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VecTor3: A. User's Manual B. Sample Coupled

1. 3 z 3 17 e 4 b5 Ls 5 mer m 5 5 35 11 11 B 1 b5 eds o Jis 4 a L b5 RO z 5 5 3 4 Sia l 10 ls 15 17 11 13 15 ee 367 114 658 628 986 307 989 878 342 109 313 081 054 537 452 336 245 034 002 294 554 089 379 629 364 484 199 Poe 596 r l 105 688 152 917 049 515 654 6535 363 367 107 672 291 842 884 187 315 112 fils 048 287 125 r n 322 HE z 1 3 359 257 591 466 052 885 315 077 244 211 foo 212 945 619 235 307 de 13 Ju Bs 4 1 eL eg 3 17 16 y 13 199 7 145 0 m x 11 17 4 4 3 zs 3 4 IO eL c5 4 10 11 10 105 204 1 zu 3 0 584 4 Shy 6 zr 930 4 ein x Pa SE Z x B 4 2125 11 957 16 z 14 10 Ls 15 5 0 245 125 Bob 3053 400 248 822 528 161 382 259 002 064 958 864 a07 449 667 885 458 979 878 406 602 525 590 266 075 650 307 TEF 659 459 5978 rol 084 594 351 151 125 335 455 150 9556 090 391 472 954 615 501 873 128 284 070 314 Hoe 511 959 4 456 G l 520 12 1 db eo Jl l l l l n A de al 1 eb d d l l dock l F HE uud uud gc gt p i Lu T p L TE p gt rupe 2 F J ioo E PE Il
2. 555 l1 247 1 387 161 768 0 539 0 420 0 367 0 558 l u27 1 421 483 l 353 1 158 0 944 0 902 1 131 1 570 1 870 250 1 210 573 0 082 0 152 0 135 0 027 0 011 003 0 z 018 0 083 0 179 0 141 0 055 0 335 5606 0 842 1 137 1 556 2 006 2 365 2 645 2 974 403 3 905 4 360 4 779 4 955 4 702 4 177 3 695 zou 3 156 5 05 3 06 2 611 2 147 1 536 1 590 0 814 385 0 095 0 557 0 876 1 010 1 033 297 1 865 2 400 2 703 3 038 3 291 3 593 3 948 184 4 235 4 152 4 068 4 015 4 053 4 088 4 015 Bad 3 361 3 473 3 503 3 298 3 941 4 081 4 15 10 4 073 3 755 3 368 3 1653 3 156 3 323 3 411 498 3 3 3 513 3 450 3 427 3 33 3 145 Z 3 289 3 795 4 311 4 550 4 929 1 206 J 268 O60 4 737 4 425 4 121 3 746 3 275 2 728 2 200 263 1 290 0 677 0 007 0 495 742 0 759 0 665 0 639 0 850 1 087 1 200 1 143 0 928 0 714 453 0 142 0 130 s41 0 521 0 271 1 030 Lata 454 1 772 2 096 2 464 2 4856 2 2342 2 043 1 5663 320 1 201 1 20 1 300 1 528 1 665 2 147 2 308 309 2 205 2 0153 1 827 1 8353 Zolak 2 496 2 900 2264 3 634 4 015 4 468 3 011 1 393 B 077 5 454 226 5 881 5 873 z 098 7 161 7 141 7 082 7 054 079 r 082 6 989 6 049 5 538 5 314 3 891 3 452 Sa 4 478 3 832 3 214 2 822 2 00 2 791 2 910 390 3 108 3 301 3 3235 3 742 3 748 3 524 3 304 052 2 716 2 413 2 051 1 513 3 7 0 5351 0 250 16 331 0 541 0 655 0 88
3. e Base Curve e Modified Park Kent Kent and Park 1971 Park et al 1982 e Montoya 2003 Montoya 2003 e Popovics Mander Popovics 1973 Mander et al 1988 e Hoshikuma 1997 Hoshikuma et al 1997 e Saenz Spacone Saenz 1964 Kwon and Spacone 2002 e FRC Lee 2011 e Attard Setunge Attard and Setunge 1996 e Elastic Plastic Compression Softening Model e No Compression Softening e Vecchio 1992 A el e2 Form Vecchio and Collins 1993 e Vecchio 1992 B el e0 Form Vecchio and Collins 1993 e Vecchio Collins 1982 Vecchio 1982 e Vecchio Collins 1986 Vecchio and Collins 1986 e Vecchio 1992 C e Maekawa 1978 Miyahara et al 1987 1988 e Mehlhorn 1990 Kollegger and Mehlhorn 1990 e Noguchi 1989 Shirai and Noguchi 1989 48 VecTor3 User s Manual Tension Stiffening Model e No Tension Stiffening e Modified Bentz 2003 Sato and Vecchio 2003 e Vecchio 1982 Vecchio 1982 e Collins Mitchell 1987 Collins and Mitchell 1987 e Bentz 1999 Bentz 2000 e Izumo 1991 Izumo et al 1991 e Lee 2010 w Post Yield Tension Softening Model e Not Considered e Linear e Bilinear e Nonlinear Yamamoto Yamamoto 1999 e Nonlinear Hordijk Hordijk 1991 Spinella Spinella et al 2010 e Custom Input Strain Based user defined stress strain curve in the auxiliary tab e Custom Input Crack Based user defined stress strain curve in the auxiliary tab e FRC Lee 20
4. Figure A 76 Apply Impulse Forces Case node nodes dnode nodes dnode nodes d node d o f T F Total i i ng T T keere F pw e Selection Mode Pointer Window Figure A 77 75 VecTor3 User s Manual As previously explained there are two ways to define impulse loading records on specific nodes The first one 1s associated with the Analysis Mode titled Dynamic Nonlinear General which can be selected in the Job Control tab in the Job Definition step Section A 2 4 1 of the VecTor3 User s Manual This Analysis Mode allows the user to define the impulse loading record at each node using a maximum of three force time key points However this type of input is not available through Formworks Plus and can only be entered in the text load file that has the extension L3R as previously explained The second way to define impulse loading records and also the one available through Formworks Plus 1s associated with the Analysis Mode titled Dynamic Nonlinear Impulse Record which can be selected in the lob Control tab in the Job Definition step Section A 2 4 1 of the VecTor3 User s Manual This Analysis Mode allows the user to define the impulse loading record of specific nodes using a maximum of 50 force time key points entered one at a time for each node For each node the time T and the corresponding force F represent one for
5. Maximum Aqgregate Size a Ultimate Strength Fu 600 MPa Reinforcement Components eee Elastic Modulus Ez 500000 MPa Component Add Thermal Diffusivity Kc strain Hardening Strain esh 5 me E Average Crack Spacing Minato x noo perpendicular to relnforcement Sw I Thermal Expansion Coefficient Es l E Delete perpendicular to y reinforcement Su perpendicular to z reinforeement 52 Frestrain Dep lo m Unsupported Length Ratio bt E Color Reinforced concrete material types to be used for solid elements only Enter T for VT 3 default value k Cancel Figure A 19 For defining steel fibre reinforced concrete the Reference Type in the Smeared Reinforcement Properties drop list should be chosen as Steel Fibre Straight or Steel Fibre Hooked for straight or end hooked types of fibres respectively When either these options is chosen the window changes to the form shown in Figure A 20 where the properties of SFRC can be entered by the user The properties to be entered are the Fibre Volume Fraction Vg Fibre Length lg Fibre Diameter df Fibre Tensile Strength fu and Fibre Bond Strength tu Also for this input the user is required to press the Add button in the lower part on the left hand side of the window shown in Figure A 20 and can use the Update and Delete buttons as previously explained 17 VecTor3 U
6. Prestrain Dep Unsupported Length Ratio bt Color Reinforcement material types to be used for truss elements only k Lancel Figure A 23 As previously explained the total number of material types allowed in VecTor3 including base material types discrete reinforcement types and bond types is 50 20 VecTor3 User s Manual A 2 2 3 Bond Properties Definition This step is responsible for defining the properties of the bond between concrete and discrete reinforcing bars This allows for the modelling of imperfect bond conditions or totally unbonded conditions for post tensioned reinforcement cases This step is accessible through the fifth button from the left in the toolbar shown in Figure A 4 The shape of the button is shown in Figure A 24 This button opens the window shown in Figure A 25 Figure A 24 Define Bond Properties Bond Type Type Reference Type Emebedded Deformed Rebars Bond Properties for Embedded Bars Confinement Pressure Factor li Min Bar Clear Cover Spacing Chlir Mo of Reinforcement Layers thru Depth li Hooked Color Bond material types to be used for interior or exterior bonded elements k Lancel Figure A 25 21 VecTor3 User s Manual The first user input required for modelling the bond type is the type of reinforcing bar from the drop list titled Reference Type The types available in VecTor3 are the Embedded Deformed Re
7. reinforcement of the column in an isometric view The concrete was batched using calcareous aggregates and had a compressive strength of 55 MPa based on three cylinder compression tests carried out on the day of testing For the longitudinal steel reinforcing bars the yield stress and the ultimate strength were reported as 444 MPa and 730 MPa respectively The yield stress and the ultimate strength of the ties were reported as 427 MPa and 671 MPa respectively The column was loaded to an axial load of 1590 kN applied from the bottom prior to the start of fire Rotation was restrained at both ends of the column With the start of fire the lateral displacement was applied to the top of the column following the profile shown in Figure B 3 The lateral displacement was kept at its maximum value of 50 mm which was reached at 120 minutes from the start of fire until the failure of the column 305 010 305 co un 4025 229 Figure B 1 83 VecTor3 Sample Coupled Thermal and Structural Analysis 1 ig 1 1 VN NN SN X s os ls a E xi XI NN 3810 13 910 305 AN PT NOE NO Se NE NE NE Us AN p yum N EE Us TEES m N Figure B 2 The simulation of fire conditions was done in the NRC Column Furnace Facility shown in Figure B 4 following the CAN U
8. 1 Factor 1 000 W 1 000 s 0 000 0 000 Vy HH Ww W W Ww Ww Ww W W Ww Ww W W Ww Ww Ww FH HH w STEP NO 1 R 0 00000000 al Vy W Ff W W W W W W W W W W W W W Ww W W w Analysis Convergence Convergence 2999999 9 999999 9 999999 1 000000 006735 1 144997 9 999999 1 477601 00 108 1 006533 1 005609 1 405853 003251 1 003408 1 005955 1 337848 001155 1 001 484 1 0052435 1 285651 0 5 1 001141 1 001677 1 241457 000564 1 004615 1 000752 1 205836 000830 1 002092 1 000221 1 174754 000925 1 000000 1 0000 6 1 150856 000931 1 002915 1 000242 1 128775 O00890 1 003763 1 000326 1 110461 Q ssl 1 001114 1 000364 1 0534007 0761 1 000000 1 000375 1 079997 O00692 1 O00000 1 000371 1 068151 Q00624 1 000000 1 000358 1 057987 000561 1 000000 1 000340 1 049364 000502 1 000000 1 000319 1 042032 000449 1 000000 1 000297 1 035815 000400 1 000000 1 0002 44 1 030506 Q s37 1 000000 1 000252 1 025989 VecTor3 Sample Coupled Thermal and Structural Analysis Ur W W W W W W W W W W W W WW W WW W W HF HF W W W W W W W W Ww W W WW W W 7 a LOAD STAGE 2 bi Load case Factor bi w FLT 1 000 w w AXIAL 1 000 x H LATERAL 1 000 B LATERAL 0 000 i H Ww Ww W Ww W W Ww W W W W Ww W W WW Ww 7 Ww HH Ww H FH W W Ww Ww W Ww W Ww Ww Ww Ww w TIME STEP H 2 w Time 60 00000000 w Ur W H W W W W H W W W W H HH OH WW H WW W WW W W W W W W W W W W W WW W W w Transient Heat Flow Convergen
9. 546 339 268 447 110 909 104 245 312 020 a 267 304 220 166 950 910 253 161 502 121 044 799 282 458 335 55 dl 400 154 36 daq 322 558 990 E G z 190 357 948 568 l 451 080 298 333 313 ada 414 037 als 037 er 874 015 2 318 Appendix A Sample VECTOR EQR File L2 13 359 53 5 323 354 865 132 l 18 L 23 9 852 802 292 1 Ss 390 454 L 27 003 2575 882 015 083 585 27 513 353 NIE 261 54 346 99 080 962 5 227 2 5 S 445 470 628 6 m zs 4 ele de m L l O94 eb l2 ls 21 aa Bi 12 13 Lz 854 K LA r unb p LJ DO ES o uo Chh n 367 fad 902 448 832 615 361 130 329 113 477 582 284 602 962 219 871 685 945 110 078 335 640 517 388 983 378 133 847 106 606 O33 130 315 347 l D m E E an zi M E Ll l ru P na K D b o J Ch o FR SOF 506 126 azl 2779 50 2352 051 998 Bel 41 _ 22 454 Su l4 4 z Z 4 l l gis B l La ss L z 4 4 174 157 447 adu 403 213 pud 960 i Es eda m ea eu Edu B m m e ails 4 4 4 11 e
10. 1192 1786 1088 585 447 612 651 1780 711 431 879 414 740 421 570 1563 1093 869 1011 458 525 49 1061 338 498 EIE 237 118 500 310 13 526 als 658 856 517 _ 2 125 578 525 F 960 409 331 589 744 HE 461 485 728 377 541 980 374 244 46 Br EE 318 07 1230 1447 932 r 705 72d 733 210 125 422 405 7B 239 99 44 342 1028 251 20 460 122 329 176 225 21 249 490 416 102 33 50 3 113 306 153 4 462 646 _ 2 B 119 334 283 146 640 7 61 fl 517 00 232 524 fs 432 262 175 511 453 239 315 176 300 3435 415 81 35 89 125 242 fe 530 1442 1250 1545 406 53602 568 617 245 5 327 53 202 45 61 sil 244 223 1100 211 299 175 391 168 293 170 224 44 Yo 471 494 9 353 207 5327 114 265 230 58 228 563 0 187 175 260 301 5 503 629 80 9q 311 81 414 489 308 58 398 340 571 847 217 388 466 366 Appendix A 95 EIE 238 223 174 352 142 752 1702 1170 1656 1025 246 411 361 251 3l 203 158 ju 181 5 167 428 250 566 21 yal 119 339 32 494 47 378 275 186 57 336 535 163 415 298 2fe 3 521 178 122 91 577 168 245 141 148 134 250 m r 91 442 54 251 3 1 9q 136 565 147 66
11. 908 1 203 652 7 104 6 480 1 8 7 5 451 3 36565 3 342 35 410 3 383 3 2 6 020 56 338 5 156 5 979 3 619 4 986 4 512 3 987 3 957 3 626 2 965 2 677 2 317 2 037 1 815 1 547 1 342 1 811 2 191 2 977 2 554 2 487 2 547 2 5654 2 755 3 048 2 991 2 170 1 859 1 154 Q 227 0 486 1 0 3 1 462 2 606 _ 3 064 3 307 3 581 4 221 4 496 5 069 5 185 5 214 7 011 548 8 164 8 849 9 427 9 869 10 464 11 545 12 599 12 964 13 205 13 16 13 605 153 468 14 310 14 092 14 506 14 640 15 635 16 671 16 772 15 881 13 133 14 098 13 065 11 596 9 705 G 223 5 515 4 271 2 387 45 0 2335 a 942 1 964 2 916 4 097 3 434 5 637 z 908 3 293 10 754 11 557 12 998 13 69 14 204 14 500 14 502 14 341 14 126 13 82 13 318 12 744 12 168 11 407 10 740 10 076 9 420 8 634 z 954 F 170 5 525 1 675 J 202 4 551 4 095 3 705 3 651 3 679 3 585 3 357 3 293 3 493 3 555 3 601 3 510 3 501 3 385 3 009 2 553 2 405 2 365 2 206 1 954 1 674 1 512 1 495 1 596 1 703 1 662 1 645 1 646 1 56 1 538 1 445 1 284 1 157 0 974 0 689 0 516 0 03d 0 289 0 584 0 992 1 352 eds 1 616 1 706 1 841 1 9455 2 020 2 211 2 500 2 7 2 879 53 021 3 228 3 378 3 103 3 581 53 876 3 982 4 038 4 052 4 120 4 153 4 141 4 178 4 269 4 320 4 590 4 521 4 123 4 465 4 422 4 380 4 327 4 314 372 4 525 4 767 5 113 5 563 5 966 5 274 5 555 5b 745 5 855 6 866 6 774 6 648 6 412 6 094 5
12. CEBI9S8 Concrete Structures under Impact and Impulsive Loading Bulletin D Information No 187 1988 Comit Euro International du Beton Lausanne Switzerland 184 p Centre Technique Industriel de la Construction Metallique CTICM Saint Aubin France M thode de Pr vision par le Calcul du Comportement au Feu des Structures en Acier Construction Metallique No 5 1982 Chak I N 2013 Janus A Post Processor for VecTor Analysis Software M A Sc Thesis University of Toronto Toronto ON 193 p Chang C H and Jau W C 2001 Study of Fired Concrete Strengthened with Confinement M Sc Thesis National Chiao Tung University Hsinchu Taiwan Chang Y F Chen Y H Sheu M S and Yao G C 2006 Residual stress strain relationship for concrete after exposure to high temperatures Cement and Concrete Research 36 10 1999 2005 Cheng F P Kodur V K R and Wang T C 2004 Stress strain curves for high strength concrete at elevated temperatures Journal of Materials in Civil Engineering 16 1 84 90 Collins M P and Mitchell D 1987 Prestressed Concrete Basics Canadian Prestressed Concrete Institute Collins M P and Porasz A 1989 Shear design for high strength concrete Bulletin d Information No 193 Design Aspects of High Strength Concrete Comit Euro International du Beton CEB 75 83 Coulomb C A 1776 Essai sur une application des regles de maximis et minimi
13. Element Surface refers to the heat transfer through conduction where the temperatures of the specified nodes are required to be entered Atmosphere refers to the heat transfer through convection where the specified nodes are subjected to a surrounding environment with elevated temperatures through fire for example hence their temperatures are unknown and need to be determined through the analysis The convection heat transfer analysis carried out using VecTo3 considers both convection and radiation The checkbox titled Pore Pres which stands for pore pressure provides the user with the option whether to consider heat transfer only where the checkbox should be left blank or to consider coupled heat and moisture transfer where the checkbox should be ticked While the first option is less time costly and less computationally expensive the second option provides a calculation of the increase in the pressure in the pores of concrete subjected to elevated temperatures The value of this pressure is used by VecTor3 to estimate the occurrence of a phenomenon known as explosive spalling which involves a forcible ejection of large fragments of concrete separating violently and abruptly when subjected to fire accompanied by a loud explosive noise VecTor3 constantly deactivates the elements that are estimated to be spalled as the analysis progresses This enables VecTor3 to better estimate the heat transfer process as layers of
14. It should be noted that this type of temperature definition does not involve any heat transfer between the elements However the thermal expansion strains and the modified mechanical properties of the materials will be calculated based on the temperatures assigned to the elements A 2 5 5 Concrete Elements Prestrains The eleventh button from the left in the toolbar shown in Figure A 57 whose shape 1s shown in Figure A 68 allows the user to define prestrains in specific concrete elements in the structural model Pressing the button opens the window shown in Figure A 69 While the option to apply non uniform prestrains through the elements are planned to be added to VecTor3 they are still under development At this moment only a uniform prestrain through the element can be defined The user is required to specify the ID 69 VecTor3 User s Manual number of the element the type of prestrain vvhich should be left as the default Uniform and the prestrain value in millistrain Figure A 68 Apply Concrete Prestrains Case Elmt Type Strain 1 Elmts d Elmt d Straini Elmts d Elmt d Strain1 Elmts d Elmt d Straini Total 1 1 wm Jo To fo fi fi fo po fi j fo fo fi fi fo po 0 Done Selection Mode Pointer Window Enter positive values for expansion and negative values for contraction including shrinkage strains Figure A 69 The user can define the prestrains of the elements individually one at a time
15. concrete no longer exist and steel reinforcing bars become directly exposed to fire It also enables VacTor3 to better estimate the structural response as the area of the load bearing cross section is reduced 72 VecTor3 User s Manual The next drop list titled Fire Curve Type provides the user with several options for the temperature time curve that controls the progress of fire or temperature with time The drop list includes the following options 1 Steady State where a constant temperature in C is assigned to the nodes for steady state heat transfer analysis This constant temperature 1s required to be entered by the user in the box titled Tp1 Other input entries are not required 2 Linear Model where the user can input a custom temperature time curve using three key points of the time in seconds at 1 Tm2 and Tm3 and the corresponding temperature in C at each of these times at Tp1 Tp2 and Tp3 respectively 3 ASTM E119 12a 2012 model where the standard temperature time curve provided by the ASTM E119 12a 2012 will be followed Other input entries are not required 4 ISO 834 1 1999 1999 model where the standard temperature time curve provided by the ISO 834 1 1999 1999 model will be followed Other input entries are not required The box titled Tcool allows the user to specify the time at which the
16. 1 2 Applying Node Restrants 95 B 2 2 1 3 Applying Node Constraints Linking Nodes 98 DB Element DO tha te E OI eI e t RETE a USQUE cote dud 100 B223 Maternal Type ASS mini ice ee saa 104 B 259 106 B 2 3 1 Analysis Job Control Parameters Definition 107 B 2 3 2 Structural Analysis Models Deflnition 112 5 2 3 9 Auxiliary Parameters DeTtmitiofi oe e cmt Dott ia te omm Dd 115 B 2 3 4 Auxiliary Thermal Parameters Definitton 116 B24 Load Deri On ayuy a OR ias 119 B 2 5 Saving the Input Files and Running VecTor3 129 Reter ICOS een eee me s s 133 Appendix A Sample VECTOR EQR File 141 VecTor3 A User s Manual F ElMohandes November 2013 VecTor3 User s Manual A 1 Introduction This user s manual provides a step by step procedure for carrying out structural analysis of reinforced concrete structures using VecTor3 with the aid of its pre processor Formworks Plus This is followed by a step by step procedure for a sample coupled thermal and structural analysis in Section B First a brief technical background on how VecTor3 operates needs to be presented VecTor3 is a
17. 112 387 35 434 33 613 268 ed 727 22 04 7 560 0 461 2 314 298 12 294 15 425 ffl 14 01 11 256 fad 2 872 1 076 Bd 1 335 2 626 068 625 3 0536 145 Cu 44 97 134 164 2 49 25 64 76 4 36 5 23 49 71 80 94 106 64 35 95 109 30 25 dry B5 a 26 78 52 MITS 12 14 12 O 18 6 56 29 a 4 16 E ds 5 2 ffs 646 920 738 108 335 232 605 434 r l 936 234 511 192 105 CMS 13 15 11 34 26 _ 20 B l8 8 2 B edu 45 89 146 152 5 6 35 13 15 24 46 36 EC 222 176 163 828 377 230 473 587 356 079 572 253 572 575 582 13 15 24 4 33 25 I 21 12 5 104 43 542 203 163 924 802 O42 913 630 819 26 386 511 129 095 609 207 416 069 2225 260 2925 387 881 83 7 883 eds 575 468 434 586 180 071 SITE 190 026 012 241 Z 871 594 949 759 527 295 367 177 G L 253 890 44 262 63d ere 508 ez 538 378 pg 2238 784 287 900 32 373 204 640 418 249 322 807 885 290 468 594 116 645 387 254 374 050 s 495 2356 258 794 l 10 293 072 457 458 280 72 ssa l4 246 7 z 882 231 676 412
18. 142 166 1 124 345 l 47 315 333 11 43 340 187 45 126 73 22 38 98 53 44 137 58 28 44 115 79 133 163 354 333 148 469 116 85 9 208 401 220 155 152 517 617 1176 379 1133 157 259 650 410 DU 308 889 351 356 135 _ 24 35 540 290 188 520 132 93 21 164 20 98 33 246 220 126 42 zr 281 113 46 332 333 46 93 1590 154 6q 147 115 Tr 28 _ 32 _ 78 118 143 19 53 35 160 Appendix A Sample VECTOR EQR File ey 28 29 sa m 82 118 133 Les 125 134 113 58 13 46 99 160 204 233 242 210 168 119 rl 49 50 42 61 35 17 11 52 89 113 92 45 11 o8 121 rl 39 12 23 1 25 40 9 45 98 148 1494 165 144 111 85 57 25 18 34 86 99 118 130 149 141 101 53 15 23 48 75 98 107 111 81 1 z 47 89 88 25 33 33 fe af 19 34 55 75 79 51 45 45 52 16 35 25 89 105 109 118 96 ala 37 9 25 33 53 64 68 33 m 61 104 103 81 34 E 59 98 104 G 33 33 30 25 22 14 46 83 123 142 95 m r 10 19 29 44 50 62 57 39 15 23 56 94 121 104 85 26 28 90 142 165 164 143 125 g9 69 25 12 48 23 15 11 1 5 4 12 1 12 26 36 25 10 5 29 50 07 71 3 07 04 57 58 75 88 10 118 114 103 90 76 65 72 82 94 107 121 131 l124 119 111 104 81 43 10 fe 115 135 133 121 108 EF 75 40 14 25 13 32 69 126 145 115 92 yu 53 33 74 By 106 107 103 106 115 121 126 115 105 F 58
19. 20 20 5 162 173 9 F 25 19 18 37 89 56 70 saz 15 62 58 35 46 87 83 22 29 65 47 49 61 44 34 9 5 _ 2 36 89 47 196 131 ja 50 04 84 11 95 109 60 EIE 135 48 47 80 y EIE 82 16 11 42 33 33 40 12 21 18 23 27 44 14 54 13 13 34 24 1332 POINTS OF VELOC EN 11 940 876 14 585 857 16 201 921 4 902 758 407 476 24 088 445 17 942 854 31 330 O21 28 303 992 4 351 437 10 259 542 21 537 be 3 989 855 _ 2 923 280 16 078 3s Appendix A Sample VECTOR EQR File 1 2 15 15 as 4 2 23 34 28 J 10 d r Lr 3 Iz 18 33 45 53 55 82 87 101 121 181 175 170 43 26 13 21 1 50 41 35 31 64 fl ala 107 112 ag 9 12 5 B2 64 51 8 3 4 1 7 5 67 67 57 45 34 62 103 95 85 120 110 97 Bu a5 EI fe 68 64 4 18 25 5 3 ala 181 158 136 ya 52 44 15 16 20 47 58 58 82 7E 81 34 14 4 8 1 14 55 49 44 56 fe 84 94 106 EF 21 15 5 _ 38 32 26 04 53 48 2 15 _5 3 11 15 46 56 72 69 130 179 4 2 82 106 160 161 79 1 51 49 8 50 22 50 69 131 ae 48 41 36 30 ff aL 96 34 0 14 30 _ 52 45 32 31 25 41 3 24 31 27 11 30 45 57 35 21 21 91 133 120 2 58 49 DATA EQUALLY SPACED AT 0 04 SEC 095 12 314 12 5 17 142 14 870 14 512 654 16 610 15 269 813 1 096 0 0259 635 8 831 12 831 yar 15 500 10 526 DU 280 759 33
20. 3 The lateral load will be applied in the positive X direction along the negative Y edge at the top of the column in a displacement control regime resembling the test conditions 125 VecTor3 Sample Coupled Thermal and Structural Analysis EE L L L T 4 E O 1 L j T T l l l L T J J 1 Saas SSS Sa SSS 1 T L SS asa J T T L5 4 1 j I Li A E 1 E T a Em EE EE pg EESENHECYEBSEHCCEEEHWEESBEg HCHEHBHEOHEOHCUHIREUEOEHCgEueuESEgIEAEREeuu EgeudeEEHIEEgeIeuERNIETJVEWESEHCIEREII Figure B 67 Recalling Section A 2 5 2 of the VecTor3 User s Manual which 1s responsible for defining this type of loading Support Displacements or Imposed Displacements the parameters required for defining this type of load can be found Pressing the button shown in Figure B 68 opens the window shown in Figure B 69 which is responsible for defining the support displacements 68 Figure B 126 VecTor3 Sample Coupled Thermal and Structural Analysis Apply Support Displacements Case node D F DISPL mm nodes dnode d dip nodes dnode ddsp nodes d node d disp Total EE o Bl H OU C UI B Mo NC C 0 Done Selection Mode Pointer window Figure B 69 The ID numbers of the nodes where the lateral displacement is to be applied can be found from Figure B 62 The line shown in Figure B 70 defines the lateral displacement to be applied in the X direction starting from node 6826 The applied displacement 1
21. 703 5 270 j 871 4 467 4 102 3 442 3 343 2 939 2 599 2 289 1 954 1 614 1 289 0 994 0 647 0 200 0 297 0 756 1 091 1 321 1 429 1 387 1 280 1 180 1 045 0 898 0 808 O sed Oo 814 0 900 1 058 1 255 1 385 1 405 1 566 1 755 1 909 2 047 2 230 dadar 2 915 3 435 4 049 4 Ol 5 365 6 023 6 674 Z 279 z 787 6 16 8 418 8 553 8 915 0 220 9 546 9 799 9 966 10 012 3 3974 9 878 a 717 9 464 Q 231 9 015 q 772 8 485 8 119 z 652 7 050 6 260 3 434 4 600 ENSE d 2 054 des 1 105 0 330 0 358 1 025 1 705 2 429 3 151 3 86 4 573 5 235 5 830 6 400 56 582 m3 549 808 798 719 mL 544 423 7 150 b5 60 6 301 5 815 5 310 4 837 4 440 4 127 3 875 53 651 3 586 3 183 3 0 08 2 788 2 475 148 End 1 78 1 _ DT sl 866 F 222 Fila 1 682 0 351 1 192 1 349 eer Appendix A 1 314 0 449 1 454 1 118 0 076 sample VECTOR EQR File 0 985 0 697 0 456 0 433 0 230 0 056 1 648 1 75 1 788 0 916 0 758 0 617 0 314 0 543 0 693 149 0 245 0 177 1 786 0 504 818 0 0350 0 524 1 227 0 397
22. Add button then pressing the Done button to close the window A view of the top plane of the model X Y plane at Z 3760 mm is shown in Figure B 29 where the constraints are shown as red dots The restraints perpendicular to the axis of symmetry can also be seen in the figure Create Linked Nodes Group DOF1 Model nodes dinnde nodes d node nodes d node Total Linked Nodes B27 3 ss HDR HE BL 32 Factor D F 2 Nodes nodes 4 node nodes d node nodes d node EH gt eso El EHEN l 6826 911 11 11 Z 1 EA Sal Add Delete Done Figure B 28 99 VecTor3 Sample Coupled Thermal and Structural Analysis OOo Oo gna g 93 pasa 295 6 3897 598 i599 1 902 98903 gave eva E80 gae 882 5883 8584 B85 6 887 238 F889 98890 gres auo 6857 gs8 863 4870 4871 872 7 74 4875 876 05877 G52 6553 6554 8855 4856 5857 4858 4559 6860 661 i862 863 5864 eias g 40 g 41 i942 6843 5844 6845 dia 847 qisas 45849 96850 5851 Lo p 6829 6830 6831 8 2 833 6834 4835 6836 46637 8838 Figure B 29 B 2 2 2 Element Definition In this test the geometric nonlinearity effects have significant influence on the overall behaviour of the column as it 1s laterally loaded Therefore the eight noded isoparametric hexahedral element type is chosen for creating the model to allow for considering those effects To define the nodes comprising
23. Files Only where only binary files are generated for every load stage 4 Last Load Stage Only where both types of files are generated for the last load stage analyzed only 5 ASCII Files Only where only text ASCII files are generated for every load stage As explained above the user can use any binary file as a seed to start an analysis job starting with the status of the structure that is saved in the binary file The binary file in this case 1s called the seed file of the new analysis job If the analysis job being defined IS new 1 e starting from the initial unloaded state of the structure the entry in the box titled Seed File Name should be set to NULL which is the default entry If the analysis being defined is starting from a seed file then the title of the binary file containing the desired initial status should be entered in the box titled Seed file name without the extension A3R 45 VecTor3 User s Manual Finally the entry in the box titled Modelling format should be left to the default entry Stand Alone Modelling if the entire structural model will be generated using the element types of VecTor3 only If the user desires to create a model that combines different element types across the different VecTor programs the option Cyrus Sub Structure should be selected The procedure of such analysis will be presented in a separate user s manual This co
24. Fire Curve Type Tmi Tpi Tm2 Tp2 Tm3 Tp3 Teool nodes d node nodesd node nodesd node Total 1 1 atmosphere z Pres steadystate 1 fo fo fo b fo fo fo fu fx fifi T T Selection Mode Pointer Window Figure B 55 It can be noticed that the loading case number Case 1 is shown at the left hand side of the window for referencing purposes Returning to Figure B 5 it can be seen that the part of the column exposed to fire starts at an elevation of 330 mm from the base of the column and ends at 305 mm from the top Also the fire should be applied on the nodes on the outer surface of the column only Referring to the nodes numbering scheme defined in Section B 2 2 1 1 of the VecTor3 Sample Coupled Thermal and Structural Analysis the first node at the level where fire 1s applied is node 547 which lies at an elevation of 300 8 mm The lines required to define the fire conditions for the entire fire exposed surface are shown in Figure B 56 and Figure B 57 Apply Nodal Thermal Loads Case node Surface Fire Curve Type Tmi Tpi Tm2 Tp2 Tm3 Tp3 Teool nodes d node nodesd node ff nodesd node Total 1 1 Atmosphere m ASTM E119 Model gt 0 lo j j fo fo j fasooo 64 El 1 Done Selection Mode Pointer Window Figure B 56 120 VecTor3 Sample Coupled Thermal and Structural Analysis Apply Nodal Thermal Loads Case node Surface Fire Curve Type Tmi Tpi Tm2 Tp2 Tm3 T
25. Fur Elastic Modulus Es Strain Hardening Strain esh Ultimate Strain eu Thermal Expansion Coefficient Cs i iE Prestrain Dep li me Unsupported Length Ratio b t o s Reinforcement material types to be used for truss elements only k Lancel Figure B 13 For the longitudinal bars Ductile Steel Reinforcement is selected in the Reference Type drop list at the top Since the bars have a diameter of 25 mm a value of 490 mm and a value of 25 mm are inserted in the boxes titled Cross Sectional Area and Reinforcement Diameter dp respectively Similarly a value of 444 MPa and a value of 730 MPa are inserted in the boxes titled Yield Stress fy and Ultimate Stress fu respectively Since the actual stress strain curve of the longitudinal reinforcing bars is not provided default values will be used for the other material properties In the Elastic Modulus E box a value of 200 000 MPa will be inserted For the Strain Hardening Strain 44 and the Ultimate Strain a value of 5 and a value of 200 will be used respectively The value entered for the Thermal Expansion Coefficient Cy in this window will not be 91 VecTor3 Sample Coupled Thermal and Structural Analysis used in the analysis as explained in the VecTor3 User s Manual It will be overridden by a value that will be calculated according to a specific temperature dependent model that
26. Properties Concrete Aggregate Type Carbonate Initial Porosity gt la Convective Heat Transfer Coeff J m2 s C 125 Emissivity 10 7 Porosity Model Gawin et al 11333 Initial Density kg m3 2400 Permeability Model Tenchew et al 2001 Initial Moisture Content 21 4 Density Model The Eurocode EM 1332 1 2 3004 2 Steel Rebar Properties Conductivity Model The Eurocode EN 13821 22004 2 Yield Stress Model The Eurocode EN 13821 2 2004 2 Specific Heat Capacity Model The Eurocode EM 1992 1 2 2004 2 Ultimate Stress Model The Eurocode EM 1992 1 2 2004 2 Compressive Strength 1 The Euracade EM 1992 1 2 2004 2 Young s Modulus Model The Euracade EM 1992 1 2 2004 2 Compressive Strength 2 Chang et al 2005 Model 1 E Thermal Expansion Strain The Eurocode EM 1992 1 2 2004 2 Peak Strain Model 1 The Eurocode ENY 1992 1 2 1995 Thermal Solution Parameters Peak Strain Madel 2 Chang et al 2006 m Thermal Time Stepping Factor to 11 0 6666 Modulus of Elasticity 1 stress factar corr strain Factor bd Modulus of Elasticity 2 Chang et al 2006 Model 1 Tensile Strength 1 The Eurocode EM 1332 1 2 2004 2 Tensile Strength 2 Chang et al 2006 Thermal Expansion Strain The Euracade 1992 1 2 1995 1 Pre Cooling 2 Post Cooling Reset Default coed ou Figure B 51 The Concrete Aggregate Ty
27. Tenchev et al 2001 Initial Moisture Content 3 Density Model The Eurocode EM 1992 1 2 2004 2 Steel Rebar Properties Conductivity Model The Euracode EN 1332 1 2 2004 ted stress Model The Eurocode EN 1332 1 2 2004 2 Specific Heat Capacity Model The Eurocode EN 1992 1 2 2004 2 gt Ultimate Stress Model The Eurocode EN 1992 1 2 2004 2 y Compressive Strength 1 The Eurocode EN 1992 1 2 2004 2 gt Young s Modulus Model The Eurocode EN 1992 1 2 2004 2 Compressive Strength 4 Chang et al 2006 Modell vi Thermal Expansion Strain The Eurocode EN 1992 1 2 2004 2 Peak Strain Model 1 The Eurocode ENY 1992 1 2 1995 gt Thermal Solution Parameters 5 Chang et al 2006 vi Thermal Time Stepping Factor 0 to 11 0 6668 Modulus of Elasticity 1 stress factar cor strain factor Modulus of Elasticity 2 Chang et al 2006 Model 1 ki Tensile Strength 1 The Eurocode EM 1332 1 z 2004 gt Tensile Strength 2 Changetal 2006 vi Thermal Expansion Strain The Eurocode ENY 1992 1 2 1995 gt 1 Pre Cooling 2 Post Cooling Reset Default coca os Figure A 56 For the thermal and structural properties of concrete and steel that are affected by the rise in temperature the following are lists of the models available for user selection for those properties More about these models can be found in ElMohandes 2013 For concrete Density e
28. Thermal Expansion Coefficient Cc 10 i u x Ultimate Strength Fu Maximum Aggregate Size a Reinforcement Components E Mod s Density Component Thermal Diffusivity Kc Strain Hardening Strain esh 0 me Average Crack Spacing Ultimate Strain u o m perpendicular to reinforeement Se Thermal Expansion Coefficient Cs E 0 PC perpendicular to y reinforcement Su perpendicular to z reinforeement 52 Prestrain Dep E ms Unsupported Length Ratio bt Color Reinforced concrete material types to be used for solid elements only Enter for T3 default value k Cancel Figure A 18 With the material type added the previously greyed out part of the window on the right hand side titled Smeared Reinforcement Properties becomes available for user input In case the Reference Type chosen was Reinforced Concrete smeared steel reinforcement can be added through this part of the window 15 VecTor3 User s Manual The drop list at the top of this part offers the following six types of smeared reinforcement available for use in VecTor3 Ductile Steel Reinforcement smooth or deformed Prestressing Steel Tension Only Reinforcement Compression Only Reinforcement Steel Fibre Hooked and Steel Fibre Straight The last two types are used for defining steel fibre reinforced concrete SFRC For typical reinforced conc
29. be 29 VecTor3 User s Manual entered in the box titled Node 2 and more nodes are allowed to be included in that group as well through the three levelled extrapolation scheme previously explained This specification will result in the following relation between the displacements of the nodes included in the first group in the direction DOF 1 denoted D and the displacements of the nodes included in the second group in the direction DOF 2 denoted D2 D1 Factor x D2 A 2 3 2 Element Definition For defining the elements shown in Figure A 27 the tenth eleventh twelfth and seventeenth buttons from the left in the toolbar shown in Figure A 28 are used for the eight noded regular hexahedral element the eight noded isoparametric hexahedral element the six noded regular wedge element and the two noded uniaxial truss bar element respectively The first three element types can model the base material reinforced unreinforced concrete steel fibre reinforced concrete or structural steel while the last one can model discrete reinforcing bars The shapes of the buttons are shown in Figure A 39 in order from left to right Pressing these buttons opens the windows shown in Figure A 40 to Figure A 43 respectively l L l si E Figure A 39 30 VecTor3 User s Manual Create Regular Hexahedral Elements emt node 1 Helmts delmt dnode Helmts delmt dnode elmts delmt d node Total Pi SEN
30. concludes the entries required in the Job Control tab in the Job Definition window B 2 3 2 Structural Analysis Models Definition The next tab in the Job Definition window titled Models is shown in Figure B 48 with the default entries This tab allows the user to select the models of the advanced structural mechanisms to be followed in the structural analysis for concrete steel reinforcing bars and bond between concrete and steel reinforcing bars This is in addition to several general analysis models Define Job Job Control Models Ausiliay Ausilary Thermal Concrete Models Compression Pre Peak Parabola Hognestad vi Confined Strength Kupfer Richart Compression Post Peak Modified ParkKert Dilation Variable Kupfer ov Compression Softening Vecchio 19924 el e2 Fom Cracking Criterion IMchrCoulamb Stess vi Crack Stress Calc Basic DSFM MCFT Crack Width Check 4099425 Crack Width M Tension Stiffening Modified Bentz 2003 vi Crack Slip Calc Wahaven Monotonic Tension Saftening linea Creep and Relaxation Net Available FAC Tension ISDEM M netonic vi Hysteretic Response Nonlinear w Plastic Offsets Reinforcement Models Bond Models Husteretic Response Bauschinger Effect Seckin id Dowel Action Tassios Crack Slip Concrete Bond Eligehausen Buckling Akkaya 2012 Refined DhakalMa Analysis Models Strain History Previous
31. displayed in the MS DOS window while the analysis is running are also saved in a text file with the title VECTOR TXT After the analysis 1s over the post processor Janus can be used for a graphical display of the results This can be done by starting Janus by pressing the button shown in Figure B 75 then opening the VECTOR JOB file in Janus Figure B 75 132 References References Asatsu Asazu N Unjo S Hoshikuma J and Kondo M 2001 Plastic hinge length of reinforced concrete columns based on the buckling characteristics of longitudinal reinforcement In Japanese Journal of Structural Mechanics and Earthquake Engineering Proceedings of Japan Society of Civil Engineers JSCE 682 177 194 Aslani F and Bastami M 2011 Constitutive relationships for normal and high strength concrete at elevated temperatures American Concrete Institute ACT Materials Journal 108 4 355 364 ASTM E119 12a Standard Test Methods for Fire Tests of Building Construction and Materials 2012 American Society for Testing and Materials ASTM West Conshohocken PA 34 p Attard M M and Setunge S 1996 Stress strain relationship of confined and unconfined concrete American Concrete Institute ACI Materials Journal 93 5 432 442 Bauschinger J 1886 Uber die ver nderung der elastizit tsgrenze und der festigkeit des eisens und stahl durch strecken und quetschen durch erwarmen und abk hlen und
32. durch oftmal wiederholte beanspruchung Mittheilungen aus dem Mechanisch Technischen Laboratorium der K niglichen Technischen Hochschule in Munchen 13 1 116 Bazant Z P and Becq Giraudon E 2002 Statistical prediction of fracture parameters of concrete and implications for choice of testing standard Cement and Concrete Research 32 4 529 556 Bazant Z P and Chern J C 1987 Stress induced thermal and shrinkage strains in concrete Journal of Engineering Mechanics American Society of Civil Engineers ASCE 113 10 1493 1511 Bentz E C 2000 Sectional Analysis of Reinforced Concrete Structures PhD Thesis University of Toronto Toronto 184 p Brockenbrough R L 1970 Theoretical stresses and strains from heat curving Journal of the Structural Division American Society of Civil Engineers ASCE 96 7 1421 1444 CAN ULC S101 07 Standard Methods of Fire Endurance Tests of Building Construction and Materials 2007 Underwriters Laboratories of Canada Toronto ON 85 p CEB FIP Model Code for Concrete Structures Buletin D Information No 124 125 1978 Comit Euro International du Beton Federation Internationale De La Pr contrainte CEB FIP Lausanne Switzerland 348 p 133 References CEB FIP Model Code 1990 Buletin D Information No 213 214 1993 Comit Euro International du Beton F d ration Internationale De La Pr contrainte CEB FIP Lausanne Switzerland 460 p
33. fire is extinguished and the nodes start to cool naturally to room temperature n air This should only be used when one of the standard temperature time curves 1s selected The fire decay model that is followed by VecTor3 is the ISO 834 1 1999 1999 model For the Linear Model option the user can specify the temperature decay using the key points and for the steady state analysis an option for temperature decay is unnecessary The user can specify the nodes with specific temperature time profiles individually one at a time or specify the ID number of a certain node with a specific temperature time profile and extrapolate the input to other nodes with the same temperature time profile by specifying the number of nodes nodes and the increment in the ID number of the subsequent nodes d node This extrapolation can be done in three levels simultaneously using the three sets of boxes available for user input as shown in Figure A 73 The Pointer and Window selection options that were explained earlier are also available 73 VecTor3 User s Manual A 2 5 8 Lumped Nodal Masses for Dynamic Analysis The fourteenth button from the left in the toolbar shown in Figure A 57 whose shape 1s shown in Figure A 74 allows the user to define additional masses lumped at specific nodes in the structural model which can be used by the user for dynamic analysis purposes Pressing the button opens the window shown in Figu
34. first node in the x y and z boxes and extrapolate them to define more nodes by specifying the number of nodes to be defined nodes and the increments of the subsequent nodes in the ID number d node the x coordinate d x the y coordinate d y and the z coordinate d z This extrapolation can be done in 25 VecTor3 User s Manual three levels simultaneously using the three sets of boxes available for user input as shovvn in Figure A 31 After each entry whether it is for an individual node or an extrapolated group of nodes the Add button on the right hand side of the window needs to be pressed This will cause the entry to show in the larger box at the bottom of the window as shown in Figure A 32 Create Nodes node z Hnodes dnode dx dz Hnodes d node dx dz Hnodes d node dx Total 1 fo po fo mm mm Ta Ta TT To Tr o m FT 3 Ta EE Delete Done Figure A 32 Unneeded entries can be deleted by selecting them from the list in the larger box at the bottom of the window then pressing the Delete button on the right hand side of the window When all the entries of all the required nodes is entered pressing the Done button on the right hand side of the window closes the window A feature that is available for facilitating the nodes definition step is the node copying feature This feature can be accessed through the second button from the lef
35. for DSFM e Not Considered e Walraven Monotonic Walraven and Reinhardt 1981 e Vecchio Lai Cyclic Vecchio and Lat 2004 e Maekawa Monotonic Okamura and Maekawa 1991 e Hybrid I Walraven Walraven and Reinhardt 1981 with preset minimum lag e Hybrid II Vecchio La1 Vecchio and Lai 2004 with preset minimum lag e Hybrid III Maekawa Okamura and Maekawa 1991 with preset minimum lag Creep and Relaxation e Not Available The input of concrete creep parameters 1s disabled in this tab but will be considered in the next tab which 1s titled Auxiliary Hysteretic Response e Linear w No Plastic Offsets e Linear w Plastic Offsets e Nonlinear w Plastic Offsets e Palermo 2002 w Decay Palermo 2002 Reinforcement Models Hysteretic Response e Linear e Bauschinger Effect Seckin Bauschinger 1886 Seckin 1981 e Elastic Hardening Curvilinear e Elastic Hardening Trilinear e Elastic Plastic Bilinear e Seckin w Local Accumulation Bauschinger 1886 Seckin 1981 Dowel Action e Not Considered 51 VecTor3 User s Manual e Tassios Crack Slip Vintzeleou and Tassios 1987 e Tassios Strength Vintzeleou and Tassios 1987 Buckling e Not Considered e Akkaya 2012 Refined Dhakal Maekawa Dhakal and Maekawa 2002 e Dhakal Maekawa 2002 Dhakal and Maekawa 2002 e Asatsu Model Asatsu Asazu et al 2001 Bond Models Concrete Bond e Perfect Bond e El
36. ill il B 3 l EN mmm mu Delete Done Figure A 40 Create Isoparametric Hexahedral Elements elmi node 1 Helmts delmt dnode elmts delmt dnode elmts delmt dnode Total EN AN EN ft B ENEE EHEHEH am o r ee ee EN Delete Done Figure A 41 Create Wedge Elements elmt node 1 Helmtz delmt d node Helmtz delmt d node Helmts delmt d node EE NENEN EEE ES EERE BB J j EH EH EH Add D Delete Done Figure A 42 Create Truss Elements elmi node 1 Helmts elmi dnode demt d node Helmts elmi d node Tatal EH EEEN paar T T T T a o Delete Done Figure A 43 31 VecTor3 User s Manual For the eight noded regular hexahedral element and the eight noded isoparametric hexahedral element the user 1s required to enter a set of four nodes composing one of the faces of the element for the first four nodes and then enter another set of four nodes composing the opposite face and in the same order This means that Nodes 1 2 3 and 4 form a face of the six faced element and Nodes 5 6 7 and 8 form the opposite face Node 1 should be opposite to Node 5 Node 2 should be opposite to Node 6 Node 3 should be opposite to Node 7 and Node 4 should be opposite to Node 8 Similarly for the six noded regular wedge element the user is required to enter a set of three nodes composing one of the faces of the element for the first three nodes and then enter another set of th
37. in the entry box titled Averaging factor which specifies a certain factor ranging from 0 to This factor represents the percentage of the value of the secant stiffness of each element that is calculated from the previous iteration to be used in the solution of the current iteration The importance of this factor lies in the difficulty of reaching convergence for the highly nonlinear procedure involved in the analyses carried out using VecTor3 A smaller averaging factor results in a more stable analysis and smoother convergence from one iteration to the next A larger averaging factor on the other hand results in faster convergence Therefore the user has to make a judgement on the value to be used for the averaging factor The option of ticking the box titled Dynamic allows the user to let VecTor3 choose an appropriate averaging factor according to the response of the structure where larger averaging factors are used for fast converging elements and smaller averaging factors are used for slow converging elements This means that with the Dynamic option each element has a different averaging factor and it keeps changing from one iteration to the next It has been found that in general flexure dominant responses do not require a small averaging factor to reach convergence where a value of 0 50 or more would be acceptable However for shear dominant responses smaller averaging factors are required Also it was found that a sm
38. in this step is saved in the VT3T AUX input file The first major entry in this tab 1s the Thermal Time Stepping Factor This factor varies from 0 to and it is required for the time discretization in the finite difference solution scheme of the heat transfer analysis For more information about this factor refer to ElMohandes 2013 The user is required to specify the type of aggregate used in the concrete mix through the drop list titled Concrete Aggregate Type where three options are available Calcareous Siliceous and Lightweight The user Is also allowed to specify the Convective Heat Transfer Coefficient and Emissivity of concrete for the convective heat transfer analysis cases Also the Initial Density of concrete and Initial Moisture Content can be specified by the user For coupled heat and moisture transfer analysis additional properties of concrete need to be specified by the user namely the Initial Porosity and the Initial Permeability 57 VecTor3 User s Manual Define Job Job Control Models Auxiliary Auxiliary Thermal Thermal Analysis Concrete Thermal Properties Concrete Moisture Transfer Properties Concrete Aggregate Type Carbonate Initial Porosity 5 8 Convectrve Heat Transfer Coeff J m2 s C 5e 01 Emiservity Porosity Model Gawin et al 1433 ki Initial Density E g m3 400 Permeability Model
39. l gd l d d lI d 11 r gt PU rJ LJ p rey L el gt rr cn ra nra c Appendix A Sample VECTOR EQR File 002 1 460 1 611 Lose 1 974 2 841 3 619 4 095 204 4 578 5 476 5 570 5 065 5 285 6 295 7 388 508 5 702 6 068 6 01 6 5341 6 452 6 775 519 641 6 793 5 910 5 586 6 751 m 7 795 7 496 571 de 37 1 5 640 5 264 6 07 6 559 8 520 6 561 310 5 428 4 569 4 695 5 026 4 305 2 806 1 20 102 0 415 0 420 0 125 0 352 1 074 1 905 2 507 315 1 411 0 436 0 676 1 887 2 4075 2 396 1 485 183 756 1 131 Li 222 1 036 600 0 220 0 175 58 1 362 2 970 4 009 4 799 4 510 3 383 2 442 Bl l 741 1 545 1 559 L ad 1 814 2 022 2 447 988 3 274 3 216 3 029 n 1 56 0 971 638 cal 0 301 0 850 0 889 0 785 0 447 0 432 1 00 1590 0 749 0 246 0 197 0 498 0 916 1 315 1 358 049 648 86 1 5306 1 865 2 2f 2 159 1 762 14 1 944 2 223 2 4530 2 56 3 252 3 5692 4 204 342 4 351 4 192 3 875 3 305 2 980 3 053 3 40 313 4 423 4 6453 4 650 4 475 3 573 2 746 2 0853 unu 1 844 1 407 l1 331 1 534 1 941 2 114 1 646 544 1 553 1 520 1 331 1 554 1 94 2 2 644 3 206 544 3 532 53 420 3 01E 2 491 1 959 s r 1 95 BZ 2 515 2 805 2 640 2 300 2 066 1 831 1 799 342 2 220 2 452 2 037 2 5067 2 372 1 968 xa 25 1 1583 1 se 789 0 5622
40. left as the default entry 60 although a stable and accurate analysis can be achieved with a smaller number of iterations The Averaging factor should be set to a small value as in compression members such as columns a small averaging factor 1s required for a stable analysis In this analysis an averaging factor of 0 15 will be chosen The Convergence limit criterion can also be slackened to a higher value than the default value of 1 00001 This is because for thermal analysis achieving such a strict convergence factor can be difficult In this analysis a value of 1 0001 will be used For the Convergence criteria the option Secant Moduli Displacements amp Reactions Weighted Average will be chosen to ensure reasonable convergence The Analysis mode for this type of analysis is Static Nonlinear Time Step as it involves a static not dynamic analysis in a time stepping procedure For the Results files the ASCII files only option can be used There is no intention to start an analysis from a seed file generated from this analysis hence there is no need to generate binary files Finally the entry in the box titled Modelling format should be left to the default entry Stand Alone Modelling since the entire structural model will be generated using the element types of VecTor3 only 111 VecTor3 Sample Coupled Thermal and Structural Analysis This
41. mm will be restrained in the X direction and the nodes lying on the axis of symmetry in the X direction at Y 152 5 mm will be restrained in the Y direction Also the plane of symmetry needs to be restrained in the perpendicular direction along the height of the column so that the response of the half model resembles the response of the full model Therefore in order to achieve the aforementioned restraints the lines shown in Figure B 22 Figure B 23 and Figure B 24 will be entered pressing the Add button after each line then pressing the Done button to close the window at the end Figure B 25 shows the restraining conditions at the base of the model of the column X Y plane at Z 0 96 VecTor3 Sample Coupled Thermal and Structural Analysis Create Support Restraints node Restrain d a F nodes Hd nude nodes nude nodes nude Total 1 EA a 3 pai 11 pai 11 Delete Done Selection Mode Pointer wron Figure B 22 Create Support Restraints node Restrain d o nodes node nodes d node nodes d node Total 7 LER p 7 is T 1 1 add 0 Delete Done Selection Mode Pointer vi Figure B 23 Create Support Restraints node Restrain dot H rodes d node nudes node H rodes H node Total 79 Dx DY DZT AIF RT 13 1 76 1 1 Delete Done Selection Mode Pointer von Figure B 24 97 VecTor3 Sam
42. or specify the ID number of a certain element with a specific prestrain and extrapolate the input to other elements by specifying the number of elements with prestrains elmts the increment in the ID number of the subsequent elements d elmt and the increment in the prestrain value from one element to the next d Strainl This extrapolation can be done in three levels simultaneously using the three sets of boxes available for user input as shown in Figure A 69 The Pointer and Window selection options that were explained earlier are also available A 2 5 6 Concrete Elements Ingress Pressures The twelfth button from the left in the toolbar shown in Figure A 57 whose shape 1s shown in Figure A 70 allows the user to define internal pressure in specific elements in the structural model Pressing the button opens the window shown in Figure A 71 The user 1s required to specify the ID number of the element and the value of the internal pressure in MPa 70 VecTor3 User s Manual Figure A 70 Apply Ingress Pressures Case elmi pressure t elmts delmt d pressure d elmts delmt d pressure Helmte d elmt d pressure Total 1 ipfo B l J O er Trpo a o Selection Mode Pointer Window Figure A 71 The user can define the internal pressure of the elements individually one at a time or specify the ID number of a certain element with a specific internal pressure and extrapolate the input to other
43. sd 9 27 64 110 155 148 134 115 96 77 35 59 53 Bs 76 82 L eu 58 29 10 3 15 21 35 33 12 4 9 17 11 4 16 33 48 55 64 49 11 28 32 34 44 34 31 36 37 25 10 3 12 19 46 82 108 101 8 53 _ 22 32 58 29 23 12 20 35 2 13 E l 25 20 16 14 _ 2 10 24 39 50 47 _ 22 17 33 95 1 2 148 130 109 83 65 yl 74 F 45 16 18 55 6 83 81 70 72 85 92 106 114 124 139 144 131 122 107 102 11 154 sss 172 17 157 126 94 50 33 _ 2 20 26 22 16 8 5 31 54 r 59 48 28 10 15 37 60 58 0 56 65 25 el 74 58 al 33 44 41 33 62 73 64 27 46 45 58 fe 83 al 82 29 F 35 24d 5 40 57 7 92 100 88 81 64 37 11 E 12 22 38 57 y eu 81 57 44 16 13 _ 27 7 50 55 47 39 E 42 80 85 96 Os 102 102 96 90 85 as 94 103 114 124 138 148 131 133 121 107 95 81 69 53 40 23 21 28 34 28 14 a 5 15 16 11 8 5 13 1 10 25 34 34 39 53 55 82 95 l s 112 109 108 106 120 133 l48 165 169 158 133 97 64 26 25 54 29 26 18 18 31 38 48 58 of 61 51 27 J 2 33 45 60 P2 85 91 83 79 71 81 95 112 13 146 134 122 107 90 73 59 08 ui 84 67 54 39 20 38 55 80 104 120 130 119 102 m r 25 17 ju 62 Je 42 24 3 3 144 TL aga da B Ts sE 11 30 28 8 iz PER B R _ 2 4u 39 E 68 167 174 100 71 32 24 60 47 29 45 l 90 18 12 _ 34 46 15 11 9 3 35 64 32 39 86 99 120 132 eu a9 84 ff 39
44. stress Ec is the Initial Tangent Elasticity Modulus and e is the Cylinder Strain at f strain corresponding to the peak compressive stress fc A typical stress strain curve for concrete under compression 15 shown in Figure A 15 showing the main material properties required to compile the curve where f and e are the compressive stress and strain in concrete respectively Ec Ec Figure A 15 If left vacant other properties will be assigned the most commonly used values independent of the input value of the cylinder compressive strength Poisson s Ratio Lu and the Maximum Aggregate Size a are assigned default values of 0 15 and 20 mm respectively The input value for the Density is used to calculate the lumped masses at the nodes comprising the elements modelled with this material for dynamic analysis purposes only These masses are not used for static dead weight loads which can be defined using a special load type that will be explained later Hence no default value will be assigned to the density of the material For the average crack spacings in the three directions Sx Sy and Sz they are calculated by default according to the CEB FIP Model Code 1978 unless their values are explicitly entered by the user in their respective boxes 12 VecTor3 User s Manual It should be noted that the value of the Thermal Expansion Coefficient C entered in this window will not
45. superimposed When the user ticks the checkbox titled Case 1 which is mandatory for an analysis to be started the greyed out entry boxes provided for this loading case become available for user input as shown in Figure A 53 At this point the user can enter the load file name which will be assigned the extension L3R as previously explained and the loading case title which is only used for referencing In the next box titled Initial factor the user is required to enter the factor by which the load values assigned to the current loading case are to be multiplied by referred to as the load factor for the first load stage to be analyzed The next box titled Final factor 1s used to enter the maximum load factor for the current loading case and the box titled Inc factor 1s used to enter the increment value in the load factor for the current loading case starting from the Initial factor and increasing up to the Final factor The Initial factor Final factor and Inc factor can all have either positive or negative values and the meaning of these factors changes with the different load types and analysis modes as will be explained later The next user input is in the form of a drop list titled Load type In this drop list the user can select the type of loading to be analyzed where the options available are Monotonic for constant or increasing loads Cyclic
46. the fire is extinguished will be assigned a large value as the fire was applied until failure A value of 36000 seconds 10 hours will be entered as the column is expected to fail a lot sooner than that Pressing the Done button closes the window when the loads definition is completed The next loading case Case 2 to be defined is the axial loading case The axial load is to be applied in a load control regime at the top of the column resembling the test conditions To define this loading case the second button from the left in the toolbar shown in Figure B 53 with the number 2 is pressed With that button pressed down all the loads to be defined will be included in Case 2 122 VecTor3 Sample Coupled Thermal and Structural Analysis Recalling Section A 2 5 1 of the VecTor3 User s Manual which 1s responsible for defining this type of loading Nodal Loads the parameters required for defining this type of load can be found Pressing the button shown in Figure B 60 opens the window shown in Figure B 61 which is responsible for defining nodal loads Figure B 60 Appiy Nodal Loads Case node Fx Fy Fz nodes d node dFx dFy dFz Hnodesdnode dF dFy dFz Hnodesdnode dfs dFy dFz Total 2 TT fo fo fo 1 Jf1fofofo rT T loloflo T Tloluo lo ulu nal pun KEN po fo po fo Selection Mode Pointer window Figure B 61 To ensure uniform loading at the top of the column besides having already l
47. the button opens the window shown in Figure A 65 The user is required to specify the ID number of the element the density of the element in kg m and the factors by which the element mass contributes to generating weight force in the X Y or Z direction GX GY and GZ It should be noted that a positive value for GX GY and GZ means that the gravity force will be applied in the positive direction of the respective axis c Figure A 64 67 VecTor3 User s Manual Apply Gravity Loads Case elmt DENSITY Ga EY GZ delmt Helmts delmt elmts d elmt Total ff Bm EE Done Selection Mode Pointer Window Enter positive value for gravity force acting in the positive direction of coordinate axis Figure A 65 The user can define the gravity loads of the elements individually one at a time or specify the ID number of a certain element whose gravity load is to be considered in the analysis and extrapolate the input to other elements by specifying the number of elements with similar density elmts and the increment in the ID number of the subsequent elements d elmt This extrapolation can be done in three levels simultaneously using the three sets of boxes available for user input as shown in Figure A 65 The Pointer and Window selection options that were explained earlier are also available A 2 5 4 Elements Temperature
48. the elements the button shown in Figure B 30 is pressed which opens the window shown in Figure B 31 Figure B 30 Create suparameftric Hexahedral Elements elmt node 1 Helmts delmt dnode Helmts demt d node Helmte demt d node Total A 1 HR EN EN E reso pm Figure B 31 100 VecTor3 Sample Coupled Thermal and Structural Analysis Adding the line shown in Figure B 32 creates all the elements of the model where 12 elements exist in the X direction 6 in the Y direction and 75 in the Z direction Returning to the nodes numbering scheme defined in Section B 2 2 1 1 of the VecTor3 Sample Coupled Thermal and Structural Analysis the ID numbers of the nodes comprising the first element can be found After all the elements are defined pressing the Done button closes the window The three dimensional view of the model with the created elements 1s shown in Figure B 33 More views can be obtained using the display features explained in Section A 2 1 1 of the VecTor3 User s Manual Create suparametric Hexahedral Elements elmt node 1 2 3 4 Helmts delmt dnode Helmts delmt dnode Helmts delmt d node Total T TrTeTsiz rt Te e 5 z 2 T 5 b 7 8 14 105 106 15 poate 1 32 33 2 14 105 106 Figure B 32 The next step is to model the reinforcing bars using the two noded uniaxial truss bar element type This can be done using the button shown in Figure B 34 which opens the window sh
49. the user should enter the material properties in their respective boxes and press the Add button on the left hand side which will make the new material type appear in the box titled Type on the left hand side as well As previously explained the user can also change the properties of any material by selecting it from the list showing in the box titled Type on the left hand side making the change and then pressing the Update button on the left hand side Also the user can delete a previously defined material by selecting it from the list showing in the box titled Type on the left hand side then pressing the Delete button also on the left hand side 23 VecTor3 User s Manual A 2 3 Structure Definition This step is required to define the elements composing the structural model to be analyzed The user input in this step is saved in the structural S3R input file This step starts with the definition of the coordinates of the nodes that will be used to define the different element comprising the structural model Next those elements can be assigned specific material types from the ones defined in the Material Definition step in Section A 2 2 of the VecTor3 User s Manual The element types available for use in VecTor3 are the eight noded regular hexahedral element with right angled corners the eight noded isoparametric hexahedral element the six noded regular wedge element with right ang
50. toolbar shown in Figure A 82 But the first step is to save the analysis job if it has not been saved yet by pressing the button shown in Figure A 5 79 VecTor3 User s Manual zi izi ki vr ii Figure A 82 As explained in the Introduction section Section A 1 of the VecTor3 User s Manual there are five main input files that are required for defining the analysis job to be carried out Pressing the first button from the left in the toolbar shown in Figure A 82 featuring the red floppy disc creates and saves the VECTOR JOB VT3 AUX and VT3T AUX files Pressing the second button featuring the blue floppy disc creates and saves the structure file with the name specified in the Job Control tab in the Job Definition step Section A 2 4 1 of the VecTor3 User s Manual and the extension S3R Finally the third button featuring the green floppy disc creates and saves the load files up to five depending on the number of the loading cases defined with the names specified in the Job Control tab in the Job Definition step Section A 2 4 1 of the VecTor3 User s Manual and the extension L3R At this point VecTor3 has all the input files it needs and is ready to run Pressing the fourth button from the left in the toolbar shown in Figure A 82 titled VT starts VecTor3 Also the user will automatically be prompted to save all input files if the VT button 1s pressed dir
51. 0 702 D uy 0 5053 0 899 0 939 0 996 1 089 1 266 1 546 1 404 1 981 2 174 2 215 2 002 1 521 1 19 1 181 1 140 0 594 0 759 0 611 535 POINTS OF DISPL DATA EQUALLY SPACED AT 0 10 SEC UNITS CM 1 350 2 579 3 857 1 214 6 082 8 187 720 11 340 13 006 14 284 15 056 15 318 15 287 15 491 15 043 13 618 dit 8 948 yarad 7 320 Ja 7 3 2 729 0 847 4 005 7 481 10 399 lt 13 155 15 8753 18 068 19 461 19 783 19 515 15 645 17 615 16 05 14 277 12 141 10 821 9 992 9 466 9 220 9 078 8 960 Sa 277 8 811 581 6 547 5 235 6 684 7 115 6 698 5 857 4 770 s 1 04 7 0 874 2 090 3 405 4 534 3 239 3 431 6 310 6 918 5536 8 080 8 331 B 24 9 1465 9 545 9 524 B 714 9 960 9 729 6 113 a 073 3 294 8 675 8 506 8 489 as 6 985 1 486 3 749 1 945 0 496 203 4 162 5 380 6 602 448 434 5 633 5 397 3 984 2 263 2 021 1 453 1 278 1 096 0 270 1 017 1 432 1 484 1 350 521 1 481 1 580 2 247 2 446 2 574 _ 2 309 20 BL 3 72 4 8532 4 510 2 169 0 576 2 474 4 256 3 075 5 063 4 4245 3 218 2 2028 2 045 1 378 0 707 0 2553 0 06 0 220 0 006 086 0 085 509 4 1 433 egi L 53 sal 2 690 3 258 3 655 3 472 3 300 5 347 3 320 3 488 3 5380 5 688 4 157 4 671 4 488 5 306 r 6 025 5 965 5 624 5 135 4 495 5 410 2 285 1 509 0 69 2 0 506 1 652 2 308 3 502 4 59 9 3060 2 73 6 025 6 16 8 627 0 839 6 919 6
52. 07133 MEE 2 fi 13 16 546 Add a 120 A Delete Done 120 d Figure B 38 103 VecTor3 Sample Coupled Thermal and Structural Analysis Figure B 39 B 2 2 3 Material Type Assignment The created elements should be assigned specific materials from the material types that were previously defined This is done by pressing the button shown in Figure B 40 opening the window shown in Figure B 41 Figure B 40 104 VecTor3 Sample Coupled Thermal and Structural Analysis Assign Material Types elmt material act delmt elmi d elmi elmts delmt 1 Waa mM Gg 93 11 93 J Selection Made Pointer Window Figure B 41 The concrete elements are assigned Material 1 through the line shown in Figure B 42 the longitudinal bars are assigned Reinforcement 1 through the line shown in Figure B 43 and the ties are assigned Reinforcement 2 through the line shown in Figure B 44 When all the elements are assigned their respective materials pressing the Done button closes the window Assign Material Types elmi material act elmts d elmt elmts delmt d elmt 1 Material m sso T 1 3 3 1 Remove Done Selection Mode Pointer Window Figure B 42 Assign Material Types elmi material act H
53. 1 320 424 315 1175 842 1652 499 394 1115 834 556 1858 202 559 68 383 165 405 23F 1 3 157 738 18 147 588 58 358 233 35 235 180 39 alu 548 289 248 179 15 422 122 111 44 57 851 740 134 351 58 206 5976 941 22 544 338 052 671 052 412 _ 80 386 202 114 _ 2 8 145 218 508 212 74 67 54 217 428 402 85 131 11 146 479 459 143 188 384 293 462 989 393 905 203 1 1 432 395 392 200 829 407 144 14 62 179 4835 401 216 5378 121 147 19 102 79 104 251 244 25 160 68 200 151 147 234 307 83 150 71 75 33 115 154 111 11 42 91 129 135 47 104 29 25 224 95 fa 134 711 223 109 203 293 33 588 680 290 508 714 58 207 855 292 566 371 191 418 123 l r 467 66 192 156 283 297 490 252 5330 104 238 102 42 211 21 230 152 172 58 212 185 129 186 248 145 236 113 201 is 27 13 71 196 174 74 111 109 F2 EL 58 147 5 Appendix A Sample VECTOR EQR File 138 338 94 166 6 379 315 107 241 394 5318 116 13 6 76 435 16 830 G L 150 r0 656 962 266 905 294 36 289 42 529 437 351 209 143 348 128 439 219 289 f 244 174 154 280 10 286 140 111 57 290 284 63 197 262 69 160
54. 11 Exponential Model e FRC fib Model Code 2010 FRC Post Crack Tension Model e Not Considered e SDEM Monotonic Lee et al 2013 e SDEM Cyclic e DEM Lee et al 2011a 2011b e VEM Voo and Foster 2003 e fib Model Code 2010 Confined Strength Model e Strength Enhancement Neglected 49 VecTor3 User s Manual e Kupfer Richart Richart et al 1928 Kupfer et al 1969 e Montoya Ottosen Ottosen 1979 Montoya 2003 Selby Selby and Vecchio 1997 e Cul amp Sheikh Cui and Sheikh 2010 Dilatation Lateral Expansion e Constant Poisson s Ratio e Variable Kupfer Kupfer et al 1969 e Variable Montoya 2003 Montoya 2003 e Variable Montoya w Limit Montoya 2003 Cracking Criterion e Uniaxial Cracking Stress e Mohr Coulomb Stress Coulomb 1776 Mohr 1900 e Mohr Coulomb Strain Coulomb 1776 Mohr 1900 e CEB FIP Model e Gupta 1998 Gupta 1998 e Mohr Coulomb w Strain History Coulomb 1776 Mohr 1900 Crack Slip Check for MCET e Crack Stress Calcs Omitted e Basic DSFM MCFT e Advanced Lee 2009 Crack Width Check e Stability Check Omitted e Agg 2 5 Max Crack Width maximum aggregate size divided by 2 5 e Agg 5 0 Max Crack Width maximum aggregate size divided by 5 0 e 10 mm Max Crack Width e 5 mm Max Crack Width 2 mm Max Crack Width e mm Max Crack Width 50 VecTor3 User s Manual Crack Slip Calculation Element Slip Distortion
55. 127 254 214 39 1 29 245 192 17 122 110 29 _ 38 67 198 26 380 415 179 201 52 658 356 35 340 416 198 195 55 548 925 243 707 6584 393 344 465 1147 70 528 315 97 489 600 163 238 221 609 147 131 184 oY 350 132 254 53 184 S 251 132 88 232 645 35 211 390 203 235 12 81 98 306 324 E 61 25 214 l 252 125 109 55 zal _ Z 134 42 143 4 59 284 275 302 167 075 31 pr 47r 347 139 186 145 415 97 484 618 179 615 586 257 1310 439 308 765 317 955 515 453 13 22 3508 192 96 69 8 247 142 220 16 166 169 352 89 157 133 2 50 17 47 456 58 22r 243 124 54 57 330 265 30 85 32 144 83 200 ff 71 97 109 71 124 50 339 270 358 370 293 329 436 eff 385 267 34 139 229 207 647 yat 468 77 869 846 47 1487 729 70 re 339 1150 492 098 114 158 441 168 65 131 41 160 222 188 15 115 42 280 6 214 a FO 104 11 x 410 585 164 278 225 25 15 syl 244 1 107 42 84 7 170 13 8 143 115 53 72 FO 245 189 278 454 477 165 514 189 196 139 64 171 313 5 371 437 203 584 825 1081 166 1338 460 414 728 366 892 400 852 254 447 328 101 15 316 176 101 250 158 20 1 158 181 49 159 121
56. 4 1 292 1 91 2 176 perl 2 091 1 884 1 790 dl aL 1 811 1 940 2 118 288 2 458 2 226 3 091 53 415 3 708 4 118 4 654 2282 5 980 6 684 336 7 837 8 122 8 2530 8 224 115 8 014 8 022 8 215 8 491 8 685 8 828 8 915 ore 8 590 8 417 8 162 7 859 464 6 736 3865 6 549 5 510 5 525 5 8518 5 806 7 185 181 7 138 7 119 7 099 7 066 7 053 7 O64 6 972 260 5 506 6 448 5 O54 5 924 5 709 277 x d r 946 4 559 4 185 3 B47 3 423 2 Del 2 485 2 106 73B 1 381 1 001 590 440 0 090 0 305 0 623 852 0 5920 0 802 O 250 0 618 0 591 0 726 1 124 Tar 2 406 3 038 3 480 3 815 4 115 4 361 4 494 6 4 681 4 745 4 650 4 825 4 685 4 455 4 145 293 3 450 3 131 2 L 2 446 2 241 2 165 2 149 144 2 156 2 155 e 094 1 598 1 664 1 467 1 374 461 1 645 1 929 Z 32 2 2 703 3 051 3 448 3 706 239 3 536 3 5360 3 457 3 20 3 03 2 045 2 643 584 2 448 2 230 2 0 1 1 900 1 61 1 698 1 719 be Log T xr 1 665 1 50 Li des 1 193 0 853 452 Q 210 297 1 163 2 030 20352 2 529 2 249 147 Appendix A Sample VECTOR EQR File 2 087 m 287 2 879 3 438 3 60 4 119 4 145 3 681 3 457 3 706 5 7 3 358 2 865 2 615 2 422 nunu 1 6 1 80 0 927 802 0 656 0 4 73 O 430 0 157 0 125 0 437 D 773 1 205 1 6541 1 958 2 039 p 533 1 946 I 512 l Z32 1 520 1 189 1 105 1 038 0 505 0 758
57. 5 1 mm which will be multiplied by the load factors defined in the Analysis Job Control Parameters as explained in Section B 2 3 1 of the VecTor3 Sample Coupled Thermal and Structural Analysis Again the loading case number Case 3 is shown at the left hand side of the window for referencing purposes Apply Support Displacements Case node D O F DISPL mm H nodes dnode d din nodes dnode ddip T nodes di node d disp 3 68 ye vc zc o B NC Y 1 Ho Bi 18 Selection Mode Pointer window Figure B 70 Figure B 71 shows the applied lateral displacements along the height of the column and Figure B 72 shows them on a cross section 127 VecTor3 Sample Coupled Thermal and Structural Analysis Figure B 71 Figure B 72 128 VecTor3 Sample Coupled Thermal and Structural Analysis As previously explained only one loading profile needs to be defined for Case 3 and Case 4 as they both involve the same type of loading and at the same nodes but with different load factors In Section B 2 3 1 of the VecTor3 Sample Coupled Thermal and Structural Analysis both Case 3 and Case 4 were assigned the same Load file name which was set to Lateral There are three ways to handle this The first one is to replicate the loading definition of Case 3 for Case 4 in the Load Definition step The second one is to define Case 3 only and opt not to save t
58. 8 915 166 465 578 4753 Sample VECTOR EQR File 606 962 988 363 746 468 427 281 243 418 643 471 280 40 297 67 267 791 584 1008 1384 574 303 66 1899 2101 1984 1202 714 385 851 453 28 1197 13772 1385 544 698 920 259 37 226 309 252 92 273 210 67 126 416 700 130 125 89 426 298 96 257 377 307 36 138 290 159 264 398 308 430 504 314 505 237 386 361 20 255 149 379 207 496 683 928 55 568 376 506 518 501 377 310 220 666 754 315 226 41 76 335 429 459 501 366 238 160 97 364 462 573 50 64 17 223 76 37 485 240 62 297 442 535 331 304 190 359 439 483 225 165 125 82 257 367 159 50 88 151 91 38 70 221 460 345 591 770 390 248 125 37 69 81 303 367 415 22 102 188 33 173 243 276 431 484 8 280 533 71 56 40 103 258 364 67 107 213 450 503 536 2072 318 448 87 107 299 165 49 252 51 242 301 287 317 257 722 812 784 33 228 410 790 948 917 735 615 363 51 86 99 362 284 160 503 453 367 491 299 117 142 451 385 138 109 305 708 1325 385 1826 85 488 1445 966 415 46 ff 1566 115 64 488 L 337 265 393 181 430 819 205 2rd 459 Ba 309 303 FU 302 187 221 3 fe 122 448 115 124 16 25 805 853 154 380 _ 73 220 546 813 69 481 5 Z 460 567 482 sual 231 146 TE 580 634 151 164 15 275 al 21 39 2
59. 847 474 1072 852 315 276 460 326 307 124 135 132 131 41 5 550 4 11 00 1099 835 824 1446 95 826 775 284 330 326 521 429 953 240 55 209 256 323 930 874 673 517 181 17 431 84 792 405 4 64 161 6 92 260 929 262 113 z 460 180 434 185 77 rog 1 602 1098 908 285 273 a5 253 700 141 66 46 180 l 401 492 15 1059 858 1092 560 1348 542 321 344 354 PEZ 351 634 260 529 934 125 169 439 261 676 1068 613 623 206 117 46 583 4 471 235 _ 2 71 420 132 181 103 131 853 96 175 471 353 229 307 427 7 32 1138 234 313 787 221 54 540 334 144 830 61 81 162 15 515 4 31 479 1070 636 1325 225 1265 1059 3 138 919 1181 320 698 486 864 588 15 230 509 615 1079 1170 258 794 07 461 140 441 405 414 167 439 661 140 366 240 695 578 BaL 470 389 199 364 032 149 1001 1223 134 205 715 52 108 935 937 161 938 133 156 23 1 51 569 562 580 999 380 1485 1481 1179 770 e 183 1109 1592 690 810 764 946 861 171 590 482 1022 770 1035 24 5630 132 716 107 11 533 138 oY 125 558 117 291 407 875 396 961 38 232 53 462 602 123 1278 1117 337 r al 1 3 300 43 1022 262 416 49 85 25 330 _ 572 280 188 936 155
60. Actions Frame Concentrated Loads Frame Uniform Loads Mone l NON ON NON HN M e a Element Filters Rectangular Quadrilateral Triangular Link Interface Hexahedral Wedge Heterosis Ring Bar Truss Figure A 8 As can be seen in this window the user 1s allowed to select what components of the structural model and loading conditions are to be displayed This can be done for the nodes in the Node Options collective frame on the left hand side of the window and for the elements in the Element Options collective frame on the right hand side of the window The collective frame in the lower part titled Element Filters allows the user to select the elements that are required to be excluded from the view to be created Not all those element types and loading conditions apply to VecTor3 but the ones that are available in VecTor3 will be discussed in detail in the following steps After selecting the VecTor3 User s Manual options of preference for the view to be created pressing the Apply button creates the desired view and pressing the Done button closes the window The next six buttons in the toolbar shown in Figure A 6 are responsible for providing better viewing features for three dimensional structures The seventh eighth and ninth buttons from the left titled XY YZ and XZ respectively allow the use
61. E ENT NE Hepetitions RS SEEN Hq emi r Cyclic Inc factor p m Initial Load Stage s me ii r Analysis Parameters seed File Name MULL Convergence Criteria Displacements Weighted Average gt Max no of Iterations 160 Analysis Mode Static Nonlinear Load Step Dynamic Averaging Factor 0 6 Results Files ASCII Files Dny o v Convergence Limit 1 00001 Modeling Format Stand Alone Modeling Figure B 46 B 2 3 1 Analysis Job Control Parameters Definition In the first tab in the Job Definition window titled Job Control four main parts need to be defined namely Job Data Structure Data Loading Data and Analysis Parameters In the collective frame titled Job Data the job file name the JOB file name should always be left as the default entry VecTor The job title can be chosen as Column 1582 and the job date can be entered In its box for referencing purposes In the collective frame titled Structural Data the structure file name the S3R file can be left unchanged as the default entry Struct the structure title can be selected as Column 1582 and the structure type needs to be left as the default entry Solid 3 D 107 VecTor3 Sample Coupled Thermal and Structural Analysis It should be noted that all the selected titles in those two collective frames are arbitrary and can be selecte
62. Elastic Modulus Ec Cylinder Strain at Pc 0 me Poisson s Ratio 2 Thermal Expansion Coefficient Cc 0 Maximum Aggregate Size a e o mm Component o Ages Thermal Diffusivity Ec l mts Average Crack Spacing perpendicular to x reinforcement Se E mm perpendicular to y reinforcement 5 mm perpendicular to z reinfarcement 52 mm Color E Reinforced concrete material types to be used for solid elements only Enter T for VT 3 default value k Cancel Figure A 14 This window enables the user to select the base material type from a drop list titled Reference Type from two options reinforced concrete and structural steel Figure A 14 shows the input boxes available for the Reinforced Concrete option As noted in the footnotes in the window the parameters designated with an asterisk are not mandatory as VecTor3 imposes default values should the user opts to leave them vacant or with a value of zero For concrete material properties only the Cylinder Compressive Strength fc is mandatory The following formulae are used to calculate default values for the other properties depending on the input value of the cylinder compressive strength 15 00 1 3320 f 6900 2 11 VecTor3 User s Manual gi 7 5 x 10 36 1 80 3 where f is the Tensile Strength cracking
63. Figure B 67 shows a section of the column along its height showing the applied axial loads at the top of the column Apply Nodal Loads Case node Fx Fy Fz Hnodesdnode dFx dFy dFz if nodes d node dFy dFz Hnodesdnode dfs dFy dFz 2 s o fem 2 T o o o z m o o T T D 0 D Selection Mode Pointer window Figure B 63 124 VecTor3 Sample Coupled Thermal and Structural Analysis Apply Nodal Loads Case node Fx Fy Fz nodes d node dFy dFz Hnodesdnode dFx dFy dFz nodesdnode dFy dFz 2 fez o ssa r r o o o 2 T T lu lolop Selection Mode Pointer Window Figure B 64 Apply Nodal Loads Case node Fx Fy Fz nodes d node dFx dFy dFz Hnodesdnode dFy dFz Hnodesdnode dfs dF dFz 2 es o fo sea 5 13 o o o f2fi2fofofo fififofofo Apply RM E Selection Mode Pointer Window Figure B 65 Apply Nodal Loads Case node Fx Fy Fz Hnodesdnode dFx dFy dFz nodes d node dFy dFz nodesdnode dFx dF dFz 2 eo o o ma n 1 T9 To o s vf Arb Selection Mode Pointer Window Figure B 66 To define the third loading case Case 3 responsible for the lateral loading the third button from the left in the toolbar shown in Figure B 53 with the number 3 is pressed With that button pressed down all the loads to be defined will be included in both Case
64. L Load case title Enter nad case title Enter nad case title Enter ad case tile ENEE EE Initial factor D oo o Final factor D n n Inc factor 7 Load bp Monotonic z Monotonics z Monotonic Monetoni zf Monotonics zl Repetitions ME Em p m G Cyclic Inc factor m mmm n Initial Load Stage 1 7 a Analysis Parameters seed File Mame NULL Convergence Criteria Displacements Weighted Average gt no of Iterations Analysis Mode Static Nonlinear Load Step Dynamic Averaging Factor V Results Files ASCII Files Ony Convergence Limit Modeling Format Stand Alone Modeling v Cancel Figure A 53 As will be explained later there are multiple analysis modes available in VecTor3 which can be selected from the drop list titled Analysis Mode in the lower part of this tab on the right hand side The input entries explained above apply to the Linear Elastic and the Static Nonlinear Load Step modes both of which will be explained later For the other analysis modes which all involve time stepping procedure the Initial factor refers to the load factor throughout the analysis on which no increment will be applied the entry of the Final factor is discarded and the Inc factor refers to the time step time increment to be used in the analysis in seconds The
65. LC 8101 07 2007 standard temperature fire curve The setup of the test required the column s top and bottom edges to be covered by insulation thus only a 3175 mm length of the 3760 mm long column was subjected to fire The mechanical and thermal loading setup of Column 1582 is shown in Figure B 5 84 VecTor3 Sample Coupled Thermal and Structural Analysis N UY A t Qs O o o o o Uu gt c O 2 O O e me A S O e 30 60 90 120 150 Time Elapsed minutes Figure B 3 Figure B 4 For the VecTor3 analysis only half of the cross section needs to be modelled taking advantage of the geometric and loading symmetry of the column The finite element discretization shown in Figure B 6 will be used to create the model where the black dots mark the locations of the longitudinal reinforcing bars Longitudinally the column will be discretized into 75 elements with a height of 50 13 mm each to achieve a total height of 3760 mm for the model The 13 ties will be modelled at 300 mm spacings instead of the actual 305 mm with appropriate compensation in cross sectional area in 85 VecTor3 Sample Coupled Thermal and Structural Analysis order to fit in the selected finite element discretization This means that a tie will be located at every sixth element along the height Lateral Load 792 305 3175 q A S ANS N ON O 2 2 O un oo e en
66. Lie and Kodur 1996 for SFRC Shin et al 2002 Kodur and Sultan 2003 for HSC Kodur and Sultan 2003 for SFR HSC The Eurocode EN 1992 1 2 2004 2005 58 VecTor3 User s Manual Thermal conductivity e The ASCE Manual of Practice Structural Fire Protection by T T Lie 1992 e The Eurocode ENV 1992 1 2 1995 1996 e Lie and Kodur 1996 for SFRC e Shin et al 2002 e Kodur and Sultan 2003 for HSC e Kodur and Sultan 2003 for SFR HSC e Kodur et al 2004 for HSC e The Eurocode EN 1992 1 2 2004 2005 e Kodur and Khalig 2011 for HSC Specific heat capacity e The ASCE Manual of Practice Structural Fire Protection by T T Lie 1992 e The Eurocode ENV 1992 1 2 1995 1996 e Shin et al 2002 e Kodur and Sultan 2003 for HSC e Kodur and Sultan 2003 for SFR HSC e The Eurocode EN 1992 1 2 2004 2005 e Kodur and Khalig 2011 for HSC Porosity e Gawin et al 1999 e Toumi and Resheidat 2010 Permeability e Gawin et al 1999 e Tenchev et al 2001 Compressive strength at elevated temperatures e No modification factor e Lie and Lin 1985 the ASCE Manual of Practice Structural Fire Protection by T T Lie 1992 59 VecTor3 User s Manual Bazant and Chern 1987 L and Guo 1993 The Eurocode ENV 1992 1 2 1995 1996 Lie and Kodur 1996 for SFRC Chang and Jau 2001 for siliceous aggregates Cheng et al 2004 for HSC Th
67. Loading Considered id Strain Rate Effects Lone Steel Inde n c Structural D amping Mat Considered Reset Options Geometic Nonlinearity Considered Basic Crack Process Uniform Advanced Cancel Figure B 48 112 VecTor3 Sample Coupled Thermal and Structural Analysis Figure B 49 shows the optimum options for the current analysis as follows Concrete Models Compression Pre Peak HSC Popovics Compression Post Peak Modified Park Kent Compression Softening Vecchio 1992 A e1 e2 Form Linear w No Plastic Offsets Reinforcement Models Reinforcement Hysteretic Response Elastic Hardening Curvilinear Reinforcement Dowel Action Tassios Crack Slip Reinforcement Buckling Akkaya 2012 Refined Dhakal Maekawa Bond Models 113 VecTor3 Sample Coupled Thermal and Structural Analysis Analysis Models Define Job Job Control Models Ausiliary Ausiliary Thermal Concrete Models Compression Pre Peak HSC Popovics Confined Strength K pfer Richat vl Compression Post Peak Modified Park Kent vl Dilation Variable Kupfer Compression Softening Vecchio 1992 4 el e2 Form Cracking Criterion MohrCoulomb Stress v Crack Stress Calc Basic DSFMAMCFT vi Crack Width Check Agg 2 5 Crack Width vl Tension Stiffening Modified Bentz2003 vi Crack Slip Cale walaven Monotonic Tension Softening Bilinsar vl Creep and Relaxation Not Ava
68. Modulus Ec Reinforcement Ratio rho Cylinder Strain at Pc eo Reinforcement Diameter Db Poisson s Ratio Mu Thermal Expansion Coefficient Cc 10 s x Ultimate Strength Fu Maximum Aggregate Size a Reinforcement Components ElastelMedulu Es Density Component Thermal Fe Strain Hardening Strain esh Average Crack Spacing Umate Set Su perpendicular to relnforcement 5x Thermal Expansion Coefficient Cs l AE perpendicular to y reinforcement Su perpendicular to z reinforcement 52 Frestrain Dep 0 ma Unsupported Length Ratio Bt 0 Color Reinforced concrete material types to be used for solid elements only Enter for WT3 default value Cancel Figure B 11 B 2 1 2 Discrete Reinforcement Material Properties Definition Using the button shown in Figure B 12 the properties of the discrete reinforcement materials can be added Pressing the button opens the window shown in Figure B 13 Two types of discrete reinforcement material should be added in this model one for the longitudinal bars and another for the ties Figure B 12 90 VecTor3 Sample Coupled Thermal and Structural Analysis Define Reinforcement Properties Reinforcement Type Reinforcement Properties Tune i Reference Type Ductile Steel Heinforeement Lross Sechonal Area Reinforcement Diameter Db eld Strength Fy Ultimate Strength
69. Repetitions in this case refers to the number of time sub steps in each time step This means that the time step entered in the Inc factor box will be divided by the number of time sub steps entered in the Repetitions box and a separate analysis will be run at time steps equal to the outcome of this calculation Yet results output files will 40 VecTor3 User s Manual only be generated at the time steps time increments entered in the Inc factor box The aim of this feature 1s to enable the user to run the dynamic analysis or heat transfer analysis with smaller time steps to achieve a more accurate and stable analysis but not have an unnecessary large number of results output files The final input box in this collective frame 15 titled Initial load stage This entry allows the user to specify the load stage at which the current loading case will be started Since five loading cases are allowed to be run simultaneously in the same analysis job the user can choose to start a certain loading case midway or at the end of the application of another loading case This can be done by specifying the Initial load stage of the loading case If the user needs all the loading cases to start simultaneously at the beginning of the analysis the Initial load stage should be left as 1 which 1s the default value The fourth part in this tab is for specifying the analysis parameters for the analysis job In ord
70. VecTor3 A User s Manual B Sample Coupled Thermal and Structural Analysis Fady ElMohandes Frank J Vecchio November 2013 VecTor3 Table of Content bis p E as 1 11 As sor Se Mania A PO E O CO E a daaa l A A IA 2 2 2 Modelim Mai EPS 4 2 T ub s n n eas 4 balal aaa l d 6 2 2 Water al DePOTUOT oo lisis uu us b al bal 10 A 2 2 1 Base Material Properties Definition 10 A 2 2 2 Discrete Reinforcement Material Properties Definition 18 0 Bond Properties Defmrtlol aid 2 Delinilioii EET DU ELTE 24 DO Wiener et ON 25 AZo Ax Deflinin Node 25 AF2 5 1 2 Applyine Node Resiram b RE e ees 27 A 2 3 1 3 Applying Node Constraints Linking Nodes 28 2 3 2 Element DENM NON seia UR a E ER lab Que alatus 30 2 20 Material Type ASSISTIDIOTL i u RAR dd 34 wa JOA AO adam auch 36 11 VecTor3 A 2 4 1 Analysis Job Control Parameters Definition 37 A 2 4 2 Structural Analysis Models Definition 46 A 2 4 3 Auxiliary Parameters Deflnition 53 A 2 4 4 Auxiliary Thermal Paramet
71. Yield Stress f and Ultimate Stress fu respectively For the other properties same default values are used as explained for the longitudinal bars material type Again the Add button is pressed and Reinforcement 2 appears in the Reinforcement Type list on the left hand side of the window as shown in Figure B 15 Once all the material types are added the OK button is pressed to close the window Define Reinforcement Properties Reinforcement Reinforcement Properties Tune l Reference Type Steel Reinforcement Heinforcement 1 x Reinforcement 2 poet CN ma Update l Reinforcement Diameter Db 1 mm Delet _Delete eld Strength Fy 427 MPa Ultimate Strength Fu E7 MPa Elastic Modulus Es 200000 MPa Strain Hardening Strain esh E me Ultimate Strain eu 200 me Thermal Expansion Coefficient Cs i YE Prestrain Dep li me Unsupported Length Ratio bt 0 Reinforcement material types to be used for truss elements only k Cancel Figure B 15 93 VecTor3 Sample Coupled Thermal and Structural Analysis B 2 1 3 Bond Properties Definition Since bond slip is not expected to be significant in this analysis bond between concrete and discrete reinforcing bars will not be discretely modelled Therefore this step will be skipped B 2 2 Structure Definition B 2 2 1 Node Definition B 2 2 1 1 Defining Node Coordi
72. a 1111111 T Newmark Constant Not Considered Not Considered Not Considered E Reset Default Cancel Figure B 50 115 VecTor3 Sample Coupled Thermal and Structural Analysis The input entered for the properties of concrete related to the thermal analysis will be overridden by the input entered in the Auxiliary Thermal tab Therefore the default entries can be left unchanged This applies to the Concrete Aggregate Type Concrete Thermal Conductivity and Thermal Time Stepping Factor All the other entries in the General Dynamic Analysis and Tension Softening collective frames do not relate to this analysis hence they can be left unchanged B 2 3 4 Auxiliary Thermal Parameters Definition The next tab in the Job Definition titled Auxiliary Thermal is shown in Figure B 51 This tab allows the user to define several additional parameters that are required for the coupled thermal and structural analysis The default entries are set to the models and criteria that have proven reasonable agreement with experimental results based on the experience of the developers of VecTor3 116 VecTor3 Sample Coupled Thermal and Structural Analysis Define Job Job Control Models Auxiliary Auxiliary Thermal Thermal 4nalysis Concrete Thermal Properties Concrete Moisture Transfer
73. ain and 0 30 for Poisson s ratio The density will not be assigned a default value for the same reason that was explained earlier for the Reinforced Concrete material type Figure A 17 shows the shape of a typical stress strain curve for structural steel showing the main material properties required to compile the curve where f and are the stress and strain in steel respectively For structural steel as well the thermal expansion coefficient entered in this window will be overridden by the value calculated according to the model to be chosen for the temperature dependent thermal expansion coefficient of steel Thermal diffusivity of steel entered in this window will also be discarded for the same reason that was explained for the Reinforced Concrete material type 13 VecTor3 User s Manual Define Material Properties Material Types Maternal Properties Type Reference Type Structural Steel z Yield Strength Fy l MPa Ultimate Strength Fu 0 MPa Elastic Modulus Es Strain Hardening Strain esh Ultimate Strain eu Thermal Expansion Coefficient Es Poisson s Ratio Density Thermal Diffusivity Ez Unsupported Length Ratio b t LULLLLLLLIL Color Reinforced concrete material types to be used for solid elements anl Enter for VT 3 default value k Cancel Figure A 16 Esh Eu Figure A 17 14 VecTor3 User s Manual After the material properties
74. all averaging factor is required for the analysis of reinforced concrete members that are subjected to uniform stresses without any weak or overly stressed part where failure 1s expected to initiate such as columns subjected to pure axial loads It should be noted that in VecTor3 if the number of iterations selected by the user 1s greater than 100 the averaging factor selected 1s reduced by 5 every 5 iterations It has been found that this constantly changing averaging factor leads to faster convergence and a more stable analysis This 1s because the analysis starts with a large averaging factor 43 VecTor3 User s Manual which results in faster convergence but this averaging factor slowly decreases in order to fine tune for better convergence Also in this user input part which is responsible for the analysis parameters of the analysis job the drop list titled Analysis mode is available for the user to select the type of the analysis required to be carried out The options available are 1 Linear Elastic where a static loading procedure that 1s independent of the loading rate and time is followed A linear elastic analysis is followed for both concrete and steel material behaviour 2 Static Nonlinear Load Step where a static loading procedure that 1s independent of the loading rate and time 1s followed The material behaviour is nonlinear 3 Static Nonlinear Time Step where a static time ste
75. at the bottom of the window then pressing the Delete button on the right hand side of the window When the input of all the required elements is entered pressing the Done button on the right hand side closes the window A 2 3 3 Material Type Assignment In this step the elements that were defined in the Elements Definition step Section A 2 3 2 of the VecTor3 User s Manual are assigned material types from the types that were defined in the Material Definition step Section A 2 2 of the VecTor3 User s Manual This can be done through the eighteenth button from the left in the toolbar shown in Figure A 28 The shape of the button 15 shown in Figure A 47 Figure A 47 Pressing this button opens the window shown in Figure A 48 where the ID number of the element can be entered in the box titled elmt and a material type can be assigned to it from the drop list titled Material The drop list includes all the material types that were defined in the Material Definition step Section A 2 2 of the VecTor3 User s Manual including the base material types the discrete reinforcement material types and the bond types The user can choose to deactivate the element in the analysis job by unticking the box titled Act Deactivated elements are considered to be completely non existent in the current analysis but can be activated in subsequent analyses 34 VecTor3 User s Manual Assign Mat
76. aterial Definition This step 1s required for defining the material properties to be used for the different elements that will be defined afterwards in order to compose the structural model to be analyzed The user input in this step is saved in the structural S3R input file Three main material types can be defined in VecTor3 with only the first one the base material being mandatory for proceeding with the analysis Those material types are the base material the discrete reinforcement material and the bond material The buttons in the toolbar shown in Figure A 12 are responsible for all user input data for the Material Definition step ie Figure A 12 A 2 2 1 Base Material Properties Definition This step is required in order to define the base material type of the structural model The options available in VecTor3 for the base material are concrete or structural steel Defining at least one base material 1s mandatory for proceeding with the analysis job Pressing the button shown in Figure A 13 which is the third button from the left in the toolbar shown in Figure A 4 the window shown in Figure A 14 opens allowing the user to input the material properties 10 VecTor3 User s Manual Figure A 13 Define Material Properties Maternal Types Material Properties Type Reference Type Reinforced Concrete x Cylinder Compressive Strength Fe l MPa Tensile Strength Ft MPa Initial Tangent
77. ation Method drop list namely Newmark Constant and Newmark Linear The constant factors y and D which determine the variation of acceleration within the time step are set according to this selection Newmark Constant refers to constant acceleration within the time step based on an average of its value at the beginning and the end of the time step For this option y is set to 1 and p is set to 1 Newmark Linear refers to linear variation of the acceleration within the time step For this option y is set to 1 and p is set to 1 The next three entries titled Ground Acceleration in X Direction Ground Acceleration in Y Direction and Ground Acceleration in Z Direction are responsible for determining the directions in which the ground acceleration record 1s to be applied This type of structural analysis involving a ground acceleration record requires the selection of a special analysis type as explained earlier and a special loading input as will be explained later Finally the lower part on the right hand side of the tab presents a collective frame titled Material Resistance Creep Factors The first four entries in this collective frame aim at facilitating the structural design and structural assessment processes where a resistance factor can be assigned to the material properties of the various types of material that were defined in the Material Definition step including concre
78. bars Embedded Smooth Rebars Unbonded Bars or Tendons and Unbonded Tendons w Friction Losses Three other options are available to provide more flexibility for the user The first two are the Interface or Bonded Plates Fabrics and the Embedded Bars Custom Input options where the user can specify custom bond stress slip curve using three key points to define the curve The last option is the No Slip option where the user can specify perfect bond no slippage for specific bond types which will override the global model that will be selected later for the structural analysis in the Structural Analysis Models Definition step in Section A 2 4 2 The properties required by the user in this window besides the type of reinforcing bar are the Confinement Pressure Factor which defines the level of confinement of concrete in the section Min Bar Clear Cover Spacing which defines the minimum clear cover or spacing of the reinforcing bar and the Number of Reinforcement Layers Through the Depth of the concrete section It should be noted that VecTor3 has the ability to calculate these properties automatically should the user assigns them a value of zero Finally the user is required to tick the Hooked Bar checkbox if the bars used are hooked ended When the properties are entered the user 1s required to press the Add button on the left hand side of the window shown in F
79. be used in the analysis It will be overridden by a value that will be calculated according to a specific temperature dependent model that will be chosen for the thermal expansion coefficient of concrete as will be explained later Also the value entered for the Thermal Diffusivity a will be discarded since separate temperature dependent models for the thermal conductivity specific heat capacity and density will be used instead Those models will be defined later Should the user choose Structural Steel as the Reference Type in the window shown in Figure A 14 the properties defining the material will change to steel material properties as shown in Figure A 16 The user is then required to enter the various material properties of structural steel including the Yield Strength fy Ultimate Strength fu Elastic Modulus Young s Modulus Es Strain Hardening Strain Esh Ultimate Strain u Poisson s Ratio u Density p and Unsupported Length Ratio b t for buckling consideration The yield strength is a mandatory input value but for the other properties 1f left vacant or are assigned a value of zero the following default values and formulae will be used to calculate them one and half times the value of the yield stress for the ultimate strength 200 000 MPa for the elastic Young s modulus 5 0 millistrain for the strain hardening strain 150 0 millistrain for the ultimate str
80. cTor3 User s Manual Y FormWorks Workspace1 d Fie Edit View Job Structure Li Analysis Window Help Dae Gaqgaa o n Nj Ki LEY i Figure A 3 MEAR St e a m o 8 nl 9 faf 55 B Be BP Ba 1 gt Figure A 4 Figure A 5 A 2 1 1 Display Features Formworks Plus provides two and three dimensional graphical representation of the structural model defined by the user This helps the user to visualize the structure and the loading profiles as they are defined With the definition of every structural component or loading condition as will be explained in the following steps a graphical representation is displayed in the workspace view VecTor3 User s Manual Formvvorks Plus also provides many features that facilitate the control of the user over the properties of the graphical representation to be displayed These features can be accessed at any point through the analysis job definition through the buttons of the toolbar shown in Figure A 6 AR amp Q amp ooh EJ Evi E EN Figure A 6 The first button from the left titled Zoom All allows the user to view the entire structural model in the workspace view This can also be done without pressing the Zoom All button by double clicking the left mouse button The second and third buttons titled Zoom In and Zoom Out respectively allow the user to incrementally view the structural model in a larger or smaller scale resp
81. ce Iteration convergence 1 0 1183926 01 2 0 1230996 03 3 0 11 594E 05 dl 0 1104 E 0 5 0 1039356 08 O 9 396RE 12 i 48114 7E 14 8 0 239304 15 structural Analysis convergence Iteration Convergence 1 1 218516 1 679316 9 999999 999999 9 999994 1 153831 2 1 014961 1 007398 1 002158 1 155551 9 999994 1 115678 3 1 008226 1 001 774 1 002948 1 001153 1 000746 1 091576 dl 1 001488 1 001596 1 00 64 1 000000 1 000160 1 O64 744 5 1 003917 1 001407 1 002330 1 000000 1 000255 1 047567 1 000771 1 001216 1 002010 1 000000 1 000245 l 034420 n 1 000581 1 001043 1 001721 1 000000 1 000217 1 027052 1 000446 1 000890 1 001468 1 000000 1 000186 1 038493 a 1 000360 1 000759 1 001250 1 000000 1 000155 1 042812 10 1 000283 1 000645 1 001 061 1 000000 1 000126 1 039921 11 1 000235 1 00054 4 1 000804 1 000000 1 000101 1 037565 d 1 000156 1 000466 1 000757 1 000000 1 000080 1 035531 13 1 000163 1 000396 1 000550 1 000000 1 000062 1 033876 14 1 0007 51 1 000335 1 000551 1 000000 1 00004 7 1 032533 13 1 000124 1 000282 1 000463 1 000000 1 000036 1 039696 16 1 0000927 1 000434 1 000393 1 000000 1 000028 1 0389242 17 1 000102 1 000202 1 000331 1 000000 1 000014 1 038275 la 1 005070 1 00016 1 0002 78 1 000000 1 000012 1 025646 18 1 000141 1 000145 1 000235 1 000000 1 000000 1 028754 20 1 000096 1 00011 4 1 0001 946 1 000000 1 000005 1 028236 STORING LOAD STAGE RESULTS IM ASCII FILE T3 Q2 A3E For future reference all the data
82. ce time key point on the impulse force time loading record The direction DOF should be maintained the same for each sequence of key points entries for each node Should the same node be subjected to impulse loads in more than one direction the record of the first direction should be entered in full for the entire time domain then the entries of the next record can be entered To allow the user to check the input for possible input errors the user can select the entry of a certain node in the box in the lower part of the window then press the Graph button on the right hand side of the window This will generate a graphical representation of the force time impulse loading record at that node The user can specify the nodes with impulse loading records individually one at a time or specify the ID number of a certain node with an impulse loading record and extrapolate the input to other nodes with the same record This can be done by specifying the number of nodes nodes and the increment in the ID number of the subsequent nodes d node This extrapolation can be done in three levels simultaneously using the three sets of boxes available for user input as shown in Figure A 77 The Pointer and Window selection options that were explained earlier are also available 76 VecTor3 User s Manual A 2 5 10 Ground Acceleration The sixteenth button from the left in the toolbar shown in Figure A 57 who
83. d la EE 11 17 15 fs ls 13 TL s 862 334 848 224 320 589 824 227 162 787 865 648 295 185 831 34 121 005 216 899 855 805 108 661 397 353 999 955 hoe 216 962 297 386 153 zl 40 497 754 814 998 411 255 294 859 246 733 fl 929 754 sl 859 146 de 18 ds B B 3 z 4 zT 14 26 s 340 272 EF B90 585 292 862 xag 4060 388 690 031 509 098 162 979 B72 saly 29 061 373 2626 097 324 2068 084 019 604 el 998 148 296 5394 220 5646 3411 2 335 Sed 476 24 205 pers 221 471 021 920 351 322 687 LES 2256 5655 sale 080 315 DGF 324 578 351 560 148 905 364 075 378 482 145 194 606 337 649 a 22 14 B B 5 z m O L 2 7 24 sizs 55 915 2360 lee 339 2655 613 046 499 552 4596 167 2315 R 206 631 570 ado 2392 828 5658 ef s122 052 325 302 890 251 2675 327 431 395 382 109 148 641 910 352 587 9307 s 2774 506 583 169 482 3 042 628 989 323 sl 838 908 160 O04 252 503 506 0353 959 323 255 028 926 EIN 200 361 287 048 9 23 l4 5 Es ds O sd 2 da 16 21 l1 1 10 2 Y
84. d according to the user s preference except for the job file name VecTor In the third collective frame titled Loading Data the title of the output files generated by the analysis can be entered in the box titled Load series ID The default entry D can be left unchanged In the box titled Starting load stage no the default value of 1 can be left unchanged as well For the last box in this line titled No of load stages a value of 500 will be selected This value depends on the load increment applied in each load stage Since the time increment will be selected as 60 seconds 1 minute and the column is expected to fail in less than eight hours 500 load stages should be enough for the analysis For defining the analysis loading scheme for the loading conditions that will be defined later four loading cases will be defined Technically there are only three distinct loading cases involved in this analysis namely axial lateral and thermal loading However since the rate of the lateral loading changes through the test after 25 minutes from the start of loading as shown in the lateral loading profile shown in Figure B 3 the loading case of the lateral loading will have to be divided into two separate loading cases one for each loading rate This means that a lateral loading case will be defined for the first 25 minutes first 25 load stages of the test and another one will be defined for the
85. d side Of the window When all the input entries are entered pressing the Done button on the right hand side of the window closes the window A 2 3 1 2 Applying Node Restraints This step enables the user to apply certain restraints on specific nodes in the structural model in order to model the support conditions of the structure to be analyzed Pressing the fourth button from the left in the toolbar shown in Figure A 28 shown in Figure A 35 opens the window shown in Figure A 36 The user can specify the ID number of a node and the directions or the degrees of freedom DOFs in which the node needs to be restrained in the global X Y and Z directions by ticking the boxes titled DX DY and DZ respectively Ticked directions mean that the node will be restrained in that direction while unticked ones mean that the node will be free to displace in that direction 27 VecTor3 User s Manual Figure A 35 Create Support Restraints node Restrain d o f rodes d node modes d node nodes node Total oP P dle ET Hi 11 MM add Done Selection Mode Pointer Window Figure A 36 As previously explained also in this window the user can define the nodes restraints individually one at a time or specify the ID number of a certain node with certain restraints and extrapolate the same restraints to other nodes by specifying the number of nodes having the same restraints nod
86. e Eurocode EN 1992 1 2 2004 2005 Li and Purkiss 2005 Hertz 2005 Aslani and Bastami 2011 Residual compressive strength No modification factor Lie et al 1986 Hertz 2005 Chang et al 2006 Model 1 Chang et al 2006 Model 2 Strain corresponding to peak compressive stress No modification factor Lie and Lin 1985 the ASCE Manual of Practice Structural Fire Protection by T T Lie 1992 Bazant and Chern 1987 The Eurocode ENV 1992 1 2 1995 1996 Lie and Kodur 1996 for SFRC Cheng et al 2004 for HSC The Eurocode EN 1992 1 2 2004 2005 Li and Purkiss 2005 Residual strain corresponding to peak compressive stress No modification factor 60 VecTor3 User s Manual e Chang et al 2006 Initial modulus of elasticity e No modification factor e Modification factor of peak compressive stress Modification factor of strain corresponding to peak compressive stress e Bazant and Chern 1987 Lu 1989 e Li and Guo 1993 e Li and Purkiss 2005 e Aslani and Bastami 2011 Residual initial modulus of elasticity strength e No modification factor e Chang et al 2006 Model 1 e Chang et al 2006 Model 2 Tensile strength e No modification factor e Bazant and Chern 1987 e Li and Guo 1993 e The Eurocode ENV 1992 1 2 1995 1996 e The Eurocode EN 1992 1 2 2004 2005 e Song et al 2007 e Moftah 2008 e Dwaikat and Kodur 2009 e Aslan
87. e load types for all the five available loading cases defined the user can view a summary of each of those loading case This can be done by selecting the loading case from the buttons shown in Figure A 58 then pressing the first button from the left in the toolbar shown in Figure A 57 whose shape is shown in Figure A 80 Figure A 80 Pressing this button opens the window shown in Figure A 81 where the Load Case Title Load Case Number Load Case File Name and Structure Title are shown together with the number of loads of each type that are applied on the structural model 78 VecTor3 User s Manual Load Information Load Case Title Enter load case title Load Case Number 1 Load Case File Name Case Structure Title Enter Structure Title Loading Nodal Loads Nodal Loads Support Displacements Lumped Masses Impulse Forces Temperature Loads Element Loads Gravity Loads Element Temperatures Concrete Prestrains Ingress Pressures Uniformly Distributed Loads Hydrostatic loads Time Varying Temperatures Frame End Actions Frame Concentrated Loads pp gm tu A AA c Frame Uniform Loads Ground 4cceleration Record Mone Cancel Figure A 81 A 2 6 Saving the Input Files and Running VecTor3 After defining all the parts of the analysis job by following the previous steps the structural model becomes ready to be analyzed This can be done using the
88. e on Bond In Concrete Paisley College of Technology Scotland Mostafae1 H Leroux P and Lafrance P S 2012 Fire Endurance Of A Reinforced Concrete Column Under Both Axial And Lateral Loads NRC Report IRC RR 327 National Research Council Canada NRC Ottawa ON 31 p Newmark N M 1959 A method of computation for structural dynamics Journal of Engineering Mechanics American Society of Civil Engineers ASCE 85 EM3 67 94 Okamura H and Maekawa K 1991 Nonlinear Analysis and Constitutive Models of Reinforced Concrete Tokyo Gihodo Shuppan Co Ottosen N S 1979 Constitutive model for short time loading of concrete Journal of the Engineering Mechanics Division American Society of Civil Engineers ASCE 105 1 127 141 Palermo D 2002 Behaviour and Analysis of Reinforced Concrete Walls Subjected to Reversed Cyclic Loading PhD Thesis University of Toronto Toronto ON 492 p Park R Priestley M J N and Gill W D 1982 Ductility of square confined concrete columns Journal of the Structural Division American Society of Civil Engineers ASCE 108 4 929 950 Popovics S 1973 A numerical approach to the complete stress strain curve of concrete Cement and Concrete Research 3 5 583 599 Rayleigh J W S 1877 The Theory of Sound reissued in 1945 Vol 1 2 ed Dover Publications New York NY 480 p Richart F E Brandtzaeg A and Brown R L 1928 A Study
89. ecTor3 These steps can be summarized in the following list 1 Starting up Material Definition Structure Definition 2 3 4 Job Definition 5 Load Definition 6 Saving the Input Files and Running VecTor3 To facilitate the process of defining the structural analysis job for the user default values and models have been predefined for most of the entries required for the analysis The default values and models have been selected based on the most commonly used values and models or based on the recommendations of the developers of VecTor3 These recommendations are based on experience on the values and models that yield the most reasonable agreement between the analyses and the experimental results VecTor3 User s Manual A 2 Modelling Main Steps A 2 1 Starting up As Formworks Plus is started Figure A 1 appears as an introductory presentation of the program and its credentials Since Formworks Plus is a universal pre processor for the entire VecTor program suite when the user clicks on the figure shown in Figure A 1 they are given the option to choose the type of structure to be anlayzed from six different available types as shown in Figure A 2 This basically decides which VecTor program will be used The list includes 1 Plane Membrane 2 D using VecTor2 program Solid 3 D using VecTor3 program Shell using VecTor4 program 2 3 4 Plane Frame 2 D using VecTor5 program 5 Axisymmetric Solid using VecT
90. ection of displacement in the X Y or Z direction DOF and the imposed displacement value in mm Figure A 62 66 VecTor3 User s Manual Apply Support Displacements Case node D 0 F DISPL mm H nodes d node ddip nodes dnode nodes dnode d disp Total gt AA O 28 B No B B Ho BB H 80 Done Selection Mode Pointer window Figure A 63 The user can define the imposed displacements on the nodes individually one at a time or specify the ID number of a certain node with specific imposed displacement and extrapolate the displacement to other nodes by specifying the number of nodes with imposed displacement nodes the increment in the ID number of the subsequent nodes d node and the increments in the imposed displacement value from one node to the next d displ It should be noted that the direction DOF of imposed displacement will be the same for all those nodes whose imposed displacements were defined together This extrapolation can be done in three levels simultaneously using the three sets of boxes available for user input as shown in Figure A 63 The Pointer and Window selection options that were explained earlier are also available A 2 5 3 Gravity Loads The ninth button from the left in the toolbar shown in Figure A 57 whose shape is shown in Figure A 64 allows the user to define elements whose gravity loads are to be considered in the analysis Pressing
91. ectively with increments of 10 in size with each press of a button This can also be done without pressing those buttons by rolling the mouse scroll wheel inwards for a larger display scale or outwards for a smaller display scale The fourth button titled Zoom Window allows the user to increase the display scale of a specific part of the structural model by pressing down the left mouse button and dragging a window around the area of interest The fifth button titled Pan allows the user to move around in the workspace view by holding down the left mouse button while dragging the mouse in the direction of interest This can also be done without pressing the Pan button by holding down the mouse scroll wheel while dragging the mouse in the direction of interest The sixth button in the toolbar shown in Figure A 6 whose shape 1s presented in Figure A 7 opens a window titled Display Options This window is shown in Figure A 8 Figure 7 VecTor3 User s Manual Display Options Mode Options Element Options Mode Numbers Inl Tap Er HFH sena Mode Numbers Out Bat Restraints Linked Nodes Nodal Loads Support Displacements Lumped Masses Impulse Forces Vapour Pressure Nodal Thermal Loads Mone Material Color Material Type Number Gravity Loads Element Temperature Concrete Prestrains Ingress Pressures Time arning Element Temperature Hydrostatic Loads Shell Uniform Loads Frame End
92. ectly The start of the analysis will appear in the form of an MS DOS window that displays the progress of the analysis For each load stage the window will show the load stage number and a list of the loading cases and their respective load factors For time stepping analyses the time step number and the time incident being analyzed in seconds will also be shown Next the progress of convergence will be displayed for each iteration being analyzed First if thermal analysis nodal thermal loads 1s included in one of the loading cases the convergence progress of the successive iterations of the heat transfer analysis or the coupled heat and moisture transfer analysis will be displayed depending on whether the user ticked the Pore Pres checkbox in the Concrete Elements Surface Temperatures in the Load Definition step or not Section A 2 5 7 of the VecTor3 User s Manual 80 VecTor3 User s Manual After the convergence of the thermal analysis is achieved the convergence progress of the successive iterations of the structural analysis will be displayed This will carry on until convergence is achieved or the maximum number of iterations allowed per load stage that was defined in the Job Control tab in the Job Definition step Section A 2 4 1 of the VecTor3 User s Manual 1s reached Then a new load stage will start For future reference all the data displayed in the MS DOS window while the analysis is r
93. ed using the display features explained in Section A 2 1 1 of the VecTor3 User s Manual Create Nodes node z Hnodes dnode dx dz Hnodes dnode dx dy dz Hnodes dnode dx Total ra rra o pe y TS ro tano e s o jo nm 616 Delete Done Figure B 18 79 go gl 93 pa 85 B6 87 88 89 90 E Figure B 19 B 2 2 1 2 Applying Node Restraints Pressing the button shown in Figure B 20 opens the window shown in Figure B 21 where nodes restraints can be defined In this model all the nodes at the plane of the base of the column at Z 0 should be fully restrained in all directions to resemble the experimental fully clamped condition 95 VecTor3 Sample Coupled Thermal and Structural Analysis Figure B 20 Create Support Restraints node Restrain d o f rodes d node modes d node nodes node Total oP P dle ET Hi 11 MM add Done Selection Mode Pointer Window Figure B 21 Therefore all the nodes at the plane of the base of the column will be restrained in the vertical direction the Z direction according to the selected orientation However in order to avoid additional stresses resulting from the expansion of the column at the plane of the base when the column is axially loaded only the nodes lying on the axes of symmetry will be restrained in the X and Y directions This means that at the base of the column the nodes lying on the axis of symmetry in the Y direction at X 152 5
94. elements by specifying the number of elements having internal pressure elmts the increment in the ID number of the subsequent elements d elmt and the increment in the value of the internal pressure from one element to the next d pressure This extrapolation can be done in three levels simultaneously using the three sets of boxes available for user input as shown in Figure A 71 The Pointer and VVindovv selection options that were explained earlier are also available A 2 5 7 Concrete Elements Surface Temperatures Nodal Thermal Loads The thirteenth button from the left in the toolbar shown in Figure A 57 whose shape 1s shown in Figure A 72 allows the user to define specific nodes in the structural model that are subjected to elevated temperatures for carrying out the heat transfer analysis through the section Pressing the button opens the window shown in Figure A 73 Figure A 72 71 VecTor3 User s Manual Apply Nodal Thermal Loads Case node Surface Ae Fire Curve Type Tm Tpi Tm2 Tp2 Tm3 Tp3 Teool nodes d node nodesd node nodesd node Total P 1 1 Atmosphere v Pres Steady State wi 0 fo 0 0 0 0 1 1 1 1 1 1 Done Selection Mode Pointer Window Figure A 73 The first user input is the ID number of the node Next in the input drop list titled Surface the user is allowed to select between two options Element Surface or Atmosphere
95. elmts delmt delmt Helmts d elmi 5401 Reinforcement 1 EZ 150 1 1 1 1 1 Done Selection Made Painter Window Figure B 43 105 VecTor3 Sample Coupled Thermal and Structural Analysis Assign Material Types elmi material act delmt Helmts delmt Helmts d elmt 5851 Reinforcement 2 ie i i i 3 Done Selection Mode Pointer Window Figure B 44 B 2 3 Job Definition This step is responsible for defining the analysis job scheme Defining the job is done through the button shown in Figure B 45 Pressing this button opens the window shown in Figure B 46 Figure B 45 106 VecTor3 Sample Coupled Thermal and Structural Analysis Define Job Job Control Models Auxiliary Auxiliary Thermal Job Data Structure Data Job file name VecT or Structure file name Struct Job title Enter Job Title Structure title Enter Structure Title Date Enter Date Structure type Solid 3 D Y Loading Data Load series ID ID Starting load stage na 1 Ma of load stages 1 Activate Case 1 Case 2 Case 3 Case 4 Case 5 Load file name NULL ur IUL a NOLL ML Load case title Enter load case title Enter load case file Enter load case title ae Enter load case tile Initial Factor li m 5 Final factor p 0 o Inc factor BB mn p a Load type Monotonic gt Monotonic EE
96. er to understand the input entries in this part a brief background of the procedure that VecTor3 follows for structural analysis needs to be presented VecTor3 performs nonlinear analysis of reinforced concrete structures based on the Modified Compression Field Theory MCFT Vecchio and Collins 1986 in a total load secant stiffness approach This means that at each load stage the total load is applied and the secant stiffnesses of the elements are used to calculate the displacements of the nodes comprising the structural model which are in turn used to calculate the strains in the elements The stresses are then calculated for the elements based on the calculated strains and the constitutive stress strain models of the elements materials Finally those strains and stresses are used to recalculate the value of the secant stiffnesses of the elements which are to be reused for the solution This procedure is referred to as an iteration in the current load stage The results of each iteration are compared to those of the previous iteration until certain criteria are met after which the analysis proceeds to the next load stage With this background of the analysis procedure in mind the entries of the fourth collective frame in this tab titled Analysis Parameters can be explained The box titled Convergence Criteria refers to the criteria that need to be met for the solution of the iteration to be deemed final so that the analys
97. ere f and e are the compressive stress and strain in steel respectively In this part as well the thermal expansion coefficient entered is overridden by the value calculated according to the model to be chosen for the temperature dependent thermal expansion coefficient of steel reinforcement After the smeared steel reinforcement material properties are entered in their respective boxes the user is required to press the Add button in the lower part on the left hand side of the window shown in Figure A 18 At this point the new reinforcement component type titled Reinforcement 1 appears in the box titled Component on the left hand 16 VecTor3 User s Manual side of the window as shown in Figure A 19 In this part as well the Update and Delete buttons can be used to update the material properties of the smeared steel reinforcement or delete the undesired ones respectively Define Material Properties Maternal Types Material Properties Smeared Reinforcement Properties Type Reference Type Reinforced Concrete Reference Type Ductile Steel Reinforcement Cylinder C ive Strength Fe 30 42532 MPa Reinforcement Orientation Tensile Strength Pt s l MPa k 1 0 m 0 Initial Tangent Elastic Modulus Ec 5 l MPa Reinforcement Ratio rho Cylinder Strain at fic eo Reinforcement Diameter Db Poisson s Ratio Thermal Expansion Coefficient Cc Yield strength Fy 400 MPa
98. erial Types elmt material act delmt elmi d elmi elmi delmt Done Selection Mode Pointer Window Figure A 48 As previously explained in the Elements Definition step Section A 2 3 2 of the VecTor3 User s Manual the user can assign material types to each element individually one at a time or extrapolate the material assignment to more elements by specifying the number of elements required to be assigned that material type 2 elmts and the increment in the ID number of the subsequent elements d elmt As previously mentioned this extrapolation can be done in three levels simultaneously using the three sets of boxes available for user input as shown in Figure A 48 There are also graphical options available for the user to assign material types to the elements These options can be accessed using the two buttons Pointer and Window which appear under the collective frame titled Selection Mode on the right hand side of the window shown in Figure A 48 The button Pointer allows the user to select one element at a time from the elements displayed in the workspace view and the button Window allows the user to select multiple elements in one step by holding down the left mouse button and dragging a window that contains the desired elements Finally a summary of the Structure Definition step can be viewed through the second button from the left in
99. ers Definition 57 AZ a Load B BIO 63 2 5 L Nodal LOIS uuu uu uu aaa qd 65 A 2 5 2 Support Displacements Imposed Displacements 66 22 9 9 GI3 IUS Oq u m PO EU amad 67 22 54 Blements Temperatur es R 68 A255 Con rete Elements PESAS uuu uuu 69 A 2 5 0 Concrete Elements Inptess Pressures u uquy a duet ias 70 A 2 5 7 Concrete Elements Surface Temperatures Nodal Thermal Loads 71 A 2 5 8 Lumped Nodal Masses for Dynamic Analys is 74 250 IMPUSE POLO C Stout setup umu s eiiim toten ule nitatem tetas iu des 75 A 2 5 T0 Cround XceelebatlOE seeded a Dala ia santa metes 71 A 2 6 Saving the Input Files and Running 79 B Sample Coupled Thermal and Structural Analysis 82 Lc O E 83 Be 2 Modeline Mal SOS 87 E 88 111 VecTor3 89 B 2 1 1 Base Material Properties Definition 89 B 2 1 2 Discrete Reinforcement Material Properties Definition 90 B 2 1 3 Bond Properties Decade 94 2 2 Structure Denil OM A a E a a q 94 B 2 2 T Node DECI o o da ada 94 B 2 2 1 1 Dehihm Node Coordina unit 94 B 2 2
100. es and the increment in the ID number of the subsequent nodes d node This extrapolation can be done in three levels simultaneously using the three sets of boxes available for user input as shown in Figure A 36 A 2 3 1 3 Applying Node Constraints Linking Nodes This step enables the user to apply certain constraints on specific groups of nodes The nodes can be linked together with specific linear displacement relations throughout the analysis This allows one or two groups of nodes to have the same displacements in specific directions or one group to have a displacement of a pre defined percentage of the displacement of another group Pressing the fourth button from the left in the toolbar shown in Figure A 28 shown in Figure A 37 opens the window shown in Figure A 38 The user can specify one group of nodes to be linked together to displace similarly using the top row of entry boxes or two groups of nodes to be linked together with a specific relation specified in the Factor entry using the two rows of entry boxes If only one group is entered the nodes included in that group will have the same displacement in the specified direction DOF 28 VecTor3 User s Manual throughout the analysis If two groups are entered then the nodes included in each group will have the same displacement in the specified direction DOF throughout the analysis and the displacements of the nodes in the second group will be linked t
101. es and saves the load files with the names specified in the Job Control tab in the Job Definition step and the extension L3R namely Thermal L3R Axial L3R and Lateral L3R At this point VecTor3 has all the input files it requires and is ready to run Pressing the fourth button from the left in the toolbar shown in Figure B 73 titled VT starts VecTor3 Pressing this button without having already saved the input files using the buttons with the red blue and green floppy discs will prompt the user to save the files When VecTor3 starts it will appear in the form of an MS DOS window that displays the progress of the analysis For each load stage the window will show the load stage number and a list of the loading cases and their respective load factors Since this is a time stepping analysis the time step number and the time incident being analyzed in seconds will also be shown Next the progress of convergence will be displayed for each iteration being analyzed First the convergence progress of the successive iterations of the heat transfer analysis will be displayed After the convergence of the thermal analysis 1s achieved the convergence progress of the successive iterations of the structural analysis will be displayed This will carry on until convergence is achieved or the maximum number of iterations allowed per load stage which was set to 60 in the Analysis Job Control Parameters i
102. finite element computer program for nonlinear analysis of three dimensional reinforced concrete structures It was originally created by Selby 1990 at the University of Toronto and was extensively further developed by ElMohandes 2013 The input of VecTor3 is in the form of ASCH text files which can be created manually or with the aid of the pre processor Formworks Plus Sadeghian 2012 Wong et al 2013 There are five main input files that are required for any analysis job The first file is titled VECTOR JOB and is responsible for defining the analysis job control parameters and the main structural mechanics models to be followed by concrete and steel in the structural analysis The second input file titled VT3 AUX is responsible for defining additional parameters that are specific to special types of structures loading conditions and analysis types The third input file titled VT3T AUX is responsible for defining the main parameters properties and structural mechanics models that control heat transfer analysis and the structural analysis in coupled thermal and structural analysis The fourth input file is the structural input file It has the extension S3R and it is responsible for defining the geometry and materials of the structure to be analyzed The fifth input file is the load file It has the extension L3R and it is responsible for defining the loads to be applied on the structure to be analyzed
103. fire safety design Magazine of Concrete Research 57 8 445 453 Hognestad E 1951 A Study of Combined Bending and Axial Load in Reinforced Concrete Members University of Illinois Engineering Experiment Station Urbana USA 128 p Hordyk D A 1991 Local Approach to Fatigue of Concrete PhD Thesis Delft University of Technology Delft 210 p 135 References Hoshikuma J Kawashima K Nagaya K and Taylor A W 1997 Stress strain model for confined reinforced concrete in bridge piers Journal of Structural Engineering American Society of Civil Engineers ASCE 123 5 624 633 ISO 834 1 1999 Fire Resistance Tests lements of Building Construction Part I General Requirements 1999 International Organization for Standardization ISO Geneva Switzerland 25 p Izumo J Shin H Maekawa K and Okarnura H 1991 An analytical model for RC panels subjected to in plane stresses Concrete Shear in Earthquake University of Houston Texas USA Jodai A 2013 Nonlinear Finite Element Analysis and Post Processing of Reinforced Concrete Structures under Transient Creep Strain M A Sc Thesis University of Toronto Toronto ON 92 p Kent D C and Park R 1971 Flexural members with confined concrete Journal of the Structural Division American Society of Civil Engineers ASCE 97 7 1969 1990 Kodur V K R and Khal q W 2011 Effect of Temperature on Thermal Properties of Differe
104. for Programs Finite Element Analysis of Reinforced Concrete EJ Vecchio University of Toronto 2012 Software Development by Peter Wong Vahid Sadeghian Sponsored by Natural Sciences and Engineering Research Council of Canada Morrison Hershfield Ltd Consulting Engineers Toronto Figure B 7 Structure Data Figure B 8 88 VecTor3 Sample Coupled Thermal and Structural Analysis B 2 1 Material Definition B 2 1 1 Base Material Properties Definition The button shown in Figure B 9 is pressed in order to define the material properties of concrete Pressing the button opens the window shown in Figure B 10 Define Material Properties Material Types Type Component un Figure B 9 Material Properties Reference Type Reinforced Concrete Cylinder Compressive Strength Fe o MPa Tensile Strength Ft s MPa Initial Tangent Elastic Modulus Ec i 0 MPa Cylinder Strain at fc Poisson s Ratio Thermal Expansion Coefficient Cc Maximum Aggregate 5126 a Density Thermal Diffusivity Ec Average Crack Spacing perpendicular to x reinfarcement 5x perpendicular to y reinforcement Sy perpendicular to z reinfarcement 52 Color Reinforced concrete material types to be used for solid elements only Enter T for VT 3 default value Figure B 10 JE JE DK Cancel To specify a compressive st
105. for a specific loading case VecTor3 allows for up to five separate loading cases of similar or different types to be analyzed simultaneously Thus up to five files with the extension L3R can be created for an analysis VecTor3 User s Manual It should be noted that the structural S3R files and the load L3R files can have any arbitrary names but the name chosen for each file has to be entered In its specific location in the VECTOR JOB file in order to identify the specific structure and the specific loading cases to be anlayzed in the analysis job defined in the VECTOR JOB file Formworks Plus Is a universal pre processor for the entire VecTor software suite including VecTor2 VecTor3 VecTor4 VecTor5 and VecTor6 It was created by Wong et al 2013 and developed further by Sadeghian 2012 A post processor Janus which was developed by Chak 2013 and Jodai 2013 1s also available for graphical display of the results of the structural analysis carried out using VecTor3 Formworks Plus provides a graphical interface for the user to facilitate the process of creating the input files of the analysis job It converts the graphical user input into the aforementioned five types of input ASCII text files and provides shortcuts to start the analysis This user s manual provides the main steps to be followed in Formworks Plus to create an analysis job of a reinforced concrete structure to be analyzed using V
106. for cyclic loads that are repetitive in the same direction and Reverse Cyclic for cyclic loads that reverse the direction of loading at the end of each cycle These loading types are further explained in the VecTor2 and FormWorks User s Manual by Wong et al 2013 Selecting the Cyclic and the Reverse Cyclic options makes the boxes Repetitions and Cyclic Inc factor available for user input For those load types the Final factor refers to the peak load factor in the loading cycle Cyclic Inc factor refers to the increment in the maximum load factor Final Factor from one cycle to the next and Repetitions refers to the number of cycles to be run at each specific value of the peak load factor before applying the increment specified in the Cyclic Inc factor More about the Cyclic and the Reverse Cyclic load types can be found in the VecTor2 and FormWorks User s Manual by Wong et al 2013 39 VecTor3 User s Manual Define Job Job Control Models Auxiliary Auxiliary Thermal Job Data Structure Data Job file name VecT or Structure file name Struct Job title Enter Jab Title Structure title Enter Structure Title Date Enter Date Structure type Solid 3 0 Loading Data Load series D ID Starting load stage no 1 of load stages 1 Activate v Case 1 2 Case 3 Case 4 Case 5 Load file name Cas ur Tm NOLL NOL
107. for dynamic loading so there is no need to use time sub steps For more information on this part refer to Section A 2 4 1 of the VecTor3 User s Manual For the Cyclic Inc factor entry it will be discarded for this type of loading Finally the Initial load stage will be set to 1 meaning that the fire conditions will be applied starting from the first load stage where the temperature 1s 20 C at the first load stage when the time elapsed is 0 seconds Define Job Job Control Models Ausiliar Auxiliary Thermal Job Data Structure Data Job file name r Structure file name Struct Jab title Column 1582 Structure title Column 1582 Date Enter Date Structure type Solid 3 D Loading Data Load series ID ID Starting load stage no 1 Ma of load stages 1500 Activate Case 1 i Case 2 W Case 3 W Case 4 Case 5 Load file name Thermal axial Lateral Lateral Load case title Fire Load Asial cad Lateral Llateral2 Epter load case title Initial Factor 1 1 O Final factor y l a qm Uu S Inc factor B osse li ooo Load ype Monotanic Monotenic Monotenic Monotonic Monotonic Repetitions IL ik 53 i HE 4 Ee Cyclic Inc factor fo n B hb l Initial Load Stage E 1 UNE PB HE Analysis Parameters seed File Name MULL Convergence Criteria Secant Modul Displacements amp F na of Iteratio
108. gt m o o x u e b Axial Load Figure B 5 86 VecTor3 Sample Coupled Thermal and Structural Analysis 12 25 417 6 25 416 Figure B 6 A time step of 60 seconds will be used for the analysis The axial load of 1590 kN will be applied prior to the start of fire at the top of the column as nodal loads in a load control regime Only half the load will be applied in order to achieve the same stress condition on the half model used in the analysis The models provided by the current version of the Eurocode EN 1992 1 2 2004 2005 will be used for the thermal analysis The exact same experimental lateral loading profile will be applied at the top of the column in a displacement control loading regime until failure The thermal loading of the fire and the lateral loading will be started at the same time resembling the experimental conditions B 2 Modelling Main Steps In order to simplify the explanation of the process of creating the finite element model and running the analysis the main steps explained in the VecTor3 User s Manual will be followed and in the same order as follows 87 VecTor3 Sample Coupled Thermal and Structural Analysis Starting up Formvvorks Plus is started and the figure shown in Figure B 7 appears When figure is clicked the window shown in Figure B 8 appears The second option Solid 3 D should be selected in order to useVecTor3 FormWorks5 Preprocessor
109. he file titled lateral 13r for Case 4 In the next step Section B 2 5 which is responsible for saving the input files when prompted to do so The third way is to choose a Load file name for Case 4 that is different from that chosen for Case 3 in Section B 2 3 1 of the VecTor3 Sample Coupled Thermal and Structural Analysis Lateral 1 and Lateral 2 for example B 2 5 Saving the Input Files and Running VecTor3 At this point the model is ready to be analyzed This can be done using the toolbar shown in Figure B 73 The first step 1s to save the analysis job if it has not been saved yet by pressing the button shown in Figure B 74 zi izi vr OER Figure B 73 Figure B 74 As explained in the Introduction section Section A 1 of the VecTor3 User s Manual there are five main input files that are required for defining the analysis job to be carried out Pressing the first button from the left in the toolbar shown in Figure B 73 featuring the red floppy disc creates and saves the VECTOR JOB VT3 AUX and VT3T AUX files Pressing the second button featuring the blue floppy disc creates and 129 VecTor3 Sample Coupled Thermal and Structural Analysis saves the structure file with the name Struct specified in the Job Control tab in the Job Definition step and the extension S3R Finally the third button featuring the green floppy disc creat
110. hich is recommended to be set to Elastic Hardening Curvilinear neglecting the Bauschinger effect B 2 3 3 Auxiliary Parameters Definition The next tab in the Job Definition window titled Auxiliary is shown in Figure B 50 In the General collective frame the default Stiffness Matrix Solver Type should be left as the default entry Solver 2 as this solver is much faster than Solver 1 Define Job Job Control Models Ausillary Auxiliary Thermal General Dynamic Analysis Stiffness Matris Solver Solver 2 Reference Mode 1 isoparametic Reference Mode 2 Concrete Aggregate Type Carbonate vl Damping Factor 1 3 TT Damping Factor 2 Concrete Fracture Energy EM m oO Concrete Thermal Conductivity v mK 228 Time Integration Method Newmark Constant Prestressing Friction Coefficient r ES Ground Acceleration in x direction Hat Considered Prestressting Wobble Coefficient m 0 0025 Ground Acceleration in y direction Not Considered m Thermal Time Stepping Factor ME Ground Acceleration in direction Mot Considered Tension Softening Tension Softening Pt 1 Strain me Tension Softening Pt 1 Stress MPa Tension Softening Pt 2 Strain ma Tension Softening Pt 2 Stress MPa Tension Softening Pt 3 Strain ma Tension Softening Pt 3 Stress MPal Tension Softening Pt 4 Strain ma Tension Softening Pt 4 Stress MP
111. his point After the loading cases are defined in the Job Definition step the load input toolbar shown in Figure B 52 becomes available for user input Mae Sap Pl E UG Th Ze V5 Z4 cl oe Wii E Figure B 52 The second to sixth buttons from the left in the toolbar shown in Figure B 52 which can be seen in Figure B 53 are used to define the various loads to be included in the four loading cases defined in the lob Definition step A A c Figure B 53 Recalling the loading cases defined in the Analysis Job Control Parameters in the Job Definition step in Section B 2 3 1 of the VecTor3 Sample Coupled Thermal and Structural Analysis the first loading case Case 1 to be defined is the thermal loading case simulating the fire conditions For this the first button from the left in the toolbar 119 VecTor3 Sample Coupled Thermal and Structural Analysis shown in Figure B 53 with the number 1 is pressed With that button pressed down all the loads to be defined will be included in Case 1 Recalling Section A 2 5 7 of the VecTor3 User s Manual which 1s responsible for defining this type of loading Nodal Thermal Loads the parameters required for defining fire conditions can be found Pressing the button shown in Figure B 54 opens the window shown in Figure B 55 which is responsible for the nodal thermal loads definition Figure B 54 Apply Nodal Thermal Loads Case node Surface Pore
112. i and Bastami 2011 Residual tensile strength e No modification factor e Xie and Qian 1998 Model 1 e Xie and Qian 1998 Model 2 l VecTor3 User s Manual e Chang et al 2006 Thermal expansion strain e The ASCE Manual of Practice Structural Fire Protection by T T Lie 1992 e Lie and Kodur 1996 for SFRC e The Eurocode ENV 1992 1 2 1995 1996 e The Eurocode EN 1992 1 2 2004 2005 e Kodur and Sultan 2003 for HSC e Kodur and Sultan 2003 for SFR HSC e Kodur and Khalig 2011 for HSC For reinforcement Yield stress e No modification factor e Brockenbrough 1970 e The Centre Technique Industriel de la Construction M tallique CTICM 1982 the ASCE Manual of Practice Structural Fire Protection by T T Lie 1992 e The European Convention for Constructional Steelwork ECCS 1983 Saab 1990 e The Eurocode ENV 1992 1 2 1995 1996 loading based e The Eurocode ENV 1992 1 2 1995 1996 tension model e The Eurocode ENV 1992 1 2 1995 1996 compression model e The Eurocode EN 1992 1 2 2004 2005 Ultimate stress e No modification factor e The Eurocode EN 1992 1 2 2004 2005 Young s modulus e No modification factor 62 VecTor3 User s Manual e Brockenbrough 1970 e The Centre Technique Industriel de la Construction M tallique CTICM 1982 the ASCE Manual of Practice Structural Fire Protection by T T Lie 1992 e The European Convent
113. igehausen Eligehausen et al 1983 e Gan Vecchio Gan 2000 e Haray l Harajli and Mukaddam 1988 e Fujii Morita and Fujii 1982 e Eligehausen No Cyclic Damage Eligehausen et al 1983 e Gan No Cyclic Damage Gan 2000 Analysis Models Strain History e Previous Loading Neglected e Previous Loading Considered Strain Rate Effects the first entry is for concrete and the second is for steel e n c n c not considered e n c Malvar Crawford Malvar and Crawford 1998 e n c CEB FIP 1988 CEB 1988 e fib MC 2010 n c fib Model Code 2010 2012 32 VecTor3 User s Manual e fib MC 2010 Malvar Crawford fib Model Code 2010 2012 Malvar and Crawford 1998 e fib MC 2010 CEB FIP 1988 fib Model Code 2010 2012 CEB 1988 e fib MC 1990 n c CEB FIP Model Code 1990 1993 e fib MC 1990 Malvar Cravvford CEB FIP Model Code 1990 1993 Malvar and Cravvford 1998 e fib MC 1990 CEB FIP 1988 CEB FIP Model Code 1990 1993 CEB 1988 Structural Damping e Not Considered e Rayleigh Damping Rayleigh 1877 e Alternative Damping Geometric Nonlinearity e Not Considered e Considered Crack Process e Uniform For VecTor3 it 1s required that the drop list of the Crack Process be left as its default and only option Uniform More about those models is available in the in the VecTor2 and FormWorks User s Manual by Wong et al 2013 and in ElMohandes 2013 Besides
114. ignated for the corresponding stress This applies for the next six boxes with the Pt 2 Pt 3 and Pt 4 for the second third and fourth key points respectively where the first box of each key point is designated for the strain and the next box is designated for the corresponding stress This curve will only be used when the option Custom Input Strain Based or the option Custom Input Crack Based is selected in the Tension Softening drop list in the Models tab as discussed in the previous section Section A 2 4 2 of the VecTor3 User s Manual The collective frame titled Dynamic Analysis in the upper part of the right hand side of this tab is responsible for defining several additional parameters related to dynamic analysis Reference Mode 1 and Reference Mode 2 refer to the first and second modes of vibration for Rayleigh damping procedure Rayleigh 1877 respectively Damping Factor 1 and Damping Factor 2 are the corresponding damping factors for these first and second modes of vibration respectively It should be noted that VecTor3 55 VecTor3 User s Manual only considers the first 100 modes of vibration in order to save time and computational resources VecTor3 uses Newmark s time integration method for the dynamic analysis solution Newmark 1959 Two options are available for the use of the method which can be selected through the Time Integr
115. igure A 25 which will add the bond type to the list titled Type on the left hand side as shown in Figure A 26 The user can use the Update Delete and Colour buttons as required as explained earlier The greyed out collective frame at the bottom of the window titled Bond Properties for Externally Bonded Plates or Sheets becomes available for user input when one of the two options Interface or Bonded Plates Fabrics and the Embedded Bars Custom Input is chosen The user is required to enter the Bonded Surface Area in mm m and three key points to compile the bond stress slip curve where U1 U2 and U3 are the bond stresses in MPa and Sl S2 and S3 are the corresponding slips in mm respectively 22 VecTor3 User s Manual Define Bond Properties Bond Type Type Reference Emebedded Deformed Hebars k Add Bond Properties for Embedded B ars Update Confinement Pressure Factor Delete Min Bar Clear Cover Spacing Clin 25 of Reinforcement Layers thru Depth 2 Hooked w Color Bond material types to be used for interior ar exterior bonded elements k Lancel Figure A 26 At this point all the material types have been entered For any of these material types base discrete reinforcement and bond the user can repeat the same steps to define more types of material For each new material type
116. ilable vl FRC Tension SDEM Monotonic vl Histeretic Response Linear w No Plastic Offsets Reinforcement Models Bond Models Husteretic Response Elastic Hardening Curvilinear Dowel Action Tassios Crack Slip Concrete Bond Eligehausen Buckling Refined D hakal M aekawa gt Analysis Models Strain History Previous Loading Considered T Strain Hate Effects Steel EZ n c d Structural Damping kat Considered Reset Options Geometric Nonlinearity Considered Basic Crack Process Uniform Advanced Lancel Figure B 49 While most of the models selected are the default ones some were changed to better suit the current structure and analysis conditions Since the concrete used had a compressive strength of 55 MPa it 1s more appropriate to use the model of high strength concrete HSC Popovics for the Compression Pre Peak model Since no reverse loading conditions are applied in the analysis the concrete Hysteretic Response can be changed 114 VecTor3 Sample Coupled Thermal and Structural Analysis to Linear w No Plastic Offsets While this is not necessary for the accuracy of the analysis it leads to a more stable analysis Therefore whenever the nonlinear response and the plastic offsets are not expected to have a major influence on any analysis it may be a good idea not to use them This also applies to the reinforcement Hysteretic Response w
117. indow that contains the desired nodes or elements Also for all those load types after each entry the Apply button on the right hand side of the input window should be pressed Once all the entries are entered the Done button should be pressed to close the window Unneeded entries can be deleted by selecting them from the list in the larger box at the bottom of the window then pressing the Delete button on the right hand side of the window At any point the last button from the left in the toolbar shown in Figure A 57 whose shape is shown in Figure A 59 can be used to delete the loads applied on the entire structure for the loading case selected in the toolbar shown in Figure A 58 from 1 to 5 Figure A 59 The following subsections Introduce each of the load types available In VecTor3 and the input entries required by the user to define them A 2 5 1 Nodal Loads The seventh button from the left in the toolbar shown in Figure A 57 whose shape is shown in Figure A 60 allows the user to define concentrated point loads on specific nodes in the structural model Pressing the button opens the window shown in Figure A 61 The user is required to specify the ID number of the node and the concentrated point loads applied on the node in the global X Y and Z directions in kN Figure A 60 65 VecTor3 User s Manual Apply Nodal Loads Case node Fx Fy Fz nodes d node dFx dFy dFz Hnodesdn
118. inked the nodes at this level to displace together vertically in the Z direction the loads are applied as concentrated loads distributed among the nodes at this level based on the tributary area The summation of the loads should add up to 795 kN which is half the axial load applied on the column since only half the column is modelled here Based on a tributary area of 161 5 mm for the corner nodes 323 mm for the edge nodes and 646 mm for the middle nodes the loads applied on those nodes are 2 76 kN 5 52 kN and 11 04 kN respectively The ID numbers of the nodes can be found from the nodes numbering scheme defined in Section B 2 2 1 1 of the VecTor3 Sample Coupled Thermal and Structural Analysis A view of the ID numbers of the nodes at the level of the application of the axial load X Y view at Z 3760 mm is shown in Figure B 62 123 VecTor3 Sample Coupled Thermal and Structural Analysis Pt tt LL EE EL LL 6877 PF L LL L IL L LL LL 6864 6916 6903 Figure B 62 The line shown in Figure B 63 defines the loads at the corner points the lines shown in Figure B 64 and Figure B 65 define the loads at the edge points and the line shown in Figure B 66 defines the loads at the middle points It can be noticed that the loading case number Case 2 is shown at the left hand side of the window for referencing purposes The negative sign of the applied loads is to apply the loads vertically downwards negative Z direction
119. ion for Constructional Steelwork ECCS 1983 e Saab 1990 e The Eurocode EN 1992 1 2 2004 2005 Thermal expansion strain e The European Convention for Constructional Steelwork ECCS 1983 e The ASCE Manual of Practice Structural Fire Protection by T T Lie 1992 e The Eurocode ENV 1992 1 2 1995 1996 e The Eurocode EN 1992 1 2 2004 2005 A 2 5 Load Definition This step is responsible for defining the loads applied on the structural model to be analyzed After the loading cases are defined in the Job Definition step the load input toolbar becomes available for user input The toolbar 1s shown in Figure A 57 Mae Sep Pl E PG Th Ze V5 Z4 cl gt Wii E Figure A 57 The second to sixth buttons from the left in the toolbar shown in Figure A 57 which can be seen in Figure A 58 allow the user to define the various loads to be included in the five separate loading cases allowed by VecTor3 When the button with the number 1 1s pressed all the loads to be defined will be included in Case 1 check the Job Control tab in the Job Definition window shown in Figure A 52 This applies to all five loading cases 63 VecTor3 User s Manual ml v5 v3 m c3 Figure A 58 The user input in this step 1s saved in the five possible L3R input files depending on the number of loading cases defined in the Job Definition step with one file for each loading case The different load ty
120. is can proceed to the next load stage The Convergence Criteria compare certain results of each iteration to the results of the 41 VecTor3 User s Manual previous iteration The options for which results are to be compared that are available in VecTor3 can be selected through the drop list and they include 1 Principal Secant Moduli Weighted Average A weighted average of the principal secant moduli of all the elements is calculated and used for testing convergence 2 Displacements Weighted Average A weighted average of all the displacements of the nodes comprising the structural model is calculated and used for testing convergence 3 Displacements Maximum Value The maximum displacement in the nodes comprising the structural model is used for testing convergence 4 Reactions Weighted Average A weighted average of all the reactions of the restrained nodes in the structural model is calculated and used for testing convergence 5 Reactions Maximum Value The maximum reaction in the restrained nodes in the structural model 1s used for testing convergence 6 Global Secant Moduli Weighted Average A weighted average of the principal secant moduli rotated to the global coordinates according to the principal stress directions of all the elements is calculated and used for testing convergence 7 Secant Moduli Displacements amp Reactions Weighted Average the values of a
121. lective frames namely Job Data Structure Data Loading Data and Analysis Parameters The user input in this step is saved in the VECTOR JOB input file 37 VecTor3 User s Manual The first user input part is designed for entering the analysis job data In the collective frame titled Job Data the job file name the JOB file job title and job date can be entered It should be noted that the job file name should always be left as the default entry VecTor The second user input part is designed for entering the analysis structure model data In the collective frame titled Structural Data the structure file name the S3R file structure title and structure type can be entered Since the analysis type described here 1s for three dimensional structures using VecTor3 the user should leave the structure type as the default entry Solid 3 D The third user input part is designed for entering the loading parameters which 1s done in the collective frame titled Loading Data In the top part of this collective frame as shown in Figure A 52 the user can enter the title of the output files generated by the analysis in the box titled Load series ID The output files will be titled using the title entered in this box followed by an underscore sign then the load stage number The output ASCII text files will have the extension A3E and the output binar
122. led corners for the rectangular sides the two noded uniaxial truss bar element for modelling discrete reinforcing bars and the dimensionless two noded link elements for modelling the bond between concrete and discrete reinforcing bars Figure 27 The buttons in the toolbar shown in Figure A 28 are responsible for all user input data for the Structure Definition step 4 cm m vu EI 22 Figure A 28 24 VecTor3 User s Manual At any point during this step the nineteenth button from the left the last button in the toolbar shown in Figure A 28 whose shape is shown in Figure A 29 can be used to delete the entire structural model including the nodes material types elements and loads 2 Figure A 29 A 2 3 1 Node Definition A 2 3 1 1 Defining Node Coordinates For defining the coordinates of the nodes the first button from the left in the toolbar shown in Figure 28 is used The shape of the button 15 shown in Figure A 30 Pressing the button opens the window shown in Figure A 31 Figure A 30 Create Nodes node z Hnodes dnode dx nodes d node dx Hnodes d node Total Pt yoyo A mmm umur HUR nu m Em EN a PIC Ta p pa o Figure A 31 In this window the user can define the nodes by specifying their coordinates in the x y and z boxes individually one at a time Another way to perform this task is to enter the coordinates of the
123. levated temperatures Nuclear Engineering and Design 212 1 3 233 241 Shirai S and Noguchi H 1989 Compressive deterioration of cracked concrete ASCE Structures Congress 1989 Design Analysis and Testing New York NY Smith G M and Young L E 1956 Ultimate flexural analysis based on stress strain curves of cylinders American Concrete Institute ACI Journal Proceedings 53 12 597 609 Song Y Zhang Z Qing L and Yu C 2007 Biaxial tensile compressive experiment of concrete at high temperatures Frontiers of Architecture and Civil Engineering in China 1 1 94 98 Spinella N Colayann P and Recupero A 2010 Simple plastic model for shear critical sfrc beams Journal of Structural Engineering American Society of Civil Engineers ASCE 136 4 390 400 Tenchev R T Li L Y and Purkiss J A 2001 Finite element analysis of coupled heat and moisture transfer in concrete subjected to fire Numerical Heat Transfer Part A Applications 39 7 685 710 Toumi B and Resheidat M 2010 Influence of high temperatures on surface cracking of concrete studied by image scanning technique Jordan Journal of Civil Engineering 4 2 155 163 Vecchio F J 1982 The Response of Reinforced Concrete to In Plane Shear and Normal Stresses Ph D Thesis University of Toronto 332 p 139 References Vecchio F J and Collins M P 1986 The modified compression field theory for rei
124. ll SIX previous options are calculated and collectively used for testing convergence The Weighted Average is calculated as the square root of the sum of squares of the ratios of the specific result value in the current to previous iteration for all the nodes or elements and the Maximum Value is calculated based on the ratio of the maximum value of the specific result value in the current iteration to its respective value in the previous iteration These values introduce what are called convergence factors which represent the relation between the results of the current iteration to the previous iteration These convergence factors have a value of one when perfect convergence is achieved 1 e when the results of the current iteration are exactly equal to those of the previous iteration For a load stage to be finalized and for the analysis to proceed to the next load stage one of two criteria needs to be met The first criterion 1s that the convergence factor calculated at 42 VecTor3 User s Manual the end of a certain iteration 15 less than a certain predefined limit which can be entered by the user in the box titled Convergence limit with a value greater than one The second criterion is that the number of iterations carried out in the current load stage reaches a predefined maximum number that can be entered by the user in the box titled Max no of iterations The final entry on this topic falls
125. lysis based on impulse loading records defined by a maximum of 50 force time 44 VecTor3 User s Manual key points applied at any number of nodes in the structural model This is similar to the Dynamic Nonlinear General for impulse loads analysis except for the ability to define the force time profile with up to fifty key points rather than three key points Also in this user input part the drop box titled Results files enables the user to select the types of results output files required to be generated by VecTor3 Two types of files can be generated for each load stage text ASCII files with the extension A3E and binary files with the extension A3R The text ASCII files are the ones that can be read using the post processor Janus for graphical display of the results or can be read as plain text files by the user The binary files on the other hand have a special purpose where they save the status of the structure at the end of the load stage enabling the user to start a subsequent analysis based on this status which acts as a seed There are five options in this drop list available for the user as follows 1 ASCII and Binary Files where both types of files are generated for every load stage 2 ASCII Files Only and Binary File for Last Load Stage where text ASCII files are generated for every load stage and a binary file is generated for the last load stage analyzed only 3 Binary
126. mt d node Helmts delmt d node Total NW Pere Perr iii EH ENEE EH EEEH ER Delete Done Figure A 44 For defining the dimensionless two noded link elements required for modelling the bond between concrete and reinforcing bars the eighth button from the left in the toolbar shown in Figure A 28 which is shown in Figure A 45 needs to be pressed This opens the window shown in Figure A 46 Figure A 45 Create Link Elements elmi node 1 B Helmts delmt dnode elmts delmt dnode Helmts d elmi d node Tatal r rr IRIS T T T T T T Dsm m Done Figure A 46 The input entries for link elements have the same format as the other types of elements However these elements are dimensionless as previously indicated meaning that the two nodes comprising the elements must coincide on each other have the exact same coordinates Since link elements model the bond between concrete and reinforcing bars one of the comprising nodes needs to be a node on a concrete element regular hexahedral element isoparametric hexahedral element or wedge element and the other node needs to be a node on a truss bar element For those elements the user is required to define two 33 VecTor3 User s Manual coincident nodes at the location of the element in the Nodes Coordinates Definition step For all types of elements unneeded entries can be deleted by selecting them from the list in the larger box
127. n Case 4 This explains why the Initial load stage will be set to 26 This is because at 110 VecTor3 Sample Coupled Thermal and Structural Analysis load stage 1 the load factor of the lateral loading case Case 3 will be 0 increasing up to a value of 25 at load stage 26 Therefore at Load Stage 26 the new lateral loading case Case 4 should start with a load factor of Initial factor of 0 which in addition to the load factor of 25 of Case 3 adds up to a total of 25 mm The load factor of Case 4 should then increase to a value of 25 Final factor of 25 within the next 95 load stages 95 minutes after the first 25 minutes to an elapsed time of 120 minutes from the start of the test to simulate the lateral loading profile shown in Figure B 3 This means that the Inc factor for Case 4 should be set to a value of 25 95 which 1s equal to 0 263158 mm min as can be seen in Figure B 47 Again the Load Type should be set to Monotonic and the default entries of 1 and 07 should be left for the Repetitions and the Cyclic Inc factor respectively as they will be discarded for this type of loading In the fourth collective frame titled Analysis Parameters the Seed file name should be left as the default entry NULL as the analysis required to be run is a new analysis The Max no of iterations can also be
128. n the Job Definition step in Section B 2 3 1 of the VecTor3 Sample Coupled Thermal and Structural Analysis 1s reached Then a new stage will start The first and second load stages progress is shown next 130 r Fr 1 r r w EC TOR 3 NONLINEAR ANALYSIS OF RC SOLIDS UNIVERSITY OF TORONTO AUGUST 16 015 VERSION 2 00 COPYRIGHT Vr HH HH W W Ww Ww W W Ww w LOAD Load case FLT AXIAL LATERAL LATERAL Vr w Ww W Ww Ww Ww Ww Ww w w Time TIME Hw HH FH FH YH W Ww W W HF w rf w WH w Tr m Y W w w WH w Tr T wf w w w Iteration 1 1 015813 2 1 300782 3 1 009958 dl 1 005847 5 1 002909 B 1 0014 72 1 000788 8 1 0004 76 9 1 0003657 10 1 000426 11 1 000274 12 1 000233 13 1 000200 14 1 0001 14 ez 1 0001 53 16 1 000135 Ta 1 000118 18 1 0001 04 19 1 000051 0 1 0000580 STORING LOAD p pbpbbmpBPHHPHBHHPHHBHPBPHBPBHBHPB structural 60001 5 4 785 004424 002016 0007252 000152 356 486 0 0542 D00546 0525 000489 000449 000408 000309 ssl 000297 000206 000237 000211 hp pe pp pe pp e e 3 A A e a A A vD STAGE RESULTS IM ASCII FILE 131 Fs Jd VECCHIO Hw Ww Ww FH Ww Ww Ww W W Ww W Ww W W Ww Ww Ww W Ww Ww w FH w W HH W W W W W W W W W W W W W W W W W H W W H VecTor3 Sample Coupled Thermal and Structural Analysis r F 1 1 T f H W W W W W W W W W W W W W W W W W W w STAGE MO
129. nates For defining the coordinates of the nodes the button shown in Figure B 16 is pressed and the window shown in Figure B 17 opens Figure B 16 Create Nodes node z Hnodes dnode dx dz Hnodes dnode dx dz Hnodes d node dx Total Papo Tu Pe TO Te TET Ta T mm mm HUN NN NEN 0 a Figure B 17 For the finite element discretization suggested in Figure B 6 the values shown in the boxes in Figure B 18 should be added The numbers of nodes are 13 7 and 76 In the X Y and Z direction respectively The coordinates of the first node are 0 0 0 The distances between the 13 nodes in the X direction are 25 4167 mm adding up to a total of 305 mm with a numbering increment d node of 1 from one node to the next In the Y direction the 7 nodes will be 25 4167 mm apart having a numbering increment d node of 13 from one node to the next The spacings between the nodes in that direction add up to a total of 152 5 mm which is half the depth of the column This means that a grid of 94 VecTor3 Sample Coupled Thermal and Structural Analysis 7x13 nodes will be created at this level with a total of 91 nodes Extrapolating those nodes in the Z direction 76 nodes will be created at distances of 50 1333 mm with a numbering increment d node of 91 from one node to the next Pressing the Add button adds the nodes to the structure The nodes can be seen in the X Y plane in Figure B 19 More views can be obtain
130. ncludes the entries required by the user in the Job Control tab in the Job Definition window A 2 4 2 Structural Analysis Models Definition The next tab in the Job Definition window is titled Models and it can be seen in Figure A 54 This tab allows the user to select the models of the advanced structural mechanisms to be followed in the structural analysis for concrete steel reinforcing bars and bond between concrete and steel reinforcing bars This is in addition to several general analysis models The tab is composed of four collective frames one for each material type with a total of three and one for the analysis models Those collective frames are titled Concrete Models Reinforcement Models Bond Models and Analysis Models 46 VecTor3 User s Manual Define Job Job Control Models Ausiliay Ausiliary Thermal Concrete Models Compression Pre Peak Parabola Hognestad Confined Strength Kupfer Richart Compression Post Peak Modified Park Kent Dilation Mariable Kupfer Compression Softening Vecchia 19924 51 62 Fom gt Cracking Criterion Mohr Loulemb Stress vl Crack Stress Calc Basic DSFMAMCFT vi Crack Width Check Agg 2 5 Mas Crack Width Tension Stiffening Modified Bentz 2003 vl Crack Slip Calc lwalrawen Monotonic vl Tension Softening linea UC Creep and Relaxation Mot Available FAL Tension SDEM Monatonic Hystere
131. nd at the same nodes they can both be defined by the same Load file name which will be set to Lateral as shown in Figure B 47 To distinguish between the two lateral loading cases each will be assigned a different Load case title Arbitrarily Case 3 will be assigned Lateral 1 and Case 4 will be assigned Lateral 2 Starting with Case 3 it will be assigned an Initial factor of 0 and a Final factor of 25 with an nc factor of 1 The increment factor Inc factor is selected based on the 60 second time step selected previously for the thermal loading case and a 1 mm displacement intended to be defined at the Load Definition step later on Section B 2 4 Returning to Figure B 3 it can be seen that the rate of lateral loading for the first 25 minutes of the test was 1 mm min Thus at each load step of 60 seconds an additional mm of lateral loading should be applied The Load Type should be set to Monotonic Repetitions and Cyclic Inc factor entries will be discarded for this type of loading Therefore they can be left as their default entries of 1 and 0 respectively Finally the Initial load stage will be set to 1 meaning that this lateral loading case will be applied starting from the first load stage The next 25 minutes of the test with the different rate of lateral loading will be defined i
132. next 95 minutes Then they will both be left with constant values to achieve the constant lateral displacement of 50 mm that was reached at 120 minutes from the start of the test Those constant values will be applied until the end of the analysis the failure of the column The final input is shown in Figure B 47 The first loading case to be defined will be the thermal loading case simulating the fire conditions Casel box in the collective frame Loading Data in the window shown in Figure B 46 1s ticked in order to define the loading case Arbitrarily the Load file name will be set to Thermal and the Load case title will be Fire Load Since this is a time stepping analysis the Initial factor refers to the load factor throughout the analysis on which no increment will be applied Therefore it will be set to 1 The entry of the Final factor will be discarded in the analysis so it can be arbitrarily set to 1 as well The 108 VecTor3 Sample Coupled Thermal and Structural Analysis Inc factor refers to the time step time increment to be used in the analysis in seconds This will be set to 60 which means that the analysis will run at increments of one minute The Load Type can be left as the default entry Monotonic The Repetitions will be set to 1 as well This is because for thermal loading the time step 15 not as small as that used
133. nforced concrete elements subjected to shear American Concrete Institute ACI Journal 83 2 219 231 Vecchio F J and Collins M P 1993 Compression response of cracked reinforced concrete Journal of Structural Engineering American Society of Civil Engineers ASCE 119 12 3590 3610 Vecchio F J and Lai D 2004 Crack shear slip in reinforced concrete elements Journal of Advanced Concrete Technology 2 3 289 300 Vintzeleou E N and Tassios T P 1987 Behavior of dowels under cyclic deformations American Concrete Institute ACI Structural Journal 84 1 18 30 Voo J Y L and Foster S J 2003 Variable engagement model for fibre reinforced concrete in tension School of Civil and Environmental Engineering University of New South Wales UNSW Sydney Australia 86 p Walraven J C and Reinhardt H W 1981 Theory and experiments on the mechanical behaviour of cracks in plain and reinforced concrete subjected to shear loading Heron 26 1A 1 68 Wong P S Trommels H and Vecchio F J 2013 VecTor2 and FormWorks User s Manual Second Edition Department of Civil Engineering University of Toronto 318 p Xie D and Qian Z 1998 Research on bond and tension of concrete after high temperature in Chinese Journal of Zhejiang University Natural Science 32 5 597 602 Yamamoto T 1999 Nonlinear Finite Element Analysis of Transverse Shear and Torsional Problems in Reinfo
134. ns E Analysis Mode Static Nonlinear Time Step Dynamic Averaging Factor 0 15 Results Files ASCII Files Dny vi Convergence Limit 1 0001 Modeling Format To Computer ea oo Figure B 47 109 VecTor3 Sample Coupled Thermal and Structural Analysis The second loading case to be defined will be the axial loading case The axial load will be applied in a load control regime to resemble the constant axial load applied during the test The Case 2 box will be ticked to define it The Load file name can be arbitrarily set to Axial and the Load case title as Axial Load Since the axial load is kept constant throughout the test both the Initial factor and the Final factor will be set to 1 with the Inc factor set to zero The Load Type should be set to Monotonic Repetitions and Cyclic Inc factor entries will be discarded for this type of loading Therefore they can be left as their default entries of 1 and 0 respectively Finally the Initial load stage will be set to 1 meaning that the axial load will be applied starting from the first load stage The third and fourth loading cases will be dedicated to the lateral loading A displacement control regime will be used for the lateral loading to resemble the test conditions The Case 3 and Case 4 boxes will be ticked Since both loading cases involve the same type of loading a
135. nt Types of High Strength Concrete Journal of Materials in Civil Engineering 23 6 793 801 Kodur V K R and Sultan M A 2003 Effect of Temperature on Thermal Properties of High Strength Concrete Journal of Materials in Civil Engineering 15 2 101 107 Kodur V K R Wang T C and Cheng F P 2004 Predicting the fire resistance behaviour of high strength concrete columns Cement amp Concrete Composites 26 2 141 153 Kollegger J and Mehlhorn G 1990 Experimentelle Untersuchungen zur Bestimmung der Druckfestigkeit des gerissenen Stahlbetons bei einer Querzugbeanspruchung Deutscher Ausschuss Fur Stahlbeton Berlin Germany 132 p Kupfer H Hilsdorf H K and Rusch H 1969 Behavior of concrete under biaxial stress American Concrete Institute ACT Journal 87 2 656 666 Kwon M and Spacone E 2002 Three dimensional finite element analyses of reinforced concrete columns Computers amp Structures 6 2 199 212 Lee S C Cho J Y and Vecchio F J 2011a Diverse embedment model for steel fibre reinforced concrete in tension model development American Concrete nstitute ACI Materials Journal 108 5 516 525 Lee S C Cho J Y and Vecchio F J 2011b Diverse embedment model for steel fibre reinforced concrete in tension model verification American Concrete nstitute ACI Materials Journal 108 5 526 535 136 References Lee S C Cho J Y and Vecchi
136. o F J 2013 Simplified diverse embedment model for steel fiber reinforced concrete elements in tension American Concrete Institute ACI Materials Journal 110 4 403 412 Li L and Purkiss J A 2005 Stress strain constitutive equations of concrete material at elevated temperatures Fire Safety Journal 40 669 686 Li W and Guo Z 1993 Experimental investigation on strength and deformation of concrete under high temperature in Chinese Journal of Building Structures 14 1 8 16 Lie T T 1992 Structural Fire Protection ASCE Manuals and Reports on Engineering Practice No 78 New York NY American Society of Civil Engineers ASCE Lie T T and Kodur V K R 1996 Thermal and mechanical properties of steel fibre reinforced concrete at elevated temperatures Canadian Journal of Civil Engineering 23 4 511 517 Lie T T and Lin T D 1985 Fire performance of reinforced concrete columns American Society for Testing and Materials ASTM Special Technical Publication SIP882 Fire Safety Science and Engineering 176 205 Lie T T Rowe T J and Lin T D 1986 Residual strength of fire exposed reinforced concrete columns American Concrete Institute ACI Special Publications SP92 Evaluation and Repair of Fire Damage to Concrete 153 174 Lu Z 1989 A Research on Fire Response of Reinforced Concrete Beams in Chinese PhD Thesis Tongji University Malvar L J and Crawfo
137. o the displacements of the first group through the specified factor Figure A 37 Create Linked Nodes Group D F1 Mode nodes di node nodes nude nodes d node Total Linked Nodes WN HT M M EM Factor DOF Made H nodes d node nodes d node nodes d node 2 EE EEEE EEEN HHEH Figure A 38 For a specific entry the user is required to select the degree of freedom to be linked for the first group in the global X Y or Z direction in the part titled DOF 1 then the ID number of the first node in the first group is entered in the box titled Node 1 For including more nodes in the group the user can use the previously explained extrapolation scheme through three sets of boxes for three levels of extrapolation If the displacements of the nodes included in the first group are to be linked to the displacements of other nodes through a specific relation the user 1s required to enter the input in the second row of boxes in the window shown in Figure A 38 The relation between the two groups is specified through a certain factor entered in the box titled Factor Then the degree of freedom of the displacements of the nodes included in the second group which is required to be linked to the degree of freedom of the displacements of the nodes included in the first group should be entered in the part titled DOF 2 Next the ID number of the first node in the second group 1S required to
138. ode dF dFy dFz Hnodesdnode dFy dFz Total 1 fo fo fo fi fir fofofo fi ftfofofo T T ToToTo i Done BEEN po FE DS Selection Mode Pointer Window Figure A 61 The user can define the concentrated point loads on the nodes individually one at a time or specify the ID number of a certain node with specific concentrated point loads and extrapolate the loads to other nodes by specifying the number of loaded nodes nodes the increment in the ID number of the subsequent nodes d node and the increments in the concentrated load value from one node to the next in the X direction d Fx the Y direction d Fy and the Z direction d Fz This increment in the load value can be beneficial in the cases of triangular and trapezoidal distributed loads This extrapolation can be done in three levels simultaneously using the three sets of boxes available for user input as shown in Figure A 61 The Pointer and Window selection options that were explained earlier are also available A 2 5 2 Support Displacements Imposed Displacements The eighth button from the left in the toolbar shown in Figure A 57 whose shape is shown in Figure A 62 allows the user to define support displacements or imposed displacements on specific nodes in the structural model Pressing the button opens the window shown in Figure A 63 The user is required to specify the ID number of the node the dir
139. of Reinforced Concrete or Structural Steel are entered in their respective boxes or left vacant or with zero values for the option to use the default values the user 1s required to press the Add button in the upper part on the left hand side of the window shown in Figure A 14 At this point the new material type named Material 1 appears in the box titled Type on the left hand side of the window as shown in Figure A 18 Should the user need to change the value of any of the properties previously entered the new value should be entered in the respective box then the button titled Update should be pressed Also the Delete button allows the user to delete the undesired material types by selecting them from the box titled Type on the left hand side of the window and pressing the button The user is also given the option to choose the colour in which the defined material will be displayed using the button titled Colour Define Material Properties Material Types Material Properties Smeared Reinforcement Properties Type Reference Type Reinforced Concrete Reference Type Ductile Steel Reinforcement M Cylinder Compressive Strength Pe 130 Update Tensile Strength Ft 0 MPa k l 0 m E Initial Tangent Elastic Modulus Ec Reinforcement Ratio rho Cylinder Strain at Pc eo x Reinforcement Diameter Db mm Poisson s Ratio 4
140. of the Failure of Concrete under Combined Compressive Stresses University of Illinois Engineering Experimental Station Urbana Illinois 104 p Saab H A 1990 Non linear Finite Element Analysis of Steel Frames in Fire Conditions PhD Thesis University of Sheffield Sheffield England 143 p Sadeghian V 2012 FormWorks Plus Improved Pre processor for VecTor Analysis Software M A Sc Thesis University of Toronto Toronto ON 147 p 138 References Saenz L P 1964 Discussion of Equation for the stress strain curve of concrete by P Desay and S Krishnan American Concrete Institute AC Journal 61 9 1229 1235 Sato Y and Vecchio F J 2003 Tension stiffening and crack formation in RC members with FRP sheets Journal of Structural Engineering American Society of Civil Engineers ASCE 129 6 717 724 Seckin M 1981 Hysteretic Behaviour of Cast in Place Exterior Beam Column Slab Subassemblies PhD Thesis University of Toronto Toronto ON 266 p selby R G 1990 Nonlinear Finite Element Analysis of Reinforced Concrete Solids Master of Applied Science Thesis University of Toronto 144 p Selby R G and Vecchio F J 1997 A constitutive model for analysis of reinforced concrete solids Canadian Journal of Civil Engineering 24 3 460 470 Shin K Y Kim S B Kim J H Chung M and Jung P S 2002 Thermo physical properties and transient heat transfer of concrete at e
141. of the record Total Duration in seconds and the total number of acceleration time key points Number of Data In the drop list at the top the user can select a certain direction X Y or Z for which the maximum and minimum ground accelerations will be 77 VecTor3 User s Manual displayed in the boxes titled Max PGA and Min PGA respectively together with the corresponding time and the corresponding acceleration values in the other two directions The second way to define ground acceleration records 1s associated with the Analysis Mode titled Dynamic Nonlinear EQ Record which can be selected in the Job Control tab in the Job Definition step Section A 2 4 1 of the VecTor3 User s Manual This Analysis Mode allows the user to define the impulse loading record using an earthquake record saved in a separate file with the title VECTOR EQR This file cannot be generated using Formworks Plus but existing files can be read by Formworks Plus to enable the user to check the input for possible errors In order to read the file the user 1s required to press the Insert button which opens a window allowing the user to select the VECTOR EQR file that needs to be read The format of a typical VECTOR EQR file is presented in in Appendix A The earthquake acceleration time record read from the VECTOR EQR file is also applied over the entire structure With all th
142. or program 6 Mixed Type using a variety of elements available in all VecTor programs linked together using Cyrus program FormWorks 4 0 Preprocessor for Vector Programs Finite Element Analysis of Reinforced Concrete EJ Vecchio University of Toronto 2012 Sponsored by Software Development by Natural Sciences and Engineering Research Council of Canada Peter Wong Morrison Hershfield Ltd Consulting Engineers Toronto Vahid Sadeghian Figure A 1 VecTor3 User s Manual Structure Data Figure A 2 For analyzing three dimensional structures using VecTor3 the user is required to choose the second option VT3 for Solid 3 D This introduces the standard user interface of Formworks Plus shown in Figure A 3 At this point the pre processor is ready for the analysis job definition to be started by the user The buttons in the toolbar shown in Figure A 4 are responsible for all the user input data required for the analysis job definition as will be shown in the following steps The workspace view in the lower part of the screen is responsible for displaying the structure and the loading profiles as they are defined by the user At any point the analysis job definition including all the structural and loading profiles that have been defined can be saved by pressing the button shown in Figure A 5 The file to be saved has the extension FVVP and it can be reopened and updated at any later time Ve
143. own in Figure B 35 101 VecTor3 Sample Coupled Thermal and Structural Analysis Figure B 33 Figure B 34 Create Truss Elements elmi node 1 2 Helmts elmi 4 node Helmts elmi dnode Helmts delmt d node Total EN EHEN jJ J ENENEN EN ENEE Delete Done Figure B 35 The line shown in Figure B 36 creates the longitudinal truss bar elements and the lines shown in Figure B 37 and Figure B 38 create the ties truss bar elements When all elements are defined pressing the Done button closes the window The view shown in 102 VecTor3 Sample Coupled Thermal and Structural Analysis Figure B 39 shows the layout of the longitudinal reinforcement and the ties in the model The coordinates of the nodes comprising the elements can be found using the various display features explained in Section A 2 1 1 of the VecTor3 User s Manual Create Truss Elements elmi node 1 a Helmts delmt dnode Helmts delmt dnode Helmts delmt d nade fa fio ml ols 2 1118 T T 1 Eli 29 120 120 121 x 120 133 13 18 548 Figure B 36 Create Truss Elements node 1 l 2 Helmts d elmt d node Helmts d elmt d node Helmts delmt d node Total propia 8 111 1 133 is T fifi Add 5758 28 120 75 2 Sl 2 1 8 1 1 1 Delete _ Done 120 133 2 1 8 13 16 546 Figure B 37 Create Truss Elements node 1 2 Helmts elmi dnode Helmts elmi d nude Helmts delmt d nude 12
144. p3 Teool nodes d node nodesd node nodesd node Total Pore 1 1 atmosphere Pres ASTM E119Model vi fo fo fo fo o o oo 2 12 e si 6 13 0 Done Selection Mode Pointer Window Figure B 57 Figure B 58 shows the nodes subjected to fire along the height of the column marked in red and Figure B 59 shows a cross section with the nodes subjected to fire around the surface also marked in red Phage bb K RE dh EEUZUUEEEFEFRERU TE BOE Hood don HON ooh ooh FEUZUSEMEFFFEBS UENM Fummmhmnuumikhmwm s Figure B 58 121 VecTor3 Sample Coupled Thermal and Structural Analysis Figure B 59 The Surface drop list should be left as the default entry Atmosphere referring to the fact that the applied temperatures are the temperatures of the fire not the actual temperatures of the nodes on which the fire conditions are applied the Element Surface option The checkbox titled Pore Pres should be left unticked here as coupled heat and moisture transfer analysis is not required For the Fire Curve Type the ASTM E119 12a 2012 model should be selected as it 1s similar to the CAN ULC S101 07 2007 standard temperature fire curve applied during the test Tml Tp1 Tm2 Tp2 Tm3 and Tp3 are used to define custom temperature time curve therefore they will be discarded for the fire curve type selected Tcool which denotes the time at which
145. pe is set to carbonate as the aggregate used in the concrete mix for this column was calcareous The default values for the Emissivity Initial Density and Initial Moisture Content are left unchanged as 0 7 2400 kg m and 4 respectively 117 VecTor3 Sample Coupled Thermal and Structural Analysis The default entries chosen are as follows For concrete Compressive strength at elevated The Eurocode EN 1992 1 2 2004 2005 temperatures Residual compressive strength Chang et al 2006 Model 1 Strain corresponding to peak compressive The Eurocode EN 1992 1 2 2004 2005 stress Residual strain corresponding to peak Chang et al 2006 compressive stress Initial modulus of elasticity Stress factor corr strain factor Residual initial modulus of elasticity Chang et al 2006 Model 1 strength Tensile strength The Eurocode EN 1992 1 2 2004 2005 Residual tensile strength Chang et al 2006 Thermal expansion strain The Eurocode EN 1992 1 2 2004 2005 118 VecTor3 Sample Coupled Thermal and Structural Analysis For reinforcement Yield stress The Eurocode EN 1992 1 2 2004 2005 Ultimate stress The Eurocode EN 1992 1 2 2004 2005 Young s modulus The Eurocode EN 1992 1 2 2004 2005 Thermal expansion strain The Eurocode EN 1992 1 2 2004 2005 B 2 4 Load Definition The loads applied to the structural model to be analyzed are to be added at t
146. pes that can be anlayzed using VecTor3 going through the buttons in the Load Definition toolbar shown in Figure A 57 from left to right can be summarized in the following list 1 Nodal Loads support Displacements Imposed Displacements Gravity Loads Elements Temperatures Concrete Elements Prestrains 2 3 4 5 6 Concrete Elements Ingress Pressures 7 Concrete Elements Surface Temperatures Nodal Thermal Loads 8 Lumped Nodal Masses for Dynamic Analysis 9 Impulse Forces 10 Ground Acceleration Pressing these buttons opens input windows that allow the user to define the loads applied on the structural model by specifying a node s ID number or an element s ID number and the load applied on it Also for all those load types except ground acceleration there are graphical options available for the user to assign the loads to the nodes and elements without the need to specify their ID number Those options can be accessed using the two buttons Pointer and Window which appear in the collective frame titled Selection Mode on the right hand side of the window of every load type The button Pointer allows the user to select one node or element at a time from the nodes and elements displayed in the workspace view The button Window allows the 64 VecTor3 User s Manual user to select multiple nodes or elements in one step by holding dovvn the left mouse button and dragging a w
147. ple Coupled Thermal and Structural Analysis OO O O 49 S 51 52 c s h co 23 24 425 a26 aG a 3 4 6 6 O 8 8 10 11 412 13 Figure 25 f f M Y E E y B 2 2 1 3 Applying Node Constraints Linking Nodes In the test the rotation was restrained at both ends of the column The restraints applied at the base of the model in the previous step Section B 2 2 1 2 of the VecTor3 Sample Coupled Thermal and Structural Analysis achieve this rotation restraint for the bottom horizontal plane of the model However the top plane cannot be vertically restrained since the model will be axially loaded and should be free to deform along it height Therefore in order to achieve the rotation restraint for the top horizontal plane of the model the nodes at this plane will have to be linked constrained to displace together vertically in the Z direction according to the selected orientation This will be done by pressing the button shown in Figure B 26 opening the window 222 Figure B 26 shown in Figure B 27 98 VecTor3 Sample Coupled Thermal and Structural Analysis Create Linked Nodes Group DOF Hodel dnode nodes node nodes d node Total ft Linked Nodes Bo tH HRT HEE AMA Factor D F 2 Node nodes d node nodes d node nodes d node Boe UM S BM BM e Figure B 27 The line shown in Figure B 28 will be entered pressing the
148. pping loading procedure that 1s independent of the loading rate is followed The material behaviour is nonlinear This is the type of analysis that 1s responsible for carrying out coupled thermal and structural analysis 4 Dynamic Nonlinear General where dynamic loading procedure is followed This 1s the type of analysis that is responsible for carrying out dynamic analysis based on ground acceleration records defined by a maximum of 50 acceleration time key points applied over the entire structure or impulse loading records defined by a maximum of three force time key points applied at any number of nodes in the structural model 5 Dynamic Nonlinear EQ Record where dynamic loading procedure is followed This is the type of analysis that is responsible for carrying out dynamic analysis based on an earthquake record generated by the user in a separate file having the title VECTOR EQR This earthquake acceleration time profile 1s applied over the entire structure This is similar to the Dynamic Nonlinear General for ground acceleration records except for the ability to define the acceleration time profile with up to five hundred key points and in a separate file The formatting of the file VECTOR EQR is shown through a sample file in Appendix A 6 Dynamic Nonlinear Impulse Record where dynamic loading procedure 1s followed This is the type of analysis that is responsible for carrying out dynamic ana
149. pported Length Ratio bt Color Reinforcement material types to be used for truss elements only Uk Lancel Figure A 22 In the drop list on the right hand side the user can choose the type of reinforcement from the four aforementioned types The properties of steel reinforcement entered in this window also follow the curve shown in Figure A 17 as explained earlier for smeared reinforcement The single additional property that is unique here is the cross sectional 19 VecTor3 User s Manual area of the reinforcing bar which substitutes for the reinforcement ratio in the case of the smeared reinforcement When the properties are entered the user is required to press the Add button on the left hand side of the window shown in Figure A 22 which will add the reinforcement material type to the list box titled Type on the left hand side as shown in Figure A 23 The user can use the Update Delete and Colour buttons as required as explained earlier Define Reinforcement Properties Reinforcement Type Reinforcement Properties Type a Reference Type Ductile Steel Reinforcement Add Cross Sectional Area 500 mmz Reinforcement Diameter Db 25 0 mm Yield Strength Fu AED MPa Update Delete Ultimate Strength Fu 40 Elastic Modulus Es 200000 MPa Strain Hardening Strain esh E me Ultimate Strain eu 1 0 me Thermal Expansion Coefficient Cs i i PL
150. r to display a cross section of the structure in the X Y Y Z or X Z planes respectively A typical view of the window that creates a cross sectional view of the structural model in the X Y plane is shown in Figure A 9 The user can specify the elevation in the Z direction at which the cross sectional view is required to be displayed For a cross sectional view in the Y Z plane the elevation in the X direction should be specified and for a cross sectional view in the X Z plane the elevation in the Y direction should be specified Also the drop list in this window allows the user to view a projection view of the structure from either of the two opposite sides top and bottom or left and right Set XY View Section zs 0 00 Cancel Figure A 9 The next two buttons shown in Figure A 10 allow the user to navigate through the cross sectional view created using the XY YZ and XZ buttons where the button on the left hand side featuring the upward arrow increases the coordinate of the displayed cross sectional view and the button on the right hand side featuring the downward arrow decreases the coordinate of the displayed cross sectional view Finally the last button from the left in the toolbar shown in Figure A 6 titled 3D which is shown in Figure A 11 creates a three dimensional isometric view of the structural model Figure A 10 VecTor3 User s Manual Figure A 11 A 2 2 M
151. rced Concrete Shells M A Sc Thesis University of Toronto 112 p 140 Appendix A Sample VECTOR EQR File Appendix A Sample VECTOR EOR File 4 MAY 18 1940 CORRECTED ACCELEROGRAM 180 DEGREES CALTECH 1 U C BERKELEY CALIFORNIA SOURCE MISEE 2674 0 02 8 G 1337 0 04 8 G 333 0 10 8 G 2674 POINTS OF ACCEL DATA EQUALLY SPACED AT 0 02 SEC UNITS MM SEC SEC 19 28 54 dz 14 96 31 G 532 528 204 Le 1128 107 1105 1589 997 247 BIz 270 1487 553 55 611 59 524 711 65 985 954 592 1532 694 465 536 1216 780 198 301 323 405 472 353 288 274 454 419 16 661 309 226 299 690 353 241 278 653 194 856 fff 182 343 50 474 305 IMPERIAL VALLEY EL CENTRO 2037 PST 33 188 40 7 646 497 147 538 1459 336 1003 1693 bd 126 1118 518 131 1183 621 459 351 511 501 54 53 147 1074 875 645 1245 06 133 1002 1100 1000 178 106 10 339 Ha 1753 154 245 719 91 41 498 113 495 388 79 220 2 419 132 160 996 841 224 343 351 119 _ 22 134 245 85 110 525 498 2153 908 1213 599 1079 1521 595 079 922 _ 38 144 768 542 206 198 926 376 2 FF 205 075 661 1053 1117 690 823 323 328 990 351 444 287 134 212 5 85 109 523 549 43 284 249 632 320 J83 3d 245 989
152. rd J E 1998 Dynamic increase factors for concrete Twenty Eighth Department of Defense Explosives Safety Seminar DDESB Orlando FL Mander J B Priestley M J N and R Park 1988 Theoretical stress strain model for confined concrete Journal of Structural Engineering American Society of Civil Engineers ASCE 114 8 1804 1826 Miyahara T Kawakami T and and Maekawa K 1987 Nonlinear behavior of cracked reinforced concrete plate element under uniaxial compression Proceedings of Japan Society of Civil Engineers JSCE No 378 V 6 306 319 Miyahara T Kawakami T and and Maekawa K 1988 Nonlinear behavior of cracked reinforced concrete plate element under uniaxial compression Concrete Library International Japan Society of Civil Engineers JSCE 11 131 144 Moftah M 2008 Numerical Modelling and Performance of Reinforced Concrete Members under Fire Condition PhD Thesis University of Western Ontario Waterloo ON 286 p 137 References Mohr C O 1900 VVelche Umstande bedingen die Elastizitatsgrenze und den Bruch eines Materials Zeitschrift des Vereins Deutscher Ingenieure 24 1524 1530 and 1572 1577 Montoya E 2003 Behaviour and Analysis of Confined Concrete PhD Thesis University of Toronto Toronto 297 p Morita S and Fuji S 1982 Bond capacity of deformed bars due to splitting of surrounding concrete Bond in concrete Proceedings of the International Conferenc
153. re A 75 The user is required to input the ID number of the node the directions DOFs in which the lumped mass contributes in the dynamic analysis in the X Y and Z directions and the mass 41 Figure A 74 value in kg Apply Lumped Masses Case Hade DOF Mass kg GF GF2 Vow YoY Vow nodes di node t node d node H nodes d node Total 1 BL Et X fel oo o flo ET i 1 a Dane Selection Made Painter Window Figure A 75 The boxes GF X GF Y and GF Z allow the user to specify the contribution of the defined lumped mass in the X Y and Z directions respectively These entries are entered as factors that will be multiplied by the gravitational acceleration g in the analysis This means that a factor of 1 in the GF Z box for example means that the real weight of the lumped mass will be applied in the positive Z direction and a factor of 1 means that the real weight of the lumped mass will be applied in the negative Z direction The boxes V X Vo Y and V Z allow the user to specify an initial velocity for the lumped mass in the X Y and Z directions in m sec respectively where these initial velocities will act as the excitation for the dynamic analysis These lumped masses are used in all the dynamic analysis types whether initial velocities have been assigned to them or not Also if a density value has been assigned to the material of an element at the Ma
154. ree nodes composing the opposite face and in the same order This means that Nodes 1 2 and 3 form a face of the two triangular faces of the element and Nodes 4 5 and 6 form the opposite triangular face Node 1 should be opposite to Node 4 Node 2 should be opposite to Node 5 and Node 3 should be opposite to Node 6 In those windows shown in Figure A 40 to Figure A 43 the user can define the elements by specifying the ID numbers of their composing nodes individually one at a time Another way to perform this task 1s to enter the composing nodes of the first element and extrapolate them to define other elements by specifying the number of elements to be defined elmts the increment in the ID number of subsequent elements d elmt and the increment in the ID number of the nodes comprising subsequent elements d node This extrapolation can be done in three levels simultaneously using the three sets of boxes available for user input as shown in Figure A 40 to Figure A 43 After each entry whether it is for an individual element or for an extrapolated group of elements the Add button on the right hand side of the window needs to be pressed This will cause the entry to show in the larger box at the bottom of the window as shown in Figure A 44 as a typical example for the regular hexahedral element input 32 VecTor3 User s Manual Create Hexahedral Elements elmt node 1 Helmts delmt d node Helmts del
155. rength of 55 MPa for the concrete of the column Reinforced Concrete is selected in the Reference Type drop list at the top and a value of 55 is inserted in the box titled Cylinder Compressive Strength f If more properties of the concrete used in this column were known their values should be inserted in their respective boxes in this window After this is done the Add button is pressed and Material 1 appears in the list of Material Types on the left hand side of the window as shown in Figure B 11 No smeared reinforcement will be used in the concrete material 89 VecTor3 Sample Coupled Thermal and Structural Analysis used in this model otherwise this would be done through the part on the right hand side of this window as explained in Section A 2 2 1 of the VecTor3 User s Manual Only one material type 1s used for this model as only one type of concrete was used in the column If more types were used they would be added to the model in the same way Once all the material types are added the OK button is pressed to close the window Define Material Properties Material Types Material Properties 5meared Reinforcement Properties Reference Type Reinforced Concrete b Type Reference Type Ductile Steel Reinforcement ki Cylinder Compressive Strength Pe 155 aaa na gan Update Tensile Strength Pt 5 l MPa k l m 0 Delete Initial Tangent Elastic
156. rete Thermal Conductivity and Thermal Time Stepping Factor The value of the Concrete Fracture Energy 1s required in case the model selected in the Tension Softening drop list in the Models tab discussed in the previous section Section A 2 4 2 of the VecTor3 User s Manual depends on it This only applies to the Nonlinear Hordijk and the FRC Lee 2011 Exponential Model options However should this entry be left at the default value 0 and one of those two options is selected for the Tension Softening model the Concrete Fracture Energy value is calculated by VecTor3 according to the model proposed by Bazant and Becq Giraudon 2002 The Prestressing Friction Coefficient and the Prestressing Wobble Coefficient are required for estimating the friction losses in unbonded tendons Therefore these entries are only used when the unbonded tendons w friction losses option is selected in the Bond Properties Definition step Section A 2 2 3 of the VecTor3 User s Manual Another collective frame titled Tension Softening allows the user to enter four key points to define a custom stress strain curve for unreinforced concrete in tension The boxes titled Tension Softening Pt 1 Strain and Tension Softening Pt 1 Strain are designated for the first key point on the curve where the former box is designated for the strain entry and the latter is des
157. rete structures modelled using smeared reinforcement the user should select Ductile Steel Reinforcement from the drop list Then the user is required to specify the orientation of the steel reinforcement by entering the values of the cosines of the angles that the reinforcement makes with the three global Cartesian coordinates X Y and Z namely k l and m respectively The summation of the squares of k l and m should obviously be equal to 1 The next step is to enter the Reinforcement Ratio p which is the percentage of the cross sectional area of the reinforcement to the area of the entire section Alternatively for the finite element analysis purposes the reinforcement ratio can be defined as the percentage of the cross sectional area of the reinforcement to the area of the section of the concrete finite element that 1s perpendicular to the reinforcement The user is then required to enter the various material properties of steel reinforcement including the Reinforcement Diameter dy Yield Stress fy Ultimate Stress fy Elastic Modulus Young s modulus Es Stram Hardening Strain sh Ultimate Strain u Prestrain for prestressed reinforcement and Unsupported Length Ratio for buckling consideration Figure A 17 presents the shape of a typical stress strain curve for steel reinforcement showing the main material properties of steel required to compile the curve wh
158. s The tenth button from the left in the toolbar shown in Figure A 57 whose shape Is shown in Figure A 66 allows the user to define the temperatures of specific elements in the structural model Pressing the button opens the window shown in Figure A 67 The user is required to specify the ID number of the element and its temperature in C Figure A 66 68 VecTor3 User s Manual Apply Element Temperature Case elmi temp elmts d elmi d temp t elmts d elmi d temp elmts d elmi d temp Tatal retro T T 0 ty yo ft E Selection Mode Pointer Window Figure A 67 The user can define the temperatures of the elements individually one at a time or specify the ID number of a certain element with a specific temperature and extrapolate the input to other elements by specifying the number of elements whose temperatures need to be specified elmts the increment in the ID number of the subsequent elements d elmt and the increment in the temperature from one element to the next d temp This increment in the temperature value can be beneficial in the cases where the user needs to apply previously known non uniform temperature distribution through a section This extrapolation can be done in three levels simultaneously using the three sets of boxes available for user input as shown in Figure A 67 The Pointer and Window selection options that were explained earlier are also available
159. s a quelques probl mes de statique relatifs l architecture M moires de Mathematique et de Physique pr sent s a l Acad mie Royale des Sciences par divers savans et lus dans ses assembl e 7 343 382 Cui C and Sheikh S 2010 Analytical model for circular normal and high strength concrete columns confined with frp Journal of Composites for Construction American Society of Civil Engineers ASCE 14 5 562 572 Dhakal R P and Maekawa K 2002 Modeling for postyield buckling of reinforcement Journal of Structural Engineering American Society of Civil Engineers ASCE 128 9 1139 1147 Dwaikat M B and Kodur V K R 2009 Hydrothermal model for predicting fire induced spalling in concrete structural systems Fire Safety Journal 44 3 425 434 134 References Eligehausen R Popov E P and Bertero V V 1983 Local bond stress slip relationships of deformed bars under generalized excitations Experimental results and analytical model Earthquake Engineering Research Center University of California Berkeley 169 p ElMohandes F 2013 Advanced Three Dimensional Nonlinear Analysis of Reinforced Concrete Structures Subjected to Fire and Extreme Loads PhD Thesis University of Toronto Toronto ON 407 p EN 1992 1 2 2004 Eurocode 2 Design of Concrete Structures Part 1 2 General Rules Structural Fire Design 2005 European Committee for Standardization CEN Brussels Belgi
160. se shape 1s shown in Figure A 78 allows the user to define ground acceleration applied on the structural model Pressing the button opens the window shown in Figure A 79 Figure A 78 Apply Ground Acceleration Load Case Time s Seca a Ace YE G Summary m o o o Rdirection Time 5 Ace X 5 Ace AceZ B Insert Done Max PGA PGA Total Duration s Humber of Data Figure A 79 As previously explained there are two ways to define ground acceleration records on the structural model The first one is associated with the Analysis Mode titled Dynamic Nonlinear General which can be selected in the Job Control tab in the Job Definition step Section A 2 4 1 of the VecTor3 User s Manual This Analysis Mode allows the user to define the ground acceleration record using a maximum of 50 acceleration time key points applied over the entire structure This can be done through the input window shown in Figure A 79 The user is required to enter the time Time s and the corresponding acceleration as a factor of the ground acceleration g in the X Y and Z directions in the boxes titled Acc X g Acc Y g Acc Z gV respectively Each entry represents one point in time The collective frame titled Summary on the right hand side of the input window shows a summary of the input including the total duration
161. ser s Manual Define Material Properties Material Types Material Properties Smeared Reinforcement Properties Type Reference Type Reinforced Concrete Reference Type Steel Fibre Hooked Cylinder Compressive Strength Fc 30 MPa Fibre Volume Fraction VE Update I Tensile Strength Ft 0 MPa E Initial Tangent Elastic Modulus Ec 5 Fibre Length Lf Cylinder Strain at Fc en 0 me Fibre Diameter DF Poisson s Ratio Mu d 0 a Fibre Tensile Strength Fur Thermal Expansion Coefficient Cc x 0 PC Fibre Bond Strength Tu Maximum Aggregate 5126 a i 0 mm Reinforcement Components Density i E kg m3 Component zem Thermal Diffusivity Fe A 0 mmes Average Crack Spacing perpendicular to amp reinfarcement Se l mm perpendicular to y reinforcement Sy mm Residual Flexural Strength Frik l MPa perpendicular to z reinfarcement 52 mm Residual Flexural Strength Fr3k l Color I Required for MC 2010 option only Reinforced concrete material types to be used for solid elements only Enter for WT3 default value Ok Cancel Figure A 20 It should be noted that VecTor3 allows for defining up to fifty different material types This includes the base material types in addition to the discrete reinforcement types and the bond types which will be explained in the next two subsections For the base material types VecTor3 allows assigning up
162. t in the toolbar shown in Figure A 28 which is shown in Figure A 33 It enables the user to duplicate certain previously defined nodes at a certain offset from the existing nodes The input window shown in Figure A 34 appears when the button is pressed The input required by the user is the ID number of the node to be duplicated the offset distance in the global X Y and Z directions DX DY and DZ and the number of duplicate layers to be generated layers Finally for defining a group of nodes to be duplicated the user is required to input the number of nodes nodes and the increment in the ID number of the subsequent nodes d node for the previously explained extrapolation scheme of nodes selection ms Figure A 33 26 VecTor3 User s Manual Mode Copy Hade D r Dz ti Layer 8 Modes d Node Total Nodes po fo l 11 3 Pa Select tm Figure A 34 The button titled Select enables the user to graphically select one node at a time from the nodes showing in the workspace view using the left mouse button After each entry of either one or multiple nodes the Add button on the right hand side of the window needs to be pressed This will cause the entry to show in the larger box at the bottom of the window Unneeded entries can be deleted by selecting them from the list in the larger box at the bottom of the window then pressing the Delete button on the right han
163. te steel reinforcing bars prestressing tendons and structural steel The strengths of those material types will be multiplied by their respective resistance factors throughout the analysis This enables the user to assign the desired material factor of safety to each of the material types that have been defined Also the second last entry in this collective frame allows the user to account for the creep of concrete with time by assigning a Concrete Creep Coefficient The initial stiffness of concrete will be divided throughout the analysis by a value of one plus this value entered for this coefficient so will the strain corresponding to the peak compressive 56 VecTor3 User s Manual stress Finally the last input box allows the user to account for the relaxation of prestressing tendons with time by assigning a P S Relaxation Coefficient Young s modulus of the prestressing tendons will be divided throughout the analysis by a value of one plus the value entered for this coefficient A 2 4 4 Auxiliary Thermal Parameters Definition This tab in the Job Definition window is titled Auxiliary Thermal and it can be seen in Figure A 56 This tab allows the user to define several additional parameters that are required for the coupled thermal and structural analysis The entries in this tab involve both the heat transfer analysis through concrete and the coupled thermal and structural analysis The user input
164. terial Definition step Section A 2 2 of the VecTor3 74 VecTor3 User s Manual User s Manual a mass 1s calculated for the element based on that density These masses are assigned to the nodes comprising that element and are added to the values of the lumped masses entered in this input window The user can specify the nodes with lumped masses individually one at a time or specify the ID number of a certain node with a specific lumped mass and extrapolate the input to other nodes with the same lumped mass directions of application factors of contribution in the different directions and initial velocity This can be done by specifying the number of nodes nodes and the increment in the ID number of the subsequent nodes d node This extrapolation can be done in three levels simultaneously using the three sets of boxes available for user input as shown in Figure A 75 The Pointer and Window selection options that were explained earlier are also available A 2 5 9 Impulse Forces The fifteenth button from the left in the toolbar shown in Figure A 57 whose shape 1s shown in Figure A 76 allows the user to define impulse loading records applied on specific nodes in the structural model Pressing the button opens the window shown in Figure A 77 The user is first required to enter the ID number of the node the direction of the impulse force DOF in the X Y or Z direction and the force time profile
165. the ability of the user to select the most preferable models according to the conditions of the structure to be analyzed there 1s a shortcut available in the lower part of the right hand side of this tab in a box titled Reset Options The user can select Basic or Advanced for two available preset groups of models that are preferred by the program s developers A 2 4 3 Auxiliary Parameters Definition The next tab in the Job Definition window is titled Auxiliary and it can be seen in Figure A 55 This tab allows the user to define several additional parameters that are 53 VecTor3 User s Manual required for special types of structures loading conditions and analysis types The user input in this step is saved in the VT3 AUX input file Define Job Job Control Models uxilar Auxiliar Thermal General Dynamic Analysis Stiffness Matris Solver Type Solver 2 T Reference Made 1 isoparametic 1 e Reference Made H2 Concrete Aggregate Type Carbonate vl Damping Factor 1 21 Damping Factor 2 2 Concrete Fracture Energy kNm Concrete Thermal Conductivity w mK Time Integration Method Newmark Constant Prestressing Friction Coefficient r Ground Acceleration in x direction Mot Considered Mi Sheapessting abla Cozieni Vmi 0 0025 Ground Acceleration in y direction Not Considered Thermal Time Stepping Factor 0 566667 Ground Acceleration in z direc
166. the toolbar shown in Figure A 4 whose shape 1s shown in Figure A 49 Pressing this button opens the window shown in Figure A 50 where the number of material types the number of elements of each type the number of nodes and the number of restrained nodes can be checked Figure A 49 35 VecTor3 User s Manual Structure Information Structure title Enter Structure Title Structure file name Struct Number of material types Continuum Materials Reinforcements Bonds Number of elements and nodes Rectangular Elements Quadrilateral Elements Triangular Elements Linkage Elements Interface Elements Hexahedral Elements Wedge Elements lsoHexahedral Elements Heterasis Elements Hing Bar Elements Truss Elements Modes Restrained Nodes Cancel Figure A 50 A 2 4 Job Definition This step 1s responsible for defining the analysis job scheme This can be done before or after the Structure Definition step Defining the job can be done through the first button from the left in the toolbar shown in Figure A 4 whose shape is shown in Figure A 51 Figure A 51 36 VecTor3 User s Manual Pressing this button opens the window shown in Figure A 52 which contains four main tabs namely Job Control Models Auxiliary and Auxiliary Thermal Each of these tabs is responsible for a certain task in the analysis job definition process Define Job Job Con
167. tic Response Nonlinear ww Plastic Offsets gt Reinforcement Models Bond Models Hysteretic Response Bauschinger Effect Seckin b Dowel Action Tassios Crack Slip gt Concrete Bond Eligehausen Buckling Akkaya 2012 Refined Dhakal Ma w Analysis Models Strain History Previous Loading Considered Strain Rate Effects Conc Steell In c m Structural Damping Not Considered Geometric Nonlinearity Considered Basic Crack Process Uniform Advanced Figure A 54 The following are lists of the models available for user selection for each advanced structural mechanism and analysis model More about these models can be found in Wong et al 2013 and ElMohandes 2013 The user input in this step is saved in the VECTOR JOB input file Concrete Models Compression Pre Peak Response e Linear e Parabola Hognestad Hognestad 1951 e NSC Popovics Popovics 1973 e HSC Popovics Collins and Porasz 1989 e Hoshikuma 1997 Hoshikuma et al 1997 47 VecTor3 User s Manual e Smith Young 1956 Smith and Young 1956 e FRC Lee 2011 e Attard Setunge Attard and Setunge 1996 e Elastic Plastic e Fire Lie and Lin ASCE Lie and Lin 1985 ASCE Manual of Practice Structural Fire Protection by T T Lie 1992 e Fire The Eurocode EN 1992 1 2 2004 2005 e Fire Aslan and Bastam Aslan and Bastam 2011 Compression Post Peak Response
168. tion Not Considered Tension Softening Tension Softening Pt 1 Strain mae Tension Softening Pt 1 Stress MPa Tension Softening Pt 2 Strain me Tension Softening Pt 2 Stress MPa Tension Softening Pt 3 Strain me Tension Softening Pt 3 Stress MPa Tension Softening Pt 4 Strain me 1111131 Tension Softening Pt 4 Stress MPa UBR Reset Default Newmark Constant Not Considered gt Not Considered 7 Not Considered gt z Figure A 55 In the first collective frame titled General the user can select between two solvers available for the solution of the equations of the displacements of the present degrees of freedom in the finite element procedure Solver 1 relies on the creation of scratch files to store the values involved in the solution while Solver 2 relies on storing those numbers in the virtual memory This makes Solver 2 much faster than Solver 1 which is why it is the default selection Since there is a separate tab the Auxiliary Thermal tab for the input of the properties of concrete related to the thermal analysis the input entered by the user in this tab for those properties will be overridden by the input entered in the Auxiliary Thermal tab Those 54 VecTor3 User s Manual properties include the Concrete Aggregate Type Conc
169. to four different types of smeared reinforcement including fibres per material type A 2 2 2 Discrete Reinforcement Material Properties Definition This step is responsible for defining the various types of discrete not smeared reinforcement in the structural model The types of discrete reinforcement available in VecTor3 are Ductile Steel Reinforcement smooth or deformed Prestressing Steel Tension Only Reinforcement and Compression Only Reinforcement This step is optional depending on the presence of reinforcement in the structure and the desire of the user to model this reinforcement as discrete uniaxial truss bar elements rather than smearing it evenly within the concrete finite element that contains it 18 VecTor3 User s Manual To start defining the discrete reinforcement material properties the fourth button from the left in the toolbar shown in Figure A 4 should be pressed The shape of the button is shown in Figure A 21 This button opens the window shown in Figure A 22 Define Reinforcement Properties Reinforcement Type na Figure A 21 Reinforcement Properties Reference Type Ductile Steel Reinforcement Cross Sectional Area li mm Reinforcement Diameter Db mm Yield Strength Fu Ultimate Strength Fur Elastic Modulus Es Strain Hardening Strain esh Ultimate Strain eu Thermal Expansion Coefficient Ls i no PE Prestrain Dep Unsu
170. trol Models Auxiliary Auxiliary Thermal Job Data Structure Data Job file name Structure file name Struct Job title Enter Job Title Structure title Enter Structure Title Date Enter Date Structure type Solid 3 D Y Loading Data Load series ID ID Starting load stage na 1 Ma of load stages 1 Activate Case 1 Case 2 Case 3 Case 4 Case 5 Load file name NULL NULLS UL mo Load case title Enter load case title Enter load case tile Enter load case tile ENTERA Enter load case tile Initial Factor Oo p o o Final factor m mm IN Inc factor p TN Load type Monotonic gt Monotonic DESEE E ETE TENE Hepetitions n ima TT Cyclic Inc factor co Ep a Initial Load Stage Sa mwa A r Analysis Parameters seed File Name MULL Convergence Criteria Displacements Weighted Average v no of Iterations 60 Analysis Mode Static Nonlinear Load Step Dynamic Averaging Factor 10 6 Results Files ASCII Files Ony el Convergence Limit 1 00001 Modeling Format Stand Alone Modeling cues vo Figure A 52 A 2 4 1 Analysis Job Control Parameters Definition This step 1s responsible for defining the main framework of the analysis This is done through the first tab in the Job Definition window titled Job Control The user input is composed of four main parts in four col
171. um 97 p ENV 1992 1 2 1996 Eurocode 2 Design of Concrete Structures Part 1 2 General Rules Structural Fire Design 1996 European Committee for Standardization CEN Brussels Belgium 63 p European Convention for Constructional Steelwork ECCS Brussels Belgium Technical Committee 3 Fire Safey of Steel Structures European Recommendations for the Fire Safety of Steel Structures Calculation of the Fire Resistance of Load Bearing Elements and Structural Assemblies Exposed to the Standard Fire 1983 Amsterdam Netherlands Elsevier 106 p fib Model Code 2010 Final Draft Bulletin No 66 2012 F d ration Internationale du Beton fib Lausanne Switzerland 370 p Gan Y 2000 Bond Stress and Slip Modeling in Nonlinear Finite Element Analysis of Reinforced Concrete Structures M A Sc Thesis University of Toronto 251 p Gawin D Majorana C E and Schrefler B A 1999 Numerical analysis of hygro thermal behaviour and damage of concrete at high temperature Mechanics of Cohesive frictional Materials 4 1 37 74 Gupta P R 1998 Shear Design of Reinforced Concrete Members Under Axial Compression PhD Thesis University of Toronto Toronto ON 189 p Harajli M H and Mukaddam M A 1988 Slip of steel bars in concrete joints under cyclic loading Journal of Structural Engineering American Society of Civil Engineers ASCE 114 9 2017 2035 Hertz K D 2005 Concrete strength for
172. unning are also saved in a text file with the title VECTOR TXT After the analysis is completed the user can use the post processor Janus for a graphical display of the results This can be done by starting Janus by pressing the sixth button from the left the last button in the toolbar shown in Figure A 82 whose shape is shown in Figure A 83 then opening the VECTOR TOB file in Janus Figure A 83 81 VecTor3 B Sample Coupled Thermal and Structural Analysis Fady ElMohandes Frank J Vecchio November 2013 VecTor3 Sample Coupled Thermal and Structural Analysis B 1 Test Introduction In this section a step by step procedure for a sample of a coupled thermal and structural analysis using VecTor3 is presented For this purpose Column 1582 tested by the National Research Council Canada NRC has been chosen This test carried out by Mostafaei et al 2012 1s the first of its kind It involved testing a full scale column specimen for fire resistance assessment under both axial and lateral loading The column had a 305 mm square cross section and a height of 3760 mm with two 25 mm thick steel loading plates at the top and the bottom It was reinforced using four 25 mm diameter longitudinal steel reinforcing bars at the four corners with a clear cover of about 48 mm The bars were tied using 10 mm diameter ties at a spacing of 305 mm Figure B 1 shows the cross section of the column and Figure B 2 shows the
173. will be chosen for the thermal expansion coefficient of concrete For the Prestrain and the Unsupported Length Ratio they will both be assigned a value of zero Once all the properties are inserted in their respective boxes the Add button is pressed Reinforcement 1 appears in the Reinforcement Type list on the left hand side of the window as shown in Figure B 14 Define Reinforcement Properties Reinforcement Type Reinforcement Properties Type l i Reference Type Ductile Steel Reinforcement Add L ross Sectional Area 1490 mme Update Update Reinforcement Diameter Db 25 mm Delet iiid Yield Strength Fy 444 MPa Ultimate Strength Fu 731 MPa Elastic Modulus Es 200000 MPa Strain Hardening Strain esh E me Ultimate Strain eu 200 me Thermal Expansion Coefficient Ls i SC Prestrain Dep Unsupported Length Ratio b t Color Reinforcement material types to be used for truss elements only Figure B 14 For the ties Ductile Steel Reinforcement is selected in the Reference Type drop list at the top Since they have a diameter of 10 mm a value of 78 mm and a value of 10 mm 92 VecTor3 Sample Coupled Thermal and Structural Analysis are inserted in the boxes titled Cross Sectional Area and Reinforcement Diameter dp respectively Similarly a value of 427 MPa and a value of 671 MPa are inserted in the boxes titled
174. y files will have the extension A3R The format of output files will be explained later The user can also specify the ID number by which the output ASCII text files should start to be titled from This 1s done by entering the desired value of the ID number of the first load stage in the box titled Starting load stage no This means that if the default output text files title D 1s chosen and the ID number of the first load stage 1s chosen to be 1 then the title of the first output ASCII text file and binary file will be ID 1 A3E and ID_1 A3E respectively The last input entry in this box 15 the total number of load stages to be analyzed in the analysis job which can be entered in the box titled No of load stages As will be explained later the analysis will run in the load increments to be specified later for a number of increments equal to the number of load stages entered in this box The next step in this part is defining the analysis loading scheme for the loading conditions that will be defined later As previously explained VecTor3 allows for five different loading cases of similar or different types to be analyzed simultaneously The number of loading cases to be analyzed should be specified in this part by ticking the 38 VecTor3 User s Manual checkboxes titled Case 1 to Case 5 as shown in Figure A 52 depending on the number of loading cases the user desires to be

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