STRUCTURAL CONCRETE SOFTWARE ADAPT-ABI. Examples

Transcription

1 STRUCTURAL CONCRETE SOFTWARE ADAPT-ABI Examples 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 support@adaptsoft.com ADAPT Corporation, Redwood City, California, USA, Tel: +1 (650) Fax: +1 (650) ADAPT International Pvt. Ltd, Kolkata, India Tel: Fax:

2 ADAPT EXAMPLES LIST OF CONTENTS 1. INTRODUCTION... EX MODELING HINTS... EX SUPPRESS ALL TIME-DEPENDENT RESPONSE...EX AGING OF CONCRETE...EX SPECIFIED MODULUS OF ELASTICITY...EX SHRINKAGE AND CREEP...EX RELAXATION IN PRESTRESSING...EX CONSTANT PRESTRESSING FORCE...EX DISREGARD CONTRIBUTION OF NONPRESTRESSED REINFORCEMENT...EX AGE OF CONCRETE...EX Casting Day...EX Stressing Date...EX LEGEND FOR SUPPORT CONDITIONS...EX EXAMPLES... EX ABI-EX1, ABI-EX1M, ABI-EXAS, ABI-EX1S, ABI-EXAU, ABI- EXAM, SIMPLY SUPPORTED BEAM...EX ABI-EX2, APPLICATION OF BOUNDARY CONDITIONS...EX ABI-EX3, SIMPLE FRAMES...EX ABI-EX4, SIMPLE PRESTRESSING...EX ABI-EX5, TRUSS STRUCTURES...EX ABI-EX6, INTERNAL HINGE WITHOUT OFFSET...EX ABI-EX8, CREEP COMPUTATIONS USING ACI AND CEB...EX ABI-EX9, TENDON GEOMETRY SPECIFICATION...EX ABI-EX10, TENDON SPECIFICATION REGULAR TENDONS...EX ABI-EX14, EXTERNAL TENDONS...EX ABI-EX16, MODELING OF COMPOSITE ACTION...EX ABI-EX18, STRESS RELAXATION...EX ABI-EX19, TRAVELER DEFLECTION...EX ABI-EX25, INCREMENTAL CONSTRUCTION ANALYSIS...EX ABI-EX26, PARKING STRUCTURE BEAM...EX ABI-EX27, TIME KEEPING AND AGING...EX ABI-EX29 CREEP AND SHIRNKAGE COMPUTATIONS USING LABORATORY TIME DEPENDENT MODELS...EX ABI-EX31, BRIDGE DECK WITH TWO DIFFERENT SECTIONS...EX ABI-EX32, CROSS SECTION WITH ABRUPT CHANGE IN GEOMETRY (USING OFFSET FEATURE)...EX ABI-EX33, CROSS SECTION WITH ABRUPT CHANGE IN GEOMETRY (USING MASTER AND SLAVE FEATURE)...EX33-1 i

3 ADAPT EXAMPLES 3.21 ABI-EX35, POST-TENSIONING IN A CROSS SECTION WITH ABRUPT CHANGE IN GEOMETRY (USING OFFSET FEATURE)...EX ABI-EX36 BASICS OF CABLE STAY MODELING...EX ABI-EX38, POST-TENSIONED BEAM WITH STEP IN THE MIDDLE...EX ABI-EX40, VARIABLE CROSS-SECTION BEAM WITH PARABOLIC TENDON...EX ABI-EX43 CAMBER SIGNIFICANCE AND ITS IMPLEMENTATION IN CONSTRUCTION...EX ABI-EX45 SPLICED GIRDER CONSTRUCTION AND HYPER- STATIC ACTIONS DUE TO PT IN INCREMENTAL CONSTRUCTION...EX ABI-EX50, SPAN-BY-SPAN BRIDGE CONSTRUCTION...EX ABI-EX51, STRUCTURAL MODELING OF BRIDGE SUPPORTS...EX51-1 APPENDIX A. EVENT SPECIFICATION... EXA-1 A.1 EVENT...EXA-1 A.2 RESPONSE BETWEEN EVENTS...EXA-1 A.3 SPECIFICATION OF EVENTS...EXA-4 A.4 REMARK ON CASTING DATE AND INITIATION OF TIME DEPENDENT EFFECTS...EXA-5 A.5 ABI-EXA, AXIALLY LOADED BEAM SUBJECTED TO CREEP...EXA-9 A.5.1 Problem...EXA-9 A.5.2 Primary objective...exa-9 A.5.3 Input Data... EXA-11 ii

4 ADAPT ABI Examples 1. INTRODUCTION This compilation of examples is a supplement to ABI manual and its software. It is intended to illustrate the basics of modeling, input generation, scope of application, and interpretation of results. For each category, the examples are organized with increased degree of complexity. Each example includes a statement of purpose, definition of the example structure with features of its discretization, other particulars of modeling, comparison with theoretical solutions - if applicable, and a listing of its ABI input data. The emphasis of each example is on one or more of the stated objective items. Some of the examples might not correspond to a realistic structure, since the examples are generally over simplified to crystallize specific issues. Examples which are taken from the prototype analysis of actual bridges and frames do not suffer from over simplification. These examples are clearly identified. 2. MODELING HINTS ABI is a general time-dependent software. Depending on the objective of the modeling, it may be desirable to suppress some of the features of ABI, such as aging of concrete, or shrinkage. The following hints describe briefly the more important features which can be suppressed, or invoked. A detailed account of each feature is given in the main ABI manual. 2.1 SUPPRESS ALL TIME-DEPENDENT RESPONSE Time-dependent response of a structure reveals itself only with lapse of time. If the time interval between two events is specified as zero, The solution obtained excludes all timedependent response. Time is specified through the Day command. Example: SOLVE Day=100 ;... implement changes; add loading SOLVE Day=100 Since the difference between the two time intervals of the two successive Solve commands is zero, the solution obtained from the second SOLVE command is time-independent. However, EX0-1

5 ADAPT ABI Examples it uses a concrete modulus of elasticity and prestressing stresses which were current at Day= AGING OF CONCRETE For concrete with constant modulus of elasticity and compressive strength for the entire analysis use the following input: CONCRETE PARAMETERS N=1 1 M=ACI a=0 b=1 For additional detail refer to Chapter 3, CONCRETE PARAMETERS command. 2.3 SPECIFIED MODULUS OF ELASTICITY To obtain a solution with a specified modulus of elasticity take the following steps: i. Suppress aging of concrete CONCRETE PARAMETERS N=1 1 M=ACI a=0 b=1 W=? Note that, W, specified here is used for computation of modulus of elasticity given below. It is not used for selfweight computation. ii. Specify a concrete strength, f c, using Fpc which gives the intended modulus of elasticity. CONCRETE PROPERTIES 1 Fpc= The concrete strength is used to compute the concrete s modulus of elasticity using the relationship (B.2.2) from Appendix B of the manual. E = 33W 1.5 [f c] 1/2 For example, in the American system of units for: W f c E = 150/1728 lb/in 3 ; and = 5000 psi = 33*(150)1.5*(5000)1/2 = 4.286x10 6 psi EX0-2

6 ADAPT ABI Examples Observe that the, E, formula does not have consistent units, but for ABI, user must enter consistent units. In SI units: where, E(t) = x10 12 W 1.5 [f c (t)] 1/2 W is in kg/mm 3 [2.4019X10-6 ]; f c (t) is in N/mm 3 ; and E(t) is in N/mm 2. In MKS units where, E(t) = x10 8 W 1.5 [f c (t)] 1/2 W is in kg/cm 3 [2.4019X10-3 ]; f c (t) is in kg/cm 2 ; and E(t) is in kg/mm 2. For MKS, W=2.4x10-3 kg/cm 3, Fpc=350 kg/cm 2, gives E=3.02x10 5 kg/cm SHRINKAGE AND CREEP To suppress creep, specify a zero coefficient for creep, Cr, in CONCRETE PROPERTIES command. Example: CONCRETE PROPERTIES N= Cr=0... To suppress shrinkage, specify a zero coefficient for shrinkage, Sh, in CONCRETE PROPERTIES command. Example: CONCRETE PROPERTIES N= Sh=0... Creep and shrinkage values can be specified independent from the another. EX0-3

7 ADAPT ABI Examples 2.5 RELAXATION IN PRESTRESSING To suppress relaxation in prestressing steel, specify, R=0, in PRESTRESSING STEEL command. Example: PRESTRESSING STEEL N= R= CONSTANT PRESTRESSING FORCE For an analysis with a constant prestressing force along the length of a tendon, specify zero values for the coefficients of friction, m, and, K, in PRESTRESSING STEEL command. Example: PRESTRESSING STEEL N= Meu=0 K=0... If, in addition, relaxation in prestressing is also to be suppressed, specify, R=0, on the same command line. 2.7 DISREGARD CONTRIBUTION OF NONPRESTRESSED REINFORCEMENT In order to suppress the contribution of nonprestressed steel in a member, specify zero percentage for nonprestressed steel of that member. Example: MILD STEEL PROPERTIES N= P= AGE OF CONCRETE The age of concrete at various stages of construction and loading affects the element s response. Each element has its own age. The age of each element is the difference between the current Day, and the casting Day of that element. The response of each element, such as its modulus of elasticity, is traced throughout the computation to the age of that element at the Day of solution. EX0-4

8 ADAPT ABI Examples Casting Day There are several options to specify the casting date of an element. These are described next: A. In FRAME command Example: FRAME N=8 7, 12,13... Day=42... It means that element number 7 is cast on day 42 B. In BUILD command The casting age of an element is overridden, if at the BUILD command used to install that element, a Day is specified Example: Stressing Date BUILD N=7 Day=56 It means that the casting date of this element is on day 56, regardless of prior entries to that effect. Each tendon has a stressing date. The stressing date of a tendon is the current date at the time the tendon is stressed. A tendon is stresses using the STRESS command. To each STRESS command, a current Day is associated. The current day is the last entry of Day on the SET, or SOLVE, command, whichever is more recent. A detailed description of events affecting the age of concrete are given in the Appendix A of this manual. 2.9 LEGEND FOR SUPPORT CONDITIONS In describing the various external support conditions of a structure and the internal connections between the different components the legends shown in Figure are used. Figure shows the legends used for internal units in bridge decks. EX0-5

9 ADAPT ABI Examples FIGURE EX0-6

10 ADAPT ABI Examples FIGURE EX0-7

11 ADAPT ABI Examples FIGURE EX0-8

12 ADAPT ABI Examples FIGURE EX0-9

13 ADAPT ABI Examples FIGURE EX0-10

14 3. EXAMPLES 3.1 ABI-EX1, ABI-EX1M, ABI-EXAS, ABI-EX1S, ABI-EXAU, ABI-EXAM Description SIMPLY SUPPORTED BEAM This first example is selected to be a very simple case - the common simply supported beam, in order to illustrate several of the basic components of the software, such as discretization of a structure into elements, data generation, execution and interpretation of the results. Six input data are given, two for each of three systems of units: US, SI, and MKS. For each case an identical problem is coded once for a single concentrated loading and once for selfweight. When executed, all the data given yield equivalent solutions in their respective units. In the preparation of data, observe the units used for selfweight (w). These are: ABI-EX1 ABI-EX1S ABI-EX1M ABI-EXAU ABI-EXAS ABI-EXAM concentrated load; American units concentrated load; SI units concentrated load; MKS units selfweight; American units selfweight; SI units selfweight; MKS units Structure The particulars of the simply supported beam of uniform cross-section are shown in Figure EX1-1. The beam is on a fixed hinge on its left support and on a roller at its right support. The beam is discretized into six elements. The aging of concrete, creep and shrinkage are all suppressed. Other particulars are: Concrete weight 150 lb/ ft 3 ; concrete strength at 28 days 5000 psi. The concrete specification leads to a modulus of elasticity E = 4.286x10 6 psi (refer to Section 2.3) Results The computer output is listed with the results of simple beam theory for deflection and moments at center of the beam. EX1-1

15 TABLE EX1-1 COMPARISON OF THEORETICAL AND SOFTWARE SOLUTIONS FOR CONCENTRATED LOADING Deflection at center (in.) Moment at center (k-in) Full beam ABI 1.654E E+2 model (EX1) Beam theory 1.654E E+2 FIGURE EX1-1 EX1-2

16 3.1.4 Input Data A. ABI-EX1 ;================================================================= ; ADAPT-BRIDGE-INCREMENTAL ABI SOFTWARE MANUAL EXAMPLES ;================================================================= ; name of this file: ABI-EX1 ; units are in lb, in START TITLE N=2 ABI-EX1 SIMPLY SUPPORTED BEAM WITH CONCENTRATED LOADING UNITS U=USA CONCRETE PARAMETERS N=1 1 M=ACI a=0 b=1 W=150/1728 MESH INPUT NODES N=7 1 X=0 Y=0! 7 X=156 Y=0 G=1,7 CONCRETE PROPERTIES N=1 1 Fpc=5000 Cr=0.0 Sh=0.0 SECTION PROPERTIES N=1 1 D=23 B=11 ELEMENTS N=6 FRAME N=6 1,1,2 C=1 X=1 St=1 Day=1 G=1,6,1,1,1 MESH COMPLETE CHANGE STRUCTURE BUILD N=1,6,1 RESTRAINTS 1 R=1,1,0 7 R=0,1,0 CHANGE COMPLETE LOADING N=4 F=0,-10000,0 SOLVE OUTPUT STOP EX1-3

17 B. ABI-EX1m ;================================================================= ; ADAPT-BRIDGE-INCREMENTAL ABI SOFTWARE MANUAL EXAMPLES ;================================================================= ; name of this file: ABI-EX1m ; units are in Kg, cm, Kg/mm^3 START TITLE N=2 ABI-EX1m SIMPLY SUPPORTED BEAM WITH CONCENTRATED LOADING; not included: creep, shrinkage, concrete aging, selfweight UNITS U=MKS ;... note command for UNIT designation CONCRETE PARAMETERS N=1 1 M=ACI a=0 b=1 W= ; W is in Kg/cm^3 MESH INPUT NODES N=7 1 X=0 Y=0! 7 X=396.2 Y=0 G=1,7 CONCRETE PROPERTIES N=1 1 Fpc= Cr=0.0 Sh=0.0 SECTION PROPERTIES N=1 1 D= B= ELEMENTS N=6 FRAME N=6 1,1,2 C=1 X=1 St=1 Day=1 G=1,6,1,1,1 MESH COMPLETE CHANGE STRUCTURE BUILD N=1,6,1 RESTRAINTS 1 R=1,1,0 7 R=0,1,0 CHANGE COMPLETE LOADING N=4 F=0, ,0 SOLVE! OUTPUT STOP EX1-4

18 C. ABI-Exas ;================================================================= ; ADAPT-BRIDGE-INCREMENTAL ABI SOFTWARE MANUAL EXAMPLES ;================================================================= ; name of this file: ABI-EXas ; units are in SI, mm, Newton START TITLE N=2 ABI-EXas SIMPLY SUPPORTED BEAM WITH SELFWEIGHT ONLY not included: creep, shrinkage, concrete aging UNITS U=SI CONCRETE PARAMETERS N=1 1 M=ACI a=0 b=1 W= ; W is in Kg/mm^3 MESH INPUT NODES N=7 1 X=0 Y=0! 7 X=3962 Y=0 G=1,7 CONCRETE PROPERTIES N=1 1 Fpc= Cr=0.0 Sh=0.0 W= ; W is in kg/mm^3 SECTION PROPERTIES N=1 1 D= B= ELEMENTS N=6 FRAME N=6 1,1,2 C=1 X=1 St=1 Day=1 G=1,6,1,1,1 MESH COMPLETE CHANGE STRUCTURE BUILD N=1,6,1 RESTRAINTS 1 R=1,1,0 7 R=0,1,0 CHANGE COMPLETE SOLVE! OUTPUT STOP EX1-5

19 D. ABI-EX1s ;================================================================= ; ADAPT-BRIDGE-INCREMENTAL ABI SOFTWARE MANUAL EXAMPLES ;================================================================= ; name of this file: ABI-EX1s ; units are in SI, mm, Newton START TITLE N=2 ABI-EX1s SIMPLY SUPPORTED BEAM WITH CONCENTRATED LOADING; not included: creep, shrinkage, concrete aging, selfweight UNITS U=SI CONCRETE PARAMETERS N=1 1 M=ACI a=0 b=1 W= ; W is in Kg/mm^3 MESH INPUT NODES N=7 1 X=0 Y=0! 7 X=3962 Y=0 G=1,7 CONCRETE PROPERTIES N=1 1 Fpc= Cr=0.0 Sh=0.0 SECTION PROPERTIES N=1 1 D= B= ELEMENTS N=6 FRAME N=6 1,1,2 C=1 X=1 St=1 Day=1 G=1,6,1,1,1 MESH COMPLETE CHANGE STRUCTURE BUILD N=1,6,1 RESTRAINTS 1 R=1,1,0 7 R=0,1,0 CHANGE COMPLETE LOADING N=4 F=0,-44482,0 SOLVE! OUTPUT STOP EX1-6

20 E. ABI-Exau ;================================================================= ; ADAPT-BRIDGE-INCREMENTAL ABI SOFTWARE MANUAL EXAMPLES ;================================================================= ; name of this file: ABI-EXau ; units are in lb, in START TITLE N=3 ABI-EXau SIMPLY SUPPORTED BEAM Not included: creep, shrinkage, concrete aging Load case : selfweight only UNITS U=USA CONCRETE PARAMETERS N=1 1 M=ACI a=0 b=1 W=150/1728 MESH INPUT NODES N=7 1 X=0 Y=0! 7 X=156 Y=0 G=1,7 CONCRETE PROPERTIES N=1 1 Fpc=5000 Cr=0.0 Sh=0.0 W=150/1728 SECTION PROPERTIES N=1 1 D=23 B=11 ELEMENTS N=6 FRAME N=6 1,1,2 C=1 X=1 St=1 Day=1 G=1,6,1,1,1 MESH COMPLETE CHANGE STRUCTURE BUILD N=1,6,1 RESTRAINTS 1 R=1,1,0 7 R=0,1,0 CHANGE COMPLETE SOLVE! OUTPUT STOP EX1-7

21 F. ABI-Exam ;================================================================= ; ADAPT-BRIDGE-INCREMENTAL ABI SOFTWARE MANUAL EXAMPLES ;================================================================= ; name of this file: ABI-EXam ; units are in Kg, cm, Kg/mm^3 START TITLE N=2 ABI-EXam SIMPLY SUPPORTED BEAM WITH SELFWEIGHT ONLY; not included: creep, shrinkage, concrete aging, selfweight UNITS U=MKS ;... note command for UNIT designation CONCRETE PARAMETERS N=1 1 M=ACI a=0 b=1 W= ; W is in Kg/cm^3 MESH INPUT NODES N=7 1 X=0 Y=0! 7 X=396.2 Y=0 G=1,7 CONCRETE PROPERTIES N=1 1 Fpc= Cr=0.0 Sh=0.0 W= ; W is in Kg/cm^3 SECTION PROPERTIES N=1 1 D= B= ELEMENTS N=6 FRAME N=6 1,1,2 C=1 X=1 St=1 Day=1 G=1,6,1,1,1 MESH COMPLETE CHANGE STRUCTURE BUILD N=1,6,1 RESTRAINTS 1 R=1,1,0 7 R=0,1,0 CHANGE COMPLETE SOLVE! OUTPUT STOP EX1-8

22 3.2 ABI-EX2 APPLICATION OF BOUNDARY CONDITIONS Description This is a variation of example 1. It illustrates a single span beam; fully fixed at the left end; rotationally fixed, but free to displace in the horizontal direction at the right end. The objective is to illustrate the application of boundary conditions through a simple example Structure The particulars of the constrained beam of uniform crosssection are shown in Figure EX2-1. The beam is fixed hinge on its left support and partially fixed as indicated in the figure. The beam is discretized into six elements. The aging of concrete, creep and shrinkage are all suppressed. Other particulars are: Concrete weight 150 lb/ cubic ft; concrete strength at 28 days 5000 psi. The concrete specification leads to a modulus of elasticity E=4.286x10 6 psi (refer to section 2.3) Results The computer output is listed with the results of simple beam theory for deflection and moments at center of the beam. TABLE EX2-1 COMPARISON OF THEORETICAL AND SOFTWARE SOLUTIONS CONCENTRATED LOADING Deflection at center (in.) Moment at center (k-in) Full beam ABI 4.136E E+2 model (EX2) Beam theory 4.136E E+2 EX2-1

23 FIGURE EX2-1 EX2-2

24 3.2.4 Input Data ;================================================================= ; ADAPT-BRIDGE-INCREMENTAL ABI SOFTWARE MANUAL EXAMPLES ;================================================================= ; name of this file: ABI-EX2 START TITLE N=2 ABI-EX2 CLAMPED SINGLE SPAN BEAM WITH CONCENTRATED LOADING UNITS U=USA CONCRETE PARAMETERS N=1 1 M=ACI a=0 b=1 W=150/1728 MESH INPUT NODES N=7 1 X=0 Y=0! 7 X=156 Y=0 G=1,7 CONCRETE PROPERTIES N=1 1 Fpc=5000 Cr=0.0 Sh=0.0 W=0.0 SECTION PROPERTIES N=1 1 D=23 B=11 ELEMENTS N=6 FRAME N=6 1,1,2 C=1 X=1 St=1 Day=1 G=1,6,1,1,1 MESH COMPLETE CHANGE STRUCTURE BUILD N=1,6,1 RESTRAINTS 1 R=1,1,1 7 R=0,1,1 CHANGE COMPLETE LOADING N=4 F=0,-10000,0 SOLVE OUTPUT STOP EX2-3

25 This Page Left Intentionally BLANK EX2-4

26 3.3 ABI-EX3 SIMPLE FRAMES Description The example is for a two story frame under a concentrated load. The objective is to illustrate the modeling and application of the software to simple frames. All timedependent parameters are suppressed Structure The two story frame as shown in the figure has uniform column and beam sections. It is fixed against movement and rotation at its supports. FIGURE EX3-1 EX3-1

27 3.3.3 Input Data ;=========================================================== ; ADAPT-BRIDGE-INCREMENTAL ABI SOFTWARE MANUAL EXAMPLES ;=========================================================== ; name of this file: ABI-EX3 START TITLE N=2 ABI-EX3 TWO STORY FRAME WITH CONCENTRATED LOADING ON UPPER BEAM UNITS U=USA CONCRETE PARAMETERS N=1 1 M=ACI a=0 b=1 W=150/1728 MESH INPUT NODES N=16 1 X=0 Y=0! 5 X=0 Y=240 G=1,5 6 X=384 Y=0! 10 X=384 Y=240 G=6,10 11 X=96 Y=120! 13 X=288 Y=120 G=11,13 14 X=96 Y=240! 16 X=288 Y=240 G=14,16 CONCRETE PROPERTIES N=1 1 Fpc=5000 Cr=0.0 Sh=0.0 SECTION PROPERTIES N=2 1 D=23 B=11 2 D=16 B=14 ELEMENTS N=16 FRAME N=16 1,1,2 C=1 X=2 St=1 Day=1 G=1,4,1,1,1 5,6,7 C=1 X=2 St=1 Day=1 G=5,8,1,1,1 9,3,11 C=1 X=1 St=1 Day=1 12,13,8 C=1 X=1 St=1 Day=1 13,5,14 C=1 X=1 St=1 Day=1 16,16,10 C=1 X=1 St=1 Day=1 10,11,12 C=1 X=1 St=1 Day=1 G=10,11,1,1,1 14,14,15 C=1 X=1 St=1 Day=1 G=14,15,1,1,1 MESH COMPLETE CHANGE STRUCTURE BUILD N=1,16,1 RESTRAINTS 1 R=1,1,1 6 R=1,1,1 CHANGE COMPLETE LOADING N=15 F=0,-10000,0 SOLVE! OUTPUT STOP EX3-2

28 3.4 ABI-EX4 SIMPLE PRESTRESSING Description This is a variation of example 1, with the objective to demonstrate the application of post-tensioning in its simplest form - that is to say, as a constant force at location of tendon. No other action other than the posttensioning is invoked. The solution will show the stresses and deformations due to post-tensioning only. The beam is simply supported at its ends Structure The particulars of the simply supported beam of uniform cross-section are shown in Figure EX4-1. A single strand with an area of in 2 is selected. The strand is stressed to 200 ksi. Since the angular- (mue) and wobble (K) coefficients of friction, as well as the seating loss are all assumed zero. The relaxation in strand force is specified as zero through the parameter. R, in PRESTRESS- ING STEEL COMMAND. The aging of concrete, creep and shrinkage are all suppressed. The beam is discretized into six elements. Other particulars are: Concrete weight 150 lb/cubic ft; concrete strength at 28 days 5000 psi. The concrete specification leads to a modulus of elasticity E=4.286x10 6 psi (refer to section 2.3) Results Since creep, shrinkage, aging of concrete and relaxation in prestressing are all suppressed, the solution is independent of concrete strength, age of concrete and date of stressing. Note that the concrete is cast on Day=1, but stressed at Day=100. In this example, the specified dates do not affect the solution, since the time-dependent parameters are all suppressed. TABLE EX4-1 COMPARISON OF THEORETICAL AND SOFTWARE SOLUTIONS, POST-TENSIONING ONLY Deflection at center (in.) Moment at center (k-in) Full beam ABI 1.752E E+2 model (EX4) Beam theory 1.752E E+2 EX4-1

29 FIGURE EX4-1 EX4-2

30 3.4.4 Input Data ;=================================================================== ; ADAPT-BRIDGE-INCREMENTAL ABI SOFTWARE MANUAL EXAMPLES ;=================================================================== ; name of this file: ABI-EX4 START TITLE N=2 ABI-EX4 SIMPLY SUPPORTED BEAM WITH CONCENTRATED LOADING + TENDON BELOW CENTROID UNITS U=USA CONCRETE PARAMETERS N=1 1 M=ACI a=0 b=1 W=150/1728 MESH INPUT NODES N=7 1 X=0 Y=0! 7 X=156 Y=0 G=1,7 CONCRETE PROPERTIES N=1 1 Fpc=5000 Cr=0.0 Sh=0.0 W=0.0 SECTION PROPERTIES N=1 1 D=23 B=11 ELEMENTS N=6 FRAME N=6 1,1,2 C=1 X=1 St=1 Day=1 G=1,6,1,1,1 PRESTRESSING STEEL N=1 1 Ep= Meu=0.0 K=0.0 Fpu= TENDON GEOMETRY N=1 1 Spans=1 M=1 Area= N=7 G=1,7,1 B=0.0, 0.0 E=156,0.0 R=0.0, 0.50, 0.0 S=-9, -9, -9 MESH COMPLETE SET Day=100 CHANGE STRUCTURE BUILD N=1,6,1 STRESS N=1 StressTo=200E+3 Anchor=0.0 RESTRAINTS 1 R=1,1,0 7 R=0,1,0 CHANGE COMPLETE SOLVE OUTPUT STOP EX4-3

31 This Page Left Intentionally BLANK EX4-4

32 3.5 ABI-EX5 TRUSS STRUCTURES Description ABI can analyze truss systems in the same manner it does frames. A truss member is defined as one which can transfer only axial loading. ABI s truss members can retain the creep, shrinkage, prestressing and aging properties which are normally associated with the frame elements. The time-dependent parameters do not affect the distribution of force among the truss members, but they affect the truss deformation. This example demonstrates how to model a truss system Structure A five-member truss is selected as shown in Figure EX5-1. Creep, shrinkage and aging are suppressed in the example selected. In the general case, however, these can each be assigned their specific values. The critical input for modeling a truss member is to specify a zero value for its moment of inertia. The truss is loaded with P = 100 lb. FIGURE EX5-1 EX5-1

33 3.5.3 Results The following table shows the results of the ABI solution compared with hand calculation. It is noted that the two are in full agreement. TABLE EX5-1 AXIAL FORCE IN TRUSS MEMBERS Member Hand calculation ABI Input Data ;================================================================= ; ADAPT-BRIDGE-INCREMENTAL ABI SOFTWARE MANUAL EXAMPLES ;================================================================= ; name of this file: ABI-EX5 START TITLE N=2 ABI-EX5, SIMPLE DOUBLE HINGED MEMBERS TRUSS WITH 4 NODES UNITS U=USA CONCRETE PARAMETERS N=1 1 M=ACI a=0 b=1 W=150/1728 MESH INPUT NODES N=4 1 X=0.0 Y=0.0 2 X=0.0 Y=100 3 X=100 Y=100 4 X=100 Y=0.0 CONCRETE PROPERTIES N=1 1 Fpc=4000 Cr=0.0 Sh=0.0 SECTION PROPERTIES N=1 1 Area=50 I=0.0 C=1,1 ELEMENTS N=5 FRAME N=5 1,1,4 C=1 X=1 St=1 Day=1 2,1,2 C=1 X=1 St=1 Day=1 3,2,3 C=1 X=1 St=1 Day=1 4,2,4 C=1 X=1 St=1 Day=1 5,3,4 C=1 X=1 St=1 Day=1 MESH COMPLETE EX5-2

34 CHANGE STRUCTURE BUILD N=1,5,1 RESTRAINTS 1 R=1,1,0 4 R=0,1,0 CHANGE COMPLETE LOADING N=2 F=100.0,0.0,0.0 SOLVE OUTPUT STOP EX5-3

35 This Page Left Intentionally BLANK EX5-4

36 3.6 ABI-EX Description INTERNAL HINGE WITHOUT OFFSET The master-slave concept is a powerful tool in modeling special structural analysis boundary conditions. The current example illustrates the use of master-slave modeling technique to introduce an internal hinge within the deck of a propped cantilever configuration Structure The particulars of the propped cantilever beam of uniform cross-section and intermediate hinge are shown in Figure EX6-1(a). The beam is fully fixed at its left support and on a roller at its right support. The beam is discretized into six elements. The aging of concrete, creep and shrinkage are all suppressed Results The computer output is listed. It should be emphasized that the introduction of the internal hinge has made the propped cantilever beam statically determinate. Subsequently, the bending moment diagram in the right segment of the beam must be zero with the concentrated load applied within the left segment. Consequently, it may be also verified that the deflected shape of the right segment is a straight line. EX6-1

37 FIGURE EX6-1(a) FIGURE EX6-1(b) EX6-2

38 FIGURE EX6-1(c) FIGURE EX6-1(d) EX6-3

39 FIGURE EX6-1(e) EX6-4

40 3.6.4 Input Data ;================================================================ ; ADAPT-BRIDGE-INCREMENTAL ABI SOFTWARE MANUAL EXAMPLES ;================================================================ ; Name of this file: ABI-EX6 START TITLE N=2 ABI-EX6 PROPED CANTILEVER BEAM WITH AN INTERNAL HINGE UNDER CONCENTRATED LOADING UNITS U=USA CONCRETE PARAMETERS N=1 1 M=ACI a=0 b=1 W=150/1728 MESH INPUT NODES N=8 1 X=0 Y=0! 5 X=360 Y=0 G=1,5 6 X=360 Y=0! 8 X=504 Y=0 G=6,8 CONCRETE PROPERTIES N=1 1 Fpc=5000 Cr=0.0 Sh=0.0 SECTION PROPERTIES N=1 1 D=23 B=11 ELEMENTS N=6 FRAME N=6 1,1,2 C=1 X=1 St=1 Day=1 G=1,4,1,1,1 5,6,7 C=1 X=1 St=1 Day=1 G=5,6,1,1,1 MESH COMPLETE! SET DAY=28 CHANGE STRUCTURE BUILD N=1,6,1 RESTRAINTS 1 R=1,1,1 8 R=0,1,0 6 R=3,3,0 M=5 ; establish a hinge at node 5/6 CHANGE COMPLETE LOADING N=4 F=0,-10000,0 SOLVE! OUTPUT STOP EX6-5

41 This Page Left Intentionally BLANK EX6-6

42 ABI-EX8 A through E DESCRIPTION CREEP COMPUTATIONS USING ACI This set of examples validates the implementation of the ACI time dependent creep model in ADAPT-ABI and illustrates how the associated hand calculations can be carried out. A rectangular specimen (Fig. EX8-1) is axially loaded at different loading ages. The resulting creep of the specimen due to the applied axial loading is monitored at a number of observation times using ADAPT-ABI. The corresponding total creep strains are hand calculated using ACI relationships as described in ADAPT-ABI manual. The hand calculations are compared with the values obtained from ADAPT-ABI program. The agreement is found to be excellent. STRUCTURE The dimensions and loading of the axially loaded column of uniform cross-section are shown in Figure EX8-1. Other particulars of the specimen are : 28 days concrete strength f c = 30 Mpa; Unit weight W = kg/mm3; Applied compressive loading P = 100 kn; Ultimate creep coefficient for a 7 days loading age Cu=3.53. Five cases A through E are considered. In Cases A through D the specimen is loaded at ages 3, 7, 28, and 50 days. The loading is sustained and the shortening of the specimen is observed on days 14, 28, 100, 200 and 20*365 days. In Case E the specimen is loaded with two concentrated axial compressive forces applied at different ages. The objective of this case is to test the formulation for multiple loading. The first loading is applied on day 7. With the first loading retained, the second loading is applied on day 28. Both loadings are kept on the specimen while its shortening is monitored with lapse of time. Table EX8-1 includes a summary of the test cases. The beam is discretized into one finite element only. The shrinkage of concrete is neglected. RESULTS The creep strain component (excluding the instantaneous elastic strain) is computed using the following ACI code equation normalized for a specimen loaded at age 7 days : EX8-1

43 C(t) (t-τ) 0.6 = (τ/7) * C u 10 + (t-τ) 0.6 where, τ t C u = the age of concrete when the load is applied in days; = the age of concrete at observation time in days; and = Ultimate creep coefficient normalized for loading at age 7. The significance of C u is that it is the ultimate creep strain if the specimen were loaded at age 7 days. Unlike the ACI creep recommendations, the CEB concrete model defines the ultimate creep strain C u for a loading at age 28 days. The discrepancy in the definition of loading age will yield different ultimate creep strains C for u the ACI and the CEB creep recommendations for a concrete specimen exposed to the the same environmental conditions. A concrete specimen loaded at a later age will creep less. This issue is discussed further in the second half of this example (ABI-EX8 F through J). The total strain is defined as the summation of the time dependent creep and the instantaneous elastic strain (Fig. EX8-2). The solutions obtained from ADAPT-ABI using the ACI material model and the associated results from hand calculations are summarized in Table EX8-1 for selected observation times. The results are in excellent agreement. Two sample hand calculations are presented in the following. One is for the total deflection for a single loading condition (Case B), and the other for a double loading condition (Case E). CASE B Verify the shortening (δ) of the specimen on day 100. The specimen is loaded on day 7. Verification: First, calculate the instantaneous shortening. Stress f = (force/area) = (100*10 3 /10,000) = 10 Mpa Concrete strength at time of loading f c(7) is: f c(7) = [7/(4+0.85*7)]*30 = MPa EX8-2

44 Modulus of elasticity at age 7 days E (7) is: E (7) = *10 12 (W) 1.5 *[f c(7) ] 1/2 = *10 12 (2.4019*10-6 ) 1.5 *[21.106] 1/2 = 23,117 Mpa Elastic shortening = 200*f/E (7) = 200*10/23,117 = mm (Solution from ADAPT-ABI mm, OK) Second, calculate the creep shortening. The creep coefficient for observation on day 100 is: (100-7) 0.6 C(100)= (7/7) * 3.53 = (100-7) 0.6 Total shortening is: δ = [ 1 + C(100)]*(instantaneous shortening) = [ ]* = mm (Solution from ADAPT-ABI mm, OK) CASE E Verify the shortening (δ) of the specimen on day 100. The specimen is loaded on day 7 with P=100 kn. Subsequently on day 28 a second load P=100 kn is added. Both loads are sustained on the specimen Verification: The loading condition of this specimen is illustrated in Fig. EX8-3a. The associated creep strain is shown in Fig. EX8-3b. For multiple loading, the creep strain is obtained using the principle of superposition. That is to say, the creep on day 100 is the sum of creeps on day 100 due to the application of the first load on day 7 and subsequently the application of the second load on day 28. The creep as well as the instantaneous displacement due to each application is treated independently from the other applications. (i) Shortening on day 100 due to the application of the first load The total shortening on day 100, due to the application of the first load on day 7, is identical to the solution obtained for Case B and verified in the preceding. It is equal to mm EX8-3

45 (ii) Shortening on day 100 due to the application of the second load First, calculate the instantaneous shortening. Stress f = 10 Mpa Concrete strength at time of loading f c(28) is 30 MPa. Hence, Modulus of elasticity at age of loading E (28) is: E (28) = *10 12 (W) 1.5 *[f (c) ] 1/2 = *10 12 (2.4019*10-6 ) 1.5 *[30] 1/2 = 27,562 Mpa Elastic shortening = 200*f/E (28) = 200*10/27,562 = mm (Solution from ADAPT-ABI mm, OK) Second, calculate the creep shortening. The creep coefficient for observation on day 100 is: (100-28) 0.6 C(100) = (28/7) * 3.53 = (100-28) 0.6 Total shortening due to the second loading is: δ = [ 1 + C(100)]*(instantaneous shortening) = [ ]* = mm (iii) Shortening on day 100 due to the application of the both loads δ = sum of deflections due to each application = = mm (Solution from ADAPT-ABI mm, OK) Table EX8-1 is a summary of the deflections computed by ADAPT-ABI and the associated hand calculations. The input data used to obtain the solutions given herein are included under INPUT section. EX8-4

46 TABLE EX8-1 : TOTAL CREEP DISPLACEMENT Cases LOADING AGES (days) OBSERVATION DATES (days) TOTAL CREEP ABI (mm) TOTAL CREEP ACI (mm) A * B * C * D * , ,.277*.204,.277 E * * For linear superposition verification, the first and second numbers represent the total displacement before and after the second concentrated load is applied. EX8-5

47 FIGURE EX8-1 FIGURE EX8-2 EX8-6

48 FIGURE EX8-3 EX8-7

49 INPUT DATA ;======================================================================= ; ADAPT-BRIDGE-INCREMENTAL ABI SOFTWARE MANUAL EXAMPLE ;======================================================================= ; Name of this file: ABI-EX8A UNITS : N, mm START TITLE N=2 One-element test for creep formulation verication ACI creep model UNITS U=SI CONCRETE PARAMETERS N=1 1 M=ACI W=2.4019E-6 MESH INPUT NODES N=2 1 Y= 0.00 X=0.0 2 Y= X=0.0 SECTION PROPERTIES N=1 1 B=100 D=100 CONCRETE PROPERTIES N=1 1 Fpc=30 Cr=3.53 Sh=0 W=0 Ac=0 M=1 MILD STEEL PROPERTIES N=1 1 Es= P=0.00 ELEMENTS N=1 FRAME ELEMENTS N=1 1,1,2 C=1 X=1 Day=0 St=1 MESH COMPLETE SET Day=3 CHANGE STRUCTURE RESTRAINTS 1 R=1,1,1 BUILD N=1 CHANGE COMPLETE ; Apply load on Day=3 LOADING! N=2 F=0,-1E5,0! SOLVE! OUTPUT SOLVE Day=14! OUTPUT! SOLVE Day=28! OUTPUT SOLVE Day=100! OUTPUT! SOLVE Day=20*365! OUTPUT STOP EX8-8

50 ;======================================================================= ; ADAPT-BRIDGE-INCREMENTAL ABI SOFTWARE MANUAL EXAMPLE ;======================================================================= ; Name of this file: ABI-EX8B UNITS : N, mm START TITLE N=2 One-element test for creep formulation verication ACI creep model UNITS U=SI CONCRETE PARAMETERS N=1 1 M=ACI W=2.4019E-6 MESH INPUT NODES N=2 1 Y= 0.00 X=0.0 2 Y= X=0.0 SECTION PROPERTIES N=1 1 B=100 D=100 CONCRETE PROPERTIES N=1 1 Fpc=30 Cr=3.53 Sh=0 W=0 Ac=0 M=1 MILD STEEL PROPERTIES N=1 1 Es= P=0.00 ELEMENTS N=1 FRAME ELEMENTS N=1 1,1,2 C=1 X=1 Day=0 St=1 MESH COMPLETE SET Day=7 CHANGE STRUCTURE RESTRAINTS 1 R=1,1,1 BUILD N=1 CHANGE COMPLETE ; Apply load on Day=7 LOADING! N=2 F=0,-1E5,0! SOLVE! OUTPUT SOLVE Day=14! OUTPUT! SOLVE Day=28! OUTPUT SOLVE Day=100! OUTPUT! SOLVE Day=20*365! OUTPUT STOP EX8-9

51 ;======================================================================= ; ADAPT-BRIDGE-INCREMENTAL ABI SOFTWARE MANUAL EXAMPLE ;======================================================================= ; Name of this file: ABI-EX8C UNITS : N, mm START TITLE N=2 One-element test for creep formulation verication ACI creep model UNITS U=SI CONCRETE PARAMETERS N=1 1 M=ACI W=2.4019E-6 MESH INPUT NODES N=2 1 Y= 0.00 X=0.0 2 Y= X=0.0 SECTION PROPERTIES N=1 1 B=100 D=100 CONCRETE PROPERTIES N=1 1 Fpc=30 Cr=3.53 Sh=0 W=0 Ac=0 M=1 MILD STEEL PROPERTIES N=1 1 Es= P=0.00 ELEMENTS N=1 FRAME ELEMENTS N=1 1,1,2 C=1 X=1 Day=0 St=1 MESH COMPLETE SET Day=28 CHANGE STRUCTURE RESTRAINTS 1 R=1,1,1 BUILD N=1 CHANGE COMPLETE ; Apply load on Day=28 LOADING! N=2 F=0,-1E5,0! SOLVE! OUTPUT SOLVE Day=14! OUTPUT! SOLVE Day=100! OUTPUT SOLVE Day=200! OUTPUT! SOLVE Day=20*365! OUTPUT STOP EX8-10

52 ;======================================================================= ; ADAPT-BRIDGE-INCREMENTAL ABI SOFTWARE MANUAL EXAMPLE ;======================================================================= ; Name of this file: ABI-EX8D UNITS : N, mm START TITLE N=2 One-element test for creep formulation verication ACI creep model UNITS U=SI CONCRETE PARAMETERS N=1 1 M=ACI W=2.4019E-6 MESH INPUT NODES N=2 1 Y= 0.00 X=0.0 2 Y= X=0.0 SECTION PROPERTIES N=1 1 B=100 D=100 CONCRETE PROPERTIES N=1 1 Fpc=30 Cr=3.53 Sh=0 W=0 Ac=0 M=1 MILD STEEL PROPERTIES N=1 1 Es= P=0.00 ELEMENTS N=1 FRAME ELEMENTS N=1 1,1,2 C=1 X=1 Day=0 St=1 MESH COMPLETE SET Day=50 CHANGE STRUCTURE RESTRAINTS 1 R=1,1,1 BUILD N=1 CHANGE COMPLETE ; Apply load on Day=50 LOADING! N=2 F=0,-1E5,0! SOLVE! OUTPUT! SOLVE Day=100! OUTPUT SOLVE Day=200! OUTPUT! SOLVE Day=20*365! OUTPUT STOP EX8-11

53 ;======================================================================= ; ADAPT-BRIDGE-INCREMENTAL ABI SOFTWARE MANUAL EXAMPLE ;======================================================================= ; Name of this file: ABI-EX8E UNITS : N, mm START TITLE N=2 One-element test for creep formulation verication ACI creep model UNITS U=SI CONCRETE PARAMETERS N=1 1 M=ACI W=2.4019E-6 MESH INPUT NODES N=2 1 Y= 0.00 X=0.0 2 Y= X=0.0 SECTION PROPERTIES N=1 1 B=100 D=100 CONCRETE PROPERTIES N=1 1 Fpc=30 Cr=3.53 Sh=0 W=0 Ac=0 M=1 MILD STEEL PROPERTIES N=1 1 Es= P=0.00 ELEMENTS N=1 FRAME ELEMENTS N=1 1,1,2 C=1 X=1 Day=0 St=1 MESH COMPLETE SET Day=7 CHANGE STRUCTURE RESTRAINTS 1 R=1,1,1 BUILD N=1 CHANGE COMPLETE ; Apply load on Day=7 LOADING! N=2 F=0,-1E5,0! SOLVE! OUTPUT! SOLVE Day=14! OUTPUT SOLVE Day=28! OUTPUT! ; Apply load on Day=28 LOADING! N=2 F=0,-1E5,0! SOLVE! OUTPUT! SOLVE Day=100! OUTPUT SOLVE Day=200! OUTPUT! SOLVE Day=20*365! OUTPUT STOP EX8-12

54 ABI-EX8 F through L CREEP COMPUTATIONS USING CEB DESCRIPTION This example serves a multiple objective. (i) (ii) By way of hand calculations for a simple case, it illustrates how creep computations using the CEB concrete model are carried out; For the same simple case used in the preceding hand calculations, it shows how an input data for ADAPT-ABI is composed. Using this input data, the creep solution obtained from ADAPT- ABI is compared with the hand calculations and commented; (iii) For advanced ADAPT-ABI users, it describes the feature of the program s extended data generation for a more precise computation of creep deformations; (iv) For the devout creep user, seeking ultimate control, it presents the details of the formulation and the inner workings of ADAPT-ABI for CEB creep computations. Frequent comparisons and comments made throughout these examples place the various aspects of the creep computation in proper perspective. For part (iv), it is important to mention that in ADAPT- ABI the graphical relationships given for the CEB material and creep model have been approximated with a number of closed form equations. These equations will be presented in detail and will be separately evaluated for the example s material and geometry data. The reader is referred to Appendix B of ADAPT-ABI manual for a discussion of the CEB graphical and closed form relationships. Details of the four parts are described next. In the first part, a specimen is loaded at day 7 and its corresponding total displacement is hand calculated for day 100 using the CEB recommendations. In the second part, the specimen described in the first part is modeled with ADAPT-ABI (This is referred to as Case K) and the corresponding total displacement is compared with the values obtained previously. In the current case, ADAPT-ABI will use interpolation to obtain the solution for 7 days loading age. In the third part (Case L) the modeling of the concrete parameters adopted in Case K is modified, in that the program is directed to generate an explicit set creep coefficients for a given loading age EX8-13

55 shortening of the specimen is observed on days 7, 14, 28, 100, 200 and 20*365 days. In Case J the specimen is loaded with two concentrated axial compressive forces applied at different ages. The objective of this case is to test the formulation for the condition of multiple loading. The first loading is applied on day 7. With the first loading retained, the second loading is applied on day 28. Both loadings are kept on the specimen while its shortening is monitored with lapse of time. For all cases, the specimen is discretized into one finite element only. The shrinkage of concrete is neglected. PART 1 - CEB Hand Calculations The CEB recommendations as discussed in the ADAPT-ABI manual will be used to determine the values of the listed parameters. The reader is referred to the ADAPT-ABI manual Appendix B and part 4 discussion of results for the definition of parameters and variables used. Notional thickness - humidity factor for H = 70% Γ = 1.50 Notional or effective thickness h 0 = 1.50*(2*100/40) = 7.5 cm Concrete strength at 7 days f c =.48*1.45*30 = 20.9 MPa Modulus of elasticity at 7 days E(7) = 45680*(20.9*100) 1/2 = 20883E2 N/cm 2 Modulus of elasticity at 28 days E(28) = 45680*(30*100) 1/2 = 25020E2 N/cm 2 Instantaneous deflection at 7 days δ i = PL/AE(7) δ I = 1E5*20/(100*20883E2) = cm = mm Equivalent 28 days deflection δ 28 = PL/AE(28) δ 28 = 1E5*20/(100*25020E2) = cm = mm Creep coefficient for 7 days loading and 100 days observation times EX8-15

56 and observation times. The loading ages and observation times generated are selected such as to coincide with the dates of interest in the example. This procedure would bypass a number of interpolation procedures which are otherwise necessary for the creep computations. Specifically, the loading age requested would be day 7 and one of the observation dates requested would be day 100. Again, the values obtained from the CEB recommendation in the first part and those of the ADAPT-ABI analysis from this part are compared. In the fourth and final part, a specific set of loading ages and observation times is selected. The internal formulations of ADAPT- ABI are presented and used to evaluate the values associated with the selected loading ages and observation times. A hand calculation is performed to check the closed form equations used by ADAPT-ABI in representing the CEB graphic and tabular relationships. STRUCTURE An axially loaded column of uniform cross-section is selected. Its dimensions are shown in Figure EX8-1. Other particulars of the specimen are: Area A = 10 cm 2 Humidity H = 70 % Temperature T = 20 o C Unit weight W = kg/mm3 28 days concrete strength f c = 30 Mpa Applied compressive loading P = 100 kn Ultimate creep coefficient C u = 3.0 for at 28 days loading age In Parts one and two, Case K, the specimen is loaded at 7 days. The loading is sustained and the shortening is monitored at 100 days only. In Part 2 the loading ages and observation times are internally generated by ADAPT-ABI using the program s default values. In part three, the specimen is again loaded at 7 days and monitored at 100 days. However, the loading ages and observation times are explicitly requested by the user to match the loading age and observation times specific to the problem. The objective is to bypass the interpolation operations which are generally performed to obtain the values of the material time dependent coefficients for the specified loading age of the problem - in this case for 7 days. The explicit request for the loading ages of interest achieves a better correlation between the CEB and the ADAPT-ABI values. In part four, five cases F through J are considered. In Cases F through I each specimen is loaded only once. The loading ages are 3, 7, 28, and 50 days respectively. The loading is sustained and the EX8-14

57 φ(100,7)= β a (7) + φ d *β d (100-7) + φ f *[β f (100)-β f (7)] =.8*(1-0.48) + 0.4* *1.78*( ) = 2.12 Ultimate creep coefficient for 28 days loading φ(,28) = β a (28) + φ d *β d ( -28) + φ f *[β f ( )-β f (28)] =.8*(1-0.69) + 0.4* *1.78*( ) = 2.79 Modified creep coefficient for user ultimate creep = 3.0 φ * (100,7) = 2.12*3.00/2.79 = 2.28 Total displacement at 100 days δ 100 = δ i +2.28*δ 28 =.278 mm In summary: Day 7 instantaneous deflection Day 100 total deflection mm mm PART 2 - ADAPT-ABI Computation for Simple Example The specimen is now monitored for 7 days loading age and day 100 observation time with ADAPT-ABI (Case K). The input data for this case is given at the end of this example. Before proceeding to the computations a brief outline of the creep curves as used in ADAPT-ABI is offered. Refer to Figure EX8-4. The solid lines represent the instantaneous and creep strains of a specimen loaded at different ages. For example, line AB signifies the instantaneous (elastic) strain of the specimen loaded on day, A. Curve BC is the variation of the creep strain of the same specimen on the assumption that the loading is retained on the specimen. Prior to the start of a creep analysis, for each material specified by the user, ADAPT-ABI generates a family of such curves as its initial data base. In the general case, the dates for which the creep curves are generated are based on the default values set in ADAPT-ABI program. The default dates cover the range of early age loading through loading several years after concrete is cast. Details of the default values are given in ADAPT-ABI manual. If a specimen is loaded on a day (such as day E in Figure EX8-4) which does not coincide with one of the default loading days initiated by the program - such as days A and D in EX8-4, ADAPT-ABI in- EX8-16

58 terpolates the creep values between the two curves immediately preceding and succeeding the user requested loading age (A and D). As a result, an approximation is entered into the analysis. The degree of approximation depends on how close is the user requested loading age (E) to the program initiated default dates (A and D). The user can eliminate this approximation by selecting the default ages to fall on the days the specimen is loaded. This feature of the program is described in part 3. Using the program generated default values, as outlined in the preceding, solution generated by ADAPT-ABI gives the following values for the instantaneous displacement at day 7 and the total displacement at day 100. Day 7 instantaneous deflection Day 100 total deflection mm mm The agreement for the instantaneous deflection is 4%. The long-term deflections differ by 11%. The primary reason for the difference between the hand calculated and ADAPT-ABI computed values is the fact that, in ADAPT-ABI the computed value is obtained through interpolation between the creep values of days which fall on the two sides of day 7, as opposed to the value associated to day 7. The interpolation method used in this example is the common engineering practice. The approximation obtained is acceptable. However, should a user wish a more precise correlation between the two values, the refinement explained in the next part can be exercised. PART 3 - ADAPT-ABI Computation With Refined Features The same specimen as in the previous part is again monitored for 7 days loading age and 100 days observation time using the refined creep feature of ADAPT-ABI (Case L). In this case, the program is instructed to generate, as its data base, the creep curve associated with loading at day 7 and, among other days, observation at day 100. Specifically, the loading age initialized and the observation times requested are listed below and shown graphically in Figure EX8-5. Age=07 T=8,14,28,50,100,200,20*365 where, Age T = day when the specimen is loaded; and = days when the creep value is computed using the code specified creep formulations. The preceding syntax signifies that for loading age 7 which coincides with the loading age of the specimen in this example, the program is requested to generate creep coefficients for days 8, 14, EX8-17

59 28, 50, 100, 200 and 20 years. The creep coefficients generated by the program for the stated days match the code formulas, but before being used by the program, a best fit curve is passed through them (broken line in Fig. Ex8-6. It is the best fit curve which is subsequently used to determine the creep for the observation days requested by the user in the analysis of the actual structure (day marked with a circle in Figure ABI-EX8-6). Using the refined creep computation option, the results of the analysis from ADAPT-ABI are (case L): Day 7 instantaneous deflection Day 100 total deflection mm mm The agreement with the hand calculation for the instantaneous response is 4%. For creep values at day 100 the difference between the two cases is less than 1%. In relation to the refined feature of ADAPT-ABI creep computation, two other items are noteworthy. First, the program needs a minimum number of points (shown with cross in Figure ABI-EX8-6) through which to fit a curve (shown with broken line in the same figure). The default value for such points is 4. Specification by user of more than four points results in improved accuracy. Second, it is important to select the first observation date close to the loading age, in order to capture the large initial rate of creep. An important observation to be made is the close agreement between the results between ADAPT-ABI values for the two cases K and L. It is confirmed that the default creep formulation implemented in ADAPT-ABI is valid and closely approximates the code recommendations. It follows that, the user need not focus his attention in requesting a specific set of loading ages and observation times that matches the user s problem, since the internally generated loading ages and observation times yield satisfactory results. PART 4 - ADAPT-ABI s Internal Working and Detailed Verification This part reviews the details of creep computation as it is carried out by ADAPT-ABI. It also presents the closed form relationships selected by ADAPT-ABI to represent the CEB code curves. The notional thickness, creep coefficient, flow coefficient and EX8-18