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1. build segments 12 33 25 25 build segments 11 34 Anchor 25 25 build segments 10 35 25 STRUCTURE BUILD 14 31 17 CHANGE COMPLETE SOLVE SOLVE Day 112 e EE Stress tendon 8 move travelers CHANGE STRUCTURE STRESS N 8 StressTo 198E3 198E3 Anchor 25 MOVE N 1 0 13 14 15 MOVE N 2 D 31 32 33 CHANGE COMPLETE SOLVE OUTPU CHANGE STRUCTURE BUILD N 13 32 19 CHANGE COMPLETE SOLVE SOLVE Day 119 Stress tendon 9 move travelers CHANGE STRUCTURE STRESS N 9 StressTo 198E3 198 MOVE N 1 0 12 13 14 MOVE 2 D 32 33 34 CHANGE COMPLETE SOLVE OUTPU CHANGE STRUCTURE BUILD N 12 33 21 CHANGE COMPLETE SOLVE SOLVE Day 126 Stress tendon 10 move travelers CHANGE STRUCTURE STRESS N 10 StressTo 198E3 198 MOVE N 1 0 11 12 13 MOVE N 2 D 33 34 35 CHANGE COMPLETE SOLVE OUTPU CHANGE STRUCTURE BUILD N 11 34 23 CHANGE COMPLETE SOLVE SOLVE Day 133 Stress tendon 11 move travelers CHANGE STRUCTURE STRESS N 11 StressTo 198E3 198E3 Anchor 25 MOVE N 1 0 10 11 12 MOVE N 2 D 34 35 36 CHANGE COMPLETE SOLVE OUTPU CHANGE STRUCTURE BUILD N 10 35 25 5 20 ADAPT
2. retta idi tu t m 50 SPRINGS usu suasana atau 51 ME dn 52 STAY ANALYSIS 53 T R A 54 5 DN 54 TENDONGEOMETRY 2 52 2 tb VR NR IUE 56 INPUT GENERATION Chapter 3 62 TRAVELERS ci a n nk eed e pu ea um aQ a Qa ala ui 62 IT 02 INPUT GENERATION Chapter 3 3 1 OVERVIEW ADAPT ABI software is a special purpose structural analysis program specifically developed for the time dependent analysis of segmentally erected prestressed concrete plane frame struc tures and bridges It accounts for variation with time of creep shrinkage relaxation in pre stressing and concrete aging as well as creep recovery The structure is modeled as a system of frame elements and prestressing tendon elements connected at nodes Time is divided into a number of time steps and the program computes the response of the structure at the end of each of these time steps 3 1 1 3 1 2 Capabilities The program can build the structure in the computer using any statically feasible construction sequence for the plane frame Frame elements springs and tendon ele ments may be installed and removed at any time st
3. Debe dier 1 2 1 2 Principal Assumptions ies PAEST LLS i PEREA EES ETET OR RIO tes A Node operations nasua DEOS Reb t te cos I aaa EHE 6 B Addition of new frame elements ee 7 C Solution scheme eee etre EE KE rete Re RE 7 22 GEOMBTRY iesu nen UR OUTRE EROR ADU 9 2 2 1 Overall Frame Geometry 2 2 2 Change in Section Along Frame Line 2 2 3 Flexibility in Selection of Cross Section Geometry ananassa 9 2 2 4 Boundary Conditions 2 5 ee p e Me RR nint 10 2 3 MATERIAL PROPERTIES IRE EAE Ae hebr 14 14 2 3 2 Nonprestressed Steel eripere anus 14 2 3 3 Prestressing Steel us 24 PRESTRESS ING a aaa aap estes 2 4 1 Tendon Number and Stressing ssim 16 2 4 2 Tendon G ommefry eene eterni i HE vei rete et tie 16 2 4 3 External Tendons Unbonded Tendons eene net 16 2 54 AC u UU 2 5 External Forces edet RR EE RE 2 5 2 External Displacements 2 Wes 2 5 3 Temperature ADU ERR ER PCR e ERRARE 2 6 TRAVELER AND FORMWORK OPERATIONS 21 CONSERUCTION PHASE 5 oer Goa RR RE 21 Chapter 3 USER S MANUAL RMEO MADE 1 S TET Capabilities e ett
4. EXAMPLES VERIFICATION move travelers CHANGE COMPLETE SOLVE SOLVE Day 140 Ke Stress tendon 12 CHANGE STRUCTURE STRESS MOVE N 1 D 9 10 11 MOVE 2 D 35 36 37 CHANGE COMPLETE SOLVE OUTPU CHANGE STRUCTURE BUILD 9 36 27 CHANGE COMPLETE SOLVE SOLVE Day 147 Stress tendon 13 CHANGE STRUCTURE N 12 StressTo 198E3 198E3 Anchor 25 move travelers STRESS MOVE N 1 MOV CO SOLVE OUT D 8 9 10 36 37 38 d D O Hd EJ rH D Q STRUCTURE BUILD N 8 37 29 COMPLETE SOLVE SOLVE Day 154 Ha D Q Stress tendon 14 N 13 StressTo 198E3 198E3 Anchor 25 move travelers CHANGE STRUCTURE STRESS MOVE N 1 7 8 9 MOVE 2 D 37 38 39 CHANGE COMPLETE SOLVE OUTPU CHANGE STRUCTURE BUILD N 7 38 31 CHANGE COMPLETE SOLVE SOLVE Day 161 Stress tendon 15 N 14 StressTo 198E3 198E3 25 move travelers CHANGE STRUCTURE STRESS MOVE N 1 D 6 7 8 MOVE 2 38 39 40 SOLVE CHANGE STRUCTURE BUILD N 6 39 33 CHANGE COMPLETE SOLVE S
5. patte 1 2 12 PBRINGIPAT ASSUMP TIONS 4 23 aie aq UR I 6 2 1 4 Inn 6 Node opetatiODSs POUR EAS EAE Pique 6 B Initialization of new frame elements pe 7 Solution sclieme on bep EDIDI nO pus 7 e ep Pd 9 22 9 2 2 2 CHANGE IN SECTION ALONG FRAME LINE 9 2 23 FLEXIBILITY IN SELECTION OF CROSS SECTION GEOMETRY 9 22 4 BOUNDARY CONDITIONS tecto tpe o edo ede 10 2260 va bee opaca ade 14 cuu am ubah hua a uito v ia s 14 2 3 2 NONPRESTRESSED STEEL PASSIVE REINFORCEMENT 14 2 5 3 BREST RESSING zz aan eei 15 PRESTRESSING Pes eM sssi iii 15 2 4 1 TENDON NUMBER AND STRESSING a a 16 2 42 TENDON GEOMETRY 16 243 EXTERNAL TENDONS UNBONDED TENDONS 10
6. Build pier and starting segment travelers build segments 20 and 25 Anchor 25 25 move travelers build segments 19 and 26 Anchor 25 25 build segments 18 and 27 CHANGE STRUCTURE RESTRAINTS 1 5 R 0 1 0 41 R 1 0 1 43 R 1 1 1 BUILD N 41 42 BUILD N 21 24 Day 35 CHANGE COMPLETE SOLVE SOLVE A 0 Day 63 OUTPUT Stress tendon 1 build CHANGE STRUCTURE STRESS N 1 StressTo 198E3 198 MOVE N 1 0 20 21 22 MOVE 2 D 24 25 26 CHANGE COMPLETE SOLVE OUTPUT CHANGE STRUCTURE BUILD N 20 25 5 CHANGE COMPLETE SOLVE SOLVE 70 Po Stress tendon 2 STRUCTURE STRESS 2 StressTo 198E3 198 MOVE N D 19 20 21 MOVE 2 D 25 26 27 CHANGE COMPLETE SOLVE OUTPU CHANGE STRUCTURE BUILD N 19 26 7 CHANGE COMPLETE SOLVE SOLVE Day 77 ADESSO Stress tendon 3 move travelers CHANGE STRUCTURE STRESS N 3 StressTo 198E3 198 MOVE N 1 18 19 20 MOVE 2 D 26 27 28 25 25 5 18 ADAPT EXAMPLES VERIFICATION 225 Anchor 25 25
7. 600 01 163 01 21 S 1501 413 401 SHRIN FACTOR 000 00 000 00 000 00 000 00 000 00 SHRIN FACTOR 000 00 000 00 000 00 000 00 000 00 6 ADAPT ABI INPUT OUTPUT EXAMPLES Appendix A 5 FRAME GEOMETRY X COORD Y COORD 5 2 FRAME ELEMENTS PRIMARY FRAME ELEMENTS N Syl ELEMENT NODE NODE CONCR SECT STEEL CASTING NO at TIPE DAY D 2 2 SPRINGS N SPRING NODE NO it 34 2 1 0000 05 1 0000 04 S 1 0000 05 1 0000 04 5 3 TENDONS TENDON NO 11 MATERIAL AREA 12 40000 T P GLOBAL COORDINATES ANGLE NODE OFFSET FROM NODE NO RADIANS NO 0 000 00 215 SIE 26 122 Et AN oar 0 5 30 618 02 1 628 02 S SIET METEO ISI 32 8 4 6 0 T 200 03 248 03 oll eh Or OS 040 03 304 03 400E 03 700E 03 000E 03 840 02 836 02 000E 00 000 01 000 00 964 01 000E 00 248E 01 000E 00 084 401 000E 00 942E 00 000E 00 993 400 000 00 833 00 000 00 958 00 000E 00 000E 00 540 02 SONS ES 92 542 02 55315 218 10 2 34 560 02 944 03 36 600 02 000 00 38 1 FP BD QVO DEO Gy x NODE NODE TOTAL ANGLE J J LENGTH LENGTH LENGTH RADIANS 225 26 26 30 30 211 32 32 32 205 34 34 36 36 38 800 01 SS OE D J 640E 02
8. COMPUTE CAMBER FOR A SEGMENTALLY CONSTRUCTED CANTILEVER U SI TE PARAMETERS N 1 1 ODES N 5 1 0 0 5 4000 0 G 1 5 CONCRETE PROPERTIES N 1 1 Fpc 34 Cr 2 5 5 0 0004 W 2 4E 6 MILD STEEL PROPERTIES N 1 1 Es 200000 0 02 SECTION PROPERTIES N 1 1 300 D 500 ELEMENTS N 4 FRAME N 4 1 1 2 0 1 1 ST 1 Day 0 2 2 3 C 1 X 1 51 1 Day 15 3 3 4 1 1 5 1 30 4 4 5 C 1 X 1 ST 1 Day 45 COMPLETE ay 10 E STRUCTURE BUILD N 1 Inslall the first segment RESTRAINTS 1 R 1 1 1 COMPLE Day 10 OUTPUT Obtain solution at day 10 E STRUCTURE BUILD N 2 D 9 ADAPT ABI BACKGROUND TO CAMBER COMPUTATION D SOLVE SOLVE Day 25 OUTPUT CHANGE STRUCTUR BUILD N 3 CHANGE COMPLETE SOLVE SOLVE Day 40 OUTPUT E CHANGE STRUCTUR BUILD N 4 CHANGE COMPLETE SOLVE SOLVE Day 60 OUTPUT E CAMBER This command triggers a printout of camber computations in the output STOP D 10
9. 1 000 Ib 160 ELEVATION SECTION a STRUCTURE ADPT317 DWG 1 2 3 4 5 NODE D 2 3 0 ELEMENT b STRUCTURAL MODEL CANTILEVER BEAM FIGURE 3 3 1 3 6 INPUT GENERATION Chapter 3 MILD STEEL PROPERTIES N 1 1 Es 29000000 0 05 PROPERTIES N 1 1 11 7 EMENTS 4 FRAME N 4 1 1 2 C 1 1 St 1 Day 0 6 1 4 1 1 1 MESH COMPLETE SET Day 0 CHANGE STRUCTURE 0 UILD 1 4 1 ESTRAINTS 1 R 1 1 1 LOADING 5 0 1000 0 SOLVE OUTPUT SOLVE Day 7 OUTPUT SOLVE Day 14 OUTPUT SOLVE Day 28 OUTPUT SOLVE Day 56 OUTPUT SOLVE 100 OUTPUT SOLVE Day 500 OUTPUT SOLVE Day 2000 OUTPUT SOLVE Day 10000 OUTPUT STOP 34 SAMPLE INPUT FOR A PRESTRESSED CONCRETE BOX GIRDER BRIDGE 3 4 1 Description of the Structure This example demonstrates ADAPT ABI Command usage and the free field input format for a simple non segmental bridge structure Input listings for an example of a segmentally constructed bridge are given in Chapter 6 A continuous prestressed concrete box girder bridge is shown in Fig 3 4 1 The three span cast in place girder is simply supported at the first and last supports It is rigidly connected to the columns at
10. 15 B 3 MATHEMATICAL MODELING OF THE CREEP STRAIN 15 B 3 1 Theoretical Background B 3 2 Calculation of the Creep Strain Increment A Constant stress and constant material parameters B Linear stress and constant material parameters C Linear stress and linear material parameters B 3 3 Determination of creep compliance Appendix REFERENCES Appendix D BACKGROUND CAMBER CALCULATION D INTRODUC HON HR GR RESET UR Eb e a on tet up te 3 D2 NUMERICAL REOR ERE UA ERE RU AERE Uds 5 D 2 1 Input data for 04124211 9 Iv ADAPT OVERVIEW Chapter 1 1 1 1 2 1 3 1 4 LIST OF CONTENTS ree E ep as uyaq Q M 1 LLI PROGRAM DEVELOPMENT 1 1 12 5 A 1 SCOPE ree 10 DISCLAIMER qc 11 PRINCIPAL STEPS IN DESIGN ANALYSIS OF SEGMENTAL BRIDGES AND n EE 11 LAT CONSTRUCTION PHASE tea M pes cei Uses eos ayasa 14 2 COMPDETED SERUCTURE eh erbe tete t o i RES 12 ADAPT OVERVIEW Chapter 1 This Page Left Intentionally BLANK OVERVIEW Chapter 1 11 GENERAL 1 1 1
11. 1 START TITLE N 1 CEB1 MKS UNITS Kg cm UNITS U MKS CONCRETE PARAMETERS N 1 1 1 Area 1935 48 P 203 20 MESH INPUT NODES 6 1 0 0 5 304 8 0 G 1 5 6 152 4 Y2 63 5 CONCRETE PROPERTIES 1 1 351 538 Cr 2 5 Sh 0 0003 W 0 0024027941 0 0000099 MILD STEEL PROPERTIES N 1 1 Es 2 038923E6 P 0 02 As 0 0000108 SECTION PROPERTIES N 1 1 Area 1935 48 9 1570913 4 C 27 94 43 18 ELEMENTS 5 FRAME 4 1 1 2 C 1 X 1 St 1 Day 1 G 1 4 1 1 1 SPRINGS 1 5 3 6 K 5357 45 PRESTRESSING STEEL 1 1 Ep 1 968615E6 Meu 0 25 0 00011811 Fpu 18983 07 R 45 Ap 0 000009 TENDON GEOMETRY N 1 1 Spans 1 M 1 Area 0 9870948 1 N 5 G 1 5 1 0 0 25 4 0 R 0 0 5 0 5 5 08 5 08 5 08 MESH COMPLETE SET Day 10 T 20 CHANGE STRUCTURE BUILD N 1 5 1 STRESS N 1 StressTo 0 14061 536 Anchor 0 0 3175 RESTRAINTS 1 R 1 1 1 6 R 1 1 1 CHANGE COMPLETE LOADING 5 15875 9 31 752 0 SOLVE OUTPUT SOLVE 500 Steps 3 OUTPUT LOADING L 1 4 1 70 70 SOLVE SOLVE Day 1000 Steps 3 OUTPUT STOP 5 35 ADAPT ABI INPUT OUTPUT EXAMPLES Appendix A ABI A MNL A INPUT OUTPUT EXAMPLES OUTPUT ORGANZA TON eet tet ee een a asta deter ertet 3 Output OVELVIEW nauunawaan ae p nte t 3 AO EXAMPLE soc te iat nha et Aas Aa a AAR tee Oia Si 11 AS INPUT BILE itp tea e RE UY ee EH ae tec e tee e ERROR 12 OUTPUT LISTING
12. 18 23 1 EXTERNAL FORCES 18 2 3 2 EXTERNALDISPLACEMENTS 18 2 53 TEMPERATURE CHANGEBES enr Ra WE DIIS 18 TRAVELER AND FORMWORK OPERATIONS 19 CONSTRUCTION PHASE ieocessccesssesssdebitcossoavesstdeveddasic vessiebeveadossedcensedeveedscdeceapesecsssdedsecdovees 21 PROGRAM DESCRIPTION Chapter 2 This Page Left Intentionally BLANK PROGRAM DESCRIPTION Chapter 2 21 OVERVIEW 2 1 1 Structural Model The bridge is modeled as a plane frame consisting of nodes in the global X Y plane The nodes may be connected by frame elements Fig 2 1 1 and springs In addition by specifying constraints the free displacement of one node with respect to another can be restricted Global displacement degrees of freedom of the nodes consist of X and Y translations and Z axis rotations The boundary condition at each nodal degree of freedom may be specified as unre strained or rigidly restrained and may be changed at any solution step The frame of the structure is generally modeled with concrete frame elements Fig 2 1 2 Each concrete frame element consists of time dependent concrete and a uniformly distributed elastic mild steel component acting in parallel to frame element Concrete and the uniformly distributed steel model the composite cross section The mild steel component of the element is intended to model the nominal
13. In the first solution step after a STRESS command has been applied to a tendon only the tendon s equivalent forces are included in the analysis In subsequent solution steps the stiffness is also included After the stressing operation a tendon is assumed bonded to the concrete at each nodal points For a refined representation of unbonded tendons the tendon need be modeled within a sheathing This type of modeling does not impact the results of the analysis to any significant degree For this reason in the general use both bonded and unbonded systems are modeled in the same fashion Examples of modeling of both systems are given in the Examples Manual ADAPT INPUT GENERATION Chapter 3 TENDON Syntax TENDON GEOMETRY N PRINT PRINT LONG This is followed by several lines of tendon geometry specification where N Total number of prestressing tendons 1 PRINT Optional if absent a table of tendon points coordinates is printed as output and PRINT LONG Optional if present a detailed table of tendon nodes in local and global coordinates and tendon segment geometries are added Use of this option produces voluminous output Explanation The TENDON GEOMETRY command is used to specify and generate the geom etry of all the prestressing tendons Each tendon is modeled as a series of segments connected at tendon points Fig 3 5 16 Each tendon point is rigidly const
14. Syntax CONCRETE PARAMETERS N 1 2 MaxShrinkageReadings n M LAB CreepSpecimens CreepReadings ShrinkageReadings Age ShrStrain Shrinkage header Shrinkage data aa 5 moo ai LoadingAge Eci Creep curve identification ObservationAge CreepStrain Creep curve header LL ZO Creep curve data n ee 5 PU L CZ AIT 5 where N Total number of concrete material models specified nl Largest number of creep specimens tested for any material model n2 Max number of creep measurements taken axShrinkageReadings n CreepSpecimens CreepReadings ShrinkageReadings Age ShrStrain on a specimen Largest number of shrinkage readings used for any material model Number of the concrete material model The number of creep specimens tested for the current material model Can be less than n1 above The largest number of creep table readings allowed for each one of the creep specimens of the current material model Different material models and different specimens in the same model can have different numbers of readings Can be less than n2 above Number of data readings for the shrinkage test Can be less than MaxShrinkageReadings above Age of concrete in days when shrinkage readings are take
15. i OY X b TENDON SEGMENT DEGREES OF FREEDOM PRESTRESSING TENDON IDEALIZATION FIGURE 4 4 2 tendon point coordinates be specified in any convenient local r s coordinate system Figure 4 4 2 which may be defined independently for each span or portion of the tendon The r s coordinates are transformed to the global X Y coordinate system using the standard transformation relationships For each span of the tendon the r and s coordinates must be either input for each tendon node or generated using one of the parametric generation schemes provided in the program The geometry of each tendon segment Figure 4 4 3 a is defined by the two tendon nodes I and J and the eccentricities of these tendon nodes from their associated frame nodes NI and NJ The tendon node eccentricities in global coordinates are given by PROGRAM BACKGROUND Chapter 4 TENDON TRUSS TENDON RENT PONT 7 e RIGID CONSTRANTS s NODE e a TENDON SEGMENT GEOMETRY M lcge 04 02 iy y y X b TENDON SEGMENT DEGREES OF FREEDOM PRESTRESSING TENDON IDEALIZATION FIGURE 4 4 3 Xq 4 4 1 Y Yr YNI Where the suffixes and NI refer to global tendon and frame node coordinates Each tendon segment has one local degree of freedom its internal strain which is transformed to six global degrees of
16. Anchor 25 CHANGE COMPLETE SOLVE OUTPUT CHANGE STRUCTURE BUILD N 18 27 9 CHANGE COMPLETE SOLVE SOLVE Day 84 Stress tendon 4 move travelers CHANGE STRUCTURE STRESS N 4 StressTo 198E3 198 MOVE N 1 D 17 18 19 MOVE N 2 D 27 28 29 CHANGE COMPLETE SOLVE OUTPU CHANGE STRUCTURE BUILD N 17 28 11 CHANGE COMPLETE SOLVE SOLVE 91 TS Stress tendon 5 move travelers CHANGE STRUCTURE STRESS N 5 StressTo 198E3 198 MOVE N 1 16 17 18 MOVE N 2 D 28 29 30 CHANGE COMPLET SOLVE OUTPU CHANGE STRUCTURE BUILD N 16 29 13 CHANGE COMPLETE SOLVE SOLVE Day 98 Stress tendon 6 move travelers CHANGE STRUCTURE STRESS N 6 StressTo 198E3 198 MOVE 1 15 16 17 MOVE 2 29 30 31 CHANGE COMPLETE SOLVE OUTPU CHANGE STRUCTURE BUILD 15 30 15 CHANGE COMPLETE SOLVE SOLVE Day 105 sts Stress tendon 7 STRUCTURE STRESS 7 StressTo 198E3 198 MOVE 1 D 14 15 16 MOVE 2 30 31 32 CHANGE COMPLETE SOLVE OUTPUT move travelers 25 25 25 25 5 19 build segments 17 and 28 build segments 16 and 29 build segments 15 and 30 build segments 14 and 31 ADAPT EXAMPLES VERIFICATION build segmente 13 32 29
17. NORMALIZED 1 GENERAL PARABOLIC TENDON FIGURE 4 4 4 4 16 4 4 3 PROGRAM BACKGROUND Chapter 4 0 s Coordinates of left tendon end fo Se Coordinates of point of zero slope low point 1 5 Coordinates of right tendon end T left end to inflexion point right end to right inflexion point These parameters provide enough information to generate a profile made up of four parabolic segments with zero slope at locations A B and C and tangent intersections at rj and The zero slope at ends 1 and r provides tangent intersections with neighboring spans Many other tendon profiles can be generated By proper specification of the parameters most commonly used profiles can be generated In special cases it is possible to use more than one portion to represent one physical span of the bridge This technique allows generation of very complex tendon geometries In some cases where non typical tendon geometries are used it may be necessary to resort to direct tendon point input With careful selection of tendon portions and with use of parametric generation in portions where it is possible the use of direct tendon point input can be minimized Determination of Initial Tendon Forces The initial forces in the tendon segments at the time of the tendon s installation are computed by the program based on input jacking forces at the tendon ends and short term losses over the length of the tendon due to
18. dsb asa I a ee RR 9 5 4 LOADINGS amp CONSTRUCTION SEQUENCE FOR THE TIME DEPENDENT ANALYSIS entren 5 5 COMPUTER INPUT 5 6 COMPARISON OF RESULTS 5 7 AMERICAN SI AND MKS SYSTEM OF UNITS EXAMPLE eene 26 5 8 dM DUBIE 26 5 9 RESUETS OU PR UR EUR CD a R Qata s haha 21 Appendix OUTPUT EXAMPLES OUTPUT ORGANIZATION A 1 1 Output Overview A 2 EXAMPLE A 3 INPUT FILE 2 ne AA OUTPUT LEISTUNG tno OR RR Pete GRAPHICAL DISPLAY OF OUTPUT ett ctos e i NER OL te Be e ER E 19 6 INPUT OUTPUT GRAPHICAL DISPLAYW tenente tnnt tenen tenete 21 Appendix B MODELING OF CONCRETE S TIME DEPENDENT BEHAVIOR B 1 STRAIN COMPONENTS AND THE SUPERPOSITION METHOD serene 4 B 1 1 Mechanical Strain eva RR EHE RD RR ORNA B 1 2 Aging Strain B 1 3 Creep Strain B 1 4 Shrinkage Strain B 1 5 Temperature Strain B 2 PREDICTION OF TIME DEPENDENT MATERIAL PROPERTIES esee 8 B 2 1 ACI Committee 209 Recommendations 8 A Strength and stiffness B Creep strain C Shrinkage strain B 2 2 CEB FIP Committee Recommendations A Strength modulus of elasticity and aging of concrete B Creepstranmm u aus ee ete DO eoe a ADAPT ABI LIST OF CONTENTS Contents C Shrnkage strdtn
19. E ette eet teet d teles 13 A 5 GRAPHICAL DISPLAY OF 19 A 6 INPUT OUTPUT GRAPHICAL 21 ADAPT ABI INPUT OUTPUT EXAMPLES Appendix A This Page Left Intentionally BLANK A 2 ADAPT ABI INPUT OUTPUT EXAMPLES Appendix A A 1 OUTPUT ORGANIZATION The results of an ABI run are organized in a compact clearly identifiable and easy to follow manner The following gives an overview of the organization of ABI output The output is subdivided into two primary parts 1 Problem definition 2 Solution Each separate entity of the problem definition or solution is placed in a data block with its own unique data block number and title The data blocks and their identification numbers are shown in the following output overview Data blocks 1 through 5 are used to reflect the input data as interpreted by ABI The solution generally consists of several stages Each stage refers to a request for output by the user The printout of each stage is organized in the group of data blocks 100 through 111 see the following output overview For example data block 108 refers to the printout of stresses If there are three stages to the solution data block 108 for stresses appears three times each time in its respective solution stage The sequence of printout strictly follows
20. FIGURE 4 1 1 4 5 PROGRAM BACKGROUND Chapter 4 a LOCAL DISPLACEMENT AND INDEPENDENT DISPLACEMENT DEGREES OF FREEDOM 2 eH ADPT347 DWG OUTLINE OF ELEMENT IN LOCAL x y PLANE b VARIATION OF AXIAL STRAIN FRAME ELEMENT LOCAL DISPLACEMENTS AND INTERNAL STRAINS FIGURE 4 1 2 The axial strain ex is obtained by differentiating u with respect to x dx du d v d 7 dx x E 4 1 3 4 6 PROGRAM BACKGROUND Chapter 4 Substituting Equation 4 1 1 into Equation 4 1 3 the resulting strain displacement relationship can be expressed as aw lu where and represent the first and second derivatives with respect to x 4 2 INTERNAL DEGREES OF FREEDOM Investigation of the strain displacement relationship Equation 4 1 4 shows that under nodal loading axial strain e varies linearly in both the x and y directions and at the centroidal axis 0 is constant over the x length of the element Figure 4 1 2 b This means that the strain or stress distribution within the element may be described uniquely by the constant strain or stress at the centroidal axis plus the strain or stress at some other y coordinate at two different x cross sections along the element Note that as with the traditional independent displacement degrees of freedom and u Figure 4 1 2 a three terms describe uniquely
21. Program Development ADAPT ABI software is a PC based computer program for the time dependent and load history analysis of prestressed post tensioned and non prestressed concrete bridges and frames in particular bridges of segmentally erected cantilever construction It is based on the wealth of over three decades of research bridge design practice and construction technology in USA with due recognition that many of the adopted construction technologies were originated in Europe Professor Alex C Scordelis and his supervisees at University of California Berkeley UCB spearheaded a series of concerted research projects since 1960s aimed at understanding the behavior of concrete bridges Many of these projects concluded with a companion analytical computer software in addition to the project s research report The works which in many cases were supported by the National Science Foundation or the California Department of Transportation have provided a solid basis for the clear understanding of concrete bridge behavior Several of the research projects account for the time dependent response of concrete under loading and environmental effects and are particularly applicable to segmentally constructed bridges The projects under professor Scordelis have led to a a series of frame software Researchers with signifi cant contribution to the related work in alphabetical order are A F Kabir M A Ketchum A R Mari M A Mukaddam S F Va
22. SOLVE OUTPUT SOLVE Day 500 Steps 3 OUTPUT LOADING L 1 4 1 T 158 158 SOLVE SOLVE Day 1000 Steps 3 OUTPUT STOP 5 33 ADAPT EXAMPLES VERIFICATION Chapter 5 ADAPT BRIDGE INCREMENTAL ABI SOFTWARE MANUAL EXAMPLES 3 name of this file 5 1 START TITLE N 1 CEB1 SI UNITS N mm UNITS U SI CONCRETE PARAMETERS N 1 1 1 Area 193548 P 2032 MESH INPUT NODES 6 1 X 0 0 5 3048 Y 0 G 1 5 6 X 1524 Y 635 CONCRETE PROPERTIES 1 1 34 4859 Cr 2 5 Sh 0 0003 W 0 0000024027941 0 0000099 MILD STEEL PROPERTIES N 1 1 Es 200018 32 P 0 02 As 0 0000108 SECTION PROPERTIES N 1 Area 193548 9 1570913 8 279 4 431 8 5 5 FRAME 4 1 1 2 1 X 1 St 1 Day 1 G 1 4 1 1 1 SPRINGS 1 5 3 6 5255 65 PRESTRESSING STEEL N 1 1 Ep 193121 Meu 0 25 0 000011811 Fpu 1862 24 R 45 Ap 0 000009 TENDON GEOMETRY N 1 1 Spans 1 M 1 Area 98 70948 1 N 5 G 1 5 1 0 0 254 0 R 0 0 5 0 5 50 8 50 8 50 8 MESH COMPLETE SET Day 10 T 20 CHANGE STRUCTURE BUILD N 1 5 1 STRESS N 1 StressTo 0 1379 437 Anchor 0 3 175 RESTRAINTS 1 R 1 1 1 6 R 1 1 1 CHANGE COMPLETE LOADING 5 155742 5 311 485 0 SOLVE OUTPUT SOLVE Day 500 Steps 3 OUTPUT LOADING L 1 4 1 70 70 SOLVE SOLVE Day 1000 Steps 3 OUTPUT STOP 5 34 ADAPT EXAMPLES VERIFICATION Chapter 5 ADAPT BRIDGE INCREMENTAL ABI SOFTWARE MANUAL EXAMPLES 3 name of this file
23. is the specific creep compliance function for observation time t under initial loading at time The inherent assumptions behind this formulation are ADAPT ABI CONCRETE MODELING Appendix B A the applicability of the principle of superposition of strain components Equation B 1 1 and B alinearrelationship between creep strain and applied stress The form of this creep strain relationship is convenient for a step by step displacement method finite element analysis but its direct evaluation is impractical because it requires integration over the entire history of stresses in an element This can require a tremendous numerical effort and data storage capacity for the solution of realistic problems The need for storing and using the complete history of stresses can be eliminated by approximating the specific creep compliance function J t t also known as the kernel with a so called degenerate kernel This basic approach has been developed by many researchers including Bresler and Selna 1964 Zienkiewicz and Watson 1966 Mukaddam 1969 Kabir and Scordelis 1976 Bazant and Wu 1973 and others Some of these researchers also include the instantaneous elastic strain in the kernel Bazant and Wittmann 1982 thoroughly analyze this formulation and also discuss convergence properties of alternative degenerate kernels The most general degenerate kernel takes the form of a Dirichlet series which can be written as Ya i C
24. 1 1 St 1 0 G 1 30 1 1 1 31 11 32 C 1 2 St 1 0 32 21 33 C 1 2 St 1 0 PRESTRESSING STEEL N 1 1 27000000 Meu 0 25 0 0004 12 Fpu 270000 R 10 TENDON GEOMETRY N 1 SPANS 3 M 1 AREA 11 54 0 900 10 900 N 11 G 1 11 R 0 11 G 11 21 8 0 N 11 G 21 31 R 0 0 1 5 29 41 84 12 29 0 1 5 12 84 12 54 0 5 12 84 29 41 N MESH COMPLETE SET Day 28 G 0 1 CHANGE STRUCTUR INPUT GENERATION Chapter 3 Px l 75 1 2 50 200 150 4 ELEVATION 66 59 RATIOS 095 05 b TENDON PROFILE 51 6 28 31 NODE 5 018 6 28 30 ELEMENT 8i 33 MODEL 11 8 0 SECTION THREE SPAN BRIDGE FIGURE 3 4 1 BUILD N 1 32 RESTRAINTS STRESS N 1 F 2 5E5 2 5E5 509 1 31 30 R 0 1 0 32 33 R 1 1 1 ADAPT INPUT GENERATION Chapter 3 CHANGE COMPLETE SOLVE OUTPUT SOLVE Day 50 OUTPUT SOLVE Day 500 OUTPUT SOLVE Day 1000 OUTPUT SOLVE Day 5000 OUTPUT SOLVE Day 10000 OUTPUT STOP 35 DETAILED DESCRIPTION OF COMMAND SYNTAX The detailed syntax of each command and a description of its use actions and output are described The commands are organized alphabetically A sample sequence in which the commands normally will be found in a typical
25. 36 5412 43 70 37 5572 38 53 38 5732 36 65 39 5892 35 37 40 6052 34 61 41 6120 34 50 42 3420 300 0 43 3420 900 0 SEQUENCE G 1 23 1 G 42 43 1 G 24 41 1 MILD STEEL PROPERTIES N 2 1 Es 29E6 0 02 2 Es 29E6 0 1 CONCRETE PROPERTIES N 1 1 5000 Cr 3 Sh 0 0008 W 155 1728 SECTION PROPERTIES N 25 1 B 744 40 349 46 D 14 375 84 18 9 00 Cant seg 2 744 40 349 07 D 14 375 85 92 9 00 3 744 40 348 00 D 14 375 89 12 9 00 4 744 40 346 45 14 375 93 77 9 00 5 744 40 344 70 D 14 375 98 36 10 34 6 744 40 342 74 D 14 375 103 02 12 79 5 14 ADAPT EXAMPLES VERIFICATION Chapter 5 7 744 40 340 41 D 14 375 108 77 15 23 8 744 40 337 75 D 14 375 115 55 17 68 9 744 40 334 75 D 14 375 123 31 20 12 10 744 40 331 44 D 14 375 132 01 22 57 11 744 40 327 83 D 14 375 141 63 25 01 12 744 40 323 92 D 14 375 152 13 27 46 13 744 40 319 73 D 14 375 163 48 29 90 14 744 40 315 26 D 14 375 175 67 32 34 15 744 40 310 52 D 14 375 188 68 34 79 16 744 40 305 51 D 14 375 202 48 37 23 17 744 40 300 24 D 14 375 217 06 39 68 18 744 40 296 26 D 14 375 228 11 41 45 Pie
26. N Total number of frame elements 1 n Frame element number n ni Node number for node I nj Node number for node J E Concrete type number X Section type number at node I and J If only one number is entered section is assumed to be uniform SE Mild Steel type number Day Casting Date days Off Offset entry number Fig 3 5 5 and 3 5 6 0 and nl nil element generation parameters optional as described below 3 26 INPUT GENERATION Chapter 3 Explanation The FRAME ELEMENTS command is used to define all the frame elements used in modeling the structure The frame element number n must be less than or equal to the total number of frame elements input on the FRAME ELE MENTS command line The frame element descriptions may be supplied in any order however each frame element description must be specified or generated once Frame elements Figs 3 5 7 consist of parallel concrete and mild steel com ponents Data supplied with the C and x identifiers specifies the concrete component Data supplied with the St and x identifiers specifies the uni formly distributed mild steel component The casting date in days may be specified with the Day identifier but this specification can be overridden under the BUILD subcommand of the CHANGE STRUCTURE command The positive direction of the local coordinated sys
27. The initial displacements of the node at the far end is determined from rigid body orientation of the newly installed ele ment Solution scheme The solution is based on combining a finite element analysis of the structure with a step forward integration scheme in the time domain The time domain is subdi PROGRAM DESCRIPTION Chapter 2 e ea lt FRAME S ORIGINAL SYSTEM LINE ORIGINAL NODE Ne DEFORMED LINE OF DISPLACED EXISTING ELEMENTS NODE POSITIONING OF NEWLY INSTALLED ELEMENT NEW ELEMENT FOLLOWS SLOPE 87 OF EXISTING DEFORMED STRUCTURE FIGURE 2 1 5 vided into a number of time steps and an analysis of the finite element system is performed for each step Time dependent strains over the time step are considered as an initial strain loading on the finite element system Time steps may be of arbitrary positive length At the beginning of each time step the complete stress strain and displacement distribution within the structure is known Over the length of the time step any external load increment is gradually applied and all resulting displacements stresses and strains in the structure are assumed to vary linearly from their initial values to their final values which are computed by the program Dead load is automatically included as an external nodal load unless specifically excluded by user The linear variation of loading increment and structural r
28. a of the figure and note that the frame elements nodes the parallel frame elements forming the section are tied by offset constraints Part b of the figure illustrates the modeling of a three component section where two offset constraints are introduced at each node Application of offset is general and efficient since it does not result in definition of new nodes Boundary Conditions The boundary condition for any degree of freedom at any node may be specified as either unrestrained restrained or restrained to zero total displacement That is to say the restraint can be imposed throughout the entire construction phase zero total dis placement or it can be imposed starting at a defined phase in construction Each node in the frame is initially assigned three degrees of freedom An unrestrained free to displace degree of freedom is assigned a corresponding equation number in the global equilibrium equations and its displacement increment in subsequent solution steps is computed by the program Nodal loads may be applied to unrestrained degrees of freedom and the program determines the response of the structure to these loads Externally applied nodal displacements may not be applied to unrestrained degrees of freedom A restrained rigidly supported degree of freedom has no corresponding equation in the global equilibrium equations and its displacement increment in subsequent solution steps is set to zero Reactions at res
29. 0585 0 5 20 7 7 18 G 23 40 1 R 0 9415 0 5 7 7 20 ntinuity tendons ch represents 8 21 Strand 1 2 Diam tendons 2 M 1 Area 25 704 18 G 1 18 1 R 0 4 2 S 46 74 100 12 6 G 18 23 1 R 0 5 0 S 12 12 12 2 M 1 Area 25 704 6 G 23 28 1 R 0 5 0 5 12 12 12 14 G 28 41 1 R 3 1 0 5 12 100 100 cal tendons ch represents 2 or 4 21 strand 1 2 Diam tendons 1 1 Area 6 426 9 G 1 9 1 R 0 874 0 5 46 74 98 15 103 34 1 1 Area 6 426 10 G 1 10 1 R 0 776 0 5 46 74 98 15 107 43 1 M 1 Area 6 426 Td GS LE R 0 698 0 5 46 74 98 15 112 64 1 M 1 Area 6 426 1 191251 R 0 634 0 5 46 74 98 15 118 91 M 1 Area 6 426 12 G 30 41 1 R 0 1 0 5 153 64 100 100 1 M 1 Area 6 426 R 0 1 0 5 143 58 100 100 M 1 Area 12 852 R 0 1 0 5 134 42 100 100 M 1 Area 12 852 0 1 0 5 126 18 100 100 M 1 Area 12 852 0 1 0 5 118 91 100 100 M 1 Area 12 852 7 G 35 41 1 R 0 1 0 5 112 64 100 100 M 1 Area 6 426 6 G 36 41 1 R 0 1 0 5 107 43 100 100 M 1 Area 6 426 5 17 Chapter 5 ADAPT 1 5 G 37 41 1 EXAMPLES VERIFICATION Chapter 5 N C R20 1 0 5 103 34 100 100 TRAVELERS 3 1 X 25 E 29E6 W 15E4 2 3 25 E 29E6 W 1E4 MESH COMPLETE SET Day 56
30. 6324 03 1655E 04 0000E 00 4118 02 4265 04 0000 00 8838 02 7831 04 0000 00 2353E 04 106 TOTAL REACTIONS AT FIXED NODES NODE X FORCE ELO ER Z MOMENT 1 0 0000 00 2 0000 02 3 2000 04 TOTAL 0 0000 00 2 0000 02 3 2000 04 107 FRAME ELEMENT ACTIONS ELEMENT BENDING BENDING AXIAL NO END I END J FORCE FORCE 3 2000 404 2 4000 04 0000E 02 0000E 00 2 4000 404 1 6000 04 0000E 02 0000E 00 1 6000 404 8 0000 03 0000 02 0000 00 SS VOOOE OS OOO 0000E 02 0000F 00 108 STRESSES AXIAL 2596 02 2596 02 6947 02 6947E 02 0 0000E 00 6947 02 6947 02 1298802 1298 02 0 0000 00 21299802 12988202 6490 01 6490E 01 0 0000 00 6490 401 6490 01 6605E 13 6605 13 0 0000E 00 CONSTRUCTION AND SOLUTION AT DAY 1000 STAGE 2 CURRENT TEPERATURE X DIRECTION GRAVITY MULTIPLIER Y DIRECTION GRAVITY MULTIPLIER STRESS CONVERGENCE FACTOR GERE A 16 ADAPT ABI INPUT OUTPUT EXAMPLES Appendix A 102 2 ACTIVE FRAME ELEMENTS 104 1 EXTERNALLY APPLIED LOAD OF THIS INCREMENT NODE X FORC SEI OS XO 2 X DISP 2 5 0 0000 00 2 0000 02 0 0000 00 0 0000 00 0 0000 00 0 0000 00 104 3 Ab OQ OUT EATERNALDY ABPLIED TEOASDTNGS THIS 5 GE JA E NODE X FORC VSO 2 2S IDES NE WD SP 5 0 0000E 00 2 0000 02 0 0000 00 0 0000 00 0 0000 00 0 0000E 00 105 NODAL BOUNDA
31. Berkeley UCB SESM 78 2 Jan 1978 pp 265 VSL 1992 H3 Viaduct in Hawaii shop drawings VSL Corporation Los Gatos Ca USA C 3 ADAPT ABI REFERENCES Appendix C Wilson E L Hoit M I 1984 A Computer Adaptive Language for the Development of Structural Analysis Programs Computers and Structures Vol 19 No 3 pp 321 338 1984 Zienkiewicz O C and Watson M 1966 Some Creep Effects in Stress Analysis with Particular Reference to Concrete Pressure Vessels Nuclear Engineering and Design No 4 C 4 ADAPT ABI BACKGROUND TO CAMBER COMPUTATION D ABLD MNL D BACKGROUND TO CAMBER COMPUTATION T INTRODUCTION S EE Saat eR Ret nente Pete E 3 D2 NUMERICALEXAMBLE rtc ei a e p t mer e bee e Pre 5 D 2 1 Input data for ADAPT ABI ee 9 ADAPT ABI BACKGROUND TO CAMBER COMPUTATION D This Page Left Intentionally BLANK D 2 ADAPT ABI BACKGROUND TO CAMBER COMPUTATION D D 1 INTRODUCTION Camber is defined as the offset from datum line built into structure at time of construction The offset is generally a distance above the horizontal line datum The purpose of the camber is to compensate for the deflection of the structure under loading and due to time dependent effects The compensation is aimed at bringing the final position of the structure to within acceptable limits for the structure s intended function The
32. EM2 Paper 9645 pp 367 378 Breen J E Cooper R L and Gallaway T M 1975 Minimizing Construction Problems in Segmentally Precast Box Girder Bridges Research Report No 121 6F Center for Highway Research The University of Texas at Austin Texas Bresler B and Selna L G 1964 Analysis of Time Dependent Behavior of Reinforced Concrete Structures ACI Symposium on Creep of Concrete American Concrete Institute SP 9 detroit ADAPT ABI REFERENCES Appendix C Brown R C Burn N H Breen J E 1974 Computer Analysis of Segmentally Erected Precast Box Girder Bridges Research Report No 121 4 Center for Highway Research The University of Texas at Austin Texas CALTRANS 1988 Bridge Design Practice Manual California Department of Transportation Sacramento Ca CEB 1978 CEB FIP Model Code for Concrete Structures Bulletin d Information 124 125E Comite Euro International du Beton Federation Internationale de la Precontrainte Paris 348 pp Collins M P and Mitchel D 1990 Prestressed Concrete Structures Prentice Hall NJ pp 776 FDOT 19892 Post Tensioning Manual Florida Department of Transportation Office of Construction October 1989 FDOT 1989b Segmental Manual Florida Department of Transportation Office of Construction October 1989 Hernandez H D and Gamble E L Time Dependent Prestress Losses in Pretensioned Concrete Construction Structural Research Series N
33. NO FORCE LOSS EL NO END I END J FORCE FORCE SOS 24 8 556 07 1 148 08 107 05 590 06 612 06 54 Sole 5602018 607 06 633 06 o HG lo SB 1e OO ROS 000 00 633 06 611 06 559 ESSE Orc ONSE OJO 000E 00 611 06 5 89 06 5 5545408 L 539 05 585 06 573 06 5 Le L Og OTIO REN SOS EE 5 570 06 10 ADAPT ABI INPUT OUTPUT EXAMPLES Appendix A 109 2 COMBINED ACTION AND FORCE OF ALL TENDONS ELEMENT NO OF BENDING BENDING SHEAR AXIAL NO TENDONS END I END J FORCE FORCE 1 SOs 0m O9 o5 15 13 580077 2505 04 0000E 00 15 752190 7 9260 06 9418 04 5180 02 9 9260 06 4957 06 6149 04 0629 01 Bro GSI TEtUG BEATE 7 0573 05 792 20EAN 0019 05 209557 55055 5328 7 078809 0077 05 SAS ATA 8119 08 2110 08 2903 05 ao DSP SOS 110 TOTAL STATIC RESULTS FOR ELEMENTS ELEMENT BENDING BENDING AXIAL TENDONS END I END J IG SF S il 2505 04 0 0000E 00 9926 ORIS 9418 04 5 5180 02 9260 06 5 4957E 06 6149 04 1 0629 01 4957 06 2 2417 07 ADDIS OS 9 51 23 SP 07 JEE SI 55249 518 0117 OOM 20 5 om HOS 111 CAMBER NODE X DIRECTION Y DIRECTION ROTATION 1 5806 01 0 0000 00 213215 920 0468E 01 52021 02 3825 04 00 0 0000 00 0000 00 1 4881 01 0261 04 0000 0
34. TOTAL CREEP STRAIN LINEAR SUPERPOSITION CREEP STRAINS FIGURE B 1 2 B 7 ADAPT ABI CONCRETE MODELING Appendix B B 1 5 Temperature Strain Temperature strain T t is a non stress originated strain defined as the deformation under temperature change The temperature strain increment T due to the temperature change T may be expressed as T ST where is the coefficient of thermal expansion B 2 PREDICTION OF TIME DEPENDENT MATERIAL PROPERTIES The experimental test data required for the analytical prediction of the time dependent strains in prestressed concrete structures are not always available In this case the required material parameters can be estimated using empirical expressions based on mix design humidity and other factors Several such empirical expressions for predicting the variation over time of concrete properties have been recommended by various researchers Based on studies by Branson et al ACI Committee 209 published a set of recommendations which have been widely applied in bridge design An alternative approach adopted by the CEB FIP recommendations 1978 is used in the bridge design examples published by the PCI PTI Both of these recommendations predict time dependent material parameters based on a few tests estimates of cylinder properties and environmental conditions Using procedures discussed in Section B 3 of this chapter the stiffness creep and shrinkage predictions found
35. ns 2 M 1 Area 12 852 N 7 G 17 23 1 R 0 1766 0 5 20 7 7 7 G 23 29 1 R 0 8234 0 5 7 7 20 2 1 Area 12 852 8 G 16 23 1 R 0 1492 0 5 20 7 7 8 G 23 30 1 R 0 8508 0 5 7 7 20 2 1 Area 12 852 9 G 15 23 1 R 0 1292 0 5 20 7 7 9 G 23 31 R 0 8708 0 5 7 7 20 2 M 1 Area 12 852 10 6 14 23 1 R 0 1139 0 5 20 7 7 10 6 23 32 1 R 0 8861 0 5 7 7 20 2 M 1 Area 12 852 11 6 13 23 1 R 0 1019 0 5 20 7 7 11 6 23 33 1 R 0 8981 0 5 7 7 20 2 M 1 Area 12 852 12 G 12 23 1 R 0 0921 0 5 20 7 7 12 G 23 34 1 R 0 9079 0 5 7 7 20 2 M 1 Area 12 852 13 G 11 23 1 R 0 0841 0 5 20 7 7 13 G 23 35 1 R 0 9159 0 5 7 7 20 2 1 Area 12 852 14 G 10 23 1 R 0 0773 0 5 20 7 7 14 G 23 36 1 R 0 9277 0 5 7 7 20 2 1 Area 12 852 15 G 9 23 1 R 0 0716 0 5 20 7 7 15 G 23 37 1 R 0 9284 0 5 7 7 20 2 1 Area 12 852 16 G 8 23 1 R 0 0666 0 5 20 7 7 16 G 23 38 1 R 0 9334 0 5 7 7 20 2 1 Area 12 852 17 G 7 23 1 R 0 0623 0 5 20 7 7 17 G 23 39 1 5 16 Chapter 5 ADAPT 16 18 20 21 22 23 24 25 26 27 28 29 30 Spans 1 N 2 N ea Spans 1 N 2 N Spans 1 N 2 N Lo ea Spans PS Spans spans spans spans Spang Spans Spans Spans Spans EXAMPLES VERIFICATION R 0 9377 0 5 7 7 20 2 M 1 Area 12 852 18 G 6 23 1 R 0
36. plotted average force at the tendon node with straight lines Figure 4 4 8 c The constant idealized force in each tendon segment can then be found by averaging the segment end force values from this smoothed profile Figure 4 4 8 c This results in a best estimate of the tendon segment forces for a smoothly curved tendon profile If there are actual concentrated angle changes in the prototype tendon geometry as found in a harped tendon then an error may be introduced since no abrupt changes in tendon force are considered This error is considered inconsequential since it disappears as the tendon discretization is refined and a minimum radius 4 21 PROGRAM BACKGROUND Chapter 4 of curvature of the tendon is always maintained in the post tensioned systems for which the program is Intended even when the tendon is harped E Equivalent prestressing loads Once forces in all the tendon segments are known the equivalent forces acting on the structure at each tendon node may be found Consider tendon node i where tendon segments 1 1 and i are connected Figure 4 4 9 The vectors from point 1 to 1 1 and from i to 1 1 are v and v respectively These can be expressed as Vi 1 Xia Xis yil ill 4 4 5 Vi ba Xio Xi yi With direction cosines viW lvii Civi 4 4 6 The components of the tendon nodal forces in the global coordinate system are given and Bio SESS 4 4
37. 1 1 M ACI 4 0 85 C 1 25 0 118 E 1 50 W 0 086805556 MESH INPUT NODES 6 1 0 0 5 120 0 G 1 5 6 60 Y 25 CONCRETE PROPERTIES N 1 Fpc 5000 Cr 2 5 Sh 0 0003 W 0 086805556 Ac 0 0000055 MILD STEEL PROPERTIES N 1 Es 29000000 0 P 0 02 As 0 000006 SECTION PROPERTIES N 1 Area 300 I 2200 C 11 17 ELEMENTS N 5 FRAME N 4 1 1 2 C 1 X 1 St 1 Day 1 G 1 4 1 1 1 SPRINGS N 1 5 3 6 K 30000 PRESTRESSING STEEL N 1 1 Ep 28000000 Meu 0 25 K 0 0003 Fpu 270000 R 45 Ap 0 000005 TENDON GEOMETRY N 1 1 Spans 1 M 1 Area 0 153 1 N 5 G 1 5 1 B 0 0 E 10 0 R 0 0 5 0 5 2 2 2 MESH COMPLETE SET Day 10 68 CHANGE STRUCTURE BUILD N 1 5 1 STRESS N 1 StressTo 0 200E3 Anchor 0 0 125 RESTRAINTS 1 R 1 1 1 6 R 1 1 1 CHANGE COMPLETE LOADING N 5 F 35000 70 0 SOLVE OUTPUT SOLVE 500 Steps 3 OUTPUT LOADING L 1 4 1 T 158 158 SOLVE Day 1000 Steps 3 OUTPUT STOP 5 30 ADAPT EXAMPLES VERIFICATION Chapter 5 ADAPT BRIDGE INCREMENTAL ABI SOFTWARE MANUAL EXAMPLE 3 name of this file 5 START TITLE N 1 ACI SI UNITS N mm UNITS U SI CONCRETE PARAMETERS N 1 1 M ACI 4 0 85 C 1 25 D 0 118 E 1 50 W 0 0000024027941 MESH INPUT NODES 6 1 X 0 0 5 3048 Y 0 G 1 5 6 X 1524 Y 635 CONCRETE PROPERTIES 1 1 34 4859 Cr 2 5 Sh 0 0003 W 0 0000024027941 0 0000099 MILD STEEL PROPERTIES N 1 1 Es 200018 32 P 0 02 As 0 0000108 SECTION PROPE
38. 7 F F C The resulting equivalent load vector Pi at tendon node i consisting of Fixi and Fivi can be expressed in terms of the two tendon force components F and F using vector addition 4 4 4 Material Constitutive Relationships The prestressing tendon steel is considered as a linear elastic material subject to time dependent strains due to relaxation Relaxation is a phenomenon similar to creep and is defined as the decrease in stress over time under constant strain The following equation proposed by Magura et al 1964 18 used for the calculation of tendon stress relaxation 2190 10800 Is 0 55 4 4 8 fi f where 4 22 PROGRAM BACKGROUND Chapter 4 1 a IDEALIZED TENDON AL ANGLE CHANGE b DISCRETIZED TENDON FORCE FORCE BEST ESTIMATE c TENDON SEGMENT FORCES IDEALIZATION OF TENDON FORCE FIGURE 4 4 8 PROGRAM BACKGROUND Chapter 4 e a co a F F TENDON FORCES CONCRETE REACTION TENDON ACTIONS AT DISCRETIZATION NODE FIGURE 4 4 9 steel stress at time t initial steel stress 0 001 offset yield stress constant 10 0 for stress relieved strand 45 0 for low relaxation strand t time in hours after stressing Figure 4 4 10 shows a typical variation of prestressing loss due to stress relaxation with time This relationship was developed assuming
39. CAST IN PLACE PR PC ECAST b DEFLECTION AND CONSTRUCTION CAMBER CAMBER FOR GEOMETRY CONTROL OF BALANCED CANTILEVER CONSTRUCTION FIGURE 1 1 2 7 ADAPT OVERVIEW Chapter 1 acast in place scheme or precast segments the construction should have a camber such as shown schematically with profiles C or B The camber curves in the figure signify where at construction time a given segment should be placed so that at the time determined by the designer the bridge superstructure be along the datum line line D D viii Most retrofit projects involve addition of fresh concrete external or internal prestressing and recently developed synthetic fabrics wrapping Mixed material properties the interaction of shrinkage and creep strains of the freshly placed concrete with the retrofitted components in resisting the applied load ing and the subsequent redistribution of loading among the new and existing components require time delayed analysis specific to segmental construction In summary where the effects of time changes in the structural system and high construction loads impact the performance and safety of a structure during construction and when complete and where the geometry of the completed structure depends on the method of construction there is need for a segmental construction analysis procedure Prime examples of segmentally constructed bridges are Prestressed precast spliced girders with post tensioning and c
40. During the solution time step when the tendon is initially stressed the tendon is considered as unbonded and only its load terms are included in the global equilibrium equations During all subsequent solution steps until the tendon is removed the tendon is considered as perfectly bonded and both load and stiffness terms are included in the global equilibrium equations Displacement compatibility between the prestressing steel segments and the frame elements is enforced at the frame nodes to which the tendon nodes are locked It is handled at the structure level through the direct stiffness assembly procedure Tendon Geometry Definition Prestressing tendon geometry is completely defined by the global X and Y coordinates of the tendon points For tendon geometry nodes the length of the frame is divided into portions which usually correspond to the actual physical spans of the frame between supports but may be arbitrarily chosen for input convenience 4 12 a E A lt PROGRAM BACKGROUND Chapter 4 CURVED TENDON a ACTUAL GEOMETRY STRAIGHT TENDON SEGMENT ANGULAR CHANGE NODE b IDEALIZED TENDON MODELING OF TENDON BY STRAIGHT SEGMENTS FIGURE 4 4 1 PROGRAM BACKGROUND Chapter 4 ADPT349DWG TENDON TRUSS TENDON ELEMENT ye POINT e e RIGID EN 242 CONSTRAINTS e FRAME e Y NODE X a TENDON SEGMENT GEOMETRY n i oz 5 5
41. OFFSET FOR ALL NODES EXAMPLES OF OFFSET APPLICATION FIGURE 3 5 6 INPUT GENERATION Chapter 3 GLOBAL SYSTEM AND DIRECTION OF POSITIVE GLOBAL ACTIONS b LOCAL SYSTEM X Y AND DIRECTION OF POSITIVE LOCAL ACTIONS ELEMENT COORDINATES FIGURE 3 5 7 INPUT GENERATION Chapter 3 Example LOADING Syntax Explanation Additional sa dd frame elements may be automatically generated using the G n1 parameters Frame elements are generated by incrementing the input parameters above by their respective increments which are input using the G identifier The generation parameters are defined as DE DP l DE ESP Pt PU 1 First element in generation sequence 2 Last element in generation sequence 3 Frame element number increment 4 Node I increment 5 J increment 6 Concrete type increment 7 Cross section type increment at node I 8 Cross section type increment at node J 9 Offset data increment 10 Mild steel type increment and 11 Casting date increment This sequence of lines must be terminated by a blank line ELEMENTS 16 FRAME 16 tyi LOADING 2 e X 1 St 1 Off 1 DAY 0 G 1 8 1 1 1 1 2 1 2 St 1 Off 2 DAY 0 0 9 16 1 1 1 To be followed by one or more lines of loading data input The LOAD NG command is used to apply concentrate
42. Texas 1975 Libby J R 1976 Segmental Box Girder Bridge Superstructure Design ACI Journal May 1976 No 12 23 pp 279 290 Lin C S 1973 Non linear Analysis of Reinforced Concrete Slabs and Shells University of California Berkeley UCB SESM 73 7 Magura D D Sozen M A and Siess C P A Study of Stress Relaxation in Prestressing Reinforcement PCI Journal Vol 9 No 2 April 1964 Mukaddam M A 1969 Behavior of Concrete under Variable Temperature and Loading Interim Report to Oak Ridge National Laboratory Reactor Division Oak Ridge Tennessee NCHRP 1992 Development of Comprehensive Bridge Specifications and Commentary National Cooperative Highway Research Program Project 12 33 Report PTI 1985 Post Tensioning Manual Post tensioning Institute Phoenix AZ 406 pp 1990 Post Tensioned Box Girder Bridge Manual Post tensioning Institute Phoenix AZ 146 pp Scordelis 1993 Ketchum Bridge Comparison of Linear Analysis Results Solution table received through private correspondence from Professor Scordelis University of California Berkeley July 1993 Scordelis A C Chan E C Ketchum M A and Van Der Walt P P 1985 Computer Programs for Prestressed Concrete Box Girder Bridges University of California Publication SESM 85 02 346 pp Van Zyl S F 1978 Analysis of Curved Segmentally Erected Prestressed Concrete Box Girder Bridges University of California
43. The beam element is based on Bernoulli Euler beam theory and a linear elastic material model This allows the approximate modeling of many types of formwork or moving auxiliary structures which may be fixed to the structure during construction Whenever a traveler is moved to a new location its element matrices and loads are recomputed for the nodal geometry of its current location These matrices and loads are then summed into the equilibrium equations during subsequent solution steps They are automatically removed from the summation when the traveler is again moved Traveler Geometry Each Traveler Figure 2 6 1 is made up of a number of traveler frame elements Traveler element geometry 15 defined the same as frame element geometry Figure 4 5 1 b Each traveler element is defined by the two nodes I and J located in the global X plane and on the centroidal axis of the traveler element The centroidal axis of the traveler element is assumed to coincide with the centroidal axis of any frame element connected to the same nodes In most cases this is a reasonable approximation of the actual traveler The origin of the local coordinate system is at node I The local x axis 18 defined by the vector joining node I and node J The local z axis is parallel to and in the direction of the global Z axis The local y axis is orthogonal to the local x and z axes and is directed according to the right hand rule The element cross section is
44. __ a INSTALLATION OF PRECAST GIRDERS b CLOSURE OF SPLICE CTI c MOMENT DUE TO SELF WEIGHT a d MOMENT DUE TO UNIFORM LIVE LOADING SEGMENTALLY CONSTRUCTED TWO SPAN GIRDER FIGURE 1 1 2 4 ADAPT OVERVIEW Chapter 1 1002 PIER SEGMENT FIELD SPLICE N FIELD SEGMENT ELEVATION CAST IN PLACE DECK TTITIT PRECAST GIRDER b SECTION I c STANDARD PRESTRESSED PRECAST SECTION EXAMPLE OF AN INCREMENTALL Y CONSTRUCTED PRECAST PRESTRESSED BRIDGE WITH CAST IN PLACE TOPPING FIGURE 1 1 2 5 1 7 ADAPT OVERVIEW Chapter 1 PCIO10 NEW SEGMENT CONSTRUCTION SEQUENCE OF AN INCREMENTALLY LAUNCHED BRIDGE FIGURE 1 1 2 6 ADAPT OVERVIEW Chapter 1 1008 a ELEVATION B CAMBER FOR PC CONSTRUCTION N CAMBER FOR 7 CONSTRUCTION lt xD DATUM LINE NO CAMBER DEFLECTION NOTE
45. amount of camber is selected to offset the entire or part of the anticipated deflection of a structure Camber computation for incrementally constructed bridges in particular balanced cantilever construction Figure D 1 1 is a critical step in the bridge design Since not only the two tips of the approaching cantilevers must closely meet at the closure the in service long time profile of the bridge must be smooth and in a position determined by design VIEW OF A TYPICAL CANTILEVER CONSTRUCTION BRIDGE FIGURE D 1 1 This writing illustrates the basics of camber computation for balanced cantilever construction It concludes with a numerical example using ADAPT ABI Consider Figure D 1 2 It shows a cantilever consisting of four segments built in four stages At each stage one segment is added to the structure Each time a new segment is added its weight increases the deflection of the previously installed segments For example the deflection of node 2 shown for stage 1 increases with the progress of construction The completed structure shown for stage 4 will have a downward deflection as indicated in the illustration The first step in camber calculation is to determine where at which height with respect to datum line each of the nodes common face of two adjacent segments should be installed during construction so that the completed structure would end up on the datum line horizontal line Since the deflection of the cantileve
46. bridges ADAPT ABI has the added capability of accounting for the time dependent effects of creep shrinkage aging of concrete loss in prestressing temperature settlement of supports and pre or post tensioning internal or external tendons and cable stays The time dependent parameters become central issues in segmentally built bridge con struction since in many instances relatively young concrete is subjected to high stresses and thereby significant time dependent deformation In the structures capable of analysis by ADAPT the cross section of the bridge can vary along its length Changes in elevation of the bridge in the vertical plane can be accommodated but horizontal curves in plan of the centroid of the bridge section are not permitted This is not a practical limitation in most cases since segmentally constructed bridges are typically straight in plan The software has no notable practical limitation on the layout number and stressing sequence of longitudinal prestressing tendons DISCLAIMER Considerable time effort and expense have gone into the development and documentation of ADAPT ABI Bridge design in general and segmentally constructed bridges with time depen dent effects are complex structural engineering tasks The software should be used by engi neers with a good understanding of concrete behavior and structural mechanics The user accepts and understands that no warranty is expressed or implied by the developer
47. cm PH 35000 1 5574E 05 1 5875E 04 me I Solution 158 70 70 5 9 RESULTS solution at day 1000 for stress deflection at node 2 of the verification model together with total top fiber concrete stress at node of element 2 are listed in Table 5 9 1 for comparison For ease of reference the values obtained for SI and MKS units are duplicated in their equivalents in the American system of units in 5 27 ADAPT EXAMPLES VERIFICATION Chapter 5 parenthesis below the computer output of the original units Solutions of each material model ACI and relate together Note that the agreement among the three systems of units 15 very good UNIT WEIGHT W ELEVATION SECTION 100 2 0 3 0D 4 0 6 gt b STRUCTURAL DISCRETIZATION VERIFICATION MODEL FOR UNITS FIGURE 5 8 1 5 28 ADAPT EXAMPLES VERIFICATION Chapter 5 TABLE 5 9 1 COMPARISON OF SOLUTIONS OBTAINED WITH DIFFERENT UNITS AMERICAN SI MKS Deflection Stress Deflection Stress Deflection Stress mm MPa cm kg cm Gn psi 1 5934E 02 1 3944E 03 4 0473E 01 1 1 7428 02 1 3433E 03 44267E 01 92647E 00 4 4267 02 94441 401 4E 5 29 ADAPT EXAMPLES VERIFICATION Chapter 5 ADAPT BRIDGE INCREMENTAL ABI SOFTWARE MANUAL EXAMPLES 3 name of this file UACI START TITLE N 1 ACI AMERICAN UNITS lb inch UNITS U USA CONCRETE PARAMETERS N
48. component 6eT 4 3 2 ey SE T 4 3 3 The significance of these strain components contributing to total strain at any point is discussed in detail in Appendix B In this chapter only the relationships required for their calculation are discussed The creep strain increment e is a function of the previous stress history and of the stress change during the current time step can be calculated recursively assuming either model A Constant stress and constant material parameters over each time step or B linear variation in stress and constant material parameters over each time step or C linear variation in stress and linear variation in material parameters over each time step For model a Equation B 3 11 Appendix B applies for computing For model b Equation B 3 14 applies for computing e For model c Equation 3 19 is used for computing The model used in the program is type that 18 to say linear variation in stress and linear variation in material properties over each time step in the analysis The assumed variation in stresses over a time step is fundamental to each creep model and must be considered when external loads are applied to the structure For model a all stress changes take place instantaneously at the ends of the time steps therefore all loads are also assumed to be applied instantaneously at the ends of the time steps Fo
49. concrete members Figure B 2 1 c shows the variation of the size correction factor with thickness B 2 2 CEB FIP Committee Recommendations The CEB FIP design recommendations include figures and tables for the estimation of time dependent material properties and strains in concrete Unlike the ACI recommendations 1978 the CEB FIP recommendations are not provided in the equation form required for computer analysis However Kristek and Smerda 1982 have proposed analytical approximations for these figures and tables These approximations are suitable for computer analysis and are incorporated in the computer program described in this report A Strength modulus of elasticity and aging of concrete il ii The compressive strength f 1 is expressed as a function of time based on the 28 day compressive strength f 28 The initial elastic modulus is estimated as a function of time and the compressive strength using the formula E t 45680 0112 B 2 5a where 0 modulus of elasticity on day t in N cn concrete strength on day t in N cn The change in modulus of elasticity with time is effected using the following relationship f t 1 45 9 75 0 75 5 5 28 B 2 5b ADAPT ABI CONCRETE MODELING Appendix B SLUMP a SLUMP CORRECTION FACTOR 10 Ku 05 0 0 RELATIVE HUMIDITY 1 b HUMIDITY CORRECTION FACTOR mI _ lt r T 1 YEAR MNM
50. continuity tendons add remaining dead load CHANGE STRUCTURE STRESS 17 18 StressTo 198E3 Anchor 25 E COMPLE d D Q LOADING L 1 40 F 0 2500 12 SOLVE OUTPUT Bes tet cea Step through time up to 10000 days 27 4 years 5 22 ADAPT EXAMPLES VERIFICATION Chapter 5 SOLVE Day 300 Steps 10 SOLVE Day 10000 Steps 10 OUTPUT STOP 5 23 ADAPT EXAMPLES VERIFICATION Chapter 5 5 6 COMPARISON RESULTS Using ABI two sets of solutions are obtained for the bridge example The solutions are compared with those obtained using SFRAME and SPCFRAME Scordelis 1993 One solution is for prestressing yield stress of 270 ksi the second for a yield stress of 210 ksi The yield stress is defined as stress at 0 196 offset from the stress strain curve of the prestressing material The values selected for the yield stress are those used in the reference analyses Observe that in the input data given in Section 5 5 the ultimate stress fpu and the yield stress f are entered with the same value In a regular ABI analysis these values would be different solutions obtained are listed with those of reference Scordelis 1993 in Table 5 6 1 The agreement among the solutions is very close values agree within 1 except for deflection at line of symmetry where ABI deflections are larger than Sframe by 11 Moments hence stresses tendon stresse
51. defined in the local y z plane and must be constant over the x length of the element The only constraint on the shape of the cross section is that it must be symmetric about the local y axis Any arbitrary cross section which meets this requirement can be modeled Any other type of structure such as the truss type travelers frequently used can be modeled approximately using these elements Material Constitutive Relationship The travelers are considered to consist of a linear elastic material Its constitutive relationship is given by 4 5 1 where total stress at time t E constant elastic modulus 4 29 4 5 4 PROGRAM BACKGROUND Chapter 4 total strain at time t Temperature strains are not considered in the traveler elements Stiffness and Load Computation During each time step the following element computations are required A The element s contribution to the global elastic stiffness matrix K B the element s internal forces due to nodal displacements and C the element s equivalent nodal loads due to initial strains and forces These computations are done using matrix transformations The total weight of the traveler is assumed constant regardless of its location in the primary structure When the traveler is installed at a new location its equivalent dead loads are computed based on the total weight of the traveler and the tributary contribution of the traveler s ge
52. edet wasta e Re le ade et teet 1 3 1 2 Input Data ede eR Let te ete pedit 1 32 5 L u e e ie e e o re ete tee teo etie 3 2 1 Natural Sequence of Commands 35 3 22 Summary OF Command a Q esee op SEHE EROR RE ee US 3 3 SAMPLE INPUT FOR NONPRESTRES SED CANTILEVER BEAM eere 5 3 3 T Description of the Structure tet on ep e ur der eet 5 ADAPT ABI LIST OF CONTENTS Contents 3 32 Input ile eet S EA ae d tes 6 3 4 SAMPLE INPUT FOR A PRESTRESSED CONCRETE BOX GIRDER 7 3 4 1 Description of the Structure eee nete SSS h ana ches 7 3 4 2 cen pA RU 8 3 5 DETAILED DESCRIPTION OF COMMAND SYNTAX ies TE 10 ACTIVATE EXTRACT trt rte AMBER CHANGE bka EE CERIS de Ee RED Qh aa CHANGE STRUCTURE tite tomi tet re Re ie em ee CONCRETE PARAMETERS CONCRETE PROPERTIES Chapter 4 THEORY 4 1 FRAME ELEMENT FORMULATION entente tete 4 1 1 Assumptions and Scope 4 1 2 Geometry of Internal Displacement Fields 4 2 INTERNAL DEGREES OF FREEDOM esee tenente tente tenente tenen enne netten 4 3 MATERIAL CONSTITUTIVE RELATIONSHIPS 8 4 31 General 5 ue RUM OD ERR RUM IDEE D Meet 8 4 3 2 Concrete Compon
53. errors are minimized b which is the ultimate creep strain closely matches the ultimate creep strain c contributions of all a 1 0 9 1 terms are approximately equal Choose a different age and repeat steps 3 through 6 to determine a new set of a 1 This is repeated for several values of to provide a table of a t for different loading ages Coefficients for different loading ages may be determined by interpolation between values given in the table This approach may be applied to experimental data or to data generated by some empirical relationship for predicting creep strain For the CEB FIP creep model discussed in Section B 2 2 this approach must be applied twice once for the total recoverable plus irreversible creep and once for the recoverable creep component only Then when the creep strain increment and the hidden state variables g are evaluated in each time step the coefficients for total creep are used when the creep strain B 22 ADAPT ABI CONCRETE MODELING Appendix B increment over the time step and the total creep strain are of the same sign and the coefficients for the recoverable component only are used when the creep strain increment over the time step and the total creep strain are of different signs B 23 ADAPT ABI CONCRETE MODELING Appendix B This Page Left Intentionally BLANK B 24 ADAPT ABI REFERENCES Appendix C ABI C MNL C REFERENCES The foll
54. for the two components are uncoupled In Bernoulli Euler beam theory only the x stress components contribute to the virtual work expressions Thus the constitutive relationships for stresses in terms of strains are one dimensional 4 3 2 Concrete Component The concrete component is considered as an aging viscoelastic material using the formulation discussed in Appendix B Refer to Appendix B for a more complete discussion of the mathematical model The constitutive relationship is given by E e e 4 3 1 where total stress at time t current elastic modulus current total strain current pseudo inelastic strain e current mechanical strain m m m The pseudo inelastic strain consists of several components To describe a time step let time be subdivided by discrete times t and let refer to increments from t _ to tj Then 4 8 PROGRAM BACKGROUND Chapter 4 t tj tji 4 6 1 The creep strain increment the shrinkage strain increment and the temperature strain increment all contribute to the virtual work expression and contribute as initial strains to the load vector for the time step The aging strain increment is a fictitious strain due to the change in elastic modulus which does not contribute to the load vector but does enter the constitutive relationship The total pseudo inelastic strain is found by summing these
55. freedom the global displacements at the nodes Figure 4 4 3 b The segment element 4 15 ADAPT PROGRAM BACKGROUND Chapter 4 matrices in local and global coordinates and the transformation are discussed in the following sections Direct tendon node input is the conceptually simplest approach for specification of tendon geometry The coordinates of each tendon point must be calculated and input and for complex tendon geometries this approach can involve a tremendous amount of hand calculation The parametric generation scheme can perform this task for most typical tendon profiles When parametric tendon geometry input is used the profile of the tendon in a span is specified as a combination of up to four parabolic and or straight line segments The tendon node coordinates in the span are then automatically generated based on a parametric description of these four segments Several combinations of automatically generated tendon geometries are given in Figure 2 4 1 It is reiterated that the tendon spans need not coincide with the frame spans As a result a frame span can be considered as several tendon spans each of which made up of four parametrically generated portions Given the length L of one span of the tendon the tendon profile is uniquely defined by the following parameters all normalized with respect to tendon span length L Figure 4 4 4 ADPT304 INFLEXION INFLEXION LOW POINT SPAN LENGTH
56. friction and anchorage slip These losses result in a variation in initial force over the length of the tendon which is finally idealized by a different initial force in each tendon segment A Friction losses Due to friction between the tendon and its sheathing during jacking the tendon force at a distance x from the jacking end is less than the force at the jacking end Figure 4 4 5 This friction loss is considered in two parts the length or wobble effect and the curvature effect The length effect is the amount of friction loss that would occur in a straight tendon due to duct imperfections and construction practice and is dependent on the friction coefficient tendon length workmanship and alignment of the duct The curvature effect results from the intended curvature of the tendon and is dependent on the friction coefficient and the total angle change between the jacking end and the point under consideration The initial tendon force F at a distance x from the jacking end can be described by the following commonly used expression 4 17 PROGRAM BACKGROUND Chapter 4 STRESSING END DEAD END ACTUAL TENDON GEOMETRY ADPT350DWG Fo TENDON FORCE Fy b ACTUAL TENDON FORCE PROFILE LOSS OF PRESTRESSING FORCE DUE TO FRICTION FIGURE 4 4 5 F F e ue Kx 4 4 2 where F Tendon force at Jacking end curvature friction coefficient cumulative angle ra
57. in the analysis take place during each cycle 1 Move traveler to location for the next segment 2 cast segment 5 12 ADAPT EXAMPLES VERIFICATION Chapter 5 3 walt three days stress the cantilever tendons anchored in the newly erected segment 5 wait four days For the actual bridge the four day period is used for moving the traveler and preparing the formwork for the next segment and the three day wait is an idle period usually scheduled to fall on a weekend gt To economize the analysis the three day wait after casting the segment and the four day period after stressing the tendons are not separately modeled Instead casting of the concrete and stressing of the tendons are assumed to take place on the same day and the concrete material parameter tables from which the elastic modulus and creep potentials are derived are generated for minimum loading age of three days The element dead load and the prestressing are applied separately in two zero length time steps then a seven day time step brings the structure to the start of the next construction cycle Thus the segmental construction analysis requires 48 solution steps The time dependent analysis for the 27 years 10 000 days following construction is performed in 20 time steps Ten time steps are used between the end of construction on day 196 and day 300 Ten more time steps are used between day 300 and day 10 000 Over each of these two time intervals the time st
58. input file is given in Section 3 2 1 Most com mands are optional and must not be used unless required for the structure under analysis For example a command such as TRAVELERS 0 need not be used as part of input data if no travelers are present Default values for input quantities where implemented in the program are indicated within square brackets by in the descriptions pv indicates a default value assumed to be equal to the previous value entered ACTIVATE EXTRACT Syntax ACTIVATE EXTRACT Explanation When included in the data file this command will cause the program to extract the components of the dead loading and the long term effects of creep and shrinkage incrementally with the progress of compu tations in ADAPT ABI It generates a set of data which will be required once ABI Gen is invoked Its location is anywhere on a line after the START com mand and before MESH INPUT Example START ACTIVATE EXTRACT Purpose The ACTIVATE EXTRACT does not change the results of ABI module but makes it somewhat slower to execute since it generates additional data for the module ABI Gen BUILD Syntax BUILD N nl n2 inc Day 3 10 INPUT GENERATION Chapter 3 Explanation CAMBER Syntax where ni Element number of first frame element in a series of elements to be installed in the structure n2 Element number of last element in
59. loading in the elements Each frame and tendon element is considered to be under an initial strain equal to the strain resulting from the temperature change acting on the element with all element degrees of freedom fixed The temperature variation within an element is specified by the temperatures at the extreme fibers of the frame element The internal temperatures are assumed to be constant over the length of the element and to vary linearly over the depth of the ele ment For the frame element this temperature field is used directly to compute the initial strains For prestressing tendon elements the element is assumed to be under constant strain so the temperature at the depth corresponding to the mid length of the tendon segment is used for computing the initial strain The initial stress free tempera ture for each element may be specified independently for each element If the temperature variation through the depth of the frame structure at any given section in not linear that frame section must be modeled as a multi layered section Combination of linear variations of temperature through each layer model the imposed nonlinear temperature change TRAVELER AND FORMWORK OPERATIONS Traveler is the generic name used for an auxiliary structure which is employed during the construction for positioning and supporting the weight of new segments or lifting of new segments into position A traveler is generally assembled and secured to the constr
60. on previous line 2 N 7 G 8 14 1 B 12 36 360 92 It means that tendon span 2 has 7 tendon points These tendon points are associated with the frame nodes 8 9 10 11 12 13 14 In the input lines to follow the geometry of this tendon span is going to be defined with respect to a set of local Cartesian coordinate axes r s which has its origin at the global point X212 36 axis passes through the global point 360 Y 92 It conveys the same specification as in Example 1 with the difference that no local coordinate axes r s for definition of tendon nodes are specified The program uses the local coordinate system associated with the preceding tendon span If none is defined in the preceding lines the global coordinate system is used ADAPT INPUT GENERATION Chapter 3 3 Example 2 N 7 List 8 9 10 14 26 5 32 It means that tendon span number 2 has 7 tendon points associated with the 7 Jrame nodes The 7 tendon points 1 2 3 4 5 6 7 are associated with the frame nodes 8 9 10 14 26 5 32 respectively The next line s provide data for generation or direct input of tendon point coordinates for the span using several options Either If parametric tendon point generation is used for the span one line with the following data must be provided R rl rc rr S sl sc sr where rl Fraction of the total span length between left end of the span and the left
61. prepared to match Ketchum Scordelis 1966 as closely as practical Taking advantage of the symmetry of the problem only one half of the bridge is modeled Figure 5 3 1 and 5 6 1 The pier and pier table region are modeled identical to previous solutions Figure 5 6 2 For a regular ABI analysis a slave element would have been used for connection between the pier top and pier table centroid The input data used to generate the ABI solutions is given in Section 5 5 The results of ABI are compared with the other available solutions in Section 5 6 BRIDGE PARTICULARS The bridge chosen for this example and verification Figure 5 2 1 is a straight three span single cell haunched box girder bridge The haunched girder is cantilevered from the piers using cast in place segments and is later made continuous with a short conventionally erected cast in place girder near the abutments and with the adjoining cantilevered girder at midspan Each cantilever segment is post tensioned to the previous 5 3 ADAPT EXAMPLES VERIFICATION Chapter 5 segments with several cantilever tendons and after the closures at the abutments and at midspan the entire bridge is prestressed with several additional continuity tendons extending the full length of the bridge and local tendons in zones of high positive moment This is common construction sequence and prestressing scheme for bridges of this type The details of the design the design criteria and the
62. since Ctop in one may have Cbot designation in the other Input either the height and width dimensions Fig 3 5 12 with the D and identifiers or the section properties with the and c identifiers When the D and B input form is used the section properties are computed by the program When the D and B identifiers are entered on an input line any additional A I and C identifiers and their data will override the internally computed values 026 TOP u bs i BOTTOM CROSS SECTIONAL GEOMETRY FIGURE 3 5 13 INPUT GENERATION Chapter 3 SEQUENCE Syntax ABHO17 b3 ACTUAL GEOMETRY b MODELLED GEOMETRY MODELING OF CROSS SECTION FIGURE 3 5 14 Figs 3 5 14 and 3 5 15 illustrate two examples of cross sectional idealizations used in the preparation of input data The 5 identifier is used to model non uniform shrinkage over the depth of the cross section The default is uniform shrinkage S EQU ENCE nl n2 vnc INPUT GENERATION Chapter 3 ABI1016 Explanation t bo 0 5 f g a ACTUAL GEOMETRY b MODELED GEOMETRY DOUBLE TEE FIGURE 3 5 15 where nl First node in a generation sequence n2 Last node in a generation sequence and inc Node number increment 1 The SEQUENCE command is an optional command u
63. solution step 25 The SET command is used to set and reset the basic environmental factors influencing the solution as well as solution convergence and acceleration which influence the accuracy of the analysis The command may be issued any number of times in order to change these factors as required with the excep tions noted below The Day identifier is used to set the date from which the age of the frame elements and hence the impact of time dependent effects can be calculated The command SET DAY can be specified only once prior to the start of the solution prior to CHANGE STRUCTURE command SET command can be used more than one time with other arguments such as c The date can also be set under the SOLVE command The identifier is used to set the element temperatures for succeeding solution steps This temperature is used for calculation of temperature strains only This temperature specification overrides any previously specified tem perature gradients entered using the LOADING command The G identifier is used to set the load multipliers for gravity loads in the global X and Y directions The gravity load multipliers gx and gy however influence only the gravity load increment and should be set only once prior to any construction operations performed under the CHANGE STRUCTURE com mand The c identifier is used to set convergence tolerances for the creep series solution The so
64. steel reinforcement usually provided in the elements of a bridge girders and post tensioned frames It is not in tended to model significant localized reinforcing steel which may be provided to resist global bending moments Significant localized steel and pre or post tensioning can be modeled separately within each concrete frame element Each element may be specified to have a uniformly varying cross sectional area be tween its ends However in the computation the program converts the stiffness of the specified non unifrom cross section to that of an equivalent prismatic member of constant cross section Short frame element modeling is recommended for increased accuracy for members with a large rate of change in cross section Dead load is automatically computed from the volumetric geometry of the frame element and its applied as equivalent concentrated forces at the nodes Each frame element may be installed into and subsequently removed from the structure at any solution step Post tensioned prestressing tendons may be of arbitrary geometry in the X Y plane Several tendons may be specified for a frame element Each tendon is approximated by a number of short piecewise linear tendon segments defined by tendon points Fig 2 1 1 c Each tendon point is associated with a frame element node to which its displacements are rigidly constrained Tendon point global coordinates may be input directly or may be generated automatically using a p
65. system Fig 3 5 10 The input X and Y node coordinates are multiplied by the scale factor immediately after input Once the scale factor is entered usually on the first line of node input data do not enter it again unless it is necessary to reset its value Additional node numbers and coordinates may be automatically generated using the G n1 n2 inc parameters Nodes and node coordinates are generated at equal intervals along a straight line between two previously specified nodes The node generation parameters are defined as 3 37 INPUT GENERATION Chapter 3 n1 apreviously specified node number n2 previously specified node number and inc node number increment defining the generated nodes If this param eter is left out a default of 1 is used shown as 1 If node coordinates are defined more than once only the last definition will be used The final set of coordinates for all nodes is printed in the output This sequence of lines must be terminated by a blank line ABI1018 STRUCTURE X GLOBAL COORDINATE SYSTEM DEFINITION OF STRUCTURE GEOMETRY IN GLOBAL COORDINATE SYSTEM FIGURE 3 5 10 OFFSET DATA Syntax OFFSET DATA N n Ol e2 2 Qg 7 where ADAPT INPUT GENERATION Chapter 3 N Total number of different offsets for all the frame elements N Total number of offset data entries n Offset number n OI x and y offset at node I s
66. t u is the ultimate shrinkage value 3 18 INPUT GENERATION Chapter 3 W 150 12 is the unit weight of concrete in pounds per cubic inch When using lb in American units is used In SI and MKS units the defaults are given The general ACI formula for elastic module of elasticity is E t 33 WP P 017 where W is in pounds per cubic foot f t is in psi and E t is in psi In the three systems of units adopted in the program the relationship assumes the following forms In American units E t 2 3704x10 WHIP 0172 where W is in pounds per cubic inch 8 6806x10 f t is in psi and E t is in psi In SI units E t 1 3518 102 WHIP 01 2 where W is in kg mm 2 4019x10 5 f t is in N mm and E t is in N mm In MKS units E t 1 3648 108 WHIP 0172 where W is in kg cm 2 4019x10 t is in kg cm and E t is in kg cm ADAPT INPUT GENERATION Chapter 3 CEB FIP CEBI FIP The next data line for each CEB or CEBI concrete type model is a control data line which takes the following form If the internally generated loading ages and observation times are used this is the only line required for the parameter type n M model Area P H where n Parameter model number Model CEB for CEB FIP recommendations 1 for one component CEB FIP model H ambient relative humidity percent 70 Area Area of
67. t time at observation t0 age of curing constants determined from experiments slump correction factor member size correction factor relative humidity correction factor Normal ranges of constants e f and using normal or light weight concrete for either moist curing or steam curing are as follows e 0 90 to 1 10 f 20 to 130 es 415 10 to 1070 x 10 6 u Standard relations be selected for the prediction of shrinkage strains by selecting appropriate constants 209 1982 for Equation B 2 4 For concrete moist cured for 7 days 5 0 800 106 t 7 35 t 7 For concrete steam cured for 3 days 5 0 730 x 106 t 3 55 t 3 The correction factors are provided to take into account different field conditions that may exist for different cases under consideration ADAPT ABI il ii CONCRETE MODELING Appendix B Slump correction factor Slump of the concrete mix is directly proportional to the water content of the mix Hence the less slump the lower will be the amount of shrinkage Figure B 2 1 a shows the variation of the slump correction factor with slump Humidity correction factor Shrinkage decreases with increases in ambient humidity Figure B 2 1 b shows the variation of the humidity correction factor with humidity Size correction factor K Shrinkage decreases with increasing thickness of
68. tendon see T18 Figure 5 6 4 Twenty four local tendons in the center span and eight local tendons in the side spans located at the bottoms of the webs are also stressed after the bridge is made continuous Figure 5 2 2 e The distribution of these tendons is shown in Figure 5 2 f Each local tendon consists of 21 1 2 inch diameter strands and is stressed from both ends Design loads on the girder include structural dead load based on 155 pcf concrete a superimposed dead load of 2 5 kips foot and AASHTO HS20 44 lane loading The design criteria and method used for proportioning the cross section and prestressing may be summarized as follows Ketchum Scordelis 1986 The cross section dimensions and top slab prestressing were proportioned based on an ultimate strength analysis of the statically determinate cantilever girder under total dead load AASHTO lane live load and prestress The draped continuity tendons and the local tendons were proportioned based on an allowable stress analysis of the final continuous system under total dead load live load and prestress Then using this preliminary design as a model the design of the tendons was finalized based on a design redistribution analysis under total dead load live load and prestress assuming 100 percent moment redistribution For checking the adequacy of the design based on this analysis an allowable stress approach was used with 0 psi tension and 2250 psi compression allowed un
69. tendons Tendons 25 through 28 each represent four actual tendons Tendons 19 through 22 are jacked from both ends with a force of 1 275 000 pounds Tendons 25 through 38 are jacked from the left end only with a force of 2 550 000 pounds Tendons 23 24 29 and 30 are jacked from the eft end only with a force of 1 275 000 pounds Material properties assumed for the time dependent analysis are as follows The concrete modeled using the ACI Committee 209 recommendations Appendix B B 2 1 has ultimate strength 28 5000 psi ultimate creep factor eo 2 5 ultimate shrinkage strain 0 0008 and unit weight W 155 pcf Time dependent 5 11 ADAPT EXAMPLES VERIFICATION Chapter 5 5 4 development of shrinkage aging utilize the standard ACI parameters derived for these properties with the default constants recommended by ACI The uniformly distributed mild steel reinforcement in the frame elements has elastic modulus E 29 000 000 psi The prestressing steel has elastic modulus E 28 000 000 psi ultimate strength fpu 270 000 psi prestressing steel is stress relieved with relaxation coefficient R 10 curvature friction coefficient u 0 25 radian wobble coefficient K 0 0004 foot and anchorage slip of 1 4 inch The ultimate strength fpu and yield stress of the prestressing steel are both assumed as 270 000 psi for one solution and 210 000 for another solution The two values are assum
70. that the strain remains constant and that the only stress applied is the initial prestress Since creep shrinkage and external loads cause additional changes in force over time this Equation 4 4 8 can not be applied directly To incorporate the additional force variations over time Hernandez and Gamble 1975 suggested the following procedure which is used in the program based on 4 24 ADAPT ADPT353 DWG PROGRAM BACKGROUND Chapter 4 the assumption that all non relaxation changes in tendon force occur at the ends of the time steps Figure 4 4 11 The initial tendon force f applied at time t relaxes by the amount to fs during the time interval 61 of Is 4 4 9 LOW RELAXATION STRESS RELIEVED TIME STRESS LOSS IN PRESTRESSING DUE TO RELAXATION FIGURE 4 4 10 At time t externally caused strain changes cause the tendon force to change to To compute the stress relaxation f during the time interval dt Equation 4 4 9a is used to calculate a fictitious initial tendon force which would have relaxed by to fl during t The stress may then be found assuming as the initial tendon force and applying Equation 4 4 11 fo 4 4 9b ADAPT PROGRAM BACKGROUND Chapter 4 STRESS ADPT354DWG to ty t 13 MODEL OF TENDON STRESS RELAXATION FIGURE 4 4 11 This procedure is applied to each tendon seg
71. the series n1 inc Element number increment Day Casting date of concrete in the specified elements The BUILD command is used to install new frame elements into the structure The elements which are installed can later be removed using the REMOVE subcommand The sequence of elements generated with the N identifier must be statically feasible in order for node displacement initialization to work properly Thus for the BUILD command backwards generation 1 inc less than 0 is allowed If a casting date is specified under this command it over rides the value input under the FRAME ELEMENTS subcommand of the MESH INPUT command The dead load of the frame element is automatically included as concentrated forces at the nodes based on the length cross section area and material unit weight of the elements input under the MESH INPUT command multiplied by the current gravity load multipliers specified with the SET command The displacements of any previously unrestrained nodes which as a result of this command are made active are initialized based on the total displacements of the node at the other end of the element and assumed rigid behavior of the element added This makes it necessary under this subcommand to generate elements in a statically feasible order More than one Build command can be specified in order to achieve a con struction Note n2 inc and Day are option
72. to interpolate solutions for days not specifically covered by the input Note that the program cannot extrapolate from the user specified data beyond the final day of shrinkage strain data collection That is to say if the final reading for shrinkage strain data is taken on day 45 and for creep strain on day 50 then the program will only be able to find a solution for days up to and including day 45 PARAMETERS N 2 T 4 8 MaxShrinkageReadings 8 pSpecimens 2 CreepReadings 6 ShrinkageReadings 7 ShrStrain 29 50E 80E 79 86 pi pi pl q 0 P 6 note there are 7 entries Eci 10894 first creep specimen ObservationAge CreepStrain 1 696E 8 5 1581E 8 3 22 INPUT GENERATION Chapter 3 10 15 20 30 LoadingAge 5 Eci 18684 ObservationAge 5 10 15 20 25 30 1842 8 2074 8 2161 8 3306 8 6 readings second creep specimen 2 CreepSpecimens 1 Ade 1 7 14 21 28 35 LoadingAge 3 Eci 16203 ObservationAge 3 7 11 22 32 CONCRETE PROPERTIES CreepStrain 493E 8 870E 8 1117E 8 1305E 8 1410E 8 1523E 8 6 readings CreepReadings 5 ShrinkageReadings 6 ShrStrain 0 6 2 29E 6 2 50E 6 2 80E 6 2 79E 6 2 86E 6 2 6 readings CreepStrain 566E 8 1291E 8 1682 8 2320 8 2683E 8 5 readings 5 Syntax C
73. using one of these recommendations can be automatically incorporated into a time dependent analysis using the computer program described in Chapter 4 The details of the assumptions and expressions of the recommendations are different and will not be discussed here The relationships recommended for predicting the behavior of concrete structures may be summarized as follows B 2 1 ACI Committee 209 Recommendations ACI Committee 209 recommendations provide a number of equations for predicting the time dependent material properties and strains in concrete A Strength and stiffness The cylinder strength f 0 is computed using an equation of the form 1 f t 1028 2 1 where f 28 is the 28 day strength t is the time in days after casting of the concrete and a and b are constants The values of a and b depend on B 8 ADAPT ABI CONCRETE MODELING Appendix B the type of cement and the curing method used for the specimen For type I cement and moist curing the recommended values are a 4 0 and b 0 85 For constant f over time a 0 0 and b 1 0 The initial elastic modulus E t is computed as a function of the cylinder strength 0 using the following formula E t 33 wl5 f 0 2 B 2 2 where w is the unit weight of the concrete in pounds per cubic foot and is the strength of the concrete in pounds per square inch Creep strain Creep strain at any time under constant stress is comput
74. 0 OUTPUT SOLVE DAY 1000 OUTPUT In the first example a solution for day 1000 is attempted immediately after day 10 This might be difficult The difficulty will show itself through high numbers of iterations 15 or more or lack of convergence The second ex ample overcomes this problem by breaking the time span into smaller inter vals without increase in output SPRINGS Syntax SPRINGS N n ni nj K kx ky kzz G nl n5 where Total number of frame springs 1 n Spring element number ni Node number for node I I is the node attached to frame for spring supports nj Node number for node J J is the node with fixed displace ment for spring supports kx Spring axial stiffness force per unit extension along the spring ky Spring shear stiffness force per unit extension perpendicular to the spring kzz Spring rotational stiffness moment per unit rotation and ml 5 Frame element generation parameters described below Explanation The SPRINGS command is used to define the spring supports of a frame Node I of the spring is defined to be attached to the frame and node J is the fixed support A spring is assumed to be an inert material having only exten sional and rotational stiffness at its node I The stiffness properties of the 3 51 ADAPT INPUT GENERATION Chapter 3 5 Syntax Explanation spring are not affected by time creep shrinkage and temperature The stiff
75. 0 0 0000 00 0000 00 SIS INE 6 6293 00 4461 01 36 76 5 2195 9 0 5 11 ADAPT ABI INPUT OUTPUT EXAMPLES Appendix A A 2 EXAMPLE The following is an example of input and output of the simple cantilever problem described next The sample input and output is for a simple non prestressed cantilever with uniform rectangular cross section subject to a concentrated loading at its tip For the purposes of illustration the weight of the cantilever is specified as zero Hence the actions moments and shears and the deformations will be due to the concentrated load only 1000 Ib BL ELEVATION SECTION STRUCTURE 2 3 4 5 NODE D 2 3 4 ELEMENT b STRUCTURAL MODEL CANTILEVER BEAM FIGURE A 2 1 The cantilever is cast at day zero loaded at day 100 at which time its moments and deformations are calculated Without changing the loading two other solutions are A 12 ADAPT ABI INPUT OUTPUT EXAMPLES Appendix A obtained one at 1000 days and the other at 10 000 days Since the loading is not changed the actions will be the same for the different ages but the deformations will increase The change in deformation is triggered by the non zero creep and shrinkage 5 coefficients entered under CONCRETE PARAMETERS command A 3 INPUT FILE ADAPT BRIDGE INCREMENTAL ABI SOFTWARE MANUAL EXAMPLE Name of th
76. 060605 STRUCTURAL CONCRETE SOFTWARE ADAPT ABI Construction Phase Modeling and Analysis Basic Module This supplemental reference manual is made available to users of ADAPT ABI 2012 to help them understand the underlying modeling and analysis capabilities of the software It references the previous text based INP file format used to define models The current version of ABI uses a similar INP file format to send model information to the analysis engine Copyright 1997 2012 support adaptsoft com www adaptsoft com ADAPT Corporation Redwood City California USA Tel 1 650 306 2400 Fax 1 650 306 2401 ADAPT International Pvt Ltd Kolkata India Tel 91 33 302 86580 Fax 91 33 224 67281 ADAPT ABI LIST OF CONTENTS Contents LIST 5 Chapter 1 OVERVIEW GENERAT n REO ep t de oe tbe d te b tert t et 1 11 1 Program u OR ats 1 1 1 2 Segmental Construction I 2 SCOPE 5 eed 1 3 DISCLAIMER 1 4 PRINCIPAL STEPS IN DESIGN ANALYSIS OF SEGMENTAL CANTILEVER BRIDGES Ic aus aS A uwa Was us hawa waina umu ated 11 Construction Phase 3 u Ne a ttle See 11 14 2 Completed Structure eerte e gU eme e nua pone 12 Chapter 2 PROGRAM DESCRIPTION 2J OVERVIEW RR p te Metern BR eR HP DER asss 1 2 Vel Structural
77. 144 01 640 02 036 01 640 402 062 00 640 402 771 00 600 01 600 01 000 02 875 00 000 02 3 958E 00 800 01 642 02 642 02 641 02 640 02 600 01 000 02 000 02 o d 1518 02 20207 26270 B2 22201402 479 03 764 03 SABER 1 Q Np MN OIN gt Q N N IO N Q 801 03 240 02 7 ADAPT ABI INPUT OUTPUT EXAMPLES Appendix A 5 4 TRAVELERS NUMBER OF TRAVELERS N TRAVELER NODE SECTION MOMENT OF ELASTIC TOTAL NO COUNT AREA INERTIA MODULUS WEIGHT 1 000 02 2 200 04 3 000E 07 1 000 04 1 000 02 2 200 04 3 000E 07 1 000 04 CURRENT X DIRECTION GRAVITY MULTIPLIER Y DIRECTION GRAVITY MULTIPLIER STRESS CONVERGENCE FACTOR 1025 STRUCTURE 102 2 ACTIVE FRAME ELEMENTS 102 3 ACTIVE SPRINGS TRAVELER 1 NODES TRAVELER 2 AT NODES A 8 ADAPT ABI INPUT OUTPUT EXAMPLES 104 LOADING 04 1 EXTERNALLY APPLIED LOAD OF THIS T N C R E M E N T 2 1 0000 02 4 0000 01 2 0000 02 4 0000 01 3 0000 02 2 0000 01 XD TSP 0 0000F 00 0 0000E 00 0 0000F 00 y D TSP 0 0000E 00 0 0000 00 0 0000 00 0 0000 00 0 0000 00 0 0000 00 EBEMENT TEMPERATURES U APED TED AL THESS N JOB E IDEE TEMPERATURE 90 0 80 0 FIBER TEM
78. 2 0 0000 00 0 0000 00 0 0000 00 0 0000E 00 105 NODAL BOUNDARY CONDITIONS AND TOTAL DISPLACEMENTS Legend 0 X DESP 16 38 1515 2 0000 00 0000 00 0000 00 8683E 03 5656E 02 22 sinr 9 SOS TO 209906 0605 02 8892 01 562598508 7473 02 9854 01 9 106 TOTAL REACTIONS AT FIXED NODES Lo 507969912 25 09 00 402 5x3 009 28 02 au SLIGHT KA 2 0000 O2 200109 A 18 ADAPT ABI INPUT OUTPUT EXAMPLES 107 FRAME ELEMENT ACTIONS ELEMENT NO 108 gt STRESSES 2638 02 7041 02 1444 02 8463 01 BENDING END I 3 2000 04 2 4000 04 1 6000 04 8 0000 03 2140 02 6543 02 0946 02 3483 01 BENDING SHEAR END J FORCE 2 4000 04 0000 02 1 6000 04 0000 02 AXIAL FORCE Bg HOM BTS 12 8 0000 403 OMNIA 09155155 0000E 02 7041E 02 1 6543 02 1444E 02 1 0946 02 8463 01 5 3483 01 4898E 00 2 4898 00 A 19 Ds Gone AXIAL 2 4898 00 2 4898 00 2 2 4898 00 4898 00 Appendix ADAPT ABI INPUT OUTPUT EXAMPLES Appendix A A 5 GRAPHICAL DISPLAY OF OUTPUT The following illustrates several graphical displays of the output generated by ABI s print option 6 03 05 8 33 24 CANT adv DISCRETIZATION OF CANTILEVER EXAMPLE FIGURE 5 1 ADAPT ABI INPUT OUTPUT EXAMPLES Appendix A CANT adv MOM
79. 3 STOP Syntax Explanation STRESS Syntax Explanation Example Example STOP The STOP command saves the entire structure database and terminates pro gram execution The analysis can be restarted to analyze for more time steps by providing the saved database files and an appropriate input file for the additional steps See the description of the START command STRESS N n1 n2 inc Ratio ra rb StressTo sa sb N Force fa fb Anchor da db where ni Tendon number of first tendon in a series of tendons with identi cal stressing specifications n2 Tendon number of last tendon in the series n1 inc Tendon number increment ra Jacking stress ratio at tendon end rb Jacking stress ratio at tendon end sa Jacking stress at tendon end sb Jacking stress at tendon end fa Jacking force at tendon end fb Jacking force at tendon end da Anchorage slip draw in at tendon end and db Anchorage slip draw in at tendon end End A of a tendon is the end first entered in the definition of tendon geometry in input data End B is the last point of the same tendon in input data TENDON GEOMETRY N 1 1 N 4 End ll co S 5 5 5 0 End B By reversing the order of entry the determination of A and B can be reversed List 6 5 4 3 In this example tendon end associated with node 6 is e
80. 3 19d g t 0 B 3 19f B 20 ADAPT ABI CONCRETE MODELING Appendix B Because the creep strain increment over the time step e is dependent on the stress change over the time step in Equation 19 this relationship must be evaluated iteratively in each time step terms in Equation B 3 19a other than stay the same for all iterations therefore all the summations can be done prior to starting the iterations and only R needs evaluation in each iteration The iteration can stop when o undergoes little change from one iteration to the next The time increment t appears in the denominators of Equation B 3 19c and B 3 19d above Thus the recursion is impossible to evaluate when dt 0 Investigation of limits as t approaches zero provides the following expressions for use in place of Equation B 3 19c and Equation B 3 19d when 0 1 B 3 20 B 0 3 21 3 3 Determination of compliance coefficients The material properties for creep strain computation in this algorithm are the creep compliance coefficients a t and retardation times They must be available as data to the subroutines implementing the creep strain algorithm Kabir 1976 demonstrated how they can be evaluated from creep data from an experimental study and also used the method to find coefficients corresponding to the ACI Committee 209 1982 recommendations The method of evaluating the coefficients is the
81. 40 5 8 6 r 300 5 2 7 r 360 5 8 It means that tendon span number 2 has seven points frame nodes to which these are associated 8 9 10 11 16 3 14 Tendon node point 5 is associated with frame node 16 The coordinates of the tendon node point 5 are r 240 s 8 The coordinates of the frame node 16 are defined elsewhere in MESH INPUT command Since the coordinates of tendon node 5 defined herein is not likely to match those of its associated frame node 16 the tendon point 5 will have an x and y offset with respect to the frame node 16 The software computes and outputs the offsets 3 61 ADAPT INPUT GENERATION Chapter 3 TITLE Syntax TITLE N 1 Problem ID text line 1 Problem ID text line Explanation The TITLE command prints a program identifier in the output file and then prints N lines of text provided on the N input lines immediately following the command line The TITLE command is optional but should be the first command interpreted in order to clearly identify the output file TRAVELERS Syntax TRAVELERS N n X E W N where the first line heading total number of travelers in the following lines number of nodes in traveler n Traveler number X section type number W Elastic modulus of material and Total weight of traveler Ib in American units Newtons in SI u
82. 83 07 R 45 Ap 0 000009 TENDON GEOMETRY N 1 1 Spans 1 M 1 0 9870948 1 N 5 G 1 5 1 0 0 25 4 0 R 0 0 5 0 5 5 08 5 08 5 08 MESH COMPLETE SET Day 10 T 20 CHANGE STRUCTURE BUILD N 1 5 1 STRESS N 1 StressTo 0 14061 536 Anchor 0 0 3175 RESTRAINTS 1 R 1 1 1 6 R 1 1 1 CHANGE COMPLETE LOADING 5 15875 9 31 752 0 SOLVE OUTPUT SOLVE 500 Steps 3 OUTPUT LOADING L 1 4 1 T 70 70 SOLVE SOLVE Day 1000 Steps 3 OUTPUT STOP 5 32 ADAPT EXAMPLES VERIFICATION Chapter 5 P ADAPT BRIDGE INCREMENTAL ABI SOFTWARE MANUAL EXAMPLE name of this file UCEBI START TITLE N 1 CEB1 AMERICAN UNITS lb inch UNITS U USA CONCRETE PARAMETERS N 1 1 1 Area 300 P 80 MESH INPUT NODES N 6 X20 0 5 120 0 G 1 5 6 X 60 Y 25 CONCRETE PROPERTIES 1 Fpc 5000 Cr 2 5 Sh 0 0003 W 0 086805556 Ac 0 0000055 MILD STEEL PROPERTIES N 1 Es 29000000 0 P 0 02 As 0 000006 SECTION PROPERTIES N 1 Area 300 I 2200 C 11 17 ELEMENTS N 5 FRAME N 4 1 1 2 C 1 X 1 St 1 Day 1 G 1 4 1 1 1 SPRINGS N 1 5 3 6 K 30000 PRESTRESSING STEEL N 1 1 Ep 28000000 Meu 0 25 K 0 0003 Fpu 270000 R 45 Ap 0 000005 TENDON GEOMETRY N 1 1 Spans 1 M 1 Area 0 153 1 N 5 G 1 5 1 B 0 0 E 10 0 R 0 0 5 0 5 2 2 2 MESH COMPLETE SET Day 10 68 CHANGE STRUCTURE BUILD N 1 5 1 STRESS N 1 StressTo 0 200E3 Anchor 0 0 125 RESTRAINTS 1 R 1 1 1 6 R 1 1 1 CHANGE COMPLETE LOADING N 5 F 35000 70 0
83. ANGE COMPLETE to terminate the command described before The cHANGE STRUCTURE command can be used any number of times in a given analysis in order to model the construction sequence The effects of the changes on the displacements and internal stresses in the structure are found by using the SOLVE command after the CHANGE STRUCTURE command and any optional loadings commands CONCRETE PARAMETERS Explanation The CONCRETE PARAMETERS command generates or concludes with either program defined tables of shrinkage strain elastic modulus and creep coeffi cients vs time or user defined values The CONCRETE PARAMETERS command must be used prior to the MESH INPUT command These tables provide the constitutive constants used in the time dependent analysis of the structure When automatic generation of the program is used the values in the tables are normalized for ultimate creep coefficient 1 ultimated shrinkage strain 1 and concrete strength f 28 1 Prior to use in each solution step these normalized values are scaled by the creep coefficient and shrinkage strain values input under the CONCRETE PROPERTIES subcommand of the MESH INPUT command The correction of concrete strength 15 also achieved through scaling to f given under the CONCRETE PROPERTIES subcommand Thus when automatic generation is used under most circumstances only one concrete parameter type is requ
84. DE U X U Y R Z X DISP Y DISP Z ROTN 1 1 1 1 0 0000 00 0 0000 400 0 0000 00 2 0 0 0 1 8925E 02 3 5619E 02 5 3428E 05 STAGE 2 NODAL TOTAL DISPLACEMENTS NODE U X U Y R Z X DISP Y DISP Z ROT 1 1 T T 0 0000E 00 0 0000E 00 0 0000E 00 2 0 0 0 8 9188 02 1 4024 01 2 3215 04 3 0 0 0 1 3540E 01 4 0959 01 2 8796E 04 STAGE 3 NODAL TOTAL DISPLACEMENTS NODE U X U Y R Z X DISP Y DISP Z ROTN 1 1 A 0 0000 00 0 0000 400 0 0000 00 2 0 0 0 1 3180E 01 3 1258E 01 5 4898E 04 3 0 0 0 2 3677 01 9 9670E 01 7 7225 04 4 0 0 0 2 8298 01 1 8062 00 8 2806E 04 STAGE 4 NODAL TOTAL DISPLACEMENTS NODE U X U Y R Z X DISP Y DISP Z ROT 1 1 1 1 0 0000 00 0 0000 400 0 0000 00 2 0 0 0 41 9008 0121 5 6346E 01 1 0220E 03 3 0 0 0 3 2102 01 1 8946E 00 1 5649 03 4 0 0 0 4 4077E 01 3 5980E 00 1 7938E 03 5 0 0 0 5 0956E 01 5 4299E 00 1 8510E 03 CAMBER NODE X DIRECTION Y DIRECTION ROTATION 0 0000E 00 0 0000E 00 0 0000E 00 2 0 1690 00 0 5635 00 0 1022E 02 3 0 3021E 00 0 1806E 01 0 1511E 02 4 0 3054E 00 0 2900E 01 0 1506E 02 5 0 2266E 00 0 2796E 01 0 1023E 02 The deflected shape and the required camber for the completed structure is shown in Figure D 2 1 from ADAPT ABI graphical output The following is the long hand calculation for camber at node 4 shown as 1 18 in the figure Refer to the Figure D 1 2 for the symbols used D 7 ADAPT ABI BACKGROUND TO CAMBER COMPUTAT
85. DESCRIPTION OF THE STRUCTUNRBE desea 7 BAD INPUTFILE 8 DETAILED DESCRIPTION OF COMMAND SYNTAX 10 ACTIVATE BX TRAC LI iiti REESE UN desse ved et tdv boni ua iat 10 E D 10 CAMBER E eoe iupra sans RIP Ue RUE CHANGE COMPLETE e SEED 12 CHANGE STRUCTEURE Sranang dU 12 CONCRETE PARAMETERS 13 CONCRETE PROPERTIES ansa aa aa a a Saa aaa 23 DE STRESS qe 25 ELEMENTS A A a Ga 26 FRAME EHI Nala usuka u ase nasa 26 LOADING 31 MESH COMPLETE dodici G N 35 IVES ER TIN PUT u naam a aan a aR aaa Qu kha aaa as 35 MILD STEEL PROPERTIES esheets 35 nui m ERE 36 NODES 2522 S 37 OFFSET DATA EIN sas 38 OUTPUT u CES 39 PRESTRESSINGSTEBL UM at t 41 rem 42 RESTRAINTS Rte a Med v Aud 42 SECTION PROPERTIES ananas ian 45 SEQUENCE gem EE 47 SED A 49
86. ENTS IN CANTILEVER EXAMPLE FIGURE A 5 2 3 2000 004 MOMENT IN ELEMENT SUPPORT FIGURE 5 3 A 21 ADAPT ABI INPUT OUTPUT EXAMPLES Appendix A Unst ksi 3 625E 001 3 593E 001 3 561E 001 3 529E 001 3 497E 001 3 465E 001 3 433E 001 3 401 001 3 370 001 3 338E 001 3 306E 001 3 274E 001 md 3 242 001 3 210 001 ADAPT STRESSES IN ELEMENT NEXT TO SUPPORT FIGURE A 5 4 A 6 INPUT OUTPUT GRAPHICAL DISPLAY The graphical display for both the input and output of the program is described in a separate package entitled ABI Viewer Interface A 22 ADAPT ABI CONCRETE MODELING Appendix B ABI B MNL B MODELING OF CONCRETE S TIME DEPENDENT BEHAVIOR 1 STRAIN COMPONENTS AND THE SUPERPOSITION METHODL a 4 Mechanical 5 ette p UE PEE ORE ERE S PROPORRE 5 Bil 2 Aging Sanz PARERE RR RH ates 6 1 3 Stam zi ees epe te eem amem e pU dee e ODER red 6 B 1 4 Shrinkage esc D beet vedete 6 B J 5 Temperature Strain nette tp eet eo e oe RR teen ete 8 2 PREDICTION OF TIME DEPENDENT MATERIAL PROPERTIES 8 B 2 1 ACI Committee 209 Recommendations us A Strength and tete te ete ep Cet B Cr ep stralh iue ge Up Ed edet tetas Shrinkage stram zs ec RR NE RR b B 2 2 CEB FIP Committee Recommend
87. H ES Cn tj RAME LEM NTS ENDON 5 2 1 PRIMARY FRAME 2 SPRINGS S RAVEL RS CONSTRUCTION AND SOLUTION 10 3 104 105 106 107 108 109 FL EMENTS Appendix A start of a stage STAGE DAY D SOLUTION CONTROL DATA STRUCTURE 102 1 ACTIVE NODES 102 2 ACTIVE FRAME ELEMENT 102 3 ACTIVE SPRINGS 102 6 ACTIVE PRESTRESSING TENDONS TRAVELERS 103 1 ACTIVE TRAVELERS AND THEIR POSITION LOADING 104 1 EXTERNALLY APPLIED LOAD OF THIS INCREMENT 104 2 ELEMENT TEMPERATURES APPLIED AT THIS INCREMENT 104 3 TOTAL OF EXTERNALLY APPLIED LOADING AT THIS STAGE 104 4 TOTAL OF ELEMENT TEMPERATURES AT THIS STAGE NODAL BOUNDARY CONDITIONS AND TOTAL DISPLACEMENTS TOTAL REACTIONS AT FIXED NODES FRAME ELEMENT ACTIONS 107 1 PRIMARY ELEMENTS 107 2 TRAVELER ACTIONS EXTREME FIBER STRESSES IN CONCRET TENDON FORCES 109 1 INDIVIDUAL TENDON ACTIONS TOTAL STATIC RESULTS FOR ELEMENTS CAMBER rt of next stage ADAPT ABI INPUT OUTPUT EXAMPLES Appendix A Data blocks 100 through 111 will be repeated for each
88. ION Appendix D 8049E 000 E 000 6E 001 Deflected Profile 5 4538E 000 b Camber ILLUSTRATION OF DEFLECTION AND CAMBER OF AN INCREMENTALLY CONSTRUCTED CANTILEVER FIGURE D 2 1 442 0 40959 deflection ofnode 3 at stage 2 05 2 8796E 4 rotation of note 3 at stage 3 44 435 03 5 13 initial position ofnode 4 at installation 0 40959 2 8796E 4 1000 0 6976 444 3 5980 final position of node 4 at completion of structure stage 4 Camber 4 0 6976 3 5980 2 900 software output is 2 900 OK D 8 ADAPT ABI BACKGROUND TO CAMBER COMPUTATION D Note that in Figure D 2 1 b for practical considerations camber shown is vertical displacement of each node But the displacement in Figure D 2 1 are the vectorial sum of displacements in the horizontal and vertical directions along x and y axis of the frame For example the displacement 3 62 shown in Figure D 2 1 for node 4 15 3 5982 0 44072 1 2 D 2 1 Input data for ADAPT ABI ADAPT BRIDGE Incremental ABI Software Manual Example Thi START TI UNITS CONCRE MESH MESH ET D HANG Q CHANGE SOLVE CHANG Name of this file CAMBER1 INP Units N mm S example illustrates the application of camber computation N 2 ABI CAMBER COMPUTATION EXAMPLE
89. IS ELEVATION CROSS SECTION a ELEMENT ELEVATION AND SECTION bi 1 L bh b BASIC LIBRARY CROSS SECTION ELEMENT COORDINATES AND THE BASIC CROSS SECTION MODULE FIGURE 2 2 2 PROGRAM DESCRIPTION Chapter 2 OFFSET CASTINPLACE TOPPING CAST IN PLACE m CONNECTION ELEMEN E CENTROD NODE Precast ONE SEGMENT ELEMENT PRECAST SECTION SECTION SECTION ELEVATION TWO COMPONENT SECTION PRECAST BASE WITH A CAST IN PLACE TOPPING 9 2 co o E 1 C1 OFFSET CENTROID CONNECTION SECTION ELEVATION b TWO COMPONENT c FINTE ELEMENT SECTION MODELING MULTI COMPONENT SECTIONS AND THEIR MODELING FIGURE 2 2 3 ADAPT PROGRAM DESCRIPTION Chapter 2 2 3 MATERIAL PROPERTIES The materials to be defined are concrete nonprestressed steel and prestressing steel Gener ally several different types for each material can be defined The multi layer modeling of a cross section is of particular value when the effects of nonlinear temperature gradient through a section is sought Depen ding on the accuracy required the section can be modeled as several layers of identical material For each layer the temperature gradient is linear Another typical application is in composite construction where a portion of the section is cast at
90. LE PIV SLIASHA SISA IVNV NOSTAVdNOO ANGIE II HO LODI 975 TI9VUL ADAPT EXAMPLES VERIFICATION Chapter 5 5 7 AMERICAN SI AND MKS SYSTEM OF UNITS EXAMPLE This example is devised to verify the correlation accuracy of the software among its built in three different systems of units American ST and MKS It achieves two objectives First by providing a complete listing of input data for each of the system of units implemented it demonstrates the specific features of data preparation for each Second it substantiates the validity of the software in changing from one system of units to the next It confirms that solutions to the same problem obtained in different systems of units are practically identical To obtain a correct solution it is imperative that units entered for each system be consistent with the listing given below AMERICAN pound inch degrees F SI Newtons mm degree C MKS Kg cm degree C The conversion factors used in the program for the more frequent items are listed in Table 5 7 1 TABLE 5 7 1 PRINCIPAL CONVERSION UNITS USED IN ABI ee om 2 54000E 01 mm 2 54000E 00 cm 6 45160E 02 mm2 6 45160E 00 cm2 4 16231E 05 mm4 4 16231E 01 cm4 4 53438E 00 kg 4 53438E 01 kg Force 4 44822E 00 N 4 53438E 01 kg Moment 1 12985E 02 N mm 1 15173E 00 kg cm 6 89476E 02 MPa 7 02830E 02 kg cm 5 55556E 01 C 5 55556E 01 C 5 8 The structural model selected for verification is
91. NCRETE NO MODEL NO ULTIMATE STRENGTH 000 03 CREEP COEFFICIENT 500 00 SHRINKAGE STRAIN 000E 04 UNIT WEIGHT 000E 00 THERM EXPN COEFF 000E 00 3 2 MILD STEEL PROPERTIES MILD STEEL ELASTIC PERCENTAGE IN THERMAL EXPANSION NO MODULUS CROSS SECTION COEFFICIENT 2 90000 07 5 00000 02 0 00000 00 SECTION 5 COMPUTED SECTION PROPERTIES SECTION 1 CROSS SECTION 700 01 OF 764 02 DISTANCE CG TONTOR 500E 00 DISTANCE 500 00 SHRIN 000 00 SHRIN BOT 000E 00 A 14 ADAPT ABI INPUT OUTPUT EXAMPLES Appendix FRAME GEOMETRY Y COORD 120 000 160 000 PRIMARY FRAME ELEMENTS 4 ELEMENT NODE NODE CONCR SECT STEEL CASTING NO LIDEN INA yp E DAY CURRENT TEPERATURE X DIRECTION GRAVITY MULTIPLIER Y DIRECTION GRAVITY MULTIPLIER STRESS CONVERGENCE FACTOR 104 LOADING 104 1 EXTERNALLY APPLIED LOAD THES ILN CREMEN NODE X FORC apas 2 X DISP YSIS Z ROTN 5 0 0000 00 2 0000 02 0 0000 00 0 0000 400 0 0000 00 0 0000 00 NODE X FORC PESOS 2 X DISP YS IDLE 5 0 0000E 00 2 0000 02 0 0000 00 0 0000 400 0 0000 00 0 0000E 00 15 ADAPT ABI INPUT OUTPUT EXAMPLES Appendix A 105 NODAL BOUNDARY CONDITIONS AND TOTAL DISPLACEMENTS X DISP DISP Z ROTN 0000E 00 0000E 00 0000 00 0000 00
92. O 1 e000 B 3 2 i l In this investigation y t is used the instantaneous elastic strain is not included in the kernel and the degenerate kernel takes the form used by Kabir 1976 Ya 0 3 3 i 1 where are creep compliance coefficients which depend on the age of loading and are retardation times in days which govern the shape of the creep curve Kabir also included a temperature shift function which is not included in this formulation This degenerate kernel can be made to approximate any creep compliance function J t t to any degree of accuracy by selecting the number of terms m and the coefficients and on the basis of least squares curve fitting This curve fitting procedure is discussed in Section B 3 3 of this Chapter Use of this kernel will result in any one of several different expressions for computing creep strain depending on the assumed variation of stresses and material parameters over the length of a time step Assuming step function stress variations and constant material parameters results in the expression given by Kabir B 16 ADAPT ABI CONCRETE MODELING Appendix B 1976 Equation B 3 11 Assuming linear stress variations and constant material parameters results in an expression similar to one given by Bazant 1982 Equation B 3 14 Assuming linear stress variations and linear variations of material parameters results in yet another express
93. OLVE Day 168 N 15 StressTo 198F3 198E3 Anchor 25 5 21 Chapter 5 build segments 9 and 36 25 build segments 8 37 25 build segments 7 38 25 build segments 6 39 25 ADAPT EXAMPLES VERIFICATION Chapter 5 p Mixes en s uds Stress tendon 16 CHANGE STRUCTURE STRESS 16 StressTo 198E3 198E3 Anchor 25 25 CHANGE COMPLETE SOLVE A 0 71 OUTPUT Build segments 1 thru 4 install closure formwork 1 build closure Segment 5 CHANGE STRUCTURE BUILD N 1 4 MOVE N 3 D 5 6 BUILD N 5 E TE SOLVE SOLVE Day 175 Steps 3 BUF an ce TUE ET Remove supports at nodes 2 thru 5 stress tendons 19 thru 22 CHANGE STRUCTURE RESTRAINTS 2 5 R 0 0 0 STRESS N 19 22 StressTo 198E3 198E3 Anchor 25 25 CHANGE COMPLETE SOLVE SOLVE Day 182 Steps 3 Move closure formwork to center span build closure segment 40 CHANGE STRUCTURE MOVE 3 D 40 41 BUILD N 40 Day 182 CHANGE COMPLETE SOLVE SOLVE Day 189 Steps 3 1j fle Stress tendons 23 thru 30 remove travelers and closure formwork CHANGE STRUCTURE STRESS N 23 30 StressTo 198E3 Anchor 25 MOVE 1 D 0 MOVE 2 D 0 MOVE 3 D 0 I CHANGE COMPLETE SOLVE SOLVE Day 196 Steps 3 hy Stress
94. ONCRETE PROPERT n Fpc f c Cr Sh W M Ac where N Total number of concrete types 1 n Concrete type number Ultimate compressive strength f lt cylinder 28 days Cr Ultimate creep coefficient 0 Sh Ultimate shrinkage coefficient 0 W Unit weight for computing gravity dead load only give units in kg This is not used in the calculation of modulus of elasticity 0 M Time dependent concrete material model number 1 and Ac Thermal expansion coefficient 0 iT E PROP ERT I Explanation CONCRE ES command is used to specify the different basic concrete material properties found in the structure The concrete type number n must be less than or equal to the total number of concrete types input on the 3 23 INPUT GENERATION Chapter 3 ABI1014 NOT NORMALIZED Lu lt gt lt CD e a LLI Lu CE C b NORMALIZED TIME TREATMENT OF CREEP AND SHRINKAGE CURVES IN DESIGN FIGURE 3 5 4 CONCRETE PROPERTIES command line The concrete types may be supplied in any order however each concrete type must be specified once The definition of the parameters C and 5 are further clarified through Fig 3 5 4 a shows symbolically the variation of either coefficient with time for three materials identified as 1 2 and 3 The maximum ordinate of each curve g
95. PERATURE 60 0 40 0 ELEMENT 5 TOTAL EXTERNALLY APPLIED LOADING AT THIS 0 0000 00 1 0000 01 1 0000 02 1 0000 02 0 0000 00 1 0000E 01 2 0 0000 00 4 0000 01 0 0000 00 0 0000 00 0 0000 00 0 0000 00 DISP 0 0000 00 0 0000 00 0 0000 00 104 4 TOTAL OF ELEMENT TEMPERATURES THIS STAGE TEMPERATURE 200 80 0 TEMPERATURE 60 0 40 0 ELEMENT 5 LS 105 NODAL BOUNDARY CONDITIONS AND TOTAL DISPLACEMENTS X DISP Y D4SPE 2826 01 TA68EF 01 2149 01 95 55295 Oil 4461 01 7457 01 1820620 0000 00 222228 Ops 2410 6 6293E 00 7952 00 6335 00 4222 01 2421 02 24 ER O PCP iy a 4 Min PR Ej Mae gt 106 TOTAL REACTIONS FIXED X FORCE 0000 00 4631E 04 8 4531 04 0 0000 00 X FORCE 2432 05 4340E 06 4121 06 25268305 Z MOMENT 0000 00 1388 07 adi 0000 00 0000 02 0957E 06 2451E D5 A 9 zu dla So 1 9a 95 7 Appendix Z ROTN 0 0000 00 0 0000 00 0 0000 00 amp Ar JG dm 0 0000 00 0 0000E 00 0 0000E 00 2 18 5 9m 9435E 04 6615E 04 22852502 TSS 3m 5984E 03 1508E 03 8462E 05 ADAPT ABI INPUT OUTPUT EXAMPLES App
96. ROUND Chapter 4 T t is the temperature T at time t and is the coefficient of thermal expansion The coefficient of thermal expansion a be different for the steel and concrete The temperature at any time may vary linearly over the y depth of each element and must be constant over the x length of the element 4 4 PRESTRESSING TENDON FORMULATION 4 4 1 4 4 2 Tendon Discretization The prestressing tendon idealization is based on representing the actual curved geometry of a post tensioned tendon by a system of piecewise linear prestressing segments intersecting at tendon points Figure 4 4 1 Each intersection point is referred to as a tendon node The tendon nodes generally do not coincide with the frame nodes which are located at the centroids of elements Each tendon node is associated with a frame node The displacements of the tendon nodes are rigidly locked to the displacements of their associated nodes Figure 4 4 2 Each tendon segment is assumed to be under uniform axial stress over its length and its stiffness and load contributions are computed as an eccentric truss element Figure 4 4 3 Initial prestressing forces are computed based on input jacking forces at each tendon end including the effects of instantaneous friction and anchorage slip losses The material model for the tendon includes relaxation strains but 15 limited to linear elasticity for its instantaneous stresses mechanical strain relationship
97. RTIES N 1 1 Area 193548 9 1570913 8 279 4 431 8 5 5 FRAME 4 1 1 2 1 X 1 St 1 Day 1 G 1 4 1 1 1 SPRINGS 1 5 3 6 5255 65 PRESTRESSING STEEL N 1 1 Ep 193121 Meu 0 25 0 000011811 Fpu 1862 24 R 45 0 000009 TENDON GEOMETRY N 1 1 Spans 1 M 1 Area 98 70948 1 N 5 G 1 5 1 0 0 254 0 R 0 0 5 0 5 50 8 50 8 50 8 MESH COMPLETE SET Day 10 20 CHANGE STRUCTURE BUILD 1 5 1 STRESS N 1 StressTo 0 1379 437 Anchor 0 3 175 RESTRAINTS 1 R 1 1 1 6 R 1 1 1 CHANGE COMPLETE LOADING 5 155742 5 311 485 0 SOLVE OUTPUT SOLVE Day 500 Steps 3 OUTPUT LOADING L 1 4 1 T 70 70 SOLVE Day 1000 Steps 3 OUTPUT STOP 5 31 ADAPT EXAMPLES VERIFICATION Chapter 5 ADAPT BRIDGE INCREMENTAL ABI SOFTWARE MANUAL EXAMPLES 3 name of this file START TITLE N 1 ACI MKS UNITS Kg cm UNITS U MKS CONCRETE PARAMETERS N 1 1 M ACI 4 0 85 C 1 25 0 118 E 1 F 50 W 0 0024027941 MESH INPUT NODES 6 1 X 0 Y20 5 304 8 Y20 G 1 5 6 152 4 Y2 63 5 CONCRETE PROPERTIES N 1 351 538 Cr 2 5 Sh 0 0003 W 0 0024027941 0 0000099 MILD STEEL PROPERTIES N 1 Es 2 038923E6 P 0 02 As 0 0000108 SECTION PROPERTIES N 1 Area 1935 48 1 9 1570913 4 C 27 94 43 18 ELEMENTS N 5 FRAME N 4 1 1 2 C 1 1 St 1 Day 1 G 1 4 1 1 1 SPRINGS 1 5 3 6 K 5357 45 PRESTRESSING STEEL 1 1 1 968615 6 Meu 0 25 0 00011811 Fpu 189
98. RY CONDITIONS AND TOTAL DISPLACEMENTS X DTSE DISE Z ROTN 0000E 00 0000F 00 0000F 00 0200 03 3624 02 013 2040 02 7519058502 798299808 8060 02 o sooo 01 4161E 03 4080E 02 7489E 01 291 TTESI AL REACTIONS AT FIXED NODES X FORCE Y FORCE 2 2340 401 1 9941 02 3 1905 04 2340 01 1 9941 02 3 1905 04 107 FRAME ELEMENT 5 ELEMENT BENDING BENDING AXIAL NO END I END J FORCE FORCE 3 1905 04 2 3929 04 9941 02 2340 01 275929 5952 024 9941 02 2340 01 5952602046 27197626208 9941 02 2340 01 Pe SaaS cds 9941 02 2340 01 108 STRESSES ELEMENT AXIAL 1 2578 02 2110 02 6992 02 1 6524E 02 2 3425 00 2 6992 02 6524 02 1406 02 1 0938 02 2 3425 00 3 1406 02 0938 02 552958 Zea rl 4 8202 01 o Sol qase 3425E 00 2 3425 00 2 3425E 00 A 17 ADAPT ABI INPUT OUTPUT EXAMPLES Appendix CURRENT TEPERATURE X DIRECTION GRAVITY MULTIPLIER Y DIRECTION GRAVITY MULTIPLIER STRESS CONVERGENCE FACTOR STRUCTURE LOADING 104 1 EXTERNALLY APPLIED LOAD OF THIS I N C R E M E N T NODE XSHORE ROF 2 X DISP Z ROTN 5 0 0000 400 2 0000 02 0 0000 00 0 0000 400 0 0000 00 0 0000 00 TOTAL OUP EXTERNALLY LOADING THIS S TA GE NODE X FORC O 2 X DISP DEIR Z ROTN 5 0 0000 00 2 0000 0
99. T ABI CONCRETE MODELING Appendix B must be evaluated iteratively in each time step All terms in Equation B 3 14a other than stay the same for all iterations therefore all the summations can be done prior to starting the iterations and only R o needs evaluation in each iteration The iteration can stop when o undergoes little change from one iteration to the next The time increment t appears in the denominator of Equation B 3 14c above Thus the recursion is impossible to evaluate when t 0 Investigation of limits as t approaches zero provides the following expression for use in place of Equation B 3 14c when t 0 1 B 3 15 Linear stress and linear material parameters Assuming dai b dyi and do t dy to be constant over the time step from t to tj and setting da t dy and da b dyi 66 the integration of Equation B 3 8 then yields exactly for uniaxial stress 80 g t at 1 66 3 16 l e i y B 3 17 D 6 B 3 18 By substituting Equation B 3 16 into Equation B 3 6b and taking y t UI Equation B 3 5 and Equation B 3 6a may be rewritten resulting in the following recursive relationship for evaluation of the creep strain increment over the time step y gti 1 amp B 3 19a 1 R a t 1 6 6 2 1 B 3 19b i 1 11 8 3 19 dt B
100. UM THICKNESS N c SIZE CORRECTION FACTOR K ACI SHRINKAGE CORRECTION FACTORS FIGURE 2 1 ADAPT ABI CONCRETE MODELING Appendix B where f t concrete strength on day t 28 concrete strength on day 28 B Creep strain The creep coefficient 0 is and defined as the ratio of creep strain to elastic strain based on the 28 day elastic modulus O t T E 28 2 6 where t t creep strain at time t under a stress applied at time t 9 67 creep coefficient for age of loading and observation time t t the age of the concrete at observation time T the age of the concrete when the load is applied The creep coefficient t t under working conditions is evaluated as the sum of three components O t t B G BO BAT B 2 7 where B G 0 8 11 B 2 8 delayed modulus of elasticity taken 0 4 Or the flow coefficient bf depends on the humidity Table B 1 1 depends on the notional thickness is a function for development over time of the delayed elastic strain 5 a function for development over time of the delayed plastic flow strain B t represents the irreversible part of the creep strain which takes place during the first few days after application of the load 6 represents the recoverable delayed elastic part of the creep strain which
101. a later stage 2 3 1 2 3 2 Concrete The program features comprehensive formulation in the definition of concrete material properties and their implementation in the computation of concrete related time dependent displacements and actions A close estimate of deformations becomes critical on the impact of time and construction schedule on the servicability and strength of the structure For each concrete material used two groups of information are defined A Creep and Shrinkage Properties The Concrete Creep and Shrinkage Parameters define the mathematical model to be used for the computation of the long term effect due to creep and shrinkage The material models included in the software are based on ACI ii CEB FIP iii Laboratory obtained or user defined according to other concrete codes B Concrete Properties These include parameters defining the specific concrete properties of each concrete material used These are crushing strength weight coefficient of thermal Aging of concrete is calculated using the parameters given for concrete properties Nonprestressed Steel Passive Reinforcement Nonprestressed steel is identified by its modulus of elasticity thermal coefficient of expansion and its percentage in the cross section Each frame element can be assigned its own type and percentage of steel Nonprestressed steel is considered as a linear elastic material uniformly distributed over the entire cross sect
102. al Example BUILD N 12 BUILD N 10 8 2 DAY 32 CAMBER C where C Displacement component to be printed 2 for X displacement ADAPT INPUT GENERATION Chapter 3 2 for Y displacement 3 for Z rotation Explanation command is used to compute and print displacement adjustment for all nodes in the structure Each time the oUTPUT command is used a record of total nodal displacements is saved Under the CAMBER command the current total nodal displacements are subtracted from the position of each node at the time of installation of that node The significance of the output camber values is as follows If each node be positioned at time of its installation with the amount of camber output by the program the structure will have zero total displacement at the time and condition associated with the call of camber command Camber command can be called several times Each camber solu tion refers to the associated time and construction phase of the camber call The background to camber calculations is given in appendices of this manual in greater detail The graphical output displays the required camber each time the OUTPUT command is invoked However a tabular printout of the nodal camber is generated only if the camber command is called The graphical output displays the vertical and horizontal components of the camber whereas the tabulated output lists all the three x y and rota
103. al from the time at the end of the previous solution to the day number specified with the Day identifier on the command line All loadings are assumed to be applied gradu ally over the length of the time step Thus any instantaneously applied loads require azero length time step A zero length time step is also required whenever the structure s configuration has been changed with the CHANGE STRUCTURE com mand zero length time step is specified by omitting the Day identifier on the command line The A identifier is used to set the convergence acceleration factor for the creep solution The default value has proven satisfactory in most cases The rt identifier is used to set the maximum number of iterations allowed in each time step After this number of iterations the solution terminates A shorter time step or higher convergence tolerances help reduce the required number of iterations INPUT GENERATION Chapter 3 If the time differences between two solutions is long due to the non linear nature of the time parameters it may be impractical for the program to ex trapolate reasonable initial values and converge to the solution For this reason it is recommended to subdivide long time spans into smaller time increments Example SOLVE DAY 10 OUTPUT SOLVE DAY 1000 OUTPUT Example SOLVE DAY 10 OUTPUT SOLVE DAY 20 OUTPUT SOLVE DAY 50 OUTPUT SOLVE DAY 150 OUTPUT SOLVE DAY 40
104. ansformation matrix is equal to the transpose of the displacement transformation matrix A as can be shown by elementary structural theory 4 5 TRAVELING FORMWORK FORMULATION 4 5 1 Traveler Function and Purpose Traveler is a frame independent from the primary bridge or other frame structure being analyzed It can be moved and attached to the primary frame It can serve principal purposes 1 It can be used to transfer the weight of newly cast concrete to the primary frame as it is done in the prototype construction through the falsework referred to in this work by the umbrella term of traveling formwork 11 It can be used to stiffen or align the structure temporarily during the construction The geometry of the traveler is independent from that of the primary frame It is defined independently and is considered pinned to the primary frame at frame nodes The traveler element is provided in order to restrain the displacements of freshly cast frame elements which have zero or near zero elastic modulus and which would otherwise undergo large incremental displacements which are prevented by the actual traveling formwork The program also automatically generates the loadings required to model the moving of the traveler 4 28 4 5 2 4 5 3 PROGRAM BACKGROUND Chapter 4 Each traveler consists of a number of beam elements Figure 4 5 1 a which can be moved to any location in the structure during the solution process
105. arametric generation scheme Initial tendon segment force computation includes the effects of instantaneous pre stressing force losses due to friction and anchorage slip seating loss Long term changes in tendon force are computed from the tendon s material property together with displacements of the nodes to which tendon is coupled 2 1 ADAPT PROGRAM DESCRIPTION Chapter 2 It is emphasized that in all cases the two points of each tendon segment must be associ ated with the end nodes of a given frame element Fig 2 1 3 The program can handle pre tensioning post tensioning cable stays and external post tensioning For example Fig 2 1 3 b segment two of tendon is associated wrongly with two elements Diagram 2 1 3 a shows the correct specification Spring elements can be specified with stiffness along their lengths stiffness perpen dicular to their direction and rotational stiffness at their connection to the structure Traveling formwork used for casting new frame elements or other construction frames Fig 2 1 4 are modeled with special frame elements which may be moved around the structure and which are not subject to time dependent strains Loading possibilities consist of i internally computed frame element dead loads ii concentrated actions forces and moments acting on the nodes 11 externally applied displacements at the nodes pressure loads iv uniformly distributed global X and Y direction l
106. are used in computing the initial tendon forces under the STRESS subcommand of the CHANGE STRUCTURE command The strength is used in calculating the initial stress in tendon when the jacking is expressed as a ratio of ultimate stress Also if Fpy is not entered Fpu is used to estimate Fpy 3 41 INPUT GENERATION Chapter 3 REMOVE Syntax REMOVE N nl n2 inc where nl Element number of first frame element in a series of elements to be removed from the structure n2 Element number of last element in the series n1 and inc Element number increment Explanation The REMOVE command is used to remove existing frame elements from the structure The elements must have been installed using the BUILD subcommand described above Once an element has been removed with this command it is permanently gone from the structure and may never be in stalled again The program automatically removes the stiffness dead load and internal forces from the system matrices when an element is removed Any additional loads applied to the element under the LOADING command described below are not automatically removed and must be removed manually by applying an equal but opposite force with another LOADING command before remov ing the element Example REMOVE N 6 REMOVE 5 9 2 In this example the frame elements 5 6 7 and 9 will be eliminated from the current configu
107. are equivalent Shrinkage strain The shrinkage strain over the time interval is given by B B 0 2 11 where the ultimate shrinkage strain E u depends on the humidity Table B 1 1 2 depends on the notional thickness a function for the development of shrinkage strain over time which also depends on the notional thickness t the age of the concrete at observation time T the age of the concrete at the beginning of the time interval The notional thickness Equation B 2 9 and the corrected age Equation B 2 10 defined for the creep model are also used for this shrinkage model B 3 MATHEMATICAL MODELING OF THE CREEP STRAIN COMPONENT Creep of concrete presents one of the most complex numerical problems in the time dependent analysis of concrete structures The modeling of creep is a statistical problem involving curve fitting and the many influential factors discussed above are involved The most important factor from the standpoint of formulating a mathematical model is that the creep strain depends on the entire stress history of the specimen This makes it desirable to formulate a creep model which stores the stress history in a compact form B 3 1 Theoretical Background Creep strain may be expressed in terms of the following convolution integral for an aging viscoelastic material t do Er w fien Lar B 3 1 where t is the creep strain at time t and
108. ase only Fig 1 1 2 1 a and b The construction loading on the bridge components either through construc tion equipment or assembly results in stresses which exceed those of the completed structure Hence the design of the components including the prestressing is in part controlled by the construction technology Prior to placing the closure segment the selfweight moment at the tip of the cantilever is zero Fig 1 1 2 2 The installation of the continuity tendons for clarity shown in Fig 1 1 2 2 b below the superstructure induces a moment which reduces the moment due to selfwieght at completion of the structure 1 1 2 2 c Weight and depending on the form of deployment of the erection equipment the stiffness of the construction equipment as shown in Fig 1 1 2 3 for the form traveler results in notable stresses and impacts the deformation of the bridge during the construction Early age loading of concrete oftentimes within the first 24 to 48 hours after casting leads to high deformation values which must be carefully evaluated and accounted for deflection and camber control of the completed structure High creep values and low modulus of elasticity of young concrete in leading segments of balanced cantilever construction result in larger displacements than normal under the weight of newly cast segments The method of construction greatly influences the initial stress in the com pleted structure to the extent that the analysi
109. at each cross section along the bridge The actions are factored and combined to assess the factor of safety of each section for strength requirements Post processor modules of ADAPT ABI featured in separate manuals offer the capability of combinations and enveloping of actions for code stipulated serviceability and strength check In all cases the immediate and long term deflections of the structure modeled are obtained directly from ADAPT ABI runs Chapter 2 of this manual provides a detailed narrative of the software features covered by ADAPT ABI Basic ADAPT ABI basic is the core module of the ADAPT ABI suite of programs Other modules are essentially post processors which expand the capabilities of the Basic or present the analysis in user desired formats 1 12 OVERVIEW Chapter 1 Chapter 3 details the preparation of data and its execution Chapter 4 presents the theoretical backeround to the computations of the program Numerical examples are given in Chapter 5 Specific features of the program such as details of implementation of time dependant effects are given the Appendices A separate volume Example Manual contains numerous cases in application of ADAPT ABI ADAPT OVERVIEW Chapter 1 This Page Left Intentionally BLANK PROGRAM DESCRIPTION Chapter 2 2 1 2 2 2 3 2 4 2 5 2 6 2 7 LIST OF CONTENTS OVERVIEW c 1 21 5 2
110. ations esee 11 A Strength modulus of elasticity and aging of concrete a 11 B Creep Stain aasawa diee IE de er te its C Shrinkage strain B 3 MATHEMATICAL MODELING OF THE CREEP STRAIN 15 B 3 1 Theoretical Background 15 B 3 2 Calculation of the Creep Strain Increment 18 A Constant stress and constant material parameters 18 B Linear stress and constant material parameters 19 C Linear stress and linear material parameters 20 B 3 3 Determination of creep compliance coefficients 21 B 1 ADAPT ABI CONCRETE MODELING Appendix B This Page Left Intentionally BLANK B 2 ADAPT ABI CONCRETE MODELING Appendix B Concrete is unique among structural materials in that it undergoes complex physical and chemical changes over time resulting in deformations and constitutive properties which are time dependent under practical service conditions These time dependent phenomena in concrete are some of the most significant factors influencing the structural behavior of segmentally erected prestressed concrete bridges Accurate consideration of time dependent concrete behavior is necessary for the accurate prediction of stresses and deflections in the structure at all load levels Nonlinear concrete behavior such as cracking crushing and the nonlinear stress strain relationship of the concrete also influence structural behavi
111. ays straightforward A time dependent analysis is necessary to obtain a realistic estimate of deflections based on which the camber is determined The prediction of deflections and the required camber during the construction phase are among strong features of ADAPT ABI Completed Structure The completed structure may differ significantly in its structural system from the construction phase configuration which may have been statically determinate With lapse of time creep shrinkage and losses in prestressing result in a change in the self weight and prestressing moments in the bridges The change in moment with time is reffered to as redistribution of moments and is illustrated in Fig 1 4 2 1 for a free cantilever bridge The response to live loading is not significantly affected by the long term effects The structural design objectives of the completed structure are A To meet stress limits under service loading service condition B To provide adequate strength for safety under design loads strength condition C To control the immediate and long term deflections typically 20 years In summary ADAPT ABI can be used to obtain the actions moments shears and axial loadings of the statically determinate and indeterminate pre and or post tensioned bridges and frames accounting for the time dependent effects and displacements The sectional actions moment shear axial force obtained from ADAPT ABI are used to check the stresses of
112. butment girder and after stressing the continuity tendons the spring elements representing the falsework would be removed Spring elements were not used in the analysis offered herein in order to retain similarity among the three solutions used for comparison 5 9 EXAMPLES VERIFICATION Chapter 5 ABUTMENT 8 NODE NUMBERING ABUTMENT PIER 1 2223 41 42 b FRAME ELEMENT NUMBERING 8 2 42 imp W Ea CROSS SECTION IDEALIZATION CATILEVER SEGMENT BEING CAST EE FRAME TRAVELER d TRAVELER IDEALIZATION ANALYTICAL MODEL OF BRIDGE EXAMPLE FIGURE 5 3 1 ADAPT EXAMPLES VERIFICATION Chapter 5 Frame elements Figure 5 3 1 b used to model the girder pier elements modeling the girder are each prismatic with the cross section of a point at the mid length of the element Figure 5 6 1 is an illustration of the frame elements used Each cantilever segment is modeled with one frame element Additional elements are used to model the closure segments the 60 foot girder segment at the abutment and the pier For section property and dead load generation the cross section of each girder element is idealized as shown in Figure 5 3 1 c The pier elements model the gross cross section of the pier Uniformly distributed mild steel reinforcement is included in all elements based on an area ratio of 2 percent in the girder and 10 percent in the p
113. cal stiffness matrix relating segment local force to local displacements Figure 4 4 3 b lt EA L gt A 1 6 displacement transformation matrix relating segment local displacements to global displacements Figure 4 4 3 b X L Y L e X L eiY L Y L e3Y L e4X L The segment end eccentricities e are defined in Equation 4 4 1 B Segment internal force due to nodal displacements The segment internal force increment is evaluated by first transforming the global displacements Figure 4 4 3 to local segment element displacement and then multiplying this displacement by the local segment element stiffness matrix k defined above This transformation can be expressed as follows U 4 4 11 where fo segment internal force 4 27 PROGRAM BACKGROUND Chapter 4 U global displacements at the nodes Figure 4 1 1 c E displacement to force transformation matrix 1 x 6 expresses segment internal force F in terms of global displacements k A k and A are defined in the preceding C Equivalent nodal loads due to initial forces The equivalent nodal forces and moments due to segment internal force are evaluated using the following matrix transformation S ATI o 4 4 12 where S global equivalent nodal loads internal segment force A 1x 6displacement transformation matrix defined above The 6 x 1 internal force to global equivalent load tr
114. ces quoted FRAME ELEMENT FORMULATION 4 1 1 Assumptions and Scope The plane frame element used in the formulation of the program is based on classical Bernoulli Euler beam kinematics Its stiffness matrix and load vector terms include the effects of axial and bending deformations only Shear deformation is neglected since it is generally of little or no significance for the concrete structures covered by this work The element formulation for this element and all other elements used in the program guarantees static equilibrium of total internal forces with the total externally applied loads The element consists of parallel concrete and mild steel components for modeling the typical composite concrete and steel bridge girder Time dependent concrete strains including mechanical strain em t aging strain 4 t creep strain t shrinkage strain and temperature strain 1 are automatically considered using the formulation discussed in Appendix B Shrinkage and temperature strains may vary linearly over the depth of each element The mild steel component is assumed to be uniformly distributed over the entire cross section Concrete and steel instantaneous stress mechanical strain laws are limited to linear elasticity focusing the applicability of the program to the service load range of fully prestressed structures Where stresses exceed the cracking limit of concrete the serviceability solutions obtained are approx
115. cessary to reset them The initial default local coordinate system is the global X Y coordinate system b The frame nodes to which the tendon points of the tendon span are associated provided the frame nodes can be generated using the G automatic generation feature described in the following The syntax of the first line of tendon span input is ns N G nl n2 inc B x0 y0 1 1 INPUT GENERATION Chapter 3 Example 1 Example 2 where ns Span number N Number of nodes in span including both end nodes ni Node number at left end of span n2 Node number at right end of span inc Node number increment for generating nodes in the span x0 y0 Global coordinates of the origin of the local r s coordinate system 0 0 and 1 1 Global coordinates of a point on the local r axis 1 0 Span numbers ns must be supplied in ascending consecutive order starting with span 1 If the node numbers cannot be generated for a particular span then the op tional G identifier above should be excluded and the next line must provide a list of the node numbers included in the span in order from start typically the left point to the end typically right point B in the span If the optional G identifier is used then this line list must not be provided List n 1 n N where n 2 Node number included in the span and Number of nodes in the span input
116. ch will ever exist in the analysis history of the structure are defined using the mesh input subcommands The erection sequence is specified later in the input using the RESTRAINTS BUILD frame element REMOVE frame element STRESS tendon and MOVE traveler subcommands of the CHANGE STRUCTURE command The mesh input subcommands include NODES SEQUENCE CONCRETE PROPERTIES MILD STEEL PROPERTIES SECTION PROPERTIES OFFSET DATA FRAME ELEMENTS PRESTRESSING STEEL TENDON GEOMETRY TRAVELERS and MESH COMPLETE as described below The MESH INPUT command can be used only once in a given analysis Also its subcommands can be used only once MILD STEEL PROPERTIES Syntax MILD STEEL PROPERTIES N n Es P 3 35 INPUT GENERATION Chapter 3 where N Total number of mild steel types 1 n Mild steel type number Es Elastic modulus P Mild steel reinforcement ratio In cross section and As Thermal expansion coefficient Explanation MOVE Syntax Explanation The MILD STEEL PROPERTIES command is used to specify the different mild passive reinforcing steel material properties found in the structure The mild
117. chosen to be simple yet contain the dimensionally critical features The model is not meant to represent a prototype STRUCTURE The model refer to Figure 5 8 1 is a post tensioned cantilever resting on a spring at its mid length It is subject to self weight applied concentrated loading temperature creep 5 26 ADAPT EXAMPLES VERIFICATION Chapter 5 shrinkage and aging of concrete Details of the model listed in Table 5 8 1 Six conditions consisting of two concrete material models ACI CEB1 each with three systems of units American SI and MKS are investigated The model s response to loading and the time dependent effects are computed at days 10 500 and 1000 The actual input files are appended to this description TABLE 5 8 1 DIMENSIONS PROPERTIES AND LOADING OF THE VERIFICATION MODEL Ib inch F Length 120 3 0480 03 3 0480 02 Area 300 1 9355 05 1 9355 03 Moment of Inertia 2200 9 1571E 08 9 1571E 04 Top fiber 11 2 7940E 02 2 7940E 01 Bottom fiber 17 4 3180E 02 4 3180 01 Concrete strength 5000 3 4486 01 3 5154 02 Unit weight 8 0806E 02 2 4019 06 2 4019 03 kg mn kg cn Thermal coef 5 5000E 06 9 9000E 06 9 9000E 06 peer STs te e 6 0000 06 10 800 06 10 800 06 2 8000 07 1 9312 05 1 9686 06 Prestressing 5 0000E 06 9 0000E 06 9 0000E 06 values C 0 25 0 25 0 25 radian W Wobble 3 0000E 04 1 1811E 05 1 1811E 04 Ib in N mm kg
118. cluded in ADAPT ABI library Since the entire variation as shown in Fig 3 5 4 b is given in the input tables of con CRETE PARAMETERS command no normalization is used DE STRESS Syntax DE STRESS N List nl n2 G nl 2 inc where N Total number of tendons 1 List List of tendons to be de stressed G This optional parameter generates the list of tendons to be de stressed nl n2 inc Generation parameters n1 Tendon number for start of generation n2 Last tendon number in generation and inc Generation increment Explanation This command is used to remove tendons previously stressed The removal of tendon will result in its stiffness being eliminated from the stiffness matrix of the 3 25 ADAPT INPUT GENERATION Chapter 3 structure If a tendon 15 being re stressed to different stress level the STRESS command mustbe used Example DE STRESS 5 LIST 2 4 6 11 14 DE STRESS 5 G 2 10 2 ELEMENTS Syntax ELEMENTS N where N Total number of frame elements destined to be used in the structure during the construction or when it is complete N is the sum of the following elements currently available in the software s library FRAME elements SPRING elements The TRAVELER elements are not included herein Stay ele ments are handled under prestressing tendons FRAME Syntax FRAME N n ni nj C St Day Off G2n1 n11 where
119. commands consisting of one or more keywords followed by optional numeri cal data required for the execution of the command The actions and the data require ments of the commands are summarized in the following pages keywords must be typed in full as they appear in this manual Mis spelled words result in error In most cases the errors are detected by the software s data verification module All numerical data are entered in the following free field form nli n2 n3 ni 1 2 3 ai 51 02 3 x bi 3 1 ADAPT INPUT GENERATION Chapter 3 where ai bi represent input data and the character pairs A and B are identifi ers specified in the input manual for the data list which follows Items in a data list must be separated by a single comma or by one or more blanks If a numerical data list requires no identification such as n1 n2 n3 in the above example the list must be located as the first data list on the line A data set of the form 1 52 3 preceded by a pair of identities B in this case may appear in any order or loca tion on the line Simple arithmetical statements are possible when entering floating point real numbers For example the following forms of data can be entered E 29600 144 C 200 12 3 5 400 12 10 20 5 2 These arithmetical statements are evaluated from left to right without operator hierar chy The statement 10 20 5 2 is evaluated a
120. concrete cross section 300 cm 30 000 mnm 46 50 in and P Perimeter of concrete section in contact with the atmosphere 10 cm 100 mm 3 937 in Modulus of Elasticity ADAPT ABI uses the following relationship to determine the modulus of elasticity when CEB or FIB concrete models are selected E t 45680 f t where E t modulus of elasticity on day t in N cm and f t concrete cylinder strength on day t in N cm Aging of Concrete Aging in concrete is effected through change in concrete strength and thereby modulus of elasticity The change in modulus of elasticity with time is effected using the following rela tionship ft 1 45 095 197 5 5 28 where concrete strength on day t and f 28 concrete strength on day 28 Note Equation B 2 5 of ADAPT ABI manual refers to concrete strength at day 1000 For modulus of elasticity at other days the curve in Figure B 2 2 a can be used The two relation ships given herein combine the equation B 2 5 of the manual and the Figure B 2 2 a 3 20 INPUT GENERATION Chapter 3 C LAB The input for laboratory generated information or for codes not programmed in the library of ADAPT ABI the LAB option of input data is used In this option the user inputs the shrinkage creep and change of modulus of elasticity of concrete with time More than one concrete material model can be defined
121. construction sequence are discussed next The span arrangement consists of a 450 foot center span and two 285 foot side spans Figure 5 2 1 a This provides for both efficient cantilever construction and satisfactory behavior of the continuous bridge The cantilevered girders are symmetrical about each pier and the 60 foot cast in place girder lengths at the abutments help eliminate interference between the traveling formwork and the abutment and also result in better structural behavior of the completed structure under superimposed loads and live load The cross section Figure 5 2 1 b consists of a single cell box with wide cantilevered slabs Transverse slab tendons are required in the top slab but are not included in this analysis The girder depth varies from a maximum of 24 feet at the piers to a minimum of 9 feet at midspan and at the abutments The bottom slab thickness varies from a maximum of 3 5 feet at the piers to a minimum of 0 75 feet at midspan The variations of these dimensions over the length of the bridge are summarized in Figure 5 3 1 c and 5 3 1 d The depth of the girder at any point is found using an expression of the form d 225 x 7 d where x is the distance from the supporting pier d is the girder depth at location x and a d are constants found by evaluating the expression at 0 and x 225 where the girder depths are known Due to the sloping webs and haunched girder the bottom slab width varie
122. creep of concrete requires the solution of two important problems which are addressed in Sections B 2 and B 3 of this chapter 1 Given the concrete mix design the proportions of the structural elements and the environmental conditions under which the structure is built find a relationship expressing the creep strain at any time under constant stress applied at any loading age Since the mechanisms of creep and shrinkage in concrete are not understood completely and correlations between field and laboratory studies are imprecise even under carefully controlled conditions no theory has explained adequately all the observed information Therefore two alternative models for predicting time dependent creep and shrinkage strains are reviewed in Section B 2 of this chapter B 3 ADAPT ABI CONCRETE MODELING Appendix B 2 Given this relationship for time dependent strains under constant stress find the actual stress and strain history in the structure under varying loads Solution of this problem requires numerical integration over time of the differential equation of which the above relationship is the kernel The choice of method to use for this numerical integration is influenced by considerations of accuracy convergence and solution economy A refined numerical integration scheme for use in a step by step finite element analysis is derived in Section B 3 of this chapter B 1 STRAIN COMPONENTS AND THE SUPERPOSITION METHOD An important assumpti
123. d If the restraint specification is 0 the degree of freedom is unrestrained The associated displacement and or rotation will be computed by the program If the restraint specification is 1 the total displacement or rotation is re strained to its current value If the restraint specification is 2 the total displacement or rotation is re strained to zero Restraint types 1 and 2 are identical except that for type 2 an imposed displacement equal and opposite to the total current displacement is applied in the next solution step If the restraint specification is 3 then the associated displacement is deter mined from that of the master node defined as M as if the connection of the slave to the master were rigid unless specific releases are defined as input This master slave relation can be present for any of the three degrees of freedom for the slave node For a node with complete dependency 3 3 3 may be used Any node defined as slave can not be set as master for another node Also note that for two specific relationships i e R 3 3 0 a hinge condition and R 3 0 0 the master as well as the slave nodes must have the same coordinates The two must coincide Any restraint change remains in effect until changed again by a subsequent RESTRAINTS subcommand All unspecified nodes are assumed to have 0 free to displace boundary condition in all three degrees of freedom Master slave relation may be prese
124. d nodal loads imposed nodal displacements uniformly distributed frame element loads and tempera ture change loadings to the structure Any node or element to which a loading is applied must be a part of the current structure All loadings remain in effect until they are removed by the application of an equal but opposite loading Each loading data line takes one of several forms depending on the type of loading The loading data lines can contain all three forms in any order INPUT GENERATION Chapter 3 ABI1027 E ACTUAL ELEMENT BOUNDARY PRISMATIC 1 SECTION ELEVATION IDEALIZATION OF NON PRISMATIC ELEMENT THROUGH A PRISMATIC ELEMENT AT ITS MID LENGTH FIGURE 3 5 8 Concentrated nodal loads The following data must be provided Nodal loads may be applied to any degree of freedom whether or not it is free to displace Loads on restrained degrees of freedom are retained for future use in case the degree of freedom is ever unrestrained N nl1 n2 inc F fx fy fzz where INPUT GENERATION Chapter 3 nl Node number of first node in a series of nodes with identical load ing n2 Node number of last node in the series n1 inc Node number increment fx force increment fy Y force increment and fzz Z moment increment Imposed nodal displacements The following data must be provided Displacements may only be applied to restrained fixed degrees of freedo
125. d the nodes to which they are connected Concentrated loads specified to act between the nodes ABI Gen Module are automatically converted to nodal loads by the program Concentrated nodal loads in the global directions are summed directly into the total external load vector Uniformly distributed frame element loads in the global directions are first converted by the program to equivalent nodal actions forces and moments and are then summed into the total external load vector These loadings remain on the structure until they are removed by application of an equal but opposite load Dead load of frame elements and travelers is automatically applied as a set of equiva lent nodal forces These forces are computed based on the calculated length and cross sectional area of the frame element and the unit weight of the concrete Gravity load multipliers which are factors by which the dead load is multiplied before summing into the total load vector may be specified for gravity load in the global X and Y directions Changing the gravity load multipliers changes the dead load factors for all frame elements currently installed in the structure Thus the entire dead load can be removed from the structure by specifying zero gravity load multipliers External Displacements External displacements and rotations may be applied on restrained degrees of freedom of the nodes These displacements and rotations can be applied only to nodes connected to curre
126. der total dead load live load and final prestress The design redistribution analysis for the 100 percent redistribution case was performed with the software using a one step construction and linear elastic analysis sequence in which all concrete segments were assumed to be cast on the average of their actual casting dates and the total dead load and prestressing were applied at the time of closure The long term prestressing force losses were estimated at seventeen percent based on this construction schedule and the AASHTO code relationships for estimating prestressing losses The material properties and tendon stressing data for this analysis were the same as for the detailed segmental analysis described herein with jacking forces and anchorage slip reduced seventeen percent to allow for long term force losses Additional information on analysis procedure and design considerations of cantilever segmental construction is given in Aalami 1993 5 5 EXAMPLES VERIFICATION Chapter 5 D 9 51 SPAN ARRANGEMENT 54 24 VARIATION OF GIRDER DEPTH D e 3 a 24 9 42 9 42 0 24 di VARIATION BOTTOM SLAB THICKNESS THREE SPAN CANTILEVER BRIDGE EXAMPLE FIGURE 5 2 1 EXAMPLES VERIFICATION Chapter 5 D y a BRIDGE ELEVATION b TYPICAL PROFILE FOR CANTILEVER TENDONS 64 tendons 4 tendons segmant qr segment 13 4 closure amp pier clo
127. dians by which the tangent to the tendon profile has changed between the Jack and location x K wobble friction coefficient x distance along the tendon PROGRAM BACKGROUND Chapter 4 In the piecewise linear tendon discretization used the angle change 18 lumped as discrete 0 deviations at the Interior tendon nodes and the length x 15 defined by the tendon segment lengths Anchor slip seating losses Anchor slip losses take place when the jacking force is transferred from the jack to the permanent tendon anchorage assembly The anchorage assembly typically displaces up to 3 8 inch during this operation resulting in a change in stress in a length of the tendon near the anchorage Figure 4 4 6 The change in stress and the length over which it is effective may be derived from fundamental principles the friction force reverses direction when the slippage takes place and the anchor set slip displacement a must equal the integral of the change in strain over the slip distance XL a dx 4 4 3 This results in the mirror image type tendon force change over the anchor slip distance Figure 4 4 6 ADPT351DWG STRESS INITIAL STRESS ipm dx F x B FINAL STRESS XL 0 X TENDON LENGTH ANCHOR SET STRESS LOSS FIGURE 4 4 6 4 19 PROGRAM BACKGROUND Chapter 4 A graphical interpretation of the fundamental principles is taken i
128. don the geometry is defined by giving the coordinates of the tendon along its path External Tendons Unbonded Tendons The external and unbonded tendons are modeled with a sheathing which serves to keep the tendon isolated from the frame elements At locations where a node of the sheath ing coincides with that of the frame structure the external or unbonded tendon is assumed to have been securely connected to the frame Force and displacement com patibility between the tendon and the frame structure is established at the connection points between the tendon sheathing and the frame structure defined by the user The sheathing of external and unbonded tendons is itself modeled as a frame element with negligible stiffness An example in the Examples Manual illustrates the applica tion of unbonded tendons 2 16 PROGRAM DESCRIPTION Chapter 2 e CD LI c lt LOW POINT a REVERSED PARABOLA w b COMBINED SIMPLE AND REVERSED PARABOLA 2 5 c PARTIAL REGULAR PARABOLA 0 HARPED TENDON EXAMPLES OF TENDON GEOMETRY FIGURE 2 4 1 ADAPT PROGRAM DESCRIPTION Chapter 2 25 LOADING 2 5 1 2 5 2 2 5 3 External Forces Concentrated external forces and moments may be applied on the frame element nodes Uniformly distributed loads may be applied on the frame elements These loads can be applied only to currently installed frame elements an
129. don numbers and geometry of each in the structure TRAVELERS Define traveling formwork MESH COMPLE H Signals end of structure definition Set Ambient Conditions SET Define ambient conditions for the solution such as day temperature and solution technique parameters Construction Operations CHANGE STRUCTURE Start construction operations for this step BUILD Install frame spring slave and hinge elements 3 4 INPUT GENERATION Chapter 3 RESTRAINTS blank line in input REMOVE STRESS DE STRESS MOVE CHANGE COMPLETE External Loading Commands LOADING Solution Command SOLVE Output Commands OUTPUT CAMBER Problem Termination Command STOP Change boundary conditions also used to define master and slave constraints Remove frame spring slave and hinge elements Stress tendons De stress remove previously stressed tendons Move traveler to new destination nodes End construction operations for this step Specify load increment which can consist of nodal loads nodal displacements and element temperatures Solve the current structure Output total structure response Output displacements to be adjusted for camber control Stop execution save for restart 33 SAMPLE INPUT FOR A NONPRESTRESSED CANTILEVER BEAM 3 3 1 Description of the Structure The following i
130. e shown in Fig 3 5 3 INPUT GENERATION Chapter 3 ABI1019 4 28 DAYS LOADING AGES AND ASSOCIATED CREEP STRAINS 4 LOADING AGES FIGURE 3 5 2 Example 2 M ACI This instruction means that the second material type selected uses ACI model Since T is not specified it uses ages and times coded in the program It uses the maximum number of loading ages and data generation points for each creep curve M ACI In addition to the optional T parameter described before eight other parameters may be described on the same line as n m ACT in order to fine tune ACI concrete model to a user defined alternative These parameters are a b C 2 t0 W All the eight preceding parameters optional User specify many of these as necessary after the two parameters of n M ACI where INPUT GENERATION Chapter 3 MEASURED OR GENERATED DATA M 6 CREEP MEASURMENTS DAYS CREEP MEASURMENTS DATA POINTS FOR CONSTRUCTION OF CREEP CURVE FIGURE 3 5 3 a 4 and b 0 85 are used in the time function for f 0 see appendices for more detail f t f 28 t a b t c 1 25 and d 0 118 are used in the age function for creep see appendices for more detail a K c t e 1 50 and t 7 are used in the time function for shrinkage g t 2 where t is shrinkage on day
131. ed the same to allow comparison between the solutions used for verification For a regular ABI solution fu and entered as different values LOADINGS amp CONSTRUCTION SEQUENCE FOR THE TIME DEPENDENT ANALYSIS The bridge is analyzed for the actual segmental construction sequence in which each segment is cast in place and post tensioned on a weekly schedule and the continuity tendons and superimposed dead load are added after closure and then for a 27 year service period afterward The construction schedule which is typical for this type and scale of bridge may be summarized as follows Days 0 to 63 Build pier and starting girder segments 21 through 24 Days 63 to 168 Build cantilever girder segments 6 through 39 stress cantilever tendons 1 through 16 with a seven day per segment cycle time Day 100 Build approach girder segments 1 through 4 Day 168 Close side span with closure girder segment 5 Day 175 Stress local tendons 19 through 22 in side span Day 182 Close center span with closure segment 40 Day 189 Stress local tendons 23 through 30 in center span remove travelers Day 196 Stress continuity tendons 17 and 18 add superimposed dead load A typical cycle of the segmental construction sequence is assumed to last seven days For the cantilever construction sequence for this bridge this results in a construction period of 105 days for the cantilever construction portion of the girder The following steps
132. ed using the following expression t 1 C t K K K K s H h 10 1 090 2 3 where creep strain time t creep coefficient initial immediate strain Cu ultimate coefficient determined by experiment C _ creep strain at time after loading initial strain at time of loading 2 35 for standard conditions slump correction factor 0 81 0 07s s is in inches humidity correction factor 1 27 0 0067 H when H gt 40 H relative humidity minimum thickness correction factor 1 0 0 0167 th 6 0 when th gt 6 inches K age at loading correction factor 1 25 1 0 118 for 7 days moist cured concrete S slump in inches th minimum size of member in inches t the age of concrete at observation time in days T the age of concrete at loading in days Standard conditions for creep for which all correction factors are equal to 1 0 are as follows B 9 ADAPT ABI CONCRETE MODELING Appendix B i slump 2 7 inches i ambient relative humidity 40 percent or less i minimum thickness 6 inches or less v age at loading 7 days for moist cured concrete Shrinkage strain Shrinkage strain is computed using the following relationship t to t e u K Kj Kj B 2 4 fat to where 5 shrinkage strain at observation time t es ultimate shrinkage strain determined from experiments
133. ee Fig 3 5 6 and OJ x and y offset at node J Explanation The OFFSET DATA command is used to define all the possible offsets that may be used for various elements in the structure The offset number n must be less than or equal to the total number of offset data entries input on the OFFSET DATA command line The offset entries must be supplied in ascend ing order starting at 1 One offset entry can only be specified once and can not be redefined Example OFFSET DATA N 2 1 OI 0 0 200 0 OU 0 0 200 0 2 01 0 0 300 0 OJ 0 0 300 0 OUTPUT Syntax OUTPUT NONE ALL SAME DISPLACEMENTS N ACTIONS REACTIONS STRESSES PRESTRESSING N PRESTRESSING LONG PRESTRESSING SHORT N STATIC No argument Prints all data blocks and ALL Same as no argument prints all data block All the other optional parameters cause data blocks 100 101 102 103 104 and 111 to be printed out together with the block specifically called by the parameter Details of each data table is given in Appendix A where DISPLACEMENTS Nodal boundary conditions and nodal displace ments Block 105 ACTIONS Moments shears and axial loading on each frame element Block 107 REACTIONS Total reactions at each fixed node Block 106 STRESSES Concrete fiber stresses at points 1 2 3 and 4 Fig 3 5 11 Data Block 108 in tabu
134. efined as the increase in strain under sustained stress of a concrete specimen under constant humidity and temperature Creep strain does not include the instantaneous elastic deformation Its rate decreases to zero over time and is only partially recoverable after load removal The main factors influencing the creep of concrete are compressive strength age at loading aggregate type ambient relative humidity and temperature the specimen size and the stress history The most important factor from the standpoint of analysis is that creep strain depends on the entire stress history of the specimen This makes it desirable to formulate a creep model which stores the stress history in a compact form Figure B 1 2 illustrates the relationship between instantaneous stress changes and the corresponding creep strain changes Shrinkage Strain Shrinkage strain S t is a non stress originated strain defined as the deformation under no load or temperature change Shrinkage of concrete is due primarily to loss of water upon drying drying shrinkage and volume change due to carbonation carbonation shrinkage The main factors influencing the shrinkage of concrete are aggregate type water cement ratio specimen size and ambient relative humidity B 6 ADAPT ABI CONCRETE MODELING Appendix B 0 taa 8012 8011 p gt time H 1 thi tn a STRESS HISTORY in rtp ESI gt time H 1 tmi tn b
135. endent analysis it only prints the results PRESTRESSING STEEL Syntax Explanation PRESTRESSING STEEL N n Meu K Fpu R where N Total number of prestressing steel types 1 n Prestressing steel type number Ep Elastic modulus Meu Angular friction coefficient K Wobble friction coefficient K Ultimate stress 0 1 yield stress for the calculation of prestress loss 0 9Fpu R Relaxation coefficient same as in relaxation equation see appendices generally specified as 10 for stress relieved and 45 for low relaxation strands to suppress relaxation altogether specify 0 0 and Ap Thermal expansion coefficient 0 use per Centigrade degree for SI and MKS and per Fahrenheit for American Units The PRESTRESSING STEEL command is used to specify the different pre stressing steel material properties found in the structure The prestressing steel type number n must be less than or equal to the total number of prestressing steel types input on the PRESTRESSING STEEL command line The prestress ing steel types may be supplied in any order however each prestressing steel type must be specified once Prestressing steel is considered as a relaxing linear elastic material The yield stress is used only in the relaxation modeling The friction coefficients
136. endix A 107 FRAME ELEMENT ACTIONS ELEMENT BENDING BENDING SHEAR AXIAL END I END J FORCE FORCE 2 Zi AS 2518 07 4 1726 04 2 7358 06 T 291 75307 8342 06 3 2276E 04 2 7359 06 2 8339E 06 9542 06 8 1127 04 2 7360 06 5 3756 407 6725E 07 6 4511 04 4 4521 06 1 0723E 08 2105 5 02925588 OE 7 5 MO REDORS 2 0403E 08 5304 08 1 8550 05 1 0650 07 SO TIS UUSEE 4 7163E 08 4404 08 5 7487 05 1 3212 07 OV OT ta 107 2 SPRING ACTIONS SPRING AXIAL BENDING FORCE MOMENT 34 514077 5511 35 4659 404 1 4110 01 3 9 4417E 04 0 0000 00 37 1191 04 0 0000 00 108 EXTREME FIBER STRESSES CONCRETE AXIAL 90502202 EO DIDI 0919 03 8924 02 9057 02 20 92504025 8931 02 5888 02 2236 02 9062 02 SOS TIERO cO PIS 2 0965 02 9042 02 4642 03 0424 01 0786 03 1604 02 2473E 03 7430E 03 1967 02 CoML Wns 2903702 S112E4 0O3 109 TENDON FORCES TENDON 1 TOTAL RESULTS SEG TOTAL PERCENT BENDING BENDING SHEAR AXIAL NO FORCE LOSS END I END J FORCE FORCE 449E 06 Los 1 084 08 1 469 08 456 05 445 06 489 06 1 494 08 1 494 08 000 00 489 06 468E 06 1 481 08 1 481 08 000 00 468 06 427 06 Abies il 442 05 422 06 TENDON 2 TOTAL RESULTS SEG TOTAL PERCENT FRAME BENDING BENDING SHEAR AXIAL
137. ent eene eie rie eee E et eterne 8 4 3 3 Nonprestressed Steel Component 4 4 PRESTRESSING TENDON FORMULATION 4 4 1 Tendon Discretization 4 4 2 Tendon Geometry Definition sees tenerent tenen enne tenens 4 4 3 Determination of Initial Tendon Forces ADAPT ABI LIST OF CONTENTS Contents Az Friction 17 B Anchor slip seating losses ee 19 C Influence of stressing procedure ee 20 D Discretized segment forces de 20 E Equivalent prestressing loads 22 4 4 4 Material Constitutive Relationships ue 22 4 4 5 Stiffness and Load Computation esee tenentem enne teens 26 A Segment stiffness Matix eco aeree tee E Rider ayu yupqa 27 B Segment internal force due to nodal displacement 2 20 27 C Equivalent nodal loads due to initial forces 4 5 TRAVELING FORMULATION 4 5 1 Traveler Function and Purpose 4 5 2 Traveler Geometry sess 35 4 5 3 Material Constitutive Relationship sees tenentes 4 5 4 Stiffness and Load Computation Chapter 5 EXAMPLES 5 1 CANTILEVER CONSTRUCTION BOX GIRDER BRIDGE EXAMBPLE eerte 3 52 BRIDGE PARTICUEARS 45 eder tee tr PE PR per ED HERREN URN UR tin 3 5 3 ANALYTICAL iot eee OT
138. entana Fe eese Pe reae eee 8 4 3 3 Nonprestressed Steel Component Ne 11 4 4 PRESTRESSING TENDON FORMULATION 12 4 4 1 Tendon Discretization 3 422 inerte de Renee ceri to auqa Sa ahus 12 4 4 2 Tendon Geometry DefIfillii oDi uu us ih ener 12 4 4 3 Determination of Initial Tendon Forces sse 17 A Ericti n oe eer Seti e 17 B Anchor slip seating losses Ne 19 C Influence of stressing procedure sse 20 D Discretized segment forces 20 E Equivalent prestressing lo0adS sse 22 4 4 4 Material Constitutive Relationships eene 22 4 4 5 Stiffness and Load Computation Ne 26 Segment stiffness matrix uestes e Re 27 B Segment internal force due to nodal 27 C Equivalent nodal loads due to initial 28 4 5 TRAVELING FORMWORK FORMULATION RN 28 4 5 1 Traveler Function and Purpose Ne 28 4 52 Traveler Geometry scho a a tie c ea eile e eic nr to 29 4 5 3 Material Constitutive 29 4 5 4 Stiffness and Load Computation 30 4 1 PROGRAM BACKGROUND Chapter 4 This Page Left Intentionally BLANK ADAPT 4 1 PROGRAM BACKGROUND Chapter 4 This Chapter presents an overview of the theoretical background to the formulation of the program Detailed description of critical formulation is given in the appendices and the referen
139. ep during the solution Prestressing tendons may be stressed from either one or both ends and may be subsequently restressed or removed Traveling formwork may be moved to any location Nodal loads may be applied or removed at any time step Nodal boundary conditions may be changed from fixed to free or free to fixed at any time step All actions are considered to occur linearly gradually over the duration of the time step Thus any instantaneous action must be modeled with a zero length time step The solution includes the effects of creep shrinkage and aging of concrete plus fric tion anchorage slip relaxation of the prestressing steel a change in stress in prestressing steel due to deformation of the structure The underlying theory and its numerical implementation in the program are discussed in Chapter 4 and the appendices of this manual Material constitutive parameters may be computed by the program to model the time dependent material properties according to laboratory measurements user defined the ACI or the CEB FIP recommendations Output can include incremental and total nodal displacements and reactions frame element stresses and sectional actions prestressing tendon forces and resultants Nu merous options exist for the specification of the type of output desired during any solution or output phase Preparation of Input Data Input data are provided to the program from an input file All input takes the form of
140. ep lengths are generated internally by the program for equal time step length on a logarithmic scale The details of this construction sequence may be found by examination of the input for the analysis given in the following 5 13 ADAPT EXAMPLES VERIFICATION Chapter 5 5 5 COMPUTER INPUT ADAPT BRIDGE INCREMENTAL ABI SOFTWARE MANUAL EXAMPLES Name of this file EX5A MNL units are all in pound inch START TITLE N 2 Three span cantilever construction prestressed concrete bridge Adapted from reference Ketchum Scordelis 1986 UNITS U USA CONCRETE PARAMETERS N l 1 MESH INPUT NODES N 43 1 0 Y 46 74 2 X 180 40 75 3 360 34 50 4 X 540 34 50 5 720 Y 34 50 6 788 34 61 7 948 35 37 8 X 1108 Y 36 65 9 1268 38 53 10 1428 43 70 11 X 1588 49 21 12 X 1748 55 10 13 1908 61 40 14 X 2068 68 12 1 15 2228 75 29 16 2388 82 90 17 X 2548 90 94 18 X 2708 99 41 19 2868 108 29 20 3028 117 58 21 3188 127 25 22 3348 137 29 23 3420 141 92 24 3492 137 29 25 3652 127 25 26 3812 117 58 27 3972 108 29 28 4132 99 41 29 4292 90 94 30 4452 82 90 31 4612 75 29 32 4772 68 12 33 4932 61 40 34 5092 55 10 35 5252 49 21
141. esponse require the use of a zero length time step when instantaneously applied loadings or changes in 2 8 PROGRAM DESCRIPTION Chapter 2 the structure configuration are considered At the end of the specified time step a new stress strain and displacement distribution within the structure is obtained In each solution step the global equilibrium equations are summed from element components using the direct stiffness method and the principle of virtual work Because of nonlinearity of the time dependent solutions an iterative procedure is adopted in the solution The convergence of the solution 15 fast 22 GEOMETRY 2 2 1 2 2 2 2 2 3 Overall Frame Geometry The program has no inherent limitation on the frame geometry so long as all members are in the same plane Multistory frames and irregular construction with or without prestressing can be treated readily by the software However most bridges are multi span one level construction toward which the examples presented herein are primarily focused Change in Section Along Frame Line Both gradual and abrupt changes in cross section along the frame line can be satisfacto rily modeled The natural frame element nodes are assumed to be at the centroid of cross section A gradual change along the frame line such as illustrated in Fig 2 2 1 a will result in different coordinates for successive nodes For each element the cross sectional properties at its be
142. et of input lines must be provided for each tendon INPUT GENERATION Chapter 3 ADPT302 CENTROIDAL AXIS STRUCTURAL SYSTEM LINE FRAME ELEMENT RIGID CONSTRAINT TENDON MODELING FIGURE 3 5 16 Tendon Geometry Specification The tendon geometry specification is repeated for each tendon For each tendon several input lines are made Details of the tendon specification input lines are described next 0 Data first line for each tendon is tendon control data line Tendon numbers must be supplied in ascending consecutive order starting with tendon 1 n Spans M Area Stay Weight where n Tendon identification number Spans Number of spans used to define the tendon point geometry M Prestressing steel type number Area Cross section area for the tendon Weight Weight per unit length of stay cable Ib in in American units N mm in SI units and kg cm in MKS units program default is zero and Stay when present the tendon is treated as a stay 3 57 ADAPT INPUT GENERATION Chapter 3 Example A tendon may be regarded as a stay if the parameter STAY appears on its control data A stay can be stressed restressed or removed in the same man ner that a tendon is treated If the parameter Weight is included the pro gram is enabled to include the sag correction for stay weight The inclusion o
143. f sag correction is invoked under the sTAY ANALYSIS command 3 Spans 4 M 2 4737 4 It means that the tendon is regarded to been made up of four contiguous parts each considered as a tendon span it has the material property type 2 as specified in the PRESTRESSING STEEL command and its area is 4737 4 mm ii Tendon Span Data For each tendon span several lines must be provided to input or generate the tendon point geometry with respect to the frame nodes for that span Note that tendon spans need not correlate with the spans of the structural frame Each tendon span is a tendon length traversing one or more frame elements Each tendon span is made up of a number of tendon point Each tendon point is defined in relation to a frame node Hence the number of tendon points of a tendon span are the same as the number of frame nodes necessary to define the geometry of that tendon span The first tendon span data line specifies the number of nodes defining the tendon span In addition optionally and depending on the geometry of the tendon span two other information items for the tendon may be entered on the same input line These are a The base vectors for the local r s coordinate system Fig 3 5 17 in which the tendon geometry is input or generated Once these base vec tors have been entered for a particular span they need not be entered again for other spans or other tendons unless it is ne
144. ginning and end are input If the change is steep for in creased accuracy shorter elements should be selected Also see the ABI example manual If the change is abrupt such as for a step at the bottom or top of a section Fig 2 2 1 b The nodes representing the centroids of the thicker and thinner elements do not coincide at the interface To complete the modeling two options are available If a prestressing tendon passes through the interface of the elements the node offset feature of the program is recommended Otherwise the master and slave feature of the pro gram can be used In either case the function of the feature is to couple the otherwise free displacements of the two interface nodes such as to uphold the plane sections remain plane assumption Flexibility in Selection of Cross Section Geometry The local coordinates of the cross section are shown in Fig 2 2 2 a Simple cross sections can be specified in two ways A Specify the area A the moment of inertia I and the location of the centroid with respect to the top and bottom fibers ADAPT PROGRAM DESCRIPTION Chapter 2 2 2 4 B Use the I section module of the program Fig 2 2 2 b to construct I rectangular T or inverted T sections For composite sections such as a precast section with a cast in place topping Fig 2 2 3 a the section is modeled with two parallel elements each at centroid of one of the section constituents Observe in part
145. hapter 3 COMMAND SUMMARY DESCRIPTION Problem Initialization Input START Start Interpreting new input data START R 1 Start interpreting data for a program re run TITLE N Print N lines of title UNITS U Set input out put units ACTIVATE EXTRACT CONCRETE PARAMETERS N Number of concrete materials used followed by the modeling scheme used for concrete s creep and shrinkage Structure Definition Input MESH INPUT Start definition of structural system NODI Input node coordinates SEQUENCE Optional input for sequence of degrees of freedom for solution optimization CONCRETE PROPERTIES Input concrete material properties strength time dependent parameters material model type MILD STEEL PROPERTIES Input mild steel properties and its amount in concrete used SECTION PROPERTIES Input cross section properties or geometry OFFSET DATA Input information on adjacent node which are shifted due to abrupt change in location of centroidal axis ELEMENTS Input total number of elements in the complete structure FRAME ELEMENTS Input elements of the structural concrete frame SPRINGS Input springs and their stiffnesses PRESTRESSING STEEL Input prestressing steel properties TENDON GEOMETRY Define ten
146. he MESH INPUT command A traveler may be moved to any INPUT GENERATION Chapter 3 location on the structure as many times as desired during analysis traveler may be removed entirely by specifying destination noden 1 0 The dead load and stiffness of the traveler are automatically included in the analysis When the traveler is moved to a new location the element geometry of the traveler is adjusted to the node geometry at the new location and all loads are automatically moved Example MOVE N 2 D 14 15 16 Means move the traveler number 2 to a new location defined by node numbers 14 15 and 16 Note that this traveler has three nodes only Others may have more nodes NODES Syntax NODES N n X Y Scale G nl n2 inc where N Total number of nodes in the structure n Node number X Global X coordinate of node n Y Global Y coordinate of node n Scale Scale factor for global X and Y coordinates and nl n2 inc Generation parameters described below Explanation NODES command states the total number of nodes of the structure The node number n must be less than or equal to the total number of nodes input on the NODES command line Node coordinates may be input or generated in any order with any number of data lines If a node is input or generated more than once the last specification is used Node coordinates are input in the global X Y coordinate
147. he analysis is based on an elastic solution A solution can be nonlinear because of the time component and the associated nonlinearity in time dependent material properties For instantaneous responses the solution is linear The element formulation used is based on classical Bernoulli Euler beam kinematics that is to say plane sections remain plane The formulation accounts for the effects of axial and bending deformations Shear deformation is not significant in the class of concrete structures addressed by the program Hence shear deformation is neglected The element formulation for the frame and all other elements used in the program guarantee static equilibrium of total internal forces with the total externally applied loads PROGRAM DESCRIPTION Chapter 2 TENDON POINT TENDON NC SEGMENT RIGID LINK gt os h FRAME ELEMENT a TENDON POINTS AND FRAME ELEMENT NODES ADPT729 DWG TENDON SEGMENT b WRONG SPECIFICATION ASSOCIATION OF TENDON POINTS WITH ELEMENT NODES FIGURE 2 1 3 ADAPT PROGRAM DESCRIPTION Chapter 2 2 1 3 2 1 4 Time dependent concrete strains including aging strain creep strain shrinkage strain and temperature strain are automatically considered Shrinkage and temperature strains may vary linearly over the depth of each element Asan alternative to discrete specification the mild steel component is assumed to be uniformly distributed over the en
148. hip corresponds to a Kelvin chain rheological model consisting of aging springs and dashpots Calculation of the Creep Strain Increment The recursive relationships for calculating the increment in creep strain over one time step can be derived from these differential equations based on any one of a number of different assumptions regarding the variation of stresses and material parameters over the length of the time step The relationships for the following sets of assumptions are derived and discussed below A Constant stress and constant material parameters over each time step B Linear variation in stress and constant material parameters over each time step C Linear variation in stress and linear variation in material parameters over each time step The recursive relationships resulting from each of these sets of assumptions are described below and are implemented in the computer program described in Chapter 4 To describe a time step let time be subdivided by discrete times t G 1 2 3 and let 6 refer to increments from tj to tj Then yit yit Constant stress constant material parameters Assuming a t and G b to be constant over the time step from t to 6 and with a step function in o t at time 4 the integration of Equation B 3 8 then yields exactly for uniaxial stress gt g t e9i a t B 3 10 ADAPT ABI CONCRETE MODELING Appendix B By s
149. ier Traveling formwork for construction of the concrete segments is included by modeling each actual traveler as two short beam elements For the construction of each segment the traveler is moved so that it supports the new concrete segment Figure 5 3 1 d Each traveler is assumed to weigh 150 000 pounds Tendon elements are used to model the cantilever continuity and local prestressing tendons described in foregoing The 30 tendons used to model all the prestressing include a total of 442 tendon segments Tendons 1 through 16 each represent four cantilever tendons anchored in each segment These tendons are straight over most of their length except for a 13 foot length at each end where they drape to their anchorage locations Each tendon is jacked from both ends with a force of 2 550 000 pounds Tendons 17 and 18 represent the eight continuity tendons in the side spans and center span respectively These tendons are parabolically draped in the webs and their geometry is generated by the program based on the control dimensions and parameters shown in Figure 5 2 2 d Each tendon is jacked from the eft end only with a force of 5 100 000 pounds Tendons 19 through 22 represent local tendons in the side span and tendons 23 through 30 represent local tendons in the center span These tendons are located at the bottom of the webs and are generated parametrically by the program Tendons 19 through 24 and 29 through 30 each represent 2 actual
150. iffness matrix bandwidth minimization The SEQUENCE command is then used to specify the internal degree of freedom numbering order for the nodes in order to minimize the stiffness matrix storage and numerical effort required in the solution of the equilibrium equations All nodes other than nodes 1 41 and 43 are free to displace in all degrees of freedom Node 1 at the abutment is restrained against displacement in the global Y direction representing a sliding bearing support Node 41 at center span is restrained against displacement in the global X direction and rotation about the global Z axis representing the symmetry condition required for modeling half the structure Node 43 at the bottom of the pier is restrained against displacement in all three degrees of freedom representing a foundation on bedrock Nodes 2 through 5 are temporarily restrained against displacement in the global Y direction in order to represent the formwork supporting this conventionally erected girder segment at the abutment These temporary restraints are released after the closure segments are cast and the local tendons are stressed In a rigorous ABI analysis the conventionally erected girder segment at the abutment would be modeled with segments resting over falsework during the construction phase The falsework will be modeled by spring elements representing the stiffness of the falsework After the closure between the cantilever section and the a
151. imate The degree of approximation depends on the level of hypothetically calculated tension stress beyond the concrete cracking limit For the determination of sectional actions moments shears axial forces it is common to assume full effectiveness of cross section For deflections however adjustments to the calculated values are necessary PTI 1990 when hypothetically calculated tension stresses exceed 12 f 2 1 0 2 in SI units Geometry of Internal Displacement Fields The geometry of the frame element Figure 4 1 1 a is defined by the two nodes I and J located in the global X Y plane and on the centroidal axis of the element The origin of the local x y coordinate system is at node I The local x axis is defined by the vector joining node I and node J The local z axis is parallel to and in the direction of the global Z axis The local y axis PROGRAM BACKGROUND Chapter 4 is orthogonal to the local x and z axes and is directed according to the right hand rule The element cross section Figure 4 1 1 b is defined in the local y z plane and must be constant over the x length of the element The only constraint on the shape of the cross section is that it must be symmetric about the local y axis Any arbitrary cross section which meets this requirement can be modeled The element has six global displacement degrees of freedom Figure 4 1 1 c consisting of two translations and one rotatio
152. inflection point a positive number Fig 3 5 17 rc Fraction of the total span length between left end of the span and the point of zero tendon slope ow point relative to the r s system a positive number Fig 3 5 17 rr Fraction of the total span length between the right inflection point and the right end of the span a positive number Fig 3 5 17 sl s coordinate of left end of tendon Fig 3 5 17 sc S coordinate of point of zero slope Fig 3 5 17 and sr S coordinate of right end of tendon Fig 3 5 17 r 0 0 4 0 1 5 12 2 16 The values given for are dimensionless but those for s are ordinates in the local s direction Or If direct tendon point coordinate input is used for the span the following N lines must be provided in place of the one above In this case the default r coordinates are the x coordinates of the nodes included in the span If para metric generation is used then these lines must not be provided np R r np S s np where INPUT GENERATION Chapter 3 ADPT304 5 INFLEXION INFLEXION LOW POINT S SPAN LENGTH NORMALIZED 1 FIGURE 3 5 17 np Tendon point number np r coordinate of tendon point and s np s coordinate of tendon point This sequence of lines must not include any blank lines Example 2 N 7 List 8 9 10 11 16 3 14 1 r 0 s 0 2 r 60 5 5 5 3 120 5 8 9 4 180 5 10 5 r 2
153. ion Equation B 3 19 The recursive relationships for computing the creep strain may be derived as follows Substituting the degenerate kernel Equation B 3 2 into the convolution integral Equation B 3 1 the resulting expression for lt may be written as dolt dy t lt Ya oft 3 4 1 1 Rearranging simplifying this expression results in equation for in the form 0 3 5 i l in which of do t aa 3 6 casi yin gt e dub ro dr B 3 6b Expressing the derivatives de ydyi and dy it can be verified by substitution into Equation B 3 6 that e 1 always satisfy the following linear differential equations Ve de do B3 7 dy dy UU dy Expressing the derivative dg dy from Equation B 3 6 it can be verified that g t always satisfy the following linear differential equations dg 2 x do dy t dy 5 B 3 8 The derivatives with respect to y may be expressed in terms of time derivatives through the following substitutions and dy2 yes ADAPT ABI CONCRETE MODELING Appendix B B 3 2 Making this substitution in equation B 3 7 results in the following differential equation Es tu 5 i 0 6 B 3 9 yi This type of constitutive relations
154. ion Fig 3 5 13 OF Area Cross section area T Cross section moment of inertia Ctop Distance from centroidal axis to extreme fiber in positive local y direction see Fig 2 2 2 and Distance from centroidal axis to extreme fiber in negative local y direction see Fig 2 2 2 and Stop Fraction of shrinkage strain at extreme fiber in positive local direction 1 and Sbot Fraction of shrinkage strain at extreme fiber in negative local y direction 1 INPUT GENERATION Chapter 3 Explanation The SECTION PROPERTIES command is used to specify the different section properties found in the frame elements and travelers making up the structure The section type number n must be less than or equal to the total number of section types input on the SECTION PROPERTIES command line The section types may be supplied in any order however each section type must be speci fied once An element s local coordinate is defined by direction of its node I to node J x direction Node I is the first node entered in input data Depending on the order of node entry of an element in input data the local y axis may look one way or the opposite way since the right hand rule for coordinate definition is used The consistent use of right hand rule for coordinate definition may necessitate the same section to be given two different section properties
155. ion of the frame ele ment PROGRAM DESCRIPTION Chapter 2 The amount of nonprestressed steel available in any cross section is expressed by a steel percentage coefficient Significant concentration of nonprestressed steel is modeled as steel bars of given cross section and properties located at user defined locations in a frame element FDOTI2 ELASTIC RECOVERY CREEP STRAIN ELASTIC STRAIN CREEP RECOVERY DEFORMATION t TIME CREEP RESPONSE OF CONCRETE FIGURE 2 3 1 2 3 3 Prestressing Steel For each prestressing steel its modulus of elasticity ultimate strength yeild strength stress relaxation coefficient and thermal coefficient of expansion are defined As an alternative laboratory measured relaxation values may be given as input data 24 PRESTRESSING Prestressing is achieved through definition of tendons and subsequently stressing of these tendons Tendons can be pretension bonded unbonded and stay ADAPT PROGRAM DESCRIPTION Chapter 2 2 4 1 2 4 2 2 4 3 Tendon Number and Stressing Multiple number of tendons each with its own geometry material properties and force characteristics can be defined Prestressing tendons defined are activated by installing them in the construction sequence When installed the tendon s contribution to the stiffness of frame elements is implemented in assembly of the next global equilibrium equatio
156. ired Time dependant concrete behavior can be modeled according to a number of model codes laboratory test data or user defined values Each parameter type can employ a different model The CONCRETE PARAMETERS details the specifics of the concrete material models used They generate data for shrinkage strain elastic modulus and creep coefficients vs time The CONCRETE PARAMETERS command must be used prior to the MESH INPUT command More than one concrete material ADAPT INPUT GENERATION Chapter 3 model be specified material models will be specified sequentially one after the other Use either i the short form input which takes advantage of default values built in the pro gram or ii detailed input which involves a comprehensive definition of concrete properties 1 Syntax Explanation SHORT FORM INPUT CONCRETE PARAMETERS N n n M mode 1 n Number of concrete material models The CONCRETE PARAMETERS specifies the number of different concrete types used from shrinkage and creep modeling standpoint where n Parameter type number model Model type used ACI ACI for ACI recommendations CEB for CEB FIP recommendations CEB1 for one component CEB FIP model In ACI 209 1978 the loading and unloading curves for creep follow the same
157. is file CANT INP START TITLE N 2 CANTILEVER BEAM EXAMPLE FIXED AT LEFT FOUR ELEMENTS MODELING units lb inch UNITS U USA CONCRETE PARAMETERS N 1 1 M ACI MESH INPUT NODES N 5 Y 0 5 X 160 Y 0 G 1 5 CONCRETE PROPERTIES N 1 1 Fpc 5000 Cr 3 5 Sh 0 0005 W 0 0 MILD STEEL PROPERTIES N 1 1 Es 29000000 0 05 SECTION PROPERTIES N 1 1 11 7 EMENTS N 4 FRAME 4 1 1 2 1 X 1 St 1 Day 0 G 1 4 1 1 1 MESH COMPLETE H Day 100 CHANGE STRUCTUR RESTRAINTS 1 R 1 1 1 E BUILD N 1 4 1 CHANGE COMPLETE LOADING N 5 F 0 1000 0 SOLVE OUTPU PERENNE stage T prev SOLVE Day 1000 Steps 10 OUTPU RA Stage Ze eor SOLVE Day 10000 Steps 10 OUTPU E RES Stage 4 5 13 ADAPT ABI INPUT OUTPUT EXAMPLES Appendix A A 4 OUTPUT LISTING AMA PE Structural Concrete Software System ADAP T BRIDGE INCREMENTAL ABI V 2 00 Jan 96 1733 Woodside Road Suite 220 Redwood City Calif 94061 Tel 415 306 2400 Name of data file of this run Date and time of this run 1 PROBLEM TITLE EXAMPLE CANTILEVER BEAM FIXED AT LEFT END FOUR ELEMENT MODELING UNITS LB INCH 2 ATERIALS CONCRETE PROPERTIES CO
158. is independent of aging ADAPT ABI CONCRETE MODELING Appendix B c D t B t represents the irreversible flow part of the creep strain which is influenced by the age of the concrete at loading The factors and p are functions of the notional thickness ho of the concrete elements The notional thickness is defined by h 2 A u B 2 9 where notional thickness humidity factor Table B 1 1 A area of concrete cross section in cn u length of the perimeter of the concrete cross section in contact with the atmosphere in cm TABLE B 1 1 BASIC COEFFICIENTS OF CREEP AND SHRINKAGE Environment humidity creep Or shrinkage Outside in 70 0 00032 general Very dry 40 3 0 00052 atmosphere The age of the concrete is adjusted to account for variations in temperature and the type of cement used For each period t during which the mean temperature is T the corrected age is obtained from the expression 3 1 0 2 0 0 a a ite ELT TII atmosphere NN X T 10 dt 30 B 2 10 where t corrected age a 1 0 for ASTM cement types I and II a 2 0 for ASTM cement type III a 3 0 for high early strength cement types T ambient temperature C during days t number of days with temperature Tn ADAPT ABI CONCRETE MODELING Appendix B When concrete cures at 20 C 68 F and normal ASTM type I cement is used the corrected age and the real age
159. ives the ultimate coefficient say C To increase the generality of the pro gram the concrete models such as the materials 1 2 and 3 shown in the figure are defined under the subcommand coNcRETE PARAMETERS Under CONCRETE PROPERTIES subcommand the ultimate coefficient will reach the 3 24 INPUT GENERATION Chapter 3 specified value at time infinity but will do so following different paths 1 2 and 3 shown in part b of the figure Example in SI units CONCRETE PROPERTIES N 1 1 36 Cr 2 5 5 0 0004 W 2 4x10 6 Where the maximum creep strain of a standard specimen for this material is 2 5 The selection of the code and concrete material for the standard creep specimen is given under the command CONCRETE PROPERTIES The value Cr 2 5 identifies the location of point A in Fig 3 5 4 b but does not specify which of the three curves 1 2 or 3 are to be used This is done in the coN CRETE PROPERTIES command Like wise the maximum value of shrinkage strain for a standard specimen for the concrete material used is Shr 0 0004 The weight in kg mm is given by w Example CONCRETE PROPERTIES N 2 1 30 Cr 1 0 5 1 0 W 0 1 2 Fpc 20 Cr 1 0 Sh 1 0 W 2 4x10 6 M 2 This example applies to when the shrinkage and creep are specified using at laboratory or a model code not in
160. jacking from tendon end When it is found that the force already existing in the tendon from end A jacking is greater than the force computed for end jacking the end B jacking procedure is terminated This method closely approximates the physical situation in the actual tendon Discretized segment forces After the initial tendon force at each tendon node is computed the initial force in each tendon segment is found by averaging the forces at its two defining tendon nodes The average tendon force scheme is applicable if the tendon has a smooth profile For tendons which are harped and have a rapid change of curvature finer frame subdivisions must be used in order to minimize the approximation 4 20 PROGRAM BACKGROUND Chapter 4 INITIAL FORCE AFTER JACKING FROM BOTH ENDS 00 08 amam Hm az LU 5200 Tu END A CONTROLLING CONTROLLING END ANCHOR AT ANCHOR AT END END INFLUENCE OF STRESSING PROCEDURE FIGURE 4 4 7 Consider a tendon with a smooth arbitrary tendon profile Figure 4 4 8 a The actual tendon force profile is a smooth curve Figure 4 4 8 b The computed tendon force profile Figure 4 4 8 b has curvature friction losses lumped at the tendon nodes and wobble friction losses distributed over the segments The best estimate of the actual tendon force profile from this computed force profile is found by connecting the
161. lated output STATIC Prints a summary of total internal forces for each frame element summed from the frame element components plus all tendon segments and traveler elements with the same nodes 3 39 INPUT GENERATION Chapter 3 1023 CENTROIDAL 3 AXIS boo FRAME ELEMENT BOTTOM FIBER X GLOBAL AXIS LOCATIONS AND ORIENTATION OF TABULATED STRESS OUTPUT FIGURE 3 5 11 NONE No output for text printout will be generated Output will be limited to graphical display SAME Output information will be the same as previous output request PRESTRESSING PRESTRESSING SHORT PRESTRESSING SHORT Prints the combined result of all tendons in the frame Block 109 2 and PRESTRESSING LONG Prints a detailed output for each tendon Block 109 1 and a summary of the combined result of all tendons Block 109 2 INPUT GENERATION Chapter 3 Explanation The amount and compilation of the printed output is controlled through the OUTPUT command Depending on the optional parameters which can follow OUTPUT command a printout with a lesser or greater detail can be obtained The output is subdivided into data blocks each numbered with a unique identification number The numbering and details of the output data blocks are given in Appendix A The OUTPUT command performs no numerical operations associated with the time dep
162. lements from the structure Any load remaining on a node which is eliminated from the assembly by removal of all frame and traveler elements at tached to it cannot be resisted by the structure and must be removed from the structure before removal of the elements PROGRAM DESCRIPTION Chapter 2 ADPT310 DWG NEW SEGMENT FORM TRAVELER ASSEMBLY TRAVELER FOR CASTING NEW SEGMENTS FIGURE 2 1 4 Initialization of new frame elements For regular linear solutions which are commonly used for completed structures node coordinates entered in input data define the geometry of the frame For incrementally constructed frames the addition of new elements accounts for the existing deformation of previously loaded and deformed elements When an element is installed in order to provide a statically feasible system one end of the element must be attached either to a restrained node or to a node already connected to another frame element In most cases this node will have been previously dis placed due to previously applied loadings If the other end of the frame element is attached to a node which is not already connected to another frame element then the displacements of that node must be initialized based on the existing displace ments at the first node These displacements are automatically initialized by the program based on the assumption that the new element is a rigid body attached to a previously displaced node Fig 2 1 5
163. loading and construction stage A 5 ADAPT ABI INPUT OUTPUT EXAMPLES Appendix A ADDRESS OF USER ADDRESS OF USER ADAPT Structural Concrete Software System D T BRIDGE INCREMENTAL ABI 9022560 Jan 96 1733 Woodside Road Suite 220 Redwood City Calif 94061 1 415 306 2400 Name of data file of this run BRIDGE 1 Date of this run B T e PROBLEM TTS ABI GEN1 EXAMPLE THREE SPAN BRIDGE BALANCED CANTILEVER CONSTRUCTION END SPANS NEXT TO ABUTMENTS CONSTRUCTED ON FALSEWORK 2 5 CONCRETE NO MODEL NO ULTIMATE STRENGTH 000 03 CREEP COEFFICIENT 000 00 SHRINKAGE STRAIN 000 00 UNIT WEIGHT 2108 4022 THERM COEFF 000E 00 3 2 MILD STEEL PROPER TEES MILD STEEL ELASTIC PERCENTAGE IN THERMAL EXPANSION NO MODULUS CROSS SECTION COEFFICIENT 1 2 90000 07 2 00000 02 0 00000 00 3 3 PRESTRESSING TENDON MATERIAL 5 STEEL ELASTIC CURVATURE WOBBLE ULTIMATE RELAX THERMAL NO MODULUS FRICTION FRICTION STRESS COEFF iL 502496 000 2521286254 01 02228852201010 50246 02101001 5010 SECTION 5 INPUT OR COMPUTED SECTION PROPERTIES SECTION 1 2 3 4 5 CROSS SECTION 456 03 564 03 996 03 860 03 5 1 5S6E 03 MOMENT OF INERTIA 493E 06 OS EOS 308E 06 152 06 438E 06 DISTANCE CG TO TOP 600 01 6 a 063 01 413 401 DISTANCE
164. lution is considered to have converged when the maximum stress change in the concrete in any element is less than the specified value over two successive iterations ADAPT INPUT GENERATION Chapter 3 SOLVE Syntax Explanation The A identifier is used to set the convergence acceleration factor for the creep solution The default value has proven satisfactory in most cases The It identifier is used to set the maximum number of iterations allowed in any solution step After this number of iterations the solution terminates A shorter time step or higher convergence tolerances help reduce the required number of iterations SOLVE Day It A where Day Day number at end of solution It Maximum iterations per time step 25 and A Convergence acceleration factor 0 70 The SOLVE command is used to solve the current structure for its displace ments and internal stresses under current loadings at the specified time This command performs the majority of the numerical operations required in the analysis Al command line data are optional and if omitted they default to their values from the previous SOLVE command or the values initialized under the SET command Once these parameters have been entered do not enter them again unless it is necessary to reset them The initial default values are those de scribed for the SET command The SOLVE command steps the solution over the time interv
165. m Applied displacements on unrestrained degrees of freedom are neglected N nl n2 inc D dx dy dzz where nl Node number of first node in a series of nodes with identical applied displacements n2 Node number of last node in the series n1 inc z Node number increment used to define nodes in the series dx X displacement increment dy Y displacement increment and azz Z rotation increment Uniformly distributed frame element loads The following data must be provided Frame element loads are in the global directions and are specified as force per unit projected length see Fig 3 5 9 Frame element loads are converted to concentrated nodal forces for the analy sis L 11 12 inc F fx fy where 11 Frame element number of first element in a series of elements with identical applied loads 12 Element number of last element the series inc Element number increment fx X force per unit Y projected length and fy Y force per unit X projected length ADAPT INPUT GENERATION Chapter 3 Temperature changeloadings The following data must be provided The temperature of each element may be different vary linearly over the depth of the element Temperature strains are included in the frame elements generated with the L identifier and also in all prestressing tendon segments with the same node numbers as the generated elements Temperature strains in the traveler
166. ment during each time step to arrive at the total stress relaxation at time t 4 4 5 Stiffness and Load Computation During each time step the following tendon segment element computations are required A The segment s contribution to the global elastic stiffness matrix B the segment s internal stress due to nodal displacements and C the segment s equivalent nodal loads due to initial stresses 4 26 PROGRAM BACKGROUND Chapter 4 During element output the equivalent segment end stress resultants must be computed for direct comparison with the frame element output These computations are done using matrix transformations All the segment element matrices are computed once prior to the time dependent solution and are reused in each time step The formulation of all the matrices follows elementary linear elastic theory for truss type elements This guarantees static equilibrium of computed internal forces with the external loads Figure 4 4 3 illustrates dimensions and properties of the tendon segment elements A Segment stiffness matrix The stiffness matrix K for each tendon segment element is evaluated by transformation of the 1 x 1 segment stiffness matrix k in local coordinates by the 1 x 6 displacement transformation matrix A as follows k A 4 4 10 where K 6 6 global stiffness matrix relating segment global forces to global displacements Figure 4 4 3 b k 1 1 lo
167. n Minimum age is 1 day Shrinkage strain readings from the lab speci men ADAPT INPUT GENERATION Chapter 3 Explanation Example CONCRETE 1 M LAB LoadingAge 1 Age 3 10 15 20 30 40 LoadingAge Age of the lab specimen in days when the creep loading is applied Minimum age is 1 day Eci Modulus of elasticity of the lab specimen at the time the creep loading is applied deter mine from the instantaneous deformation of lab specimen under applied loading ObservationAge Days when measurment of the lab creep specimen are made minimum age is 1 day and CreepStrain Observed creep strain of the lab specimen per unit stress e g strain per Mpa for SI units per psi for Ameican units per Kg cm for MKS units The above syntax for the CONCRETE PARAMETERS command is a modification of the syntax used in previous releases of the program for the laboratory generated material model option M LAB In this case the shrinkage creep and elastic modulus data to be used in program calculations are input by the user The number of different material models and the number of creep and shrinkage test specimens for each material are user defined The number of ShrStrain readings must be equal to the number specified for ShrinkageReadings The number of CreepStrain readings must be equal to the number specified for creepReadings The program then uses the input data
168. n Zyl and Y J Kang Refer to Appen dix C for references ADAPT ABI draws upon the pool of information generated in past research and prac tice It compiles modifies and expounds the reported research with the objective to meet the demands of consulting engineers engaged in concrete bridge and prestressed frame design It is important to be clear at the onset regarding the basis of the work The names and agencies mentioned in the foregoing are purely for acknowledgment and recognition of their valuable works in and their contributions to the field of analysis of concrete bridges It is neither intended to draw credence for the work presented herein nor to shed any liability on the persons and agencies named ADAPT ABI is an independent entity Segmental Construction A segmentally constructed bridge or frame is built from discrete components which are assembled to form the complete structure The assembly generally takes place over a period of time In addition a segmentally constructed bridge has one or more of the features described below 1 components called upon to carry loading in configuration through construction phase structural system other than that of the com pleted structure A good example is balanced cantilever construction where 1 1 ADAPT OVERVIEW Chapter 1 1 11 1 V vi vii the cantilevering structural system of the bridge is for construction ph
169. n at each node external loads are assumed to be applied at the nodes Any distributed loads including dead loads are converted to statically equivalent concentrated nodal actions Any element local internal effects of external loads are neglected The internal displacement fields in the element are expressed in terms of the three independent local nodal displacements 0 0 and u Figure 4 1 2 a using cubic hermitian polynomial displacement interpolation functions Equation 4 1 1 These interpolation functions represent exactly classical Bernoulli Euler beam kinematics and can be integrated exactly for linear elastic materials The axial displacements ug Figure 4 1 2 a along the element s x axis can be expressed in terms of the local nodal displacements as 0 5 0 4 1 1 u where 2 x 1 L 12 4 1 1a x x 4 1 1 2 x 3 L 4 1 1c The axial displacement u at any point in the element can be expressed in terms of the displacements u and vo along the element s x axis as dv U Uo x 0 y dx 4 1 2 PROGRAM BACKGROUND Chapter 4 a FRAME ELEMENT LOCAL COORDINATE SYSTEM iy CENTROIDAL AXIS ADPT346 DWG AXIS OF SYMMETRY b CROSS SECTION IDEAIZATION Y 97 04 ELEMENT 02 jy c GLOBAL DISPLACEMENT DEGREES OF FREEDOM FRAME ELEMENT GEOMETRY AND GLOBAL DEGREES OF FREEDOM
170. n order to arrive at the computational approach for determining anchor slip losses The area of the region between the original force and the force after seating loss Figure 4 4 6 of the tendon force diagram must equal the anchor slip displacement multiplied by A E of the tendon Area of triangle 4 4 4 Where A is the area of the tendon and E is its modulus of elasticity The tendon segments are scanned starting at the jacking end in order to locate point at distance XL Figure 4 4 6 a which satisfies this equality After this point 1s located all tendon forces between the jacking end and this point are modified to reflect the mirrored force profile Influence of stressing procedure In an actual structure one of several different jacking procedures may be used for each tendon jacking from either one of the two ends or jacking from both ends The procedure for computing initial forces for one end jacking is similar for jacking from either end of the tendon the only difference is the order in which the tendon segments are considered For two end jacking the controlling anchorage must be determined for each tendon point Figure 4 4 7 The procedure used is as follows First the tendon point forces are determined under jacking at tendon end A Next the same procedure is initiated for jacking from tendon end B but as the force at each tendon point is computed it is compared with the force already existing due to
171. nd A 3 54 INPUT GENERATION Chapter 3 The STRESS command is used to install stress restress and remove prestress ing tendons The tendons geometry and material properties must have been input under the TENDONS subcommand of the MESH INPUT command Re moval of tendons can be more readily achieved by using DE STRESS sub command Not all the parameters listed after the stress command need be specified Use as many arguments necessary to uniquely define the intended stress condition For example if jacking stress ratio at end A ra is specified the magnitude of stress at this point sa can not be specified A tendon is initially stressed by specifying its jacking force and anchorage slip values under this command The tendon segment initial forces are then calcu lated based on this input and the material properties of the prestressing steel A tendon may be restressed by specifying a new jacking force under a subse quent application of this command The jacking force is specified using either the Rat io or St ressTo Force identifier When the Rat io identifier is used the jacking force is computed using an expression of the form Jacking force Ratio Area Fpu When the Stress identifier is used the jacking force is computed using an expression of the form Jacking Force StressTo Area When the Force identifier is used the jacking force is directly the input value
172. ness properties remain unchanged throughout the analysis Additional spring elements may be automatically generated using the G n1 n5 parameters Spring elements are generated by incrementing the input parameters above by their respective increments which are input using the G identifier The generation parameters are defined as nl First spring in generation sequence n2 Last spring in generation sequence n3 Spring number increment n4 Node increment and n5 Node J increment Note Springs generated using the G generation command have all the same stiffness values START R where R Data restore flag 21 to restore database 0 The START command specifies the location in the input file at which execu tion begins All input lines before the START command are ignored All input lines after the START command are interpreted as input data Therefore the START command may be used once in the input Under most circumstances this command is the first command in the input file It may be located later in the input file when the analysis is a restart of a prior analysis terminated with the STOP command in which case the START command must be placed subsequent to the STOP command at which the previous run has successfully terminated For a restart case R 1 should be specified on the command line so the database will be restored Obviously prior to restart i the program must have successfully executed the
173. nits and kg in MKS units Explanation The TRAVELERS command is used to describe all the traveling formwork used in modeling the construction sequence Traveler numbers must be supplied in ascending consecutive order starting with traveler 1 Travelers are modeled as linear elastic frame elements linearly connecting several nodes Only the traveler properties are input under this command The locations of the travelers may change at any time and are input under the MOVE subcommand of the CHANGE STRUCTURE command UNITS Syntax UNITS U where the following three systems of units are available U SI U USA INPUT GENERATION Chapter 3 Or 0 5 51 distances in mm millimeter forces Newton USA All distances in in inch all forces in Ib pound and MKS All distances in cm centimeters all forces in kg Kilograms INPUT GENERATION Chapter 3 This Page Left Intentionally BLANK ADAPT PROGRAM BACKGROUND Chapter 4 ABI 40 MNL 4 PROGRAM BACKGROUND 4 1 FRAME ELEMENT FORMULATION Ne 3 4 1 1 Assumptions and 3 4 1 2 Geometry of Internal Displacement Fields Ne 3 4 2 INTERNAL DEGREES OF FREEDOM Ne 7 4 3 MATERIAL CONSTITUTIVE RELATIONSHIPS 8 4 3 1 General Assumptions eee eee eerte e Rr ee Red 8 4 3 2 Concre te Component cer relia ith te webiste v
174. ns In all subsequent steps the tendon s current stiffness matrices relaxation strain equivalent loads and current total forces are included This simulates a tendon which is unbonded during stressing and perfectly bonded thereafter For unbonded post tensioned systems the tendon need be encased in a sheathing as described in section 2 4 3 Prestressing tendons are removed by eliminating the contributions of their stiffness and internal forces in subsequent global equilibrium equation assembly Initial forces in the tendon segments are computed including the effects of friction and anchor set Each tendon may be stressed from either one or both ends Long term stress losses are effected through tendon s relaxation coefficient and the frame displacements to which the tendon is locked These include the effects of creep and shrinkage among other causes of strains in a frame element Tendon Geometry The only limitation on a tendon s geometry is that it is modeled as a straight segment between adjacent frame nodes to which it is associated At installation the location of a tendon with respect to a node is defined by its offset distance from the node Through out the solution the tendon offset distances are retained as constant There are a number of predefined library shapes which can be used to describe the geometry of regular tendons Fig 2 4 1 illustrates several of the profiles included in the library of the program For an irregular ten
175. nt in one stage but deleted in a later stage To achieve this redefine the restraints for the node in subsequent stage to be either 3 43 INPUT GENERATION Chapter 3 ABI 1024 APPLIED V DISPLACEMENT UV OFFSET ANALYSIS NODE NATURAL NODE CENTROIDAL AXIS X GLOBAL AXIS RESTRAINTS AND APPLIED DISPLACEMENTS ARE ALONG GLOBAL DIRECTIONS AND AT ANALYSIS NODES FIGURE 3 5 12 Oor 1 or2 without any master node definition The program automatically determines which nodes are defined in the current structure and includes only their unrestrained degrees of freedom in the global equilibrium equations Thus the user need not restrain unused nodes with this command This sequence of lines must be terminated by a blank line ADAPT INPUT GENERATION Chapter 3 Example 12 R 1 1 1 Node 12 is fully clamped fixed in 12 R 0 0 0 Restraints of node 12 are removed RESTRAINTS 4 8 3 3 3 1 Node 4 is fully dependent ees fey vis on deformations of node 1 6 R 3 3 0 M 2 This models a hinge but nodes 2 and 6 must have same coordinates SECTION PROPERTIES Syntax SECTION PROPERTIES N n 41 42 43 B b1 b2 b3 Area I N C Ctop Cbot S Stop Sbot where N Total number of section types 1 and n Section type number and 1 2 Height dimensions of section 3 5 13 and bl b2 b3 Width dimensions of the sect
176. nt variable in the concrete stress strain relationship c t E t emt B 1 3 where O t is the uniaxial concrete stress at time t and E t is the instantaneous elastic modulus at time t Neglecting any deterioration under high stress or cyclic loading the elastic modulus E t increases over time quite rapidly during the first month after casting and more slowly afterwards Thus under constant stress the mechanical strain m t decreases over time The elastic modulus E t is often estimated based on compressive strength The compressive strength of concrete 1 is defined as the maximum average stress obtained from the testing of concrete specimens such as cylinders cubes or prisms subjected to uniaxial compression B 5 ADAPT ABI CONCRETE MODELING Appendix B B 1 2 B 1 3 B 1 4 Aging Strain Aging strain t is a fictitious stress originated strain which be defined as the decrease in mechanical strain over time due to the increase in elastic modulus of the concrete Aging strain does not represent an actual physical deformation of the concrete and should instead be considered as a correction factor for the calculation of the current total stress as a function of the current total strain Under constant stress the aging strain increment occurring between time t and t may be expressed as 1 1 587 7 9 B 1 4 Creep Strain Creep strain 1 is a stress originated strain d
177. ntly installed frame elements and remain in effect until they are removed by application of an equal but opposite displacement or rotation until all elements con necting to the node are removed or until the restraint is removed from the degree of freedom The displacements and rotations are applied to the structure as an initial strain loading case in the elements Each frame tendon and traveler element connected to a node with an imposed displacement is considered to be under an initial strain equal to the strain resulting from the imposed displacements acting on the element with all other element degrees of freedom fixed This method for considering externally applied displacements and rotations eliminates the numerical problems associated with the use of stiff external springs and applied forces for simulating applied displacements Temperature Changes Temperature changes and gradients may be applied to any currently installed frame element and remain in effect until they are removed by application of an equal but 2 18 PROGRAM DESCRIPTION Chapter 2 2 6 opposite temperature change or gradient When a temperature change or gradient is applied its specification is by frame element number but the temperature change is actually applied to all tendon elements passing through the frame element in addition to the frame element itself The temperature change is applied to the structure as an initial non mechanical strain
178. o 417 Civil Engineering Studies University of Illinois Urbana May 1975 Kabir A F 1976 Nonlinear Analysis of Reinforced Concrete Panels Slabs and Loading University of California at Berkeley SESM Report No 76 6 Kang Y J and Scordelis A C 1990 Non linear Segmental Analysis of Reinforced and Prestressed Concrete Bridges Proceedings Third International Conference on Short and Medium Span Bridges Toronto Ontario Canada Vol 1 pp 229 240 Ketchum M and Scordelis A 1986 Redistribution of Stresses in Segmentally Erected Prestressed Concrete Bridges University of California Berkeley Report No UCB SESM 86 07 Kristek V and Smerda Z 1982 Simplified Calculation of the Relaxation of Stress Respecting the Delayed Elasticity Fundamental Research on Creep and Shrinkage of Concrete Edited by Wittman H F Martinus Nijhoff Publishers Boston McGregor James 1988 Reinforced Concrete Mechanics and Design Prentice Hall New Jersey 800 pp C 2 ADAPT ABI REFERENCES Appendix C Lacy G C and Breen J E 1975 The Design and Optimization of Segmentally Precast Prestressed Box Girder Bridges Research Report No 121 3 Center for Highway Research The University of Texas at Austin Texas 1975 Lacy G C and Breen J E 1969 Long Span Prestressed Concrete Bridges of Segmental Construction Research Report No 121 1 Center for Highway Research The University of Texas at Austin
179. oads on the frame elements and v linearly varying temperature changes through the depths of a frame element and vi Linearly varying shrinkage through the depths of an element The program has the ability to monitor the actions and displacements of a frame during construction All nodes frame elements prestressing tendons springs stays and travelers which will ever exist in the structure are first defined to the program prior to the analysis The construction steps are then described as part of input data For each construction step the associated elements plus additional travelers are tagged for installation or removal External loading specific to each construction step is described At the beginning of the analysis no elements are considered to have been installed Only when a node element or tendon is installed at a construction step it is included in the analysis for that and the following time steps During subsequent construction steps elements tendons and supports previously installed can be removed provided the remaining structure is statically stable When a tendon or element is undefined it is not included in the analy sis An element is installed if it has been specifically built into the structure at a construc tion stage through a BUILD command and has not yet been removed otherwise the element is undefined A node is defined if at least one defined frame element spring or traveler element is connected to it other
180. ometry to each frame node Figure 4 5 1 b 4 30 PROGRAM BACKGROUND Chapter 4 ll IY 07 J y Le ES X NEW 97 NODE J Y XY NEW ELEMENT EXISTING NODE X X X a NODE DISPLACEMENT INITLIZATION TOTAL LENGTH L 1 ADPT355DWG 6 3 Zu NODE 3 NODE 2 n NODE 1 m TRAVELER ELEMENT YA T Wi i W b TRAVELING FORMWORK DEAD LOAD FORM TRAVELER DISPLACEMENT FIGURE 4 5 1 TOTAL WEIGHT W J CONSTANT INITIALIZATION AND WEIGHT DISTRIBUTION PROGRAM BACKGROUND Chapter 4 This Page Left Intentionally BLANK 4 32 ADAPT EXAMPLES VERIFICATION Chapter 5 ABI 50 MNL 5 EXAMPLES VERIFICATION 5 1 CANTILEVER CONSTRUCTION BOX GIRDER BRIDGE EXAMPLE 20 3 5 2 BRIDGE PARTICU ARS ectetuer eee ep a e e e e a aa unata 3 5S ANALYTICAL tte ehe tenete e edet 9 5 4 LOADINGS amp CONSTRUCTION SEQUENCE FOR THE TIME DEPENDENT RE 5 5 COMPUTER 5 6 COMPARISON OF RESULTS 5 7 AMERICAN SI AND MKS SYSTEM OF UNITS EXAMPLE DB S IRUGTURE eee tete eR Sid E GEE itae te S RESUPHS eere E Ua p Pe te eee e e eter diets 5 1 ADAPT EXAMPLES VERIFICATION Chapter 5 This Page Left Intentionally BLANK 5 2 ADAPT EXAMPLES VERIFICATION Chapter 5 5 1 5 2 This Chapter includes two examples The first example is a protot
181. on in studying and predicting the time dependent behavior of concrete structures is that the total strain in the concrete may be considered as a superposition of several independent components caused by different phenomena Even though creep and shrinkage are not strictly independent and even under simple isothermal conditions the presence of shrinkage increases the magnitude of creep this commonly accepted assumption has been experimentally verified It has been used by many investigators to study the time dependent behavior of concrete structures In this investigation the total uniaxial concrete strain t at time t is considered as a superposition of the following components t em t en t B 1 1 9 50 e a t eT t B 1 2 where e t total strain P t mechanical strain the independent variable in stress strain relationship t nonmechanical strain composed of the following components et creep strain 0 shrinkage strain cea aging strain temperature strain The meanings of each of these strain components are discussed in this chapter and are illustrated for the case of a specimen under constant stress and no temperature change in Figure B 1 1 B 4 ADAPT ABI CONCRETE MODELING Appendix B e 5 DEFINITION STRAIN COMPONENTS FIGURE 1 1 B 1 1 Mechanical Strain Mechanical strain m t is a stress originated strain and is the independe
182. oncrete parameter types na Maximum loading ages in parameter tables number of creep curves 32 and nt Maximum number of data points on a single creep curve after loading for parameter tables 32 For example in Fig 3 5 2 the collection of creep curves shown consists of creep curves for four loading ages 3 7 14 and 28 days Using this set of data the program can determine the creep response of a structure loaded between days 3 and 28 but observed from day one on to the farthest extent of the curves typically 20 years The default of the program is 32 loading ages for the parameter na The extent of the loading ages stretches up to 20 years This enables determination of creep for loading applied essen tially anytime from casting day to 20 years of age The number of points used to generate the creep curve in Fig 3 5 3 is six nt 6 These points are either generated used model codes or are read from laboratory tests The next data line for each ACI concrete type model is a control data line which takes the following form If the internally generated loading ages and observation times are used this is the only line required for parameter type M ACI T nat ntt where n Concrete model number nat Number of loading ages in material type n table na This parameter is for creep curves shown in Fig 3 5 2 and ntt Number of data after loading for material type n table nc This parameter is 6 for the creep curv
183. oncrete topping Balanced cantilever construction Various schemes of span by span construction for continuous bridge frames Incrementally launched bridges Bridges retrofitted with external tendons concrete jackets and synthetic fabrics Cable stayed bridges and Suspension bridges In the traditional non segmental design the design engineer assumes the structure in its final configuration The method of construction is disregarded Selfweight and other loading are applied to the completed structure in order to calculate the design actions moments shears and axial loading and deformations It is generally assumed that there are no locked in initial stresses in the completed structure and that the profile of the completed structure is as shown on the structural drawings The design assumptions made for the traditional structures can not be extended to segmental construction The parameters which impact the safety and performance of a segmental construction and need be accounted for in design may be grouped into time dependent parameters and construction schedule and sequence 12 SCOPE ADAPT ABI software can analyze both the completed bridge structures and bridges during construction where construction procedure and sequence affect the performance of the com pleted project ADAPT OVERVIEW Chapter 1 1 3 1 4 Inaddition to capabilities of other software in determining actions and displacements of prestressed concrete
184. or but are excluded from this investigation of purely time dependent behavior Time dependent behavior of concrete may be of three different classifications time dependent material properties resulting in time dependent stress strain relationships and producing fictitious aging strains time dependent stress originated creep strain and time dependent non stress originated shrinkage and temperature change strains Strictly speaking these three classes of effects are not independent However in practice they may be treated as independent of each other and hence additive Material properties influenced by time include the strength 1 and the stiffness E t The strength and stiffness increase significantly during the first month after casting then they increase more slowly over the remainder of life of the structure Aging strains are fictitious strains used in an analysis to allow for time dependent stiffness Creep and shrinkage strains in concrete are influenced by a number of factors depending on the mix design the loading history and the environment Predicted displacements and internal stresses in the structure may be significantly in error if these strains are neglected Of these strain components creep strain is by far the most difficult to predict because it is stress originated and depends on the entire stress history of the concrete as well as other factors The analysis of a structure for the time dependent effects of
185. over the time step dt is given by eT T T t T tj1 o 4 3 7 where T t is the temperature T at time t and is the coefficient of thermal expansion which is a material property The temperature at any time may vary linearly over the y depth of each element and must be constant over the x length of the element Values of all the time dependent material parameters E t a t 50 etc are found from tables generated internally by the program Prior to the program s solution phase these tables are initialized with the values of the material parameters at a number of different concrete ages For concrete ages different from those tabulated a linear interpolation between the nearest tabulated values is used The calculation of these material parameters is discussed in Appendix B The integrations of the appropriate stresses and pseudo inelastic strain components over the volume of the element to arrive at the equivalent loads representing these stresses and strains are performed by matrix transformations of the stress and pseudo inelastic strain vectors Nonprestressed Steel Component The nonprestressed steel component is considered as a linear elastic material Its constitutive relationship is given by E e el 4 3 8 where total stress at time t E constant elastic modulus total strain at time t eT temperature strain at time t T t T ref a 4 3 9 PROGRAM BACKG
186. oving them from their current location and then installing them in the new location When a traveler is first moved to a new location its element characteristic matrices are computed for the element geometry at the new location Traveler elements are always assumed to be under zero stress when they are installed at a new location Traveler elements behave elastically and have no memory of previous locations 2 20 PROGRAM DESCRIPTION Chapter 2 2 7 For any given problem the total weight of a traveler is assumed to remain constant regardless of its location in the structure When a traveler is installed at a new location its equivalent nodal dead loads are computed based on the total weight of the traveler on a tributary area basis The final deflection and camber of a structure is generally very sensitive to the stiffness of the traveler It is essential to include realistic values for traveler parameters in the analysis CONSTRUCTION PHASE In addition to the analysis capability of completed structure the program can trace the dis placements and stresses during the construction phase The construction sequence is defined through a number of construction steps At each step which is differentiated from a previous step by lapse of time and or construction and loading operations a complete solution is ob tained Over the length of any construction time step tendon and frame elements may be installed or removed from the
187. owever if as in common construction practice it be desired that for either alignment considerations or otherwise the tip of the constructed cantilever be at a point such as D depending on whether the cantilever is constructed using 1 2 ADAPT OVERVIEW Chapter 1 1 a SPAN ARRANGEMENT CLOSURE uu FALSEWORK b CONSTRUCTION ARRANGMENT 1 DISTRIBUTION OF MOMENTS DEAD LOAD MOMENT REDISTRIBUTION IN BALANCED CANTILEVER CONSTRUCTION FIGURE 1 1 2 1 ADAPT OVERVIEW Chapter 1 001 5 ARRANGEMENT CLOSURE all SEGMENT S CAST CONTINUITY TENDON FALSEWORK b CONSTRUCTION ARRANGEMENT TENDON AT BOTTOM SHOWN AT SIDE FOR CLARITY PRIOR TO CLOSURE AFTER CLOSURE DISTRIBUTION OF MOMENT DISTRIBUTION OF MOMENT AT AND PRIOR COMPLETION OF CONSTRUCTION FIGURE 1 1 2 2 OVERVIEW Chapter 1 a b c d e f lt GROUND SUPPORT lt FORM TRAVELER lt NEWLY CAST L4 SEGMENT PROGRESSION OF CONSTRUCTION IN A FREE CANTILEVER CONSTRUCTION USING FORM TRAVELER 1009 FIGURE 1 1 2 3 ADAPT OVERVIEW Chapter 1 006
188. owing references are consulted or used in the preparation of this manual Aalami B O 1993 Analysis and Design of Segmentally Constructed Bridges Proceedings International Conference on Concrete Engineering and Technology Kuala Lumpur Institution of Engineers Malaysia May 25 27 1993 pp TS2 1 16 AASHTO 1991 Interim Specifications Bridges 1991 AASHTO 1989a Guide Specifications for Design and Construction of Segmental Concrete Bridges AASHTO 1989b Standard Specifications for Highway Bridges 14th edition Abbas S and Scordelis A C 1990 Non linear Analysis of Segmentally Erected Reinforced and Prestressed Concrete Cable Stayed Bridges Proceedings Second Workshop on Bridge Engineering Research in Progress University of Nevada Reno Nevada Oct 29 30 1990 pp 11 14 Abdel Karim A M and Tadros K 1992 Design and Construction of Spliced I Girder Bridges PCI Journal July August 92 pp 114 122 209 1982 Prediction of Creep Shrinkage and Temperature Effects in Concrete Structures Designing for Creep and Shrinkage in Concrete Structure ACI Publication SP 76 American Concrete Institute Detroit pp 193 300 Bazant Z P and Wittman F H 1982 Creep and Shrinkage in Concrete Structures Book New York John Wiley and Sons Bazant Z P and Wu S T 1973 Dirichlet Series Creep Function for Aging Concrete Journal of Engineering Mechancis Division ASCE V 99 No
189. pattern In CEB 78 the unloading curve is different in shape to the loading curve Over a long period the unloading curve tends to pick up strain contrary to observation To improve the CEB model 1 18 introduced The CEB1 model has the same unloading curve characteristic as the loading curve Fig 3 5 1 illustrates the point INPUT GENERATION Chapter 3 ABI1013 CEB1 TIME ILLUSTRATION OF CREEP STRAIN FOR CEB AND 1978 FIGURE 3 5 1 Example 1 CONCRETE PARAMETERS N 1 1 M ACI This example uses ACI model for the entire frame with ACI 209 default parameters Example 2 CONCRETE PARAMETERS N 2 1 M ACI 2 M CEB This example uses ACI model for concrete type 1 and for concrete type 2 ii DETAILED INPUT The syntax of the detailed input depends on the concrete model used The following models are available 3 15 ADAPT INPUT GENERATION Chapter 3 209 1978 CEB FIP CEB1 FIB 1978 LAB The input option LAB refers to input from laboratory generated readings or user generated values based on model codes different from those available in ABI library ACI and CEB A ACI 209 Concrete Model 1978 Syntax CONCRETE PARAMETERS N T na nt To be followed by several lines of concrete parameter specifications where N Total number of c
190. presents the sequence of commands for most common problems Not all the commands may be necessary in a given problem INPUT GENERATION Chapter 3 ACTIVATE EXTRACT CONCRETE PARAMETERS MESH INPUT NODES E blank line i9 eg SEQUENCE A rA blank line ue Mrs CONCRETE PROPERTIES MILD STEEL PROPERTIES SECTION PROPERTI OFFSET DATA ELEMENTS FRAME SPRINGS n ppp DIT blank LIne ees PRESTRESSING STEEL TENDON GEOMETRY blank line CHANGE STRUCTUR BUILD RESTRAINTS GI lt STRESS CHANGE STOP 3 2 2 Summary of Commands Element Traveler E STRESS Tendon Frame Element The following brief descriptions of each command and its input data requirements are intended as a summary of the software s command syntax and as a quick reference guide for the experienced user Detailed descriptions of each command and the mean ing of all data are provided further on in this chapter Sample inputs for a simple canti lever and a simple prestressed concrete bridge are included in this chapter for illustra tion Command necessary if ABI GEN is used ADAPT INPUT GENERATION C
191. problem up to the com mand from which a re start shall begin and i1 the data base of the former run must have been generated and be available in the subdirectory INPUT GENERATION Chapter 3 These steps are achieved by first placing a STOP command after the last SOLVE command of the first run Then after completion of the run substitute the STOP by START R 1 Example First Run Second Run START EU STOP START 1 ER pus In the first run the program will execute the first part of data appearing be tween the START andthe stop In second run when encountering R 1 after the command START the program will re create the data up to the last instruction of the first run then it will execute the remainder of the data until the next STOP command STAY ANALYSIS Syntax Explanation STAY ANALYSIS Sag include exclude where Sag sag inclusion option exclude The STAY ANALYSTS command is used to control the type of analysis to be performed The cable stay element formulation allows for nonlinearity in stiffness of the stay due to its sag under its weight To include the sag correc tion first the following commands must be included within the MESH INPUT data block STAY ANALYSIS Sag include Second the parameters of stay and weight must be added on the tendon geometry input refer to tendon geometry ADAPT INPUT GENERATION Chapter
192. r is downward it is apparent that the D 3 ADAPT ABI BACKGROUND TO CAMBER COMPUTATION D nodes must be constructed above the datum line in anticipation that the deflection of the structure will lower them to the level of datum line In bridge structures it is generally desired that the structure would conclude with a profile above the datum line The second step in camber calculation is therefore to add to the camber values from the previous step the amount of the desired upward offset from the horizontal line As an example let us review the camber calculation for node 4 of the cantilever in Figure D 1 2 for which the camber necessary to bring the final position of the bridge to the horizontal line is determined Since in the first step of computation the camber shall fully eliminate the anticipated deflection along the bridge the magnitude of camber must be Camber Initial position Final position Initial position is the location height where a node segment end is originally placed at time of construction In this example node 4 is at the right end of segment 3 and it is installed at point A Its position with respect to the datum line at time of installation is d The suffix indicates location of node 4 at the initial condition The basis for computation of the initial position of node 4 will be expounded further on After completion of the construction and lapse of time node 4 will end up in its final po
193. r models b and c all 4 9 PROGRAM BACKGROUND Chapter 4 stresses vary linearly over the length of the time steps therefore all loads are assumed to be applied gradually over the length of the time steps Therefore for models b and c any loads applied instantaneously must be applied in a zero length time step Models b and c for the calculation of the creep strain increment require iteration during each time step since the creep strain increment both contributes to the incremental load vector and also depends on the stress increment over the time step In the first iteration the stress change over the time step is taken as zero the displacement increment is computed the constitutive relationship is evaluated and a first estimate of the actual stress change over the time step is computed This computed stress change estimate is then used in the constitutive model and the process is repeated for a better estimate of the actual stress change The iteration continues until the stress change o converges to a specified tolerance In some cases the iterative solution converges very slowly therefore a simple convergence acceleration scheme has been incorporated in the program In each iteration the creep strain estimate is corrected using the following relationship 5 et 4 3 4 1 where C the convergence acceleration factor corrected creep strain estimate for itera
194. r table 19 744 40 295 00 D 14 375 231 62 42 00 Rigid zone 20 744 40 351 27 D 14 375 74 00 19 63 Near abutment 21 744 40 349 81 D 14 375 82 75 10 88 22 744 40 349 50 D 14 375 84 63 9 00 23 744 40 349 50 D 14 375 84 63 9 00 24 348 D 96 Pier 25 72 1 5 72 D 4 80 4 Traveler ELEMENTS 42 FRAME N 42 22 1 20 St 1 Day 100 G 1 4 1 1 1 0 1 0 0 55 6 C 1 1 5 1 Day 168 G 5 22 1 1 1 0 1 0 7 23 23 24 C21 18 St 1 Day 49 G 23 40 1 1 1 0 1 0 7 41 23 42 1 19 St 2 Day 0 42 42 43 1 24 St 2 Day 0 PRESTRESSING STEEL N 1 1 Ep 28E6 Meu 25 K 0004 12 Fpu 27E4 R 10 TENDON GEOMETRY 30 Be Ae es Cantiver tendons each represents 4 21 Strand 1 2 Diam tendons 1 Spans 2 M 1 Area 12 852 R 0 6638 0 5 20 7 7 2 3 G 23 25 1 R 0 3362 0 5 7 7 20 2 Spans 2 M 1 12 852 1 4 G 20 23 R 0 3929 0 5 20 7 7 2 N 4 G 23 26 R 0 6071 0 5 7 7 20 3 Spans 2 M 1 Area 12 852 1 N 5 G 19 23 1 R 0 2790 0 5 20 7 7 2 5 G 23 27 1 R 0 7210 0 5 7 7 20 4 Spans 2 1 12 852 1 6 G 18 23 R 0 2163 0 5 20 7 7 2 N 6 G 23 28 1 R 0 7837 0 5 7 7 20 5 15 ADAPT 10 11 12 T3 14 15 5 1 2 5 1 5 1 5 1 5 1 5 1 5 1 5 1 5 1 5 1 5 1 n N N n N N n N N n N EXAMPLES VERIFICATION
195. rained to a specified node which is usually different for each tendon point Each tendon segment must correlate entirely within one frame element In other words there must be a one to one correspondence between each tendon segment and an associated element frame The global X and Y coordinates of the tendon points com pletely define the tendon s geometry These coordinates may be input directly for each tendon point or they may be generated using a parametric generation scheme The input or generation can be in an alternative translated and rotated local r s coordinate system specified by the user The r and s coordinates are converted internally to the global X Y system For input convenience each tendon may be viewed to consist of several contiguous lengths referred to as spans The number and lengths of tendon spans need not correlate with that of the structure These spans are defined by the node numbers corresponding to the tendon points along their length and need not correspond to the actual spans of the bridge The tendon geometry of each span may be either directly input or parametrically generated Tables of tendon points and segment geometry may be printed in the output The PRINT identifier on the TENDON GEOMETRY command line is used to set the amount of output and the number of tables printed Several lines of input described below are required to specify the geometry of each span of each tendon This s
196. ration is performed PROGRAM DESCRIPTION Chapter 2 JOINT SEGMENT SUPPORT TRUSS LEFT SPAN ERECTED hosce b LEFT SPAN STRESSED RIGHT SPAN BEING ERECTED ADPT358 DWG e Lr 2 d TENDONS SPAN BY SPAN EXAMPLE CONSTRUCTION FIGURE 2 7 2 PROGRAM DESCRIPTION Chapter 2 TEMPORARY TOWER AND TIE BACKS 22555 sss ADPT362DWG PROGRESSIVE PLACING CONSTRUCTION USING ERECTION TOWER AND PRECAST SEGMENTS FIGURE 2 7 3 PROGRAM DESCRIPTION Chapter 2 FORM TRAVELER BALASTED SPAN y ce LI a lt PROGRESSIVE BALANCED CANTILEVER CONSTRUCTION USING CAST IN PLACE SEGMENTS FIGURE 2 7 4 PROGRAM DESCRIPTION Chapter 2 This Page Left Intentionally BLANK INPUT GENERATION Chapter 3 3 1 3 2 3 3 3 4 3 5 LIST OF CONTENTS OVERVIEW 1 DLT CAPABILITIES E 1 3 1 2 PREPARATION OF INPUT DATA 1 COMMAND SUMMARY 2 3 2 1 NATURAL SEQUENCE OF COMMANDS ppp 2 322 SUMMARY OF COMMANDS 3 SAMPLE INPUT FOR A NONPRESTRESSED CANTILEVER BEAM 5 3 3 DESCRIPTION OF THE STRUCTURE 5 33 2 INPUT FILE 55 A E T US A 6 SAMPLE INPUT FOR PRESTRESSED CONCRETE BOX GIRDER BRIDGE 7 3 4 L
197. ration of the structure RESTRAINTS Syntax RESTRAINTS nl n2 inc R rx ry r M m1 m2 minc where nl Node number of first node in a series of nodes with identical re straint specifications n2 Node number of last node in the series n1 inc Node number increment used to define nodes in the series Ex X displacement restraint specification ry Y displacement restraint specification rzz Z rotation restraint specification m1 Node number of first node in a series of nodes which is master node for nl node 3 42 INPUT GENERATION Chapter 3 Explanation m2 Node number of last node in the series which is master node corre sponding to n2 m1 and minc Node number increment used to define master nodes for nodes n1 through n2 The RESTRAINTS command is used to specify the boundary conditions of the structure The data line is repeated as many times as required to specify the desired boundary condition changes Each node has three displacement degrees of freedom Fig 3 5 12 each of which may be specified with one of three restraint types r 0 Free to displace 1 Fixed at current total displacement current position r 2 Fixed with zero displacement and r 3 Fixed with displacement corresponding to that of its master node If this option is used a master node must be defined on the same line corresponding to the node for which restraints are being define
198. s 10420 5 2 Blank spaces within arithmetical statements are not allowed The command interpreter in the program recognizes several special characters used to delimit multiple command lines on one physical line continuation of a command line on the next physical line and comments to be ignored by the command interpreter The exclamation mark is a special character used to delimit several command lines provided on one physical line The data to the right of an exclamation point are not considered to be part of the current command line and are instead consid ered as the next command line Any number of command lines may be input on one physical input line by separating them with this character N The backslash is a special character used for continuation of a command on the next physical line AII data to the right of the backslash are ignored and the following input line is interpreted as a continuation of the first line This option allows a maximum of 160 characters to be entered as one line of data The maxi mum number of characters permitted on any physical line is 80 semicolon is a special character used to delimit comments in the input stream All characters to the right of the semicolon up to the end of the line are ignored by the program If the semicolon is located in the first column in a command line the entire command line is ignored 32 COMMAND SUMMARY 3 21 Natural Sequence of Commands The following re
199. s and the reactions are from an engineering standpoint almost identical with Sframe solutions 5 24 Chapter 5 EXAMPLES VERIFICATION K uo Jo uonp no e2 10 889115 1 19sJJo 95170 paumsse sr aoN I S0 HIV I S 0 HOY I I 60 H00 T 60 HvO T 608491 60 HrC L LO HLV I LO H8V I 90 H6C T 90 H8C T 90 H9C T 90 HSC T I S0 HIV I 0 H6 I I 60 HvO T 60 HOT T 60 HO0CL 60 H6CL LO H8V I LO H8V I 1 I I 60 MIO T 60 HS0 T 60 HOC L 60 H8CL LO H8V I 0 48771 LO H8V I 90 H8C T 90 HSC T 90 HSC T 90 HSC T SO HTL I SO HTL I S0 HTO9 I S0 HTO9 I 804666 80459 6 60 H8CL 60 H6C L LO HS8V I SO0 HYTL TI SO HYTL TI S0 HYTO9 I S0 HYTO9 I 80 6 6 808869 6 60814261 60 906 1 LO HSY I LO HSY TI 90 HYvC T 90 HSC T 184 559176 uopu r 0 1 0 I 0 9 1 0 9 I 012 OLC 80 H6t 6 012 80 HS9 6 OLT 012 OLT Id 19W39 Ju uro A 60 H8CL 60 H6C L LO HS8Y I LO HS8Y I 90 HSC I 90 HSC I ueuuoJN UOLIA juaunnqy UOLIA uon opedg Ienu o 5 25 ADAPT 0L CT 18 01 Or TI vr OI 79 8 606 45 8 5 OLS 012 0 SET OLC 4 uon nnsuoo V
200. s are not included The reference temperature for all elements is taken as the ambient temperature see the SET command on the day the element was installed L 11 12 inc T ttop tbot Where 11 Frame element number of first element in a series of elements with identical temperatures ADPT315 7 X FRAME GLOBAL ELEMENT COORDINATES REPRESENTATION OF PRESSURE LOADING ON ELEMENT FIGURE 3 5 9 3 34 INPUT GENERATION Chapter 3 12 Element number of last element in the series inc Element number increment ttop Temperature at top fiber of cross section and tbot Temperature at bottom fiber of cross section This sequence of lines must be terminated by a blank line MESH COMPLETE Syntax Explanation MESH COMPLETE The MESH COMPLETE command has no arguments It signals the program that the mesh input phase of the analysis is complete No mesh input commands are allowed after this command has been interpreted MESH INPUT Syntax Explanation MESH INPUT To be followed by mesh input subcommands lines The MESH INPUT command has no arguments of its own but is followed by a series of mesh input subcommands which specify the node coordinates material and section properties and frame and tendon element geometries for the plane frame structure nodes frame elements tendons and travelers whi
201. s from a maximum of 29 feet at midspan and the abutments to a minimum of 24 feet at the piers All other cross section dimensions are constant over the full length of the bridge The details of the dimensions of the bridge may be found by examination of the input listing for the analysis given in Section 5 5 Four cantilever prestressing tendons located in the top slab are anchored at the end of each girder segment during the construction phase Figure 5 2 2 b This results in a final total of 64 tendons in the top slab over the piers dropping off uniformly toward center span Figure 5 2 2 c Each cantilever tendon consists of 21 1 2 inch diameter strands and is stressed from both ends Eight continuity prestressing tendons extending over the full length of the bridge with a draped profile in the webs are stressed after the bridge is made continuous with mid span closures Figure 5 2 2 d The center span continuity tendons are stressed from both ends at coupler anchorages over the piers and are then coupled to the side span continuity tendons which are stressed from the abutment end only Each continuity tendon consists of 21 1 2 inch diameter strands The continuity tendon between the abutment and the coupler over the first pier is modeled as one tendon see T17 Figure 5 6 3 The 5 4 ADAPT EXAMPLES VERIFICATION Chapter 5 continuation of the continuity tendon from the coupler to the centerline of center span is modeled as a second
202. s of the completed structure without regard to its construction scheme becomes irrelevant Consider classical case of the span by span construction of a two span bride made continuous over the common support Fig 1 1 2 4 At completion of the bridge the selfweight moment at interior support is primarily governed by the method of construction The distribution follows that of the preconstruction simply supported girders The moment due to live loading however is distributed following the structural system of a two span continuous girder Fig 1 1 2 4 d The bridge undergoes significant changes in its load carrying structural system during its erection Spliced precast prestressed girder bridges are generally assembled with interm supports As simply supported members they carry their self weight When spliced they take the load of freshly placed topping before the composite action sets in Fig 1 1 2 5 Another example is the incrementally launched bridge Fig 1 1 2 6 where each section of the bridge will be subject to both the negative moment associated with the support and the positive moment associated with the midspan location Geometry control during the construction is a central consideration in achiev ing the design dictated profile of the completed bridge Consider the balanced cantilever shown in Fig 1 1 2 7a If built with no consideration to geometry control the finished structure is likely to have a deflected profile marked A H
203. s or the distributors in the accuracy or the reliability of the program The user must clearly understand the basic assumptions of the program and must independently verify the results produced by the software PRINCIPAL STEPS IN DESIGN ANALYSIS OF SEGMENTAL BRIDGES AND FRAMES The common steps in the analysis and design of segmentally constructed bridges during the construction phase and when complete are 141 Construction Phase The objective during the construction phase is A To carry self weight and construction loads with stresses in concrete limited to permissible construction phase values B To sustain a code prescribed factor of safety against overload through adequate strength reserve C 1 To predict the deflection of the structure during each phase of construction and 11 to ADAPT OVERVIEW Chapter 1 1 4 2 adjust the formwork for construction of each new segment such as to control the projected profile of the bridge The necessary adjustments to the vertical align ment of the frame during the construction is reffered to as camber or adjustment The stress and strength calculations are in many cases straightforward since the frame under construction may be statically determinate Free cantilever bridges are good examples of this category Prior to attachment of the cantilever tips approaching one another from opposite piers the structure is determinate The deflection and camber computations are not alw
204. s sample input for a simple non prestressed cantilever with uniform rectangular cross section subject to a concentrated loading at its tip For the purposes of illustration the weight of the cantilever is specified as zero Hence the actions mo ments and shears and the deformations will be due to the concentrated load only The cantilever is cast at day zero loaded at day 100 at which time its moments and deformations are calculated Without changing the loading two other solutions are obtained one at 1000 days and the other at 10 000 days Since the loading is not changed the actions will be the same for the different ages but the deformations will increase The change in deformation is triggered by the non zero creep and shrink age Sh coefficients entered under CONCRETE PARAMETERS command Cantilever selfweight w is not included The output of this example is given in Appendix A ADAPT INPUT GENERATION Chapter 3 3 3 2 JInput File ADAPT BRIDGE INCREMENTAL ABI SOFTWARE MANUAL EXAMPLE name of this file CANT MNL units are in lb in START TITLE N 2 CANT MNL CANTILEVER BEAM EXAMPLE FOUR ELEMENTS FIXED AT LEFT UNITS lb in UNITS U USA CONCRETE PARAMETERS N 1 1 MESH INPUT NODES N 5 1 0 0 5 160 0 G 1 5 CONCRETE PROPERTIES N 1 1 Fpc 5000 Cr 3 5 5 0 0005 W 0 0
205. same whether the creep strains are measured in a laboratory or computed using some formula for their estimation such as those discussed in Chapter B 2 The test data required for the concrete are the values of total creep strain under unit stress J t t for a number of loading ages t and observation times t Then the following procedure is followed in order to make a best fit approximation of the test data with the degenerate kernel Equation B 3 3 m and 1 1 m are chosen on a trial basis A particular age is chosen Various times t J 1 2 n are chosen such that tj gt Values of J t t5 are found at j 1 2 n points The following system of equations 15 set up pode cS dm B 21 ADAPT ABI ti t0 T1 2 Lac tn 10 T 1 CONCRETE MODELING Appendix B 15 m e C 50 J ti T0 e Od x ee a lat 1 e CIT Uf e mM iG or in condensed form 1 ali Plx gt m B 3 14 The method of least squares is applied to solve the overdeterminate system of equations for the values of a n blu Solution of Equation B 3 14 for the unknown vector a gives the classical least squares solution alui ATA Tags Choose a different m and and go through steps 2 through 6 for a new a Optimum m and I s are chosen based on the following criteria a Least square
206. sed to specify the node number order used for numbering the nodal displacement degrees of freedom of the structure Skillful use of this command can reduce the profile of the stiffness matrix and increase the program s efficiency in solving the equilib rium equations If this command is not used degrees of freedom will be numbered in node numerical order 1 The SEQUENCE command must be placed after the NODES command and before MESH command Data lines must be provided to generate a list of node numbers in the order in which their degrees of freedom are to be numbered Each node number must appear not more than once in this list Any nodes which are omitted from this list will be numbered in numerical order after all other nodes This sequence of lines must be terminated by a blank line Example SEQUENCE G 5 9 2 G 1 4 The above example is interpretated as 5 7 9 1 2 3 4 3 48 INPUT GENERATION Chapter 3 SET Syntax Explanation SET Days T G gx gy C A Tte where Day Current date days 0 T Current temperature Consistent with input units 70 if American else 20 C gx X direction gravity load multiplier fraction 0 gy Y direction gravity load multiplier fraction 1 E Stress change convergence tolerance 1 psi 0 007 Mpa 0 07 Kg cm A Convergence acceleration factor 0 70 and It Maximum iterations per
207. sition having a computed displacement equal to d4 4 This is the displacement of node 4 at stage 4 Hence the camber for this node 18 Camber 44 d44 In regards to the initial position of node 4 the following consideration applies Refer to Figure D 1 2 stage 2 5 It is assumed that the form traveler is positioned as an extension of segment 2 ready to receive the new segment 3 The form traveler shown in the figure with a straight broken line has the same slope at node 3 as segment 2 Hence the initial position of node 4 on the form and prior to placement of concrete is d4i d32 65 713 Where dy displacement of node 3 at stage 2 This displacement already includes the effects from the weight of the form traveler 0 rotation of node 3 at stage 2 Once concrete is placed the form traveler would deflect Point A stage 2 5 will move below its initial position by an amount controlled by the stiffness of the form traveler Once D 4 ADAPT ABI BACKGROUND TO CAMBER COMPUTATION D D 2 concrete is set and post tensioning is applied segment 3 lifts off the formwork Point 4 assumes a new position Hence the final position of point 4 depends largely on the stiffness of the form traveler deflection of the forms and the traveler truss under selfweight of concrete and the amount and time of prestressing Once segment 3 is stripped the form traveler is moved and positioned to cast segment 4 In s
208. steel type number n must be less than or equal to the total number of mild steel types input on the MILD STEEL PROPERTIES command line Mild steel types may be supplied in any order however each mild steel type must be specified once and only once Mild reinforcing steel is considered as a linear elastic material uniformly distributed over the entire element cross section The area reinforcement ratio Steel area Total area defines the total amount of steel used A table of mild steel properties is printed in the output Mild steel can also be specified by its position and cross sectional area in an element In this case mild steel is defined as a prestressing tendons with zero initial stress Obviously for mild steel the tendon properties shall be adjusted to reflect that of non prestressed reinforcement MOVE N D n 1 n n where N Traveler number D Destination of traveler is the location where the traveler is being installed The traveler s position Is described by the node numbers of the structure frame Number of nodes entered herein must equal to the number of nodes specified for each traveler in TRAVELER com mand n Destination nodes for the new traveler location and n Number of nodes in traveler The MOVE command is used to install move and remove traveling formwork The traveler description must have been input under the TRAVELER subcommand of t
209. structure traveling formwork may be installed moved or removed from the structure and nodal boundary conditions may be changed This permits the analysis of struc tures built with a variety of segmental erection schemes including cantilever construction Fig 2 7 1 span by span construction Fig 2 7 2 incrementally launched construction and pre cast girder cast in place deck construction Figs 2 7 3 and 2 7 4 illustrate examples of other incremental construction techniques in use KOKORO OK KOKORO OK 27151311 21418138 FORM TRAVELER ADPT357 DWG BALANCED CANTILEVER CONSTRUCTION USING CAST IN PLACE AND GANTRY FIGURE 2 7 1 2 21 ADAPT PROGRAM DESCRIPTION Chapter 2 For cantilever and span by span construction schemes the global X Y coordinate system can be considered fixed in space The construction operations described below can be applied directly and the structure can be built in the computer following the same operations used in the actual construction For incrementally launched construction schemes the global X Y coordinate system should be considered as a reference system which moves with the girder Then to model the launching operations the supports are moved along the girder by restraining and releasing nodal bound ary conditions Since construction operations are usually considered as instantaneous and not gradual a zero length time step is required when a construction ope
210. sure DISTRABUTION OF CANTILEVER TENDONS BRIDGE EXAMPLE TENDON LAYOUT CONT D FIGURE 5 2 2 continued EXAMPLES VERIFICATION Chapter 5 D 2 3 o d jv 100 12 100 f 9037 9027 d PROFILE FOR CONTINUITY TENDONS 8 TYPIGAL PROFILES FOR LOGAL TENDONS 2 tendons segment f DISTRABUTION OF LOCAL TENDONS BRIDGE EXAMPLE TENDON LAYOUT CONT D continued FIGURE 5 2 2 ADAPT EXAMPLES VERIFICATION Chapter 5 5 3 ANALYTICAL MODEL analytical model for the complete time dependent analysis with the software Figure 5 3 1 is of a symmetrical half of the structure includes the pier and girder and consists of 43 nodes 42 frame elements and 30 prestressing tendons Units used in the analysis are inches and pounds The analytical model selected is identical to Ketchum Scordelis 1986 to afford comparison The model as generated in the computer is shown in Figure 5 6 1 and 5 6 2 For the ABI analysis a slave element between the pier top and the pier table centroid is recommended However none is used herein to keep the two models similar The nodes Figure 5 3 1 a are located at segment joints along the centroidal axis of the box girder Additional nodes are used in the 60 foot cast in place girder length at the abutment and near the pier in order to accurately model the prestressing The nodes are numbered for ease of node and element generation without regard for st
211. tem of an element is from its node I to its node J Fig 3 5 7 Node I is the node entered first in the input data under the ELEMENTS command The top and bottom fibers of an element are defined by the orientation of its local coordinate system as shown in Fig 3 5 7 More than frame element be generated with different Off subcommands at an analysis node This will result in elements to be located at different physical locations with respect to the reference nodes Fig 3 5 6 Elements with different cross sections at their ends I and J are idealized as a prismatic uniform section The idealization is for mid length of the element and it is obtained through linear interpolation of values entered for the ends I and J The idealized section is used for stiffness and time dependent computations However at completion of the computation the actions at nodes I and J are applied to the actual section properties entered for I and J to determine fiber stresses in concrete Fig 3 5 8 INPUT GENERATION Chapter 3 ABI 1025 ELEMENT S NATURAL NODE X GLOBAL AXIS n OJ Jx Jy NOTE ly Jx AND Jy HAVE NEGATIVE VALUES ILLUSTRATION OF OFFSET AT ELEMENT NODES FIGURE 3 5 5 INPUT GENERATION Chapter 3 ABI 1022 CENTROIDAL AXIS OFFSET y ANALYSIS NODES a OFFSET FOR SELECTED NODES NATURAL NODES b
212. the numerical order given in the output overview regardless of the sequence of data entry and solution path Several features are used to enhance readability and compress the solution If an item is not present such as springs the associated data block is automatically deleted If loading is removed from a node or at nodes where there are no loading no printout is made Printout is limited to items which exit for the stage at which printout is requested The exception is for the solution items where computed zero values of stresses displacements and actions are printed A maximum of 80 columns are used for output organization This allows printout on letter size paper An optional pagination command paginates the output to the user specified number of lines per page with each page numbered and bearing the identification of the problem A 1 1 Output Overview The computer output starts with the following blocks A user identification block B software identification block C current data identification A 3 ADAPT ABI D INPUT OUTPUT EXAMPLES date and time of data execution The preceding information is followed by data blocks listed below 1 PROBLEM TITLE 2 UNITS 3 MATERIALS 3 1 CONCRE E PROPERTI ES 3 2 MILD 5 EL PROPERTI ES 3 93 PRESTR ESSING PROP ECTION GEOMET RIES RAME GEOMETRY
213. the second and third supports The prismatic cross section is a single cell box with cantilevered top slab Six post tensioned prestressing tendons extending the full length of the bridge are draped in each web The structural model consists of 33 nodes 32 frame elements and one prestressing tendon The piers and girder are erected in one step on day 28 from concrete cast on day 0 After the initial analysis for dead load and prestressing the time dependent structural behavior of the bridge is traced over a 10000 day 27 year period 3 7 ADAPT INPUT GENERATION Chapter 3 3 4 2 Input File ADAPT BRIDGE INCREMENTAL ABI SOFTWARE MANUAL EXAMPLES H name of this file EX1 MNL units are lb in START EX1 MNL TITLI GI N 3 EX1 MNL CONTINUOUS PRESTRESSED BRIDGE EXAMPLE SINGLE STEP CONSTRUCTION THEN 27 YEAR ANALYSIS ALL UNITS ARE POUNDS AND INCHES UNITS U USA CONCRETE PARAMETERS N 1 1 M ACI MESH INPUT NODES N 33 1 0 Y 870 59 11 X 18000 Y 870 59 G 1 11 21 4200 870 59 G 11 21 1 31 6000 870 59 G 21 31 32 1800 0 33 4200 0 CONCRETE 5 N 1 1 Fpc 5000 Cr 3 5 Sh 0 0005 W 155 1728 Lt MILD STEEL PROPERTIES N 1 1 Es 29000000 0 02 SECTION PROPERTIES N 2 1 14 73 9 540 36 204 2 D 96 B 180 ELEMENTS 32 FRAME N 32 325552
214. the strain or stress distribution within the element The x and y coordinates for tracking strains and stresses are located at the y extreme fibers of the cross section and at the x extreme ends of the element Figure 4 2 1 y FIBER NODE 5 NODE J AXS X 2 9 4 BOTTOM FIBER FRAME ELEMENT STRAIN AND STRESS POINTS ADPT316 DWG FIGURE 4 2 1 ADAPT PROGRAM BACKGROUND Chapter 4 4 3 The linear variation of stresses and strains within the element simplifies the integrations required in the computation of the element characteristic matrices integrations over the volume of the element are performed exactly eliminating the need for numerical integration for stiffness and load terms and reducing most such integrations to simple matrix transformations A simple matrix transformation from stresses to stress resultants is also performed so that traditional element end stress resultants can be output in addition to the stresses and strains at the integration points In the following these integration and transformation matrices are derived and discussed in detail MATERIAL CONSTITUTIVE RELATIONSHIPS 4 3 1 General Assumptions Each frame element consists of parallel concrete and mild steel components The interaction between these components is handled on the structure level by enforcing compatibility at the nodes and therefore within the elements Thus the constitutive relationships
215. tion displacements CHANGE COMPLETE Syntax Explanation CHANGE COMPLETE The cHANGE COMPLETE command has no arguments It is the closing compan ion to CHANGE STRUCTURE command It signals the program that the interpre tation of CHANGE STRUCTURE commands should stop The effects of the changes on the displacements and internal stresses in the structure are found by using the SOLVE command CHANGE STRUCTURE Syntax Explanation CHANGE STRUCTURE The cHANGE STRUCTURE command has no arguments of its own but is fol lowed by a series of construction operation subcommands which specify the current boundary conditions the installation and removal of frame elements and prestressing tendons and the movement of travelers in the plane frame structure The structure to be analyzed is completely defined by the cumulative effects of CHANGE STRUCTURE commands 3 12 INPUT GENERATION Chapter 3 The construction operation includes one or more subcommands nested be tween the two commands CHANGE STRUCTURE and CHANGE COMPLETE CHANGE STRUCTURE RESTRAINTS to change nodal boundary conditions BUILD to install frame elements REMOVE to remove frame elements STRESS to stress or to restress prestressing tendons DE STRESS to remove prestressing tendons OVE to move traveling formwork CH
216. tion i and uncorrected creep strain estimate for iteration i This scheme reliably accelerates convergence in cases where the computed solution oscillates around the final solution It will slow convergence when the solution converges monotonically however in such cases convergence is very fast and the impact of the slowed convergence on total solution time is very small An acceleration factor of C 0 is equivalent to no acceleration The value C 0 71 was used in the numerical examples discussed in Chapter 5 and is the default value for the program The shrinkage strain increment es is a function of the age of the concrete t and the ultimate shrinkage strain It may vary linearly over the y depth of each element and is constant over the x length of the element It may be expressed as e t 1 4 3 5 4 10 4 3 3 PROGRAM BACKGROUND Chapter 4 The aging strain increment is a fictitious strain used to take into account the increase in elastic modulus E t over the time step During the time step dt the elastic modulus changes from E t to E t In the absence of creep shrinkage and a load increment the total stresses o and strains remain constant Therefore is introduced as an increment in the pseudo inelastic strain so that the constitutive relationship still applies 5 1 1 I E t 4 3 6 temperature strain increment de
217. tire cross section The frame element consists of parallel concrete and mild steel components for modeling the typical composite con crete and steel Concrete and steel instantaneous stresses are limited to linear elasticity Since cracking of concrete is not accounted for solutions which exceed the tensile limit of concrete involve some approximation in deformation Output The output of the analysis consists of Mirror image of input data Geometry and material properties generated by the program Nodal actions moments shears and axial loading Nodal displacements translation and rotation Reactions at supports Stresses in the elements Forces in pre stressing and prestress losses Prestressing moments primary moments and hyperstatic secondary Camber Gy at Sa ba The volume and detail of printout is controlled by the user when generating input data Solution A Node operations Nodal degrees of freedom are included in the equilibrium equations only when the node is attached to at least one currently installed frame element spring or traveler element When no frame spring or traveler elements are attached to a node its degrees of freedom are neglected Loads and displacements may be applied only to nodes of the currently installed frame elements Loads which are applied between the nodes are covered by the program to their equivalents at the nodes This is an important consideration when removing e
218. trained degrees of freedom are summed by the program from external nodal load and element internal resisting force components If the boundary condition is subsequently changed to unrestrained the reactions are automatically applied as part of the loading increment on the structure Nodal loads may be applied to a restrained degree of freedom but these loads are resisted by the reactions and do not influence the stresses in the structure Externally applied nodal displacements may be applied to any restrained degrees of freedom A restrained to zero degree of freedom is a special case of the restrained case discussed above The only difference between the two is that in the restrained to zero case an external displacement is applied in the first solution step after the specification is made so that the total displacement in the degree of freedom is zero Rotational and extensional spring supports are simulated through spring elements PROGRAM DESCRIPTION Chapter 2 CENTROIDAL AXIS FRAME ELEMENT a FRAME WITH GRADUAL CHANGE IN CR0SS SECTION b FRAME WITH ABRUPT CHANGE IN IN CR0SS SECTION e ex LI lt FRAME ELEMENT c MODELING OF ABRUPT CHANGE IN CROSS SECTION WITH OFFSET MODELING OF CHANGE IN GEOMETRY ALONG FRAME LINE FIGURE 2 2 1 PROGRAM DESCRIPTION Chapter 2 ADPT300 DWG YA P 7 CENTROID SYMMETRY AX
219. ubstituting Equation B 3 10 into Equation B 3 6b and taking y t UI Equation B 3 5 and Equation B 3 6a may be rewritten resulting in the following recursive relationship for evaluation of the creep strain increment over the time d gt 1 eri 3 11 gt 23 t eri at B 3 11b gt 0 B 3 11c where g are called the hidden state variables and are updated during each time step for re use in the next time step This relationship for evaluating the creep strain increment over the time step is equivalent to the relationship used by Kabir 1976 although its derivation 15 different Linear stress and constant material parameters Assuming 0 and do t dy to be constant over the time step from t to tj and setting do t dy the integration of Equation B 3 8 then yields exactly for uniaxial stress 841 g t sk a t B 3 12 1 e i 6y B 3 13 By substituting Equation B 3 12 into Equation B 3 6b and taking y t Equation B 3 5 and Equation B 3 6a may be rewritten resulting in the following recursive relationship for evaluation of the creep strain increment over the time step R y 9 061 e amp ri 3 14 i 1 b L l e amp Tij 8t B 3 14c gto O B 3 14e Because the creep strain increment over the time step is dependent on the stress change over the time step in Equation B 3 14a this relationship ADAP
220. ucted portion of the bridge adjacent to the position of new construction The weight of the traveler and the new piece to be added is reacted by the existing portion of the bridge A simplified traveler extending over one segment is shown in Fig 2 1 3 Unlike a gantry Fig 2 7 1 a traveler is commonly short Fig 2 6 1 illustrates the idealization of a traveler which extends over three segments Part of the figure shows the traveler positioned for receiving the weight of a new segment Part b of the figure shows the traveler elements Note that in this example the traveler is made up of three elements When in position the traveler is locked into the bridge frame elements at nodes I J and K shown in the figure ADAPT PROGRAM DESCRIPTION Chapter 2 INSTALLED FRAME SEGMENT TO BE ELEMENTS dicun in FRAME NODE INSTALLED SEGMENTS TRAVELER POSITION FOR CASTING NEW SEGMENT e x ce e 0 TRAVELER FRAME STRUCTURE TRAVELER MODELING FIGURE 2 6 1 In the solution travelers are installed at a particular location by including the contributions of their current stiffness matrices dead loads and internal stresses in subsequent global equilib rium equation assemblies Travelers are removed by neglecting the contributions of their stiffness dead load and internal stresses in subsequent global equilibrium equation assem blies Travelers are automatically moved by the program by first rem
221. ummary the final deflection of the construction and the camber calculation are very sensitive to the stiffness details of the form traveler prestressing and the construction sequence The ADAPT ABI allows for these effects in its deflection and camber calculations The outcome of the computations however would be as accurate as the input data justifies NUMERICAL EXAMPLE For illustration purposes a cantilever with dimensions given in the input data presented herein is selected For simplicity and without compromising the concept of computations neither prestressing nor a traveler is included in the example The omission of form traveler and prestressing would require that each segment be several days old at time of installation refer to input data for details The construction ofthe cantilever is shown in Figure D 1 2 The time sequence for installation of segments is Stage 1 Day 10 Stage 2 Day 25 Stage 3 Day 40 Stage 4 Day 60 ADAPT ABI BACKGROUND TO CAMBER COMPUTATION Appendix D DEFLECTION AN INGREMENTALLY CONSTRUCTED CANTILEVER FIGURE D 1 2 D 6 ADAPT ABI BACKGROUND TO CAMBER COMPUTATION Appendix D The solution for the displacement of the nodes at each stage and the camber are reproduced from the ADAPT ABI output in the following STAGE 1 NODAL TOTAL DISPLACEMENTS NO
222. wise the node is undefined For the analysis of either immediate response moving live load or long term effects of completed frames it is not necessary to go through the construction steps For com pleted structures the entire frame is installed in one step and analyzed accordingly PROGRAM DESCRIPTION Chapter 2 c e e lt GLOBAL COORDINATE SYSTEM TENDON b PROTOTYPE TENDON GEOMETRY FRAME NODE TENDON SEGMENT RIGID LUN POINT NM ELEMENT c DISCRETIZED TENDON STRUCTURAL MODELING FIGURE 2 1 1 ADAPT PROGRAM DESCRIPTION Chapter 2 CD e 2 1 2 CENTROIDAL AXIS ELEVATION FRAME ELEMENT LOCAL COORDINATES POSITIVE DIRECTIONS OF FRAME ACTIONS FIGURE 2 1 2 Module ABI Gen of the programs allows specification of loading at any point on the structure Further it has the capability to obtain patterned solutions skipping of live loading in order to obtain the maximum value of an action at any points together with its associated other actions such as maximum moment with associated shear and axial loading Principal Assumptions The frame of the structure is in one plane As a result all sections are implicitly as sumed to be symmetrical with respect to the plane of the frame all loads are assumed to be applied in the plane of the frame Torsional effects if any do not enter the compu tations T
223. ype bridge selected to illustrate details of input generation modeling and application of the software to a practical problem Also since the first example is adapted from the available literature it provides a good basis for comparison of ABI solutions to other software The second example is a simple prestressed structure devised to illustrate the application of the software in different systems of units American SI and MKS It demonstrates the correlation of the solution among them Numerous examples illustrating the many facets of the software are given in the Examples Manual which is compiled in a different volume CANTILEVER CONSTRUCTION BOX GIRDER BRIDGE EXAMPLE This example is an adaptation from Ketchum Scordelis 1986 It is presented with two objectives in mind First it demonstrates the capabilities of ADAPT ABI for analysis of a realistic multi span prestressed concrete box girder bridge using cantilever construction method cast in place segments traveling formwork and conventionally erected girder segments near the abutments Second it serves as a basis for comparison of results obtained from ABI with two other software from which analysis solutions for this example are available Scordelis 1993 The structural behavior of the bridge under dead load construction loads and prestressing is traced through the construction phase and over a 27 year service period thereafter The input data for the computer analysis is

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