

Depth is the depth of the section

Name

Is the problem file name (character*256)

NUMNP, nstr, kbent

Numnp is the number of nodes in the structure, including pile cap and the tops of the piles.

Nstr is not used.

kbent is the model type

kbent = -1: Pile and Cap Only & Single Pile

kbent = 1: General Pier

kbent = 3: High Mast / Lighting Sign

kbent = 4: Retaining Wall

kbent = 5: Sound Wall

kbent = 6: Stiffness Formulation

kbent = 7: Pile Bent

kbent = 8: Column Analysis

ncol, NCL V, NCANTN, NADMEM, NADPRP, NCLNOD, NBMNOD, NBPAD, kmetr

ncol is the number of columns in the structure

439

nclv is the

ncantn is the number of cantilever nodes

nadmem is the number of additional members

nadprp is the number of additional properties

nclnod is the number of node in the columns

nbmnod is the number of nodes in the pier cap

nbpad is the number of bearing locations

kmetr is the metric flag (0=english,1=meters/KN, 2=mm,KN)

space, height, offset, CANTIL, PADOFF

These are double precision.

Space is the spacing between columns

Height is the height of the columns

Offset is the distance from x=0 to start the structure.

Cantil is the length of the cantilevers

Padoff is the offset from the left column where the first bearing location starts.

X, Y, Z

There are numnp records. These are the X, Y and Z coordinates of the structure nodes (Not

including the piles below the pile cap).

Idx, idy, idz, idrx, idry, idrz

There are numnp records. There are the structural DOF for the problem. They are for the x, y, z

and then rotation x, y and z.

440

There are three sets of the following. For the beam type elements (mtype=3), for the shell

elements (mtype=6) and for the spring elements (mtype=8).

Mtype, nume

Mtype is the element type.

Nume is the number of elements of this type.

NELM, NND, (LT(J), J=1, NND) (this line is repeated nume times)

Nelm is the element number

Nnd is the number of nodes saved for this element

Lt() is the list of node numbers for this element.

DX, DY, DZ, RX, RY, RZ

There are numnp records. These are the displacements in the X, Y and Z and the rotations in the

X, Y and Z directions for the structure nodes (Not including the piles below the pile cap).

MAXIMUMS

lmsh2,lpsh2,lmsh3,lpsh3,lmrm2,lprm2,lmrm3,lprm3,

lmaxl,lpaxl,lmtor,lptor,lmsax,lpsax,lmsdx,lpsdx,

lmsdy,lpsdy,lmsto,lpsto,lmdiz,lpdiz,lmdix,lpdix,

lmdiy,lpdiy

lmsh2 is the load case with the max pile shear-2

lpsh2 is the pile number with the max pile shear-2

lmsh3 is the load case with the max pile shear-3

lpsh3 is the pile number with the max pile shear3

441

lmrm2 is the load case with the max pile moment-2

lprm2 is the pile number with the max pile moment-2

lmrm3 is the load case with the max pile moment-3

lprm3 is the pile number with the max pile moment-3

lmaxl is the load case with the max axial force

lpaxl is the pile number with the max axial force

lmtor is the load case with the max torsion

lptor is the pile number with the max torsion

lmsax is the load case with the max soil axial force

lpsax is the pile number with the max soil axial force

lmsdx is the load case with the max soil lateral-x force

lpsdx is the pile number with the max soil lateral-x force

lmsdy is the load case with the max soil lateral-y force

lpsdy is the pile number with the max soil lateral-y force

lmsto is the load case with the max soil torsion

lpsto is the pile number with the max soil torsion

lmdiz is the load case with the max pile axial-displacement

lpdiz is the pile number with the max pile axial-displacement

lmdix is the load case with the max pile x-displacement

lpdix is the pile number with the max pile x-displacement

lmdiy is the load case with the max pile y-displacement

lpdiy is the pile number with the max pile y-displacement

MINIMUMS

lmsh2,lpsh2,lmsh3,lpsh3,lmrm2,lprm2,lmrm3,lprm3,

lmaxl,lpaxl,lmtor,lptor,lmsax,lpsax,lmsdx,lpsdx,

lmsdy,lpsdy,lmsto,lpsto,lmdiz,lpdiz,lmdix,lpdix,

lmdiy,lpdiy

442

lmsh2 is the load case with the min pile shear-2

lpsh2 is the pile number with the min pile shear-2

lmsh3 is the load case with the min pile shear-3

lpsh3 is the pile number with the min pile shear3

lmrm2 is the load case with the min pile moment-2

lprm2 is the pile number with the min pile moment-2

lmrm3 is the load case with the min pile moment-3

lprm3 is the pile number with the min pile moment-3

lmaxl is the load case with the min axial force

lpaxl is the pile number with the min axial force

lmtor is the load case with the min torsion

lptor is the pile number with the min torsion

lmsax is the load case with the min soil axial force

lpsax is the pile number with the min soil axial force

lmsdx is the load case with the min soil lateral-x force

lpsdx is the pile number with the min soil lateral-x force

lmsdy is the load case with the min soil lateral-y force

lpsdy is the pile number with the min soil lateral-y force

lmsto is the load case with the min soil torsion

lpsto is the pile number with the min soil torsion

lmdiz is the load case with the min pile axial-displacement

lpdiz is the pile number with the min pile axial-displacement

lmdix is the load case with the min pile x-displacement

lpdix is the pile number with the min pile x-displacement

lmdiy is the load case with the min pile y-displacement

lpdiy is the pile number with the min pile y-displacement

Pile Data

443

File: name.PIL

This file contains the pile information data.

NUMPN, NUMLC

Numpn is the total number of pile nodes

Numlc is the number of load cases or combinations written to results file.

NPX, NPY, nmpil, npil, kfix, nplnod

Npx is the grid in the X direction

Npy is the grid in the Y direction

Nmpil is the number of missing piles.

Npil is the number of actual piles

Kfix is the flag for pile head fixity (0=pinned, 1=fixed)

Nplnod is the number of nodes in a pile (including the top)

Mpilx, mpily (There are nmpil records)

Mpilx is the x index for the missing pile

Mpily is the y index for the missing pile.

Dxsp1, dxsp2, dxsp3,… (npx-1 values)

These are the pile spacings for the X direction.

444

Dysp1, dysp2, dysp3,… (npy-1 values)

These are the pile spacings for the y direction.

The following line is written ONCE FOR EACH PILE in the system (NPIL times)

(ipp(i), i=1, nplnod-1)

This index tells which cross section to use for each segment of pile.

(numpset(I), I=1, npil)

This index tells which pile set number to use for each pile in the system.

Ndfrln

This is the number of nodes in the free length (above the ground surface). This matches nsub in

the input file.

The next line is written for EACH PILE. (npil times).

TPL, GSE

Tpl is the total pile length.

Gse is the height above the ground of the pile cap

Batx, baty, batl (There are npil records)

Batx is the slope in the x direction for a battered element.

Baty is the slope in the y direction for a battered element.

445

Batl is the actual element segment length.

DX, DY, DZ, RX, RY, RZ (There are nplnod*npil records)

There are numpn records. These are the displacements in the X,y and Z and the rotations in the

X,Y,and Z directions for the pile nodes.

Axial Forces for Beam Elements

File: name.AXL

This file contains the axial forces for each beam type element (structure and pile).

Numtrs, numfrm

Numtrs is the number of truss type members (=0)

Numfrm is the number of bending type members.

The next two sections are repeated twice and both are repeated NUMLC times, for each load case.

Mtype, nume

Mtype is the element type (=3 for structure, =2 for piles)

Nume is the number of elements

446

Axial

Axial is the axial force for the member for the appropriate load case.

Maximum Moments in Beam Elements

File: name.MOM

This file contains the maximum moment forces for each beam type element (structure and pile).

numfrm

Numfrm is the number of bending type members.

The next two sections are repeated twice and both are repeated NUMLC times, for each load case.

Mtype, nume

Mtype is the element type (=3 for structure, =2 for piles)

Nume is the number of elements

Rmom

Rmom is the maximum moment in the member for the appropriate load case.

447

Stresses of Pile Cap

File: name.STR

This file contains the shell element stresses for the pile cap. There are eight records per load case.

Each record contains eight values per element times the number of cap elements. The eight

records represent:

Mxx, Myy, Mxy, Sxz, Syz, Sy, Sx, Sxy

Therefore, the loops are:

Do I=1,numlc

Do j=1,8 (the eight sets of results)

Read() (stress(k), k=1, 8* #elements)

Enddo

Enddo

Capacity Information

File: name.SLI

This file contains the capacity information for each cross section used in the structure.

Nxpile, nxstruc

Nxpile is the number of cross section in the piles

Nxstruc is the number of cross sections in the structure.

448

idflg is the flag to tell if cross section capacity information (for interaction diagrams) exists in

the file. One flag is written for each cross section.

=1, information is not present

=0, information is present

The next set of records is repeated for each cross section for which capacity information exists.

Nlcv is the number of contour slices for this cross section

PTUV, YPC, ZPC

Ptuv is the ultimate axial tension strength

Ypc is the y shift for the plastic centroid

Zpc is the z shift for the plastic centroid

(PNC(J)J=1, 13) (repeated nlcv times)

pnc is the table of capacity results. Where the values are:

pnc(1) = φ* Compression capacity

pnc(2) = φ* moment capacity about local 3 axis (M1)

pnc(3) = φ* moment capacity about negative local 2 axis (M2)

pnc(4) = φ* moment capacity about negative local 3 axis (M3)

pnc(5) = φ* moment capacity about local 2 axis (M4)

pnc(6) = α1

pnc(7) = β1

pnc(8) = α2

pnc(9) = β2

pnc(10) = α3

449

pnc(11) = β3

pnc(12) = α4

pnc(13) = β4

100

=

+

βα

y

ny

z

nz

M

M

M

M

The α and β’s are used as a pair for the following capacity equation:

If the compression is in the 1st quadrant (+2,+3) then use M1, M2, α1, β1

If the compression is in the 2nd quadrant (-2,+3) then use M3, M2, α2, β2

If the compression is in the 3rd quadrant (-2,-3) then use M3, M4, α3, β3

If the compression is in the 4th quadrant (+2,-3) then use M1, M4, α4, β4

Shear and Moment Results

File: name.VMD

This file contains the bending element shears, moments and capacities for the pile and structure

elements. This is a direct access file (A fixed record size) of 56 bytes. There is one set of records

for all elements in the piles and structure. The number of elements (records per set) is:

number of records per load case =NPEL + NUMFRM

where NPEL=NPIL*(nplnod-1).

Note that the numbers NPIL and NPLNOD can be found in the name.PIL file and NUMFRM can

be found in the name.AXL file. The set of results is repeated for each load case. Each record

contains fourteen values per element. The fifteen values represent:

450

W, V2I, V3I, V2J, V3J, XMI2, XMI3, XMJ2, XMJ3, XMMAX, XML, FRATI, FRATJ, AXLI, AXLJ

Where

W is the uniform load on the element.

V2I is the shear on the I end in the local 2 direction.

V3I is the shear on the I end in the local 3 direction.

V2J is the shear on the J end in the local 2 direction.

V3J is the shear on the J end in the local 3 direction.

XMI2 is the moment on the I end about the local 2 axis.

XMI3 is the moment on the I end about the local 3 axis.

XMJ2 is the moment on the J end about the local 2 axis.

XMJ3 is the moment on the J end about the local 3 axis.

XMMAX is the maximum midspan moment if uniform loads exist.

XML is the distance from the I end where the maximum midspan moment exists.

FRATI is the capacity ratio at the I end.

FRATJ is the capacity ratio at the J end.

AXLI is the axial force at the I end of the member.

AXLJ is the axial force at the J end of the member.

NOTE: All values are single precision real numbers (4 bytes). Also, the pile elements come first,

then the structure elements.

Analysis Convergence Information

File: name.NCV

This file contains analysis parameters and convergence information.

451

Nconv

Where

Nconv is the number of converged load cases (for static analyses)

is the number of converged load combinations (for AASHTO load combination

problems)

is the number of converged time steps (for dynamic analyses)

Phiovr

Where

Phiovr is the user-defined strength reduction "phi" factor to use when factoring the interaction

diagrams.

NPlt

Where

NPlt is the results version number (currently version 1)

Ndynam

Where

Ndynam is the type of analysis (0 – for static, 1 – for dynamic, 2 – for response spectrum analysis)

NTimeStep

Where

452

NTimeStep is the time step used (for time domain dynamic analysis, otherwise 0)

NVEC

Where

NVEC is the number of eigenvectors (for response spectrum analysis, otherwise 0)

Mode Shape and Frequency Information (Response Spectrum Analysis)

File: name.EIG

This file contains eigenvalues (frequencies) and eigenvectors (mode shapes) used in the response spectrum

analysis.

NVEC

Where

NVEC is the number of number of eigenvectors

NNODE

Where

NNODE is the number of nodes in the model

453

FREQ1, FREQ2, FREQ3, ….. FREQN

Where

FREQx is the vibration frequency for mode x.

Loop over the number of eigenvectors and over each node in the model

NODE, PHIXX, PHIYY, PHIZZ, PHIRX, PHIRY, PHIRZ

Where

NODE is the model node number (integer)

PHIXX is the eigenvector in the x-direction (double)

PHIYY is the eigenvector in the y-direction (double)

PHIZZ is the eigenvector in the z-direction (double)

PHIRX is the eigenvector about the x-axis (double)

PHIRY is the eigenvector about the y-axis (double)

PHIRZ is the eigenvector about the z-axis (double)

Eigenvector data read example:

Do I=1,NVEC

Do j=1,NNODE

Read() NODE, (PHI(k), k=1, 6)

Enddo

Enddo

454

AASHTO Load Combination Results

File: name.ASH

This file contains design code and limit state information.

nCodeType

Where

nCodeType is the AASHTO design code used for load combinations

(0 – for LRFD, 1 – for LFD)

nGroup1, nGroup2, …, nGroup11

Where

nGroup1… are the limit states that were analyzed

(0 – for analyzed, 1 – for not analyzed)

(CritPl(J),J=1,11)

Where

CritPl is load combination number with the maximum pile demand/capacity ratio for each

analyzed limit state (0 – if not analyzed)

(CritCol(J),J=1,11)

Where

CritPl is load combination number with the maximum pier column demand/capacity ratio for

each analyzed limit state (0 – if not analyzed)

455

(CritPierCap (J),J=1,11)

Where

CritPl is load combination number with the maximum pier cap demand/capacity ratio for each

analyzed limit state (0 – if not analyzed)

References

References

Brown, D., Morrison, C., and Reese, L. (1988), "Lateral Load Behavior of a Pile Group in Sand," ASCE

Journal of Geotechnical Engineering, Vol. 114, No. 11, pp. 1261-1276.

Gazioglu, S. M., and O’Neill, M. W. "Evaluation of P-Y Relationships in Cohesive Soils," from Analysis

and Design of Pile Foundations, proceedings of a symposium sponsored by the ASCE

Geotechnical Engineering Division, ASCE National Convention, San Francisco, CA, pp. 192-213.

Georgiadis, M. "Development of P-Y curves for Layered Soils," Proceedings, Geotechnical Practice in

Offshore Engineering, American Society of Civil Engineers, pp. 536-545.

Kulhawy, F. and Mayne, P. "Manual for Estimating Soil Properties for Foundation Design." Electric

Power Research Institute (EPRI) Report. EPRI EL-6800. Project 1493-6. Aug. 1990, pp. 5-17.

Matlock, H. "Correlations for Design of Laterally Loaded Piles in Soft Clay," Paper No. OTC 1204,

Proceedings, Second Annual Offshore Technology Conference, Houston, Texas, Vol. 1, 1970, pp.

577-594.

McVay,M. C., O'Brien, M., Townsend, F. C., Bloomquist, D. G., and Caliendo, J. A. "Numerical

Analysis of Vertically Loaded Pile Groups," ASCE, Foundation Engineering Congress,

Northwestern University, Illinois, July, 1989, pp. 675-690.

456

McVay,M. C., M., Niraula, L. "Development of Modified T-Z Curves for Large Diameter Piles/Drilled

Shafts in Limestone for FB-Pier," Report Number 4910-4504-878-12, National Technical

Information Service, Springfield, VA June 2004.

Kim, Myoung-Ho, "Analysis of Osterburg and Stanamic Axial Load Testing and Conventional Lateral

Load Testing", Master’s Thesis, University of Florida, Gainsvelli, Florida, 2001.

Murchison, J. M. and O’Neill, M. W. "Evaluation of P-Y Relationships in Cohesionless Soils," from

Analysis and Design of Pile Foundations, proceedings of a symposium sponsored by the ASCE

Geotechnical Engineering Division, ASCE National Convention, San Francisco, CA, pp. 174-191.

Reese, L. C., Cox, W. R. and Koop, F. D "Analysis of Laterally Loaded Piles in Sand," Paper No. OTC

2080, Proceedings, Fifth Annual Offshore Technology Conference, Houston, Texas, 1974 (GESA

Report No. D-75-9).

Reese, L. C., Cox, W. R. and Koop, F. D. "Field Testing and Analysis of Laterally Loaded Piles in Stiff

Clay," Paper No. OTC 2312, Proceedings, Seventh Offshore Technology Conference, Houston,

Texas, 1975.

Reese, L. C. and Welch, R. C. "Lateral Loading of Deep Foundations in Stiff Clay," Journal of the

Geotechnical Engineering Division, American Society of Civil Engineers, Vol. 101, No. GT7,

Proceedings Paper 11456, 1975, pp. 633-649 (GESA Report No. D-74-10).

Sayed, S. M. and Bakeer, R. M. "Efficiency Formula For Pile Groups," Journal of the Geotechnical

Engineering, American Society of Civil Engineers, Vol. 118, No. 2, Paper No. 26553, 1992, pp.

278-299.

Itani, A. M. "Future Use of Composite Steel-Concrete Columns in Highway Bridges." AISC Engineering

Journal.33, No.3 pp. 110-115 1996.

Mander, J. B., Priestley, M. J. N.,Park R., "Theoretical Stress Strain Model for Confined Concrete"

ASCE Journal of Structural Engineering 114,pp. 1804-1826, 1988.

Mander, J. B., Priestley, M. J. N.,Park R., "Observed Stress-Strain Behavior of Confined Concrete"


457

Chai, Y., H., Preistly, M., J., N., and Seible, F., "Flexural Retrofit of Circular Reinforced Bridge

Columns by Steel Jacketing,", University of California, San Diego, La Jolla, 1991.

Mirza, S., A., and MacGregor, J., G., "Variability of mechanical properties of reinforcing bars,", ASCE

Journal of Structural Engineering, 105(ST5):921-937, May 1979.

Scott, B., D., Park R., and Priestly, M., J., N., "Stress-strain Behavior of concrete confined by

overlapping hoops at low and high strain rates,", ACI Journal , 79(1): 13-27, Jan./Feb 1982.

Stone, W., C. and Cheok, G., S., Inelastic Behavior of Full-Scale Bridge Columns Subjected to Cyclic

Loading.. Report No. NIST/BSS-166, National Institute of Standards and Technology, U.S.

Department of Commerce, Gaithersberg, MD 20899, Jan. 1989.

Pinder, Terrence, "A Model for Concrete Under The Effect of Transverse Confinement", Report

presented to the graduate committee of the Department of Civil Engineering, University of

Florida, Summer 1997.

Randolph, M.F., "Piles Subjected to Torsion," Journal of the Geotechnical Division, ASCE, Vol. 107,

No. GT8, August, 1981, pp. 1095-1111.

Stoll, U.W., "Torque Shear Test of Cylindrical Friction Piles," Civil Engineering, ASCE, Vol. 42, No. 4,

April., 1972, pp.63-64.

Wang, S. T., and Reese, L. C., "COM624P – Laterally loaded pile analysis for the microcomputer, ver.

2.0" FHWA-SA-91-048, Springfield, VA, 1993.

Peck, R.B., Hanson, W. E. and Thornburn, T. H., "Foundation Engineering", John Wiley & Sons, 1974.

Bowles, J. E., "Foundation Analysis and Design", McGraw-Hill, New York, 1977.

O’Neill, M. W. and Dunnavant, T. W., "A Study of Effect of Scale, Velocity, and Cyclic Degradability

on Laterally Loaded Single Piles in Overconsolidated Clay.", Rep. No. UHCE 84-7, Dept. of Civil

Engineering, Univ. of Houston, Houston, TX, 1984.

Welch, R. C., and Reese, L.C., "Lateral Load Behavior of Drilled Shafts", Research Rep. No. 3-5-65-99,

conducted for Texas Highway Department and U.S. Department of Transportation, Federal

458

Highway Administration, Bureau of Public Roads, Center for Highway Research, Univ. of Texas

at Austin, TX, 1972.

FHWA, PCSTABLS-Users Manual, Federal Highway Administration, Springfield, VA 1988.

Mitchell, J. S., "A Nonlinear Analysis of Bi-Axially Loaded Beam-Columns Using a Discrete Element

Model," Ph. D. Dissertation, The University of Texas at Austin, August, 1973.

Andrade, P., "Materially and Geometrically Non-Linear Analysis of Laterally Loaded Piles Using a

Discrete Element Technique," Masters Report, Universtiy of Florida, Gainesville, 1994.

Precast Conrete Institute, PCI Design Handbook, 4th

Ed., Chicago IL, 1992.

California Department of Transportation (CALTRANS), Bridge Design Practice Manual, Sacrament,

CA, 1981.

O’Neill, M.W., Townsend, F. C., Hassan, K. M., Buller, A., and Chan, P. S., "Load Transfer for Drilled

Shafts in Intermediate Geomaterials," Report No. FHWA-RD-95-172, November 1996.

University of Florida, "Development of Modified T-Z Curves for Large Diameter Piles/Drilled Shafts in

Limestone for FBPier", UF Project #4910-4504-878-12.

Tutorials

Tutorial Index The following two tutorials are included with the Help Manual. (Click Link to view) Overview (9 minutes 8 seconds) This demo provides an overview of the FB-MultiPier program and explains the most commonly used features. Convergence Problem (3 minutes 45 seconds) This tutorial shows how to overcome convergence problems when analyzing a model using FB-MultiPier.

The tutorials below require an Internet connection and are located on the BSI server. (Click Link to download)

Covers the Element Forces Dialog.

459

Help About The Help About displays important program information. Explains how to update a license in FB-MultiPier. Max Min Covers the Max Min Dialog. Percentage Steel Explains how to use the Percentage Steel method to enter reinforcing steel. Pile Sets Explains how to create Pile Sets. Printable Forces Covers the Printable Forces Dialog. Soil Plot Covers the Soil Plot Dialog. Soil Table Demonstrates how to enter data in the Soil Table. Zoom Feature Covers the Zoom features in FB-MultiPier.

FB MultiPier

460

Segment Selection

Select the member segment to view its interaction diagram.


Confined Concrete Model References

461

1. Itani, A. M. "Future Use of Composite Steel-Concrete Columns in Highway Bridges." AISC Engineering

Journal.33, No.3 pp. 110-115 1996.

2. Mander, J. B., Priestley, M. J. N.,Park R., "Theoretical Stress Strain Model for Confined Concrete"


3. Mander, J. B., Priestley, M. J. N.,Park R., "Observed Stress-Strain Behavior of Confined Concrete"


5. Chai, Y., H., Preistly, M., J., N., and Seible, F., "Flexural Retrofit of Circular Reinforced Bridge

Columns by Steel Jacketing,", University of California, San Diego, La Jolla, 1991

6. Mirza, S., A., and MacGregor, J., G., "Variability of mechanical properties of reinforcing bars,", ASCE

Journal of Structural Engineering, 105(ST5):921-937, May 1979

7. Scott, B., D., Park R., and Priestly, M., J., N., "Stress-strain Behavior of concrete confined by

overlapping hoops at low and high strain rates,", ACI Journal , 79(1): 13-27, Jan./Feb 1982

8. Stone, W., C. and Cheok, G., S., Inelastic Behavior of Full-Scale Bridge Columns Subjected to Cyclic

Loading.. Report No. NIST/BSS-166, National Institute of Standards and Technology, U.S.

Department of Commerce, Gaithersberg, MD 20899, Jan. 1989

9. Pinder, Terrence, "A Model for Concrete Under The Effect of Transverse Confinement", Report

presented to the graduate committee of the Department of Civil Engineering, University of

Florida, Summer 1997.

Note: For cases when it is infeasible to contact a BSI representative during normal business hours, it is possible to obtain the numerical codes by fax or email. For this case, the user must fax or email the following information to the BSI:

1) 1) 1) 1) 1) 1) 1) 1) 1) Name of the user 2) 2) 2) 2) 2) 2) 2) 2) 2) Program License ID 3) 3) 3) 3) 3) 3) 3) 3) 3) Password used for the BSI account 4) 4) 4) 4) 4) 4) 4) 4) 4) Session Code 5) 5) 5) 5) 5) 5) 5) 5) 5) Machine ID

Upon receipt of the above information and verification of the user’s account status, the numerical codes to unlock the program will be provided by fax or email. After obtaining the numerical codes, the user can enter them and complete the license update.

462

Figure G5

License File Update by Internet (Preferred) This option allows the user to update the software license through an Internet connection. This is the preferred method, since it can be done at a convenient time for the user. The Update via Internet Connection option requires that the user enter a License ID and password, both of which were provided to the user when purchasing the product. After entering both items, click the Next button to continue. The FB-MultiPier program will now automatically connect the BSI web server to process the account information. If the account status is verified, the screen will tell you that the license has been updated successfully in green text. If there are problems with the account status or the License ID or password are incorrect, various error messages will be displayed in red text. In the event that the user cannot connect to the BSI web server, the Update by Phone/Fax option should be used. This can be done by clicking the Back button.

463

Figure G6

After successfully updating the software license, click the Next button to view the Update Complete wizard page. In order to apply the changes to the program configuration, the FB-MultiPier program needs to be restarted. Clicking the Finish button will update and automatically close the program. The program will now run in an unlocked state.


AASHTO Table



1. Table Format

2. Table Edit Options

3. Load Case Options

464


AASHTO Table

popup link to the AASHTO Table

P-Y Multiplier Reduction for Shaft with Torsion

465

A p-y multiplier reduction factor should be used for drilled shafts subjected to combined lateral and torsional loading. The results for various centrifuge tests with different L/D and Torque/Lateral load ratios are given below. The reduced capacity is plotted on the vertical axis. As an example, suppose there is a mast arm on a single drilled shaft with L/D = 5 and the Torque/Lateral Load ratio is 10. The resulting capacity would be approximately 90% of the original capacity. As a result, a p-y multiplier of 0.9 should be used to reduce the lateral capacity of the shaft.

466

Barge Impact

This section allows the user to define barge impact parameters. The external forcing function will

be modified to simulate a barge impact with the pier. This is an experimental option that is

currently not available in the graphical interface.

BARGE

The next line specifies barge impact parameters.

L=LVLOUT V=VBINI M=MB C=ABY T= BFT N=NABPB

Where

LVLOUT is the level of output flag (greater than 0 indicates full output

VBINI is the initial velocity of the barge

MB is the mass of the barge

ABY is the crush level at which yielding occurs

BFT is Barge Force Tolerance

NABPB is the number of points in ABPB (displacement v. load) array

The following lines describe the load-displacement crushing curve for the barge. A maximum of

200 lines can be used.

DIS LOAD (one per line)

Where

DIS is the displacement value (first column of ABPB array)

LOAD is the load value (second column of ABPB array)

467


3D Bridge View

Figure A90: 3D Bridge View Window

All the options available for the 3D View Window are available for the 3D Bridge View.


468

Calculating Foundation Stiffness Using FB-MultiPier

FB-MultiPier can be used to calculate the foundation stiffness of a pile and cap system. The

purpose is to calculate the stiffness of the foundation structure including the piles, the pile cap the

soil etc. The stiffness is reported at a single point and therefore it is a 6x6 matrix. The point at

which the stiffness is reported is the pile head if it is a single pile or the center of the pile cap if it

is a pile and cap problem. The point (node) at which the stiffness is reported is internally generated

by the program.

The stiffness of the foundation is calculated as follows:

6. 6. 6. 6. 6. 6. 6. 6. The foundation (pile cap, piles,

soil) is analyzed based on the applied load. The load can only be applied at the additional node

that the program internally generates (see Figure E5).

7. 7. 7. 7. 7. 7. 7. 7. Once the solution is obtained for

the applied load, the program calculates the flexibility matrix of the structure at the particular

equilibrium state following general principles. To do that the program internally applies unit

forces (actually 0.01 load and then scales the results) at the additional point that is internally

created by the program. The forces are applied successively in all six possible directions (Fx, Fy,

Fz, Mx, My, Mz).

8. 8. 8. 8. 8. 8. 8. 8. The displacements from each

solution at the additional node comprise the columns of the flexibility matrix ie the displacements

from the solution under the application of the Fx load comprise the first column of the flexibility

matrix.

9. 9. 9. 9. 9. 9. 9. 9. Once the flexibility matrix is

obtained the program calculates the inverse of that which is the stiffness.

10. 10. 10. 10. 10. 10. 10. 10. In the output data file the program

reports both of the matrices.

The calculated stiffness (or flexibility) matrix is calculated after the equilibrium state of the

structure is obtained. This is necessary since the foundation is usually comprised from nonlinear

elements (including the soil springs). Therefore the snapshot in time (equilibrium state) that the

stiffness is calculated is very important.

If the program was not following the particular sequence ie not obtaining the equilibrium solution

first, then the calculation of the stiffness would be incorrect since it would be obtained using

information for a state of the structure other than the equilibrium.

469

The stiffness can be thought of as being the tangent stiffness (instead of secant) for the simple

reason that it is calculated for a particular instance in time.

The program makes the decision that the loading on the pile cap is applied at the center. The

reason for that is because the stiffness is reported at the particular point. Therefore to be consistent

with the theory the load could not be applied at any other place. It is therefore imperative for the

engineer to make sure that the resultant of the loads from the superstructure (bridge pier) passes

through the particular point.

Additional node created by the program in Orange

Figure E5: Stiffness model in thin mode showing additional node in orange

470

Sound_Wall_Eplanation

3D 3D Display Control

3D 3D Results

3D Display Control

471

3D Node Information

3D Results Dynamic Options

3D Results Window

AASH AASHTO Load Factors Table

AASH Automated AASHTO Loads

472

AASH Limit States to Check

AASHTO Load Case Options

AASHTO Load Combination Preview Table

AASHTO Load Combination Results

AASHTO Load Manager

473

AASHTO Load Table

AASHTO Table Edit Options

AASHTO Table Format

Add Substructure


Analysis Convergence Information

474

Analysis Type


AP 1020 Pile Pier Behavior

AP 1033 Iteration Control

AP 1123 Print Control

475

AP 1211 Soil Behavior

AP 1258 Design Options

AP 1708 Interaction Diagram Phi Factor

Axial Forces for Beam Elements

Axial Skin Friction for Florida Limestone

476

Axial Soil Pile Interaction

Axial T Z Curve for Side Friction

Axial T Z Q Z Curve for Tip Resistance

Batch Mode

Bearing Connection

477

Bearing Location Loads

Bearing Pad Properties

Bearing Rotation

Bridge Multiple Piers Option

Bridge Span Overview

478

Bridge Spring Toggle

Bridge Tab

Cap Behavior

CAP Edit Cap Thickness

Capacity Information

479

CD Custom Stress Strain

Clay API

ClayEnd

ClaySide

Column Connection to the Pile Cap

Column Information

480

Combination AASHTO

Concentrated Nodal Loads

Conclusions

Concrete

CONFINED CONCRETE MODEL

481

Control Menu

Converting FB Pier Coordinates to a Standard Coordinate System

Deck Modeling

DESCRIPTION OF TOOLBAR ICONS


482

DrilledEnd

DrilledSide

Driven Pile Clay API

Driven Pile Clay API QZ

Driven Pile Sand API

483

Driven Pile Sand API QZ

DrivenEnd

DrivenSide

Dynamic Control Parameters

Dynamic Load Function Application

Dynamic Step by Step Integration

484

Dynamics Tab

Edit Custom Bearings

Edit Load Functions

Edit Span

Edit Supports

485


Element Dialog

Element End Forces

Element Stiffness

Engine Input Overview

486

Equivalent Stiffness Generation

Expanding Memory

Failure Ratio for Cross Sections

FB PIER LICENSE INSTALLATION HELP

FB Pier1

487

Figure B 2

Figure B 3

File Menu

FINITE ELEMENT

Flat Shell Elements

488

Full Scale Column without Steel Casing

General Control

General Pier Wizard

Generalized Stress and Strain

Geometry and Control Information

489

GRID 2094 Grid Spacing Table

GRID Custom Grid Spacing

Gross Pier Component Properties

Gross Pile Properties

Group Interaction

490

Half Scale Column With Steel Retrofitting Jacket

Header

Help Menu


HP H Pile Properties

491

HP Section Dimensions

HP Section Orientation

Hyperbolic Curve

ID Interaction Diagram

ID Interaction Diagrams

ID Pier Selection

492

ID Pile Selection


INTERACTION DIAGRAMS

Intermediate GeomaterialQZ

Intermediate GeomaterialTZ

493

Lateral Soil Pile Interaction

LE Database Section Selection

LE Parabolic Taper Cantilever Properties

LE Pier Components

LE Section Data

494

LE Section Properties

License File

Limestone McVay use 2 3 Rotation

Load Function Edit Table

LOAD Load Case Options

LOAD Load Table

495

LOAD Table Edit Options

LOAD Table Format

Longitudinal Reinforcement

LP Database Section Selection

LP Full Cross Section Pile Properties

496

LP Load Case

LP Loads

LP Node Applied

LP Pile Set Info

LP Pile Shaft Segment List

LP Section Properties

497

LP Section Type

LP Segment Dimensions

Mander Models for Confined Concrete

Mass Damper Tab

Mass Dampers in 3D View

498

Matlock s Soft Clay Below Water Table

Max Min Forces Dialog

Maximum Moments in Beam Elements

MEM Extra Member Sections

MEM Extra Members List

499

MEM Nodes Attached

Membrane Element

Mesh Correctness and Convergence

Mild Steel

Mindlin Theory

500

Missing Pile Data

MLE Section Type

Mode Shape and Frequency Information Response Spectrum Analysisi

Modify Load Factors

Multiple Pier Generation

501

Multiple Pier Substructure Information

Multiple Pile Sets

Multiple Soil Sets

NLE Full Pier Component Properties

NLE Section Dimensions

NLP Material Properties

502

NLP Section Dimensions

NLP Section Type

NONLINEAR BEHAVIOR


O Neill s Clay

503

O Neill s Sand

OP Bullet Section Properties

OP Cross Section Orientation

OP Group Data

OP Void Data

504

P Y Resistance for Florida Limestone

PAD Bearing Locations

PI Pile Data

Pier Cross Section Table

Pier Element Selection

Pier Rotation Angle

505

Pier Segment Selection

Pier to Superstructure Connectivity

Pile Batter Information

Pile Cap Properties

Pile Data

506

Pile Element Selection

Pile Information

Pile Segment Selection

Pipe Pile Properties

Plate Element

507

Point Dampers

Point Mass

Poisson s Ratio

POST PROCESSING FILE FORMATS

PP 1044 Pile Cap Grid Geometry

508

PP 1087 Pile Cross Section Type

PP Pile Cap Data

PP Pile Length Data

PP Pile Shaft Type

PP Pile to Cap Connection

PR Graphs

509

PR Pile Results

PR Pile Selection

PR Plot Display Control

PR Printable Forces

Print Control

510

Printable Soil Graph

Program Settings

PRP 1049 General Pier Option

PRP 1050 High Mast Light Sign Option

PRP 1051 Retaining Wall Option

511

PRP 1052 Sound Wall Option

PRP 1059 Pile and Cap Option

PRP 1060 Single Pile Option

PRP 1061 Stiffness Option

PRP 1062 Column Analysis Option

PRP 1063 Pile Bent Option

512

PRR Graphs

PRR Pier Results

PRR Pier Selection

PRR Printable Forces Dialog

Pushover

513

PYM Advanced Soil Data

Reese and Welch s Stiff Clay Above Water Table

Reese s Stiff Clay Below Water Table

References

Reinforcement

514

Removed Pier Cap Element

Removed Pile Cap Element

Result Forces Dialog

Results Viewer

RET Retaining Wall Soil Layer Data

RET Soil Layer

515

RET Soil Layer Data

RET Surcharge

RET Wall and Layer Geometry

RET Wall Load Data

Retaining Wall Explanation

516

Rigid Link Properties

RP Circular Section Properties

RP Confined Concrete Option

RP Edit Bar Groups

RP Group Data

RP Miscellaneous

517

RP Shear Reinforcement

Running FBPier eng in Batch Mode

Sand API

Sand of Reese Cox and Koop

SandEnd

518

SandSide

SECTION Detailed Cross Section

Section Properties

Self Weight and Buoyancy Load Factors

Set Path for a License File on a Network Server

519

Shear and Moment Results

Shear Modulus

Soil Dynamics Dialog

Soil Information

SOIL PILE INTERACTION

520

Soil Properties

Soil Resistance Due to Pile Rotation

Soil Table

SOILPLOT Soil Model Plot

Sound Wall Explanation

SP Elevations

521

SP Rectangular Section Properties

SP Soil Layer Data

SP Soil Layer Models

SP Soil Strength Criteria

SP Void Data

522

Span Concentrated Nodal Loads

Span End Condition

Special Element for FB-PIER

Spectrum Analysis

SPR Spring Nodes

523

SPR Spring Stiffness

Spring Properties

SPT Window

SS Default Stress Strain Curves

SSPLOT Section Stress Strain Plot

Steel Jacket

524

STP Cross Section Type

STP Pier Geometry

STP Taper Data

Stress Strain Curves

Stresses of Pile Cap

525

Structural Information

Subgrade Modulus

Superstructure Information

TAB 130 Soil Tab

TAB 132 Pile and Cap Tab

526

TAB 134 Pier Tab

TAB 135 Load Tab

TAB 136 Analysis Tab

TAB 137 Problem Tab

TAB 243 Spring Tab

TAB 282 X Members Tab

527

TAB 285 AASHTO Tab

TAB 290 Retaining Tab

TAB 298 Pushover Tab

Taper Modeling

Torsional Soil Pile Interaction

528

Transfer Beam Properties

Transfer License to a Different Computer

Transverse Reinforcement

Tutorials

Unconfined Concrete

529

Undrained Strength

Update a License on a Network Server

Update a License on a Stand Alone Workstation

User Defined Bearing Connection

User DefinedPY

530

User DefinedQZ

User DefinedTq

User DefinedTZ

View Menu

Water Table

What s New in Version 3

531

WIN 3D View Window

WIN Pile Edit Window

WIN Soil Edit Window


Wind Load Generation Table

532

Wizard Menu


Young s Modulus

533

Index

2

2D Bridge View...................................................................................................................... 47, 133

3

3D 3D Display Control ................................................................................................................. 470 3D 3D Results.............................................................................................................................. 470 3D Bridge View............................................................................................................................ 467 3D Display Control............................................................................................................... 199, 470 3D Node Information ................................................................................................................... 471 3D Results ................................................................................................................................... 193 3D Results Dynamic Options............................................................................................... 196, 471 3D Results Window ..................................................................................................................... 471 3D View Window.................................................................................................................. 170, 173 3D_Results_Window ................................................................................................................... 193

A

AASH AASHTO Load Factors Table........................................................................................... 471 AASH Automated AASHTO Loads.............................................................................................. 471 AASH Limit States to Check........................................................................................................ 472 AASHTO Load Case Options .............................................................................................. 147, 472 AASHTO Load Combination Preview Table.......................................................................... 43, 472 AASHTO Load Combination Results................................................................................... 454, 472 AASHTO Load Factors Table........................................................................................................ 39 AASHTO Load Manager........................................................................................................ 41, 472 AASHTO Load Table........................................................................................................... 146, 473 AASHTO Tab................................................................................................................................. 39 AASHTO Table Edit Options ............................................................................................... 146, 473 AASHTO Table Format ....................................................................................................... 146, 473 Add Substructure ................................................................................................................. 163, 473 Adjustment for Prestressing ........................................................................................................ 473 Advanced Soil Data ..................................................................................................................... 112 Analysis Convergence Information...................................................................................... 450, 473 Analysis Tab .................................................................................................................................. 33 Analysis Type ........................................................................................................................ 36, 474 Angle of Internal Friction...................................................................................................... 261, 474 AP 1020 Pile Pier Behavior ......................................................................................................... 474 AP 1033 Iteration Control ............................................................................................................ 474 AP 1123 Print Control .................................................................................................................. 474 AP 1211 Soil Behavior................................................................................................................. 475 AP 1258 Design Options ............................................................................................................. 475 AP 1708 Interaction Diagram Phi Factor..................................................................................... 475 ASSHTO Table ............................................................................................................................ 463 Automated AASHTO Loads........................................................................................................... 40 Axial Efficiency............................................................................................................................. 255 Axial Forces for Beam Elements ................................................................................................. 475 Axial Skin Friction for Florida Limestone ............................................................................. 284, 475 Axial Soil Pile Interaction ............................................................................................................. 476 Axial Soil-Pile Interaction............................................................................................. 281, 283, 293

534

Axial T Z Curve for Side Friction.................................................................................................. 476 Axial T Z Q Z Curve for Tip Resistance....................................................................................... 476 Axial T-Z Curve for Side Friction ......................................................................................... 283, 288

Drilled and Cast Insitu Piles/Shafts.................................................................. 288, 289, 290, 291 Driven Piles .............................................................................................................................. 283 User Defined ............................................................................................................................ 288

Axial T-Z(Q-Z) Curve for Tip Resistance..................................................................... 293, 294, 296 Drilled and Cast Insitu Piles/Shafts.......................................................................... 296, 297, 299 Driven Piles .............................................................................................................................. 294 User Defined ............................................................................................................................ 294

B

Barge Impact ............................................................................................................................... 466 Batch Mode.................................................................................................................. 249, 250, 476 Bearing Connection ............................................................................................................. 430, 476 Bearing Location Loads....................................................................................................... 141, 477 Bearing Locations ........................................................................................................................ 120 Bearing Pad Properties ....................................................................................................... 221, 477 Bearing Rotation .................................................................................................................. 121, 477 Bridge (Multiple Piers) Option........................................................................................................ 31 Bridge Multiple Piers Option ........................................................................................................ 477 Bridge Span Dead Load ...................................................................................... 224, 225, 226, 228 Bridge Span Element Numbering ................................................................................................ 235 Bridge Span Overview................................................................................................................. 477 Bridge Spring Toggle........................................................................................................... 348, 478 Bridge Tab ................................................................................................................... 156, 157, 478 Bullet Section Properties ............................................................................................................. 130 Buoyancy ............................................................................................................................. 140, 348

C

Calculating Foundation Stiffness Using FB-MultiPier.................................................................. 468 Cap Behavior ......................................................................................................................... 34, 478 CAP Edit Cap Thickness ............................................................................................................. 478 capacity........................................................................................................................................ 326 Capacity Information.................................................................................................................... 478 CD Custom Stress Strain ............................................................................................................ 479 Circular Section Properties............................................................................................................ 67 Clay (API) .................................................................................................................................... 281 Clay API....................................................................................................................................... 479 ClayEnd ....................................................................................................................................... 479 ClaySide ...................................................................................................................................... 479 Column Analysis Option ................................................................................................................ 30 Column Connection to the Pile Cap .................................................................................... 206, 479 Column Information ..................................................................................................................... 479 Combination (AASHTO) .............................................................................................................. 349 Combination AASHTO................................................................................................................. 480 Concentrated Nodal Loads.......................................................................................................... 480 Conclusions ........................................................................................................................... 91, 480 Concrete ................................................................................................................................ 74, 480 Confined ........................................................................................................................................ 74 CONFINED CONCRETE MODEL............................................................................................... 480 Confined Concrete Model References ........................................................................................ 460 Confined Concrete Option ............................................................................................................. 71 Control Menu ......................................................................................................................... 20, 481 Converting FB Pier Coordinates to a Standard Coordinate System ........................................... 481

535

Cross Section Orientation............................................................................................................ 132 Cross Section Type ..................................................................................................................... 122 Custom Grid Spacing .................................................................................................................. 169 Custom Stress/Strain..................................................................................................................... 97

D

Database Section Selection .................................................................................................. 61, 124 Deck Modeling ..................................................................................................................... 217, 481 Default Stress/Strain Curves ......................................................................................................... 96 Demo ........................................................................................................................................... 237 DESCRIPTION OF TOOLBAR ICONS ....................................................................................... 481 Design Options .............................................................................................................................. 37 Detailed Cross Section .................................................................................................................. 65 Discrete Element Model ...................................................................... 311, 312, 313, 314, 317, 481

Element Deformation Relations ............................................................................................... 312 Element End Forces ................................................................................................................ 317 Element Stiffness ..................................................................................................................... 318 Integration of Stresses ............................................................................................................. 314

Display Control ............................................................................................................................ 200 DrilledEnd .................................................................................................................................... 482 DrilledSide ................................................................................................................................... 482 Driven Pile Clay (API) .................................................................................................................. 282 Driven Pile Clay (API)_QZ........................................................................................................... 295 Driven Pile Clay API .................................................................................................................... 482 Driven Pile Clay API QZ ............................................................................................................. 482 Driven Pile Sand (API)................................................................................................................. 282 Driven Pile Sand (API)_QZ.......................................................................................................... 295 Driven Pile Sand API ................................................................................................................... 482 Driven Pile Sand API QZ ............................................................................................................ 483 DrivenEnd .................................................................................................................................... 483 DrivenSide ................................................................................................................................... 483 Dynamic Control Parameters .............................................................................................. 353, 483 Dynamic Load Function Application .................................................................................... 432, 483 Dynamic Step by Step Integration ....................................................................................... 356, 483 Dynamics Tab........................................................................................................................ 45, 484

E

Edit Cap Thickness..................................................................................................................... 169 Edit Bar Groups ............................................................................................................................. 69 Edit Custom Bearings.......................................................................................................... 159, 484 Edit Load Functions............................................................................................................... 49, 484 Edit Span ............................................................................................................................. 160, 484 Edit Supports ....................................................................................................................... 158, 484 Element Deformation Relations................................................................................................... 485 Element Dialog .................................................................................................................... 173, 485 Element End Forces .................................................................................................................... 485 Element Stiffness......................................................................................................................... 485 Elevations .................................................................................................................................... 102 Engine Input Overview ........................................................................................................ 335, 485 Equivalent Stiffness ..................................................................................................................... 329 Equivalent Stiffness Generation .................................................................................................. 486 Expanding Memory.............................................................................................................. 235, 486 Extra Member Sections ............................................................................................................... 135 Extra Members List...................................................................................................................... 135

536

F

Failure Ratio ........................................................................................................................ 326, 327 Failure Ratio for Cross Sections.................................................................................................. 486 FB MultiPier ................................................................................................................................... 17 FB PIER LICENSE INSTALLATION HELP ................................................................................. 486 FB Pier1....................................................................................................................................... 486 FB-Pier......................................................................................................................................... 459 Figure B 2 .................................................................................................................................... 487 Figure B 3 .................................................................................................................................... 487 File Menu ............................................................................................................................... 19, 487 FINITE ELEMENT ....................................................................................... 303, 304, 306, 309, 487 Fixed License............................................................................................................................... 240 Flat Shell Elements.............................................................................................................. 307, 487 Full Cross-Section Pile Properties................................................................................................. 64 Full Pier Component Properties .................................................................................................. 127 Full Scale Column without Steel Casing ..................................................................................... 488

G

General Control ........................................................................................................................... 488 General Pier Option....................................................................................................................... 23 General Pier Wizard ............................................................................................................ 248, 488 Generalized Stress and Strain............................................................................................. 309, 488 Geometry and Control Information .............................................................................................. 488 Global Damping ............................................................................................................................. 47 Global Mass................................................................................................................................... 47 Graphs ......................................................................................................................... 176, 177, 180 GRID 2094 Grid Spacing Table................................................................................................... 489 GRID Custom Grid Spacing ........................................................................................................ 489 Grid Spacing Table ........................................................................................................................ 59 Gross Pier Component Properties............................................................................................... 489 Gross Pile Properties................................................................................................................... 489 Group Data ............................................................................................................................ 70, 131 Group Interaction ................................................................................................................. 252, 489

H

Half Scale Column With Steel Retrofitting Jacket ....................................................................... 490 Header ......................................................................................................................................... 490 Help Menu ............................................................................................................................. 21, 490 High Mast Light/Sign Option.......................................................................................................... 25 High Strength Prestressing Steels............................................................................................... 490 HP H Pile Properties.................................................................................................................... 490 HP Section Dimensions............................................................................................................... 491 HP Section Orientation ................................................................................................................ 491 H-Pile Properties............................................................................................................................ 95 Hyperbolic Curve ......................................................................................................................... 491

I

ID Interaction Diagram................................................................................................................. 491 ID Interaction Diagrams............................................................................................................... 491 ID Pier Selection .......................................................................................................................... 491 ID Pile Selection .......................................................................................................................... 492 INPUT FILE .........................................336, 339, 340, 362, 387, 388, 389, 414, 418, 419, 425, 427

Column Information.................................................................................................................. 418 Concentrated Nodal Loads ...................................................................................................... 419

537

General Control........................................................................................................................ 337 Header ..................................................................................................................................... 335 Missing Pile Data ..................................................................................................................... 388 Pile Batter Information ............................................................................................................. 387 Pile Cap Properties .................................................................................................................. 427 Pile Information ........................................................................................................................ 362 Print Control ............................................................................................................................. 336 Soil Information ........................................................................................................................ 389 Spring Properties ..................................................................................................................... 425 Structural Information............................................................................................................... 398

Integration of Stresses................................................................................................................. 492 interaction .................................................................................................................................... 326 Interaction Diagram ............................................................................................................. 188, 189 Interaction Diagram Phi Factor...................................................................................................... 36 Interaction Diagrams ................................................................................................................... 185 INTERACTION DIAGRAMS ................................................................................ 323, 324, 325, 492 Intermediate GeomaterialQZ ....................................................................................................... 492 Intermediate GeomaterialTZ........................................................................................................ 492 Iteration Control ............................................................................................................................. 35

L

Lateral Soil Pile Interaction.......................................................................................................... 493 Lateral Soil-Pile Interaction.................................................. 265, 266, 269, 270, 271, 273, 274, 280 LE Database Section Selection ................................................................................................... 493 LE Parabolic Taper Cantilever Properties ................................................................................... 493 LE Pier Components ................................................................................................................... 493 LE Section Data........................................................................................................................... 493 LE Section Properties .................................................................................................................. 494 license.......................................................................................................................................... 239 License ........................................................................................................................ 237, 238, 239 license file .................................................................................................................................... 239 License File.................................................................................................................. 237, 238, 494 License Path ................................................................................................................................ 242 License Transfer .......................................................................................................................... 246 license update.............................................................................................................................. 239 Limestone (McVay use 2 - 3 Rotation ........................................................................................ 277 Limestone McVay use 2 3 Rotation............................................................................................. 494 Limit States to Check..................................................................................................................... 44 Linear Pier Component Properties .............................................................................................. 122 Linear Pile Properties .................................................................................................................... 59 Load Case ................................................................................................................................... 139 Load Case Options...................................................................................................................... 144 Load Factor.................................................................................................................................. 348 Load Function Edit Table....................................................................................................... 51, 494 LOAD Load Case Options ........................................................................................................... 494 LOAD Load Table ........................................................................................................................ 494 Load Tab...................................................................................................................... 137, 138, 139 Load Table........................................................................................................................... 143, 144 LOAD Table Edit Options ............................................................................................................ 495 LOAD Table Format .................................................................................................................... 495 Loads ........................................................................................................................................... 141 Longitudinal ................................................................................................................................... 84 Longitudinal Reinforcement......................................................................................................... 495 LP Database Section Selection ................................................................................................... 495 LP Full Cross Section Pile Properties ......................................................................................... 495 LP Load Case .............................................................................................................................. 496

538

LP Loads...................................................................................................................................... 496 LP Node Applied.......................................................................................................................... 496 LP Pile Set Info ............................................................................................................................ 496 LP Pile Shaft Segment List.......................................................................................................... 496 LP Section Properties .................................................................................................................. 496 LP Section Type .......................................................................................................................... 497 LP Segment Dimensions ............................................................................................................. 497

M

Mander..................................................................................................................................... 74, 76 Mander Models for Confined Concrete ....................................................................................... 497 Mass Damper Tab ....................................................................................................................... 497 Mass Dampers in 3D View .......................................................................................................... 497 Mass/Damper Tab ....................................................................................................................... 149 Mass/Dampers in 3D View .......................................................................................................... 149 Material Properties......................................................................................................................... 96 Matlock s Soft Clay Below Water Table ...................................................................................... 498 Matlock's Soft Clay Below Water Table....................................................................................... 271 Max Min Forces Dialog........................................................................................................ 202, 498 Maximum Moments in Beam Elements ....................................................................................... 498 MEM Extra Member Sections...................................................................................................... 498 MEM Extra Members List ............................................................................................................ 498 MEM Nodes Attached.................................................................................................................. 499 Membrane Element ............................................................................................................. 304, 499 Mesh Correctness and Convergence.................................................................................. 310, 499 Mild Steel ..................................................................................................................................... 499 Mindlin Theory ..................................................................................................................... 307, 499 Miscellaneous ................................................................................................................................ 73 Missing Pile Data ......................................................................................................................... 500 MLE Section Type ....................................................................................................................... 500 Mode Shape and Frequency Information (Response Spectrum Analysisi) ................................ 452 Mode Shape and Frequency Information Response Spectrum Analysisi ................................... 500 Model ............................................................................................................................................. 74 Model Analysis Damping ............................................................................................................... 49 Modify Load Factors ............................................................................................................ 351, 500 Multiple Pier Generation ...................................................................................................... 433, 500 Multiple Pier Substructure Information ................................................................................ 340, 501 Multiple Pile Sets ................................................................................................................. 386, 501 Multiple Soil Sets ................................................................................................................. 397, 501

N

Network License .......................................................................................................................... 241 Network Path ............................................................................................................................... 242 Network Server ............................................................................................................................ 241 Network Server Path ................................................................................................................... 242 New Project/Problem Tab.............................................................................................................. 21 NLE Full Pier Component Properties .......................................................................................... 501 NLE Section Dimensions............................................................................................................. 501 NLP Material Properties .............................................................................................................. 501 NLP Section Dimensions............................................................................................................. 502 NLP Section Type........................................................................................................................ 502 Node Applied ............................................................................................................................... 140 Node Information ......................................................................................................................... 202 Node Numbering.......................................................................................................................... 213 Nodes Attached ........................................................................................................................... 136

539

NONLINEAR BEHAVIOR ........................................................................................................... 311 NONLINEAR BEHAVIOR ............................................................................................................ 502 Nonlinear Solution Strategies .............................................................................................. 327, 502

O

O Neill s Clay ............................................................................................................................... 502 O Neill s Sand.............................................................................................................................. 503 O'Neill's Clay................................................................................................................................ 270 O'Neill's Sand .............................................................................................................................. 266 OP Bullet Section Properties ....................................................................................................... 503 OP Cross Section Orientation ..................................................................................................... 503 OP Group Data ............................................................................................................................ 503 OP Void Data............................................................................................................................... 503

P

P Y Resistance for Florida Limestone ......................................................................................... 504 PAD Bearing Locations ............................................................................................................... 504 Parabolic Taper Cantilever Properties ........................................................................................ 126 partial Fixity.................................................................................................................................. 362 PI Pile Data.................................................................................................................................. 504 Pier Components ......................................................................................................................... 123 Pier Cross Section Table..................................................................................... 182, 183, 184, 504 Pier Element Selection ........................................................................................................ 191, 504 Pier Geometry.............................................................................................................................. 117 Pier Results ................................................................................................................................. 179 Pier Rotation Angle.............................................................................................................. 119, 504 Pier Segment Selection ....................................................................................................... 190, 505 Pier Selection....................................................................................................................... 179, 189 Pier Tab ....................................................................................................................................... 116 Pier to Superstructure Connectivity ..................................................................................... 434, 505 Pile and Cap Option ...................................................................................................................... 23 Pile and Cap Tab........................................................................................................................... 54 Pile Batter Information ................................................................................................................. 505 Pile Bent Option............................................................................................................................. 29 Pile Cap Data................................................................................................................................. 57 Pile Cap Grid Geometry ................................................................................................................ 57 Pile Cap Properties...................................................................................................................... 505 Pile Cross Section Type ................................................................................................................ 55 Pile Data .............................................................................................................................. 168, 505 Pile Edit Window.......................................................................................................... 166, 167, 168 Pile Element Selection......................................................................................................... 188, 506 Pile Information............................................................................................................................ 506 Pile Length Data ............................................................................................................................ 54 Pile Results.................................................................................................................................. 174 Pile Segment Selection ....................................................................................................... 187, 506 Pile Selection ....................................................................................................................... 175, 185 Pile Set Info ................................................................................................................................... 61 Pile to Cap Connection.................................................................................................................. 56 Pile/Pier Behavior .......................................................................................................................... 34 Pile/Shaft Segment_List ................................................................................................................ 60 Pile/Shaft Type .............................................................................................................................. 56 Pipe Pile Properties ............................................................................................................... 96, 506 Plate Element .............................................................................................. 305, 306, 307, 309, 506 Plot Display Control ..................................................................................................................... 175 Point Dampers ..................................................................................................................... 431, 507

540

Point Mass ........................................................................................................................... 430, 507 Poisson s Ratio............................................................................................................................ 507 Poisson's Ratio ............................................................................................................................ 259 POST PROCESSING FILE FORMATS .............................. 433, 437, 442, 445, 446, 447, 449, 507

Axial Forces for Beam Elements.............................................................................................. 445 Capacity Information ........................................................................................................ 447, 448 Geometry and Control Information........................................................................................... 437 Maximum Moments in Beam Elements ................................................................................... 446 Pile Data................................................................................................................................... 442 Shear and Moment Results ..................................................................................................... 449 Stresses of Pile Cap ................................................................................................................ 447

PP 1044 Pile Cap Grid Geometry................................................................................................ 507 PP 1087 Pile Cross Section Type ............................................................................................... 508 PP Pile Cap Data......................................................................................................................... 508 PP Pile Length Data .................................................................................................................... 508 PP Pile Shaft Type....................................................................................................................... 508 PP Pile to Cap Connection .......................................................................................................... 508 PR Graphs ................................................................................................................................... 508 PR Pile Results............................................................................................................................ 509 PR Pile Selection ......................................................................................................................... 509 PR Plot Display Control ............................................................................................................... 509 PR Printable Forces .................................................................................................................... 509 Preliminary Soil Values................................................................................................................ 216 Print Control........................................................................................................................... 37, 509 Printable Forces Dialog ....................................................................................................... 177, 181 Printable Soil Graph .................................................................................................... 110, 111, 510 Problem Tab .................................................................................................................................. 22 Program Settings ................................................................................................................. 236, 510 PRP 1049 General Pier Option ................................................................................................... 510 PRP 1050 High Mast Light Sign Option ...................................................................................... 510 PRP 1051 Retaining Wall Option ................................................................................................ 510 PRP 1052 Sound Wall Option ..................................................................................................... 511 PRP 1059 Pile and Cap Option ................................................................................................... 511 PRP 1060 Single Pile Option....................................................................................................... 511 PRP 1061 Stiffness Option.......................................................................................................... 511 PRP 1062 Column Analysis Option............................................................................................. 511 PRP 1063 Pile Bent Option ......................................................................................................... 511 PRR Graphs ................................................................................................................................ 512 PRR Pier Results......................................................................................................................... 512 PRR Pier Selection ...................................................................................................................... 512 PRR Printable Forces Dialog....................................................................................................... 512 Pushover.............................................................................................................................. 349, 512 Pushover Tab ................................................................................................................................ 52 P-Y Resistance for Florida Limestone......................................................................................... 275 PYM Advanced Soil Data ............................................................................................................ 513

R

Rayleigh Damping Fractors ........................................................................................................... 48 Rectangular Section Properties..................................................................................................... 92 Reese and Welch s Stiff Clay Above Water Table ...................................................................... 513 Reese and Welch's Stiff Clay Above Water Table ...................................................................... 274 Reese s Stiff Clay Below Water Table......................................................................................... 513 Reese's Stiff Clay Below Water Table......................................................................................... 273 References .......................................................................................................................... 455, 513 Reinforcement ....................................................................................................................... 83, 513 Remove License.......................................................................................................................... 244

541

removed....................................................................................................................................... 428 Removed Cap.............................................................................................................................. 428 Removed Pier Cap Element ................................................................................................ 428, 514 Removed Pile Cap Element ................................................................................................ 427, 514 Result Forces Dialog ........................................................................................................... 198, 514 Results Viewer............................................................................................................. 205, 206, 514 RET Retaining Wall Soil Layer Data............................................................................................ 514 RET Soil Layer............................................................................................................................. 514 RET Soil Layer Data.................................................................................................................... 515 RET Surcharge ............................................................................................................................ 515 RET Wall and Layer Geometry.................................................................................................... 515 RET Wall Load Data.................................................................................................................... 515 Retaining Tab .............................................................................................................................. 152 Retaining Wall Explanation.................................................................................................. 154, 515 Retaining Wall Option.................................................................................................................... 26 Retaining Wall Soil Layer Data.................................................................................................... 155 Rigid Link Properties ........................................................................................................... 220, 516 RP Circular Section Properties.................................................................................................... 516 RP Confined Concrete Option ..................................................................................................... 516 RP Edit Bar Groups ..................................................................................................................... 516 RP Group Data ............................................................................................................................ 516 RP Miscellaneous ........................................................................................................................ 516 RP Shear Reinforcement............................................................................................................. 517 Running FBPier eng in Batch Mode ............................................................................................ 517

S

Sand (API) ................................................................................................................................... 280 Sand API...................................................................................................................................... 517 Sand of Reese

Cox and Koop .............................................................................................................................. 269

Sand of Reese Cox and Koop ..................................................................................................... 517 SandEnd ...................................................................................................................................... 517 SandSide ..................................................................................................................................... 518 Section Data ................................................................................................................................ 125 SECTION Detailed Cross Section ............................................................................................... 518 Section Dimensions......................................................................................................... 66, 95, 129 Section Orientation ........................................................................................................................ 96 Section Properties ................................................................................................... 35, 63, 126, 518 Section Stress-Strain Plot.............................................................................................................. 98 Section Type.................................................................................................................... 62, 67, 130 Segment Dimensions .................................................................................................................... 63 Segment Selection ...................................................................................................................... 460 Self Weight .................................................................................................................................. 348 Self Weight and Buoyancy Load Factors ............................................................................ 348, 518 Set Path for a License File on a Network Server ........................................................................ 518 Shaft with Torsion ........................................................................................................................ 464 Shear and Moment Results ......................................................................................................... 519 Shear Modulus............................................................................................................. 259, 260, 519 Shear Reinforcement..................................................................................................................... 73 Single Pile Option .......................................................................................................................... 24 Soil Behavior.................................................................................................................................. 35 Soil Dynamics Dialog........................................................................................................... 108, 519 Soil Edit Window.................................................................................................................. 165, 166 Soil Information.................................................................................................................... 389, 519 Soil Layer..................................................................................................................................... 152

542

Soil Layer Data .................................................................................................................... 101, 154 Soil Layer Models ........................................................................................................................ 104 Soil Model Plot............................................................................................................................. 108 SOIL PILE INTERACTION .......................................................................................................... 519 Soil Properties ............................................................................. 258, 259, 260, 261, 262, 263, 520 Soil Resistance Due to Pile Rotation................................................................................... 255, 520 Soil Strength Crirteria .................................................................................................................. 113 Soil Tab........................................................................................................................................ 100 Soil Table..................................................................................................................... 102, 103, 520 SOIL-PILE INTERACTION .................................................................................. 252, 265, 281, 301 SOILPLOT Soil Model Plot .......................................................................................................... 520 Sound Wall Explanation ...................................................................................................... 133, 520 Sound Wall Option......................................................................................................................... 27 SP Elevations .............................................................................................................................. 520 SP Rectangular Section Properties ............................................................................................. 521 SP Soil Layer Data ...................................................................................................................... 521 SP Soil Layer Models .................................................................................................................. 521 SP Soil Strength Criteria.............................................................................................................. 521 SP Void Data ............................................................................................................................... 521 Span Concentrated Nodal Loads ........................................................................................ 360, 522 Span End Condition............................................................................................................. 164, 522 Span Length ................................................................................................................................ 216 Span Modeling............................................................................................................................. 211 Special Element for FB-MultiPier................................................................................................. 309 Special Element for FB-PIER .............................................................................................. 309, 522 Spectrum Analysis ....................................................................................................... 357, 358, 522 Spiring_Stiffness.......................................................................................................................... 148 SPR Spring Nodes....................................................................................................................... 522 SPR Spring Stiffness ................................................................................................................... 523 Spring Nodes ............................................................................................................................... 148 Spring Properties ......................................................................................................................... 523 Spring Tab ................................................................................................................................... 148 SPT Window........................................................................................................................ 114, 523 SS Default Stress Strain Curves ................................................................................................. 523 SSPLOT Section Stress Strain Plot............................................................................................. 523 Stand Alone License.................................................................................................................... 240 Steel Jacket ..................................................................................................................... 87, 88, 523 Stiffness ............................................................................................... 329, 330, 331, 332, 333, 334 Stiffness Conversion.................................................................................................................... 331 Stiffness Coordinate .................................................................................................................... 331 Stiffness Option ............................................................................................................................. 28 STP Cross Section Type ............................................................................................................. 524 STP Pier Geometry...................................................................................................................... 524 STP Taper Data........................................................................................................................... 524 Stress Strain Curves.................................................................................................................... 524 Stresses of Pile Cap .................................................................................................................... 524 Stress-Strain Curves ........................................................................................... 319, 320, 321, 322

Adjustment for Prestressing..................................................................................................... 322 Concrete........................................................................................................................... 319, 320 High Strength Prestressing Steels ........................................................................................... 321 Mild Steel ......................................................................................................................... 320, 321

Structural Information .................................................................................................................. 525 Subgrade Modulus .............................................................................................................. 263, 525 Superstructure Information .................................................................................................. 342, 525 Surcharge .................................................................................................................................... 156

543

T

TAB 130 Soil Tab......................................................................................................................... 525 TAB 132 Pile and Cap Tab.......................................................................................................... 525 TAB 134 Pier Tab ........................................................................................................................ 526 TAB 135 Load Tab ...................................................................................................................... 526 TAB 136 Analysis Tab ................................................................................................................. 526 TAB 137 Problem Tab ................................................................................................................. 526 TAB 243 Spring Tab .................................................................................................................... 526 TAB 282 X Members Tab ............................................................................................................ 526 TAB 285 AASHTO Tab................................................................................................................ 527 TAB 290 Retaining Tab ............................................................................................................... 527 TAB 298 Pushover Tab ............................................................................................................... 527 Table Edit Options ....................................................................................................................... 144 Table Format ............................................................................................................................... 144 Taper Data................................................................................................................................... 116 Taper Modeling.................................................................................................................... 207, 527 Time Functions .............................................................................................................................. 49 Time Stepping Patameters ............................................................................................................ 48 TOOLBAR ICONS ....................................................................................................................... 246 Torsional Soil Pile Interaction ...................................................................................................... 527 Torsional Soil-Pile Interaction.............................................................................................. 301, 303

Hyperbolic Curve.............................................................................................................. 301, 302 User Defined ............................................................................................................................ 303

Transfer Beam..................................................................................................... 229, 230, 231, 232 Transfer Beam Properties ................................................................................................... 219, 528 Transfer License.......................................................................................................................... 244 Transfer License to a Different Computer ................................................................................... 528 Transverse..................................................................................................................................... 87 Transverse Reinforcement .......................................................................................................... 528 Tutorials ............................................................................................................................... 458, 528

U

Unconfined............................................................................................................................... 82, 83 Unconfined Concrete................................................................................................................... 528 Undrained Strength ............................................................................................................. 262, 529 Unlock.......................................................................................................................................... 236 Update a License on a Network Server....................................................................................... 529 Update a License on a Stand Alone Workstation........................................................................ 529 User Defined Bearing Connection ....................................................................................... 346, 529 User DefinedPY........................................................................................................................... 529 User DefinedQZ........................................................................................................................... 530 User DefinedTq............................................................................................................................ 530 User DefinedTZ ........................................................................................................................... 530

V

View Menu ....................................................................................................................... 19, 20, 530 Void Data ............................................................................................................................... 94, 132

W

Wall and Layer Geometry............................................................................................................ 152 Wall Load Data ............................................................................................................................ 155 Water Table ......................................................................................................................... 101, 530 What s New in Version 3 ....................................................................................................... 17, 530 WIN 3D View Window ................................................................................................................. 531

544

WIN Pile Edit Window.................................................................................................................. 531 WIN Soil Edit Window.................................................................................................................. 531 Wind Generator ........................................................................................................................... 232 Wind Load Generation......................................................................................................... 422, 531 Wind Load Generation Table................................................................................................. 42, 531 Wizard Menu.................................................................................................................... 20, 21, 532

X

X-Members Tab........................................................................................................................... 134 XML Report Generator ........................................................................................................ 204, 532

Y

Young s Modulus ......................................................................................................................... 532 Young's Modulus ......................................................................................................................... 259

135640720 FB MultiPier Help Manual

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