Add_v4.50
060305
STRUCTURAL CONCRETE SOFTWARE
ADAPT-ABI
Addendum to Construction Phase
Modeling and Analysis
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
[email protected] 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
ADDENDUM TO THE USER MANUAL
ABI
TABLE OF CONTENTS
1. CHAPTER 3 ADDENDUM
1.1 ACI-209 Concrete Model (1992)…………………………………...………….....2
1.2 AASHTO Concrete Model (1994)……………………………………………..…3
1.3 Eurocode 2 Concrete Model (2004)……………………………………………....4
1.4 British Concrete Model………………………………………………….…….….5
1.5 Hong Kong Concrete Model…………………………………………………..….7
1.6 Definition of Generic Material Properties……………………………………..….9
1.7 Cable Stay Modeling…………………………………………………………….10
2. APPENDIX A ADDENDUM – Comments on the Tabular Output…………...…17
3. APPENDIX B ADDENDUM
3.1 ACI Committee 209 Recommendation (1992)………………………….……...19
3.1.1 Strength and stiffness…………………………………………………….19
3.1.2 Creep strain…………………………………………………………...….19
3.1.3 Shrinkage strain………………………………………………….………22
3.2 AASHTO Recommendations (1994)…………………………………………...24
3.2.1 Strength and stiffness……………………………………………….……24
3.2.2 Creep strain…………………………………………………………...….25
3.2.3 Shrinkage strain………………………………………………………….25
3.3 Eurocode 2 Recommendation (2004)……………………………………….…..26
3.3.1 Strength and stiffness………………………………………………….…26
3.3.2 Creep strain…………………………………………………………...….27
3.3.3 Shrinkage strain…………………………………………………….....…28
3.4 British Code Recommendations………………………………………………..29
3.4.1 Creep strain………………………………………………………………29
3.4.2 Shrinkage strain…………………………………………………...……..32
3.5 Hong Kong Code Recommendations…………………………………………..33
3.5.1 Creep strain………………………………………………………………33
3.5.2 Shrinkage strain………………………………………………….……....33
4. APPENDIX D ADDENDUM – Comments on Camber Computations…………35
5. APPENDIX E
4.1 Cable Stay……………………………………………………………………….37
4.2 Modeling of Composite Constructions………………………………………….53
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ADDENDUM TO THE USER MANUAL
ABI
1. CHAPTER 3 ADDENDUM
1.1
ACI-209 Concrete model (1992)
Syntax:
CONCRETE PARAMETERS N=?
n M=ACI92
To be followed by several lines of concrete parameter specifications.
where,
N
n
= Total number of concrete parameter types;
= Concrete model number.
Syntax described refers to “standard conditions” for which creep correction factors are
equal to 1. To describe conditions other than standard, the user should specify additional
parameters such as:
A=? B=? C=? D=? E=?
AC=? W=? CURE=? T0=?
F=?
HM=?
TH=?
VS=?
S=?
P=?
CC=?
where,
A
AC
B
C
CC
CURE
D
E
F
HM
P
S
TH
T0
VS
W
kg/cm3].
= Strength factor [4.0];
= Air content (percent) [6];
= Strength factor [0.85];
= Creep factor [0.6];
= Cement content [0.015 lb/in3, 4.15x10-7 kg/mm3, 4.15x10-4 kg/cm3];
= Curing method of concrete (1 for moist, 2 for steam curing) [1];
= Creep factor [10.0];
= Shrinkage factor [1.0];
= Shrinkage factor (35 for moist, 55 for steam cured concrete) [35];
= Ambient relative humidity (percent) [40];
= Fine aggregate content (percent) [50];
= Slump [2.65 in, 67 mm, 6.7 cm];
= Average member thickness [6 in, 152 mm, 15.2 cm];
= Duration of curing (days) [7];
= Volume to surface ratio [1.5 in, 38mm, 3.8cm]; and,
= Density of concrete [8.6806x10-2 lb/in3, 2.4019x10-6 kg/mm3, 2.4019x10-3
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The values in the brackets are default, “standard condition” values coded in the program.
The detailed description of creep and shrinkage strain calculation, and application of the
listed parameters are given in the Appendix B.2.3.
Example:
CONCRETE PARAMETERS N=1
1 M=ACI92 HM=60
First material type selected uses ACI-209 (1992) concrete model. The input value of
humidity is 60% while all other concrete parameters that are not specified have
default values.
1.2
AASHTO Concrete Model (1994)
Syntax:
CONCRETE PARAMETERS N=?
n M=AASHTO
To be followed by several lines of concrete parameter specifications.
where,
N
n
= Total number of concrete parameter types;
= Concrete model number.
This instruction means that the “n” material type selected uses AASHTO concrete
model. Other concrete parameters are optional and user may specify as many of
these as necessary. They are:
A=? B=? C=? HM=? VS=? W=? CURE=? T0=?
FPC=?
where,
= Strength factor [4.0];
= Strength factor [0.85];
= Creep correction factor [1.56];
= Ambient relative humidity, (percent) [70];
= Volume-to-surface ratio [38 mm,3.8 cm, 1.5 in];
= Density of concrete [2.4019x10-6 kg/mm3, 2.4019x10-3 kg/cm3
-2
8.6806x10 psi];
CURE = Curing method (1 for moist, 2 for steam cured concrete) [1];
T0
= Duration of curing, (days) [7]; and
FPC
= The 28-day compressive strength of concrete [35 MPa, 350 kg/cm2
5000 psi].
A
B
C
HM
VS
W
The values in the brackets are default, “standard condition” values coded in the program.
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The detailed description of creep and shrinkage strain calculation, and application of the
listed parameters are given in the Appendix B.2.4.
1.3
Eurocode 2 Concrete Model (2004)
Syntax:
CONCRETE PARAMETERS N =?
n M=EC2
To be followed by several lines of concrete parameter specifications.
where,
N
n
= Total number of concrete parameter types;
= Concrete model number;
Concrete parameter specifications are optional. If user doesn’t specify any concrete
parameter, program will consider default, “standard condition” values. To describe nonstandard condition user can specify the following:
HM=? AC= U=? CTYPE=? T0=? FPC=?
Where,
HM
AC
U
CTYPE
T0
FPC
= Ambient relative humidity, (percent) [70];
= Area of cross section [7.75x10-2 in2, 50 mm2, 0.5 cm2];
= Perimeter of section exposed to drying [3.937x10-2 in, 1 mm, 0.1cm];
= Cement type (1 for Class S, 2 for Class N, 3 for Class R of cement) [2];
= Duration of curing, (days) [7]; and,
= The 28-day compressive strength of concrete [5000 psi, 350 kg/cm2, 35
MPa].
The values in the brackets are default, “standard condition” values coded in the program.
The detailed description of creep and shrinkage strain calculation, and application of the
listed parameters are given in the Appendix B.2.5.
NOTE:
The ultimate creep and shrinkage coefficients are calculated internally by the program and
therefore, in “CONCRETE PROPERTIES” data block, the user should use 1.0 for creep and
shrinkage multipliers (Cr and Sr respectively) unless the user wants to have a different
ultimate creep and shrinkage strains. In this case the user should input the ratio between the
desired coefficient and the one calculated by the program.
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1.4
ADDENDUM TO THE USER MANUAL
ABI
British Concrete Model
The time dependent material specifications can now be defined in accordance with the
British code requirements under the CONCRETE PARAMETER command block. The
PRESTRESSING STEEL as well as the CONCRETE PROPERTIES command block have been
expanded for additional features. The syntax of these two command blocks are partially
listed for a description of the new features.
Syntax:
CONCRETE PARAMETERS N=?
n M=BS
where,
N
n
= Total number of concrete parameter types;
= Concrete model number.
For the British code requirements, the age at loadings and observation times are only
internally generated by the program. Consequently, the G=? identifier described in the
Concrete Material Generic Input line is not active. Following the Material Generic Input
line, an additional line of input data in the following format is needed for the British
model. Other parameters needed are defined under the SET command line (such as
temperature) in which case the first occurrence of the SET command within the input file
is used or under the MESH INPUT block (such as concrete 28 days strength, ultimate
creep or creep scale factor, ultimate shrinkage or shrinkage scale factor, mild steel elastic
modulus and percentage of mild steel reinforcement).
Humidity=?, Thickness=?, Cement=?, WCratio=?, CemType=?
where,
Humidity
= relative humidity in percent [70 %]
Thickness
= effective thickness
= sectional area divided by half perimeter
= in., mm, cm [200 mm]
= cement content
= lb/yd3,kg/m3,kg/m3, [300 kg/m3]
= water-cement ratio [0.5]
= RAPID for rapid hardening cement
= PORTLAND for ordinary Portland cement [PORTLAND]
Cement
wCratio
CemType
Syntax:
PRESTRESSING STEEL
n Ep=? ... R=?
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or
StressRatio=? Hours=? LossRatio=?
where,
Either
= Relaxation coefficient;
R
or
StressRatio
= Initial stress to ultimate stress (Fpu)
in the test used to determine the relaxation
characteristics of the strand [0.80];
Hours = Number of hours of duration of test [1000];
LossRatio
= Observed stress loss ratio in the test [0.045]
The PRESTRESSING STEEL command has been expanded to allow the specification of
the relaxation coefficient (R or C) directly through the R=? identifier or indirectly
through the use of the StressLoss=?, Hours=? and LossRatio=? identifiers in which
case the relaxation coefficient is internally computed using these three parameters.
The command syntax as described in the manual remains unchanged with the above
format needed when the indirect method is adopted.
Syntax:
CONCRETE PROPERTIES N=?
n Fpc=?
W=?
M =? Ac=? \
CrScale=?
or
ShScale=?
or
Weight=?
or
(Cr=? or CrUltimate=?) (Sh=? or ShUltimate=?)
where,
Either
CrUltimate or Cr= Ultimate Creep Coefficient [0]
or
CrScale= Scaling coefficient for ultimate creep computed from user
specified concrete model [1]
else
Ultimate creep coefficient assumed zero
Either
ShUltimate or Sr= Ultimate Shrinkage Coefficient [0]
or
ShScale= scaling coefficient for ultimate shrinkage computed from user
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ADDENDUM TO THE USER MANUAL
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specified concrete model [1]
else
Ultimate shrinkage coefficient assumed zero
The CONCRETE PROPERTIES command has been modified and expanded to allow scaling
and resetting of the creep and shrinkage ultimate coefficients. Either the W=? or Weight=?
identifier can be used to define the unit weight of concrete. For the British creep model, the
ultimate creep coefficient is reset by normalizing the 28 days internally generated value to
the specified value given under the Cr=? and CrUltimate=? identifiers. The ultimate creep
coefficient at other loading ages are scaled with the same factor. The ultimate creep
coefficient can be scaled up or down by using the CrScale=? identifier instead. The same
concept is applicable to the shrinkage time effects where the ultimate shrinkage coefficient
is reset with the Sr=? or SrUltimate=? identifier and is scaled up or down with the
SrScale=? identifier. For the British model only, the concrete ultimate strength at 28 days,
the ultimate creep and shrinkage coefficients are used in conjunction with the data defined
under the CONCRETE PARAMETER block to set up the material time dependent representation.
1.5
Hong Kong Concrete Model
The syntax is similar to British concrete model.
Syntax:
CONCRETE PARAMETERS N=?
n M=HK
where,
N
n
= Total number of concrete parameter types;
= Concrete model number.
Additional parameters that has to be specified are:
Humidity=?, Thickness=?, Cement=?, WCratio=?, CemType=?
where,
Humidity
= relative humidity in percent [70 %]
Thickness
= effective thickness
= sectional area divided by half perimeter
= in., mm, cm [200 mm]
= cement content
= lb/yd3,kg/m3,kg/m3, [300 kg/m3]
= water-cement ratio [0.5]
= RAPID for rapid hardening cement
Cement
wCratio
CemType
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ABI
= PORTLAND for ordinary Portland cement [PORTLAND]
Syntax:
PRESTRESSING STEEL
n Ep=? ... R=?
or
StressRatio=? Hours=? LossRatio=?
where,
Either
= Relaxation coefficient;
R
or
StressRatio
= Initial stress to ultimate stress (Fpu)
in the test used to determine the relaxation
characteristics of the strand [0.80];
Hours = Number of hours of duration of test [1000];
LossRatio
= Observed stress loss ratio in the test [0.045]
Syntax:
CONCRETE PROPERTIES N=?
n Fpc=?
W=?
or
Weight=?
M =? Ac=? \
CrScale=?
ShScale=?
or
or
(Cr=? or CrUltimate=?) (Sh=? or ShUltimate=?)
where,
Either
CrUltimate or Cr= Ultimate Creep Coefficient [0]
or
CrScale= Scaling coefficient for ultimate creep computed from user
specified concrete model [1]
else
Ultimate creep coefficient assumed zero
Either
ShUltimate or Sr= Ultimate Shrinkage Coefficient [0]
or
ShScale= scaling coefficient for ultimate shrinkage computed from user
specified concrete model [1]
Else
Ultimate shrinkage coefficient assumed zero
For more detailed explanation refer to write-up for British concrete model
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ADDENDUM TO THE USER MANUAL
ABI
1.6 Definition of Generic Material Properties
Besides concrete, the user can define other materials. These are defined in a separate data
block called “GENERIC PROPERTIES”. The generic materials do no have time-dependent
properties.
Syntax:
GENERIC PROPERTIES N=?
n ES=Eg NAME=?
Where,
N
n
ES
NAME
= Total number of generic material types
= Generic material type number
= Modulus of elasticity of generic material (Eg)
= Name of generic material
Note: When defining generic material property for each frame element in the “ELEMENTS”
data block use “S = ?” instead of “C = ?”.
Example:
The following is the example of input file for generic material:
MESH INPUT
NODES N=5
1 X=0.0 Y=0.0 ! 5 X=0 Y=200 G=1,5
; Fixed base column
CONCRETE PROPERTIES N=1
1 FPC=35.00 CR=0.0 SH=1.0 W=0 M=1
; Laboratory model
GENERIC PROPERTIES N=1
1 ES=35.00 NAME=STEEL
SECTION PROPERTIES N=1
1 Area=7854 I=4.909E6 C=50, 50
ELEMENTS N=4
FRAME N=4
1,1,2 C=1
2,2,3 C=1
3,3,4 C=1
4,4,5 S=1
X=1
X=1
X=1
X=1
ST=1
ST=1
ST=1
ST=1
; Circular section
Day=0
Day=0
Day=0
Day=0
; Laboratory model
; Generic material
property
MESH COMPLETE
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ADAPT
ADDENDUM TO THE USER MANUAL
ABI
1.7 Cable Stay Modeling
The following is an addendum to the User’s Manual of ADAPT-ABI. It describes the
commands specific to cable stay modeling.
1.7.1 Command Summary and Sequence
The natural sequence of cable stay related commands within the body of the entire problem
is given in the following.
START
TITLE
UNITS
CONCRETE PARAMETERS
MESH INPUT
NODES
......................blank line ..............
SEQUENCE
......................blank line ..............
CONCRETE PROPERTIES
MILD STEEL PROPERTIES
STAY MATERIAL PROPERTIES
STAY ANALYSIS
SECTION PROPERTIES
OFFSET DATA
ELEMENTS
FRAME
SPRINGS
STAY ELEMENT
........................blank line ............
PRESTRESSING STEEL
TENDON GEOMETRY
........................blank line ............
TRAVELERS
MESH COMPLETE
SET
CHANGE STRUCTURE
BUILD (Frame Element)
RESTRAINTS
........................blank line ..............
REMOVE
; Elements
STRESS
; Tendons
DE-STRESS
; Tendons
STAY STRESS
; Stays
MOVE
; Travelers
CHANGE COMPLETE
LOADING
STAY=?
; Stay temperature
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...........................blank line ...............
SOLVE F=?
OUTPUT
CAMBER
STOP
1.7.2
List of Commands
The commands are organized in alphabetical order.
LOADING
Syntax :
LOADING
Stay= n1,n2,inc
Temp= ?
where,
n1
n2
inc
Temp
= first stay element number in series
= last stay element in series
= stay element increment
= uniform stay element temperature
[ 0]
[ 0]
[ 0]
[20C, or 70F]
Explanation : A detailed discussion of the LOADING command and the different load
categories handled is provided in the user’s manual. The following category
is added to process temperature effects in cable stay elements. Uniform dead
loading over the length of stay is specified under the STAY MATERIAL
PROPERTIES command.
Temperature effects can be individually specified for each stay element.
The reference temperature for all stay elements is taken as the ambient
temperature provided within the SET command. The stay element
temperature is assumed uniform over the full cable length.
SOLVE
Syntax :
SOLVE...
F= ?
where,
F= displacement increment scale factor
[0.9]
Explanation : The SOLVE command is expanded to control the solution convergence
strategy. The features and options of the SOLVE command remain unchanged
and are described in detail in the ABI manual. The cable stay element
formulation allows geometrical as well as sag nonlinearities to be included
or excluded independently in the solution. The displacement increment scale
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ADDENDUM TO THE USER MANUAL
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factor is used to scale the full displacement vector by the value specified
with the F= ? identifier. A smaller F= ? value will improve convergence. A
larger F= ? value will speed up the execution . A compromising F= ? value
should be used. The 0.9 default value have been found adequate for
common problems.
STAY ANALYSIS
Syntax :
STAY ANALYSIS
Geometry={include][exclude}\
Sag={[include][exclude]}
where,
Geometry
Sag
= geometrical nonlinearity option
= sag inclusion option
[exclude]
[exclude]
Explanation : The STAY ANALYSIS command is used to control the type of analysis to be
performed. The cable stay element formulation allows geometrical as well
as sag nonlinearities to be included independently in the solution. Small
displacement effects also known as geometrical nonlinearities considers the
cable stay elements geometry and equilibrium in the deformed
configuration. The ‘Geometry= include’ identifier must be specified to
activate this option. Similarly, the ‘Sag= include’ identifier must be
specified to invoke the sag nonlinearity.
STAY ELEMENT
Syntax :
STAY ELEMENT N= ?
n,ni,nj Material= ?
where,
N
= number of stay elements
n
= stay element number =< N
ni
= stay element node I
nj
= stay element node J
Material = material type number
[1]
[0]
[0]
[0]
[0]
Explanation : The STAY ELEMENT command is used to define all the cable stay elements
used in modeling the structure. The stay element number n must be less
than or equal to the total number of stay elements set on the STAY
ELEMENTS command line. The stay element descriptions may be supplied in
any order; however each stay element description must be specified or
generated once.
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STAY MATERIAL PROPERTIES
Syntax :
STAY MATERIAL PROPERTIES N= ?
n Ecable=? Area=? Weight=? Fpu=? Astay=? [[R=?]or
[StressRatio=?][LossRatio=?][Hours= ?]]
where,
N
= number of cable materials
n
= stay material number = < N
Ecable = cable elastic modulus
Area = cable area
Weight = stay unit weight per length
Fpu = cable ultimate stress
R
= cable relaxation coefficient
Acable = cable thermal expansion coefficient
Hours = number of hours of duration of test
LossRatio
= observed stress loss ratio in the test
StressRatio
= initial stress to ultimate stress (Fpu)
in the test to determine the relaxation
characteristics of the strand
[ 1]
[ 0]
[0.0]
[0.0]
[0.0]
[0.0]
[0.0]
[0.0]
[0.0]
[ 0]
[0.8]
Explanation : The STAY MATERIAL PROPERTIES command is used to specify the
material properties of the different stay elements defined in the structure.
The stay material type number n must be less or equal to the total number
of stay material types set on the STAY MATERIAL PROPERTIES command
line. The cable modulus of elasticity Ecable is the stretched elastic modulus
value independent of the cable sag. The unit length Weight is used to
compute the equivalent modulus of elasticity and the equivalent dead load
forces. The Ecable, Area, Fpu, R and Acable parameters relate to the
structural resisting cable material of the stay element while the Weight
parameter can implicitly account for any additional dead load per unit
length over the stay. The stay material types may be supplied in any order;
however each cable material type must be specified once.
STAY STRESS
Syntax :
STAY STRESS N=n1,n2,inc /
{[Ratio=?][StressTo=?][Force=?]}
where,
n1
n2
= first stay element in series
= last stay element in series
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[0]
[0]
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ADDENDUM TO THE USER MANUAL
inc
= element increment
Ratio = stress ratio to ultimate stress
StressTo= actual stress
Force = actual stressing force
ABI
[1]
[0]
[0]
[0]
Explanation : The STAY STRESS command is used to install, stress, restress and remove
cable stay elements. The stay elements’ geometry and material properties
must have been input under the STAY MATERIAL PROPERTIES and STAY
ELEMENT subcommands of the MESH INPUT command.
A stay element is initially stressed by specifying its stressing force under
this command. The stressing force can be set with either the Ratio= ?,
StressTo= ? or Force= ? identifier. The cable force is initialized to zero and
subsequently overridden, when applicable, with the force derived from the
stay element ultimate stress specification and its cross sectional area listed
under the STAY MATERIAL PROPERTIES subcommand in conjunction with
the Ratio= ? value specified above. The latter cable force is superseded
with the StressTo= ? value, when specified, in conjunction with the cable
cross sectional area. When applicable, the force defined under the Force= ?
identifier will take precedence over all previously derived cable forces.
Subsequently, a single selection from the { [Ratio= ?] [StressTo= ?]
[Force= ?] } list will be sufficient to initialize the stay element stressing
force.
A stay element can be restressed by specifying a new stressing force under
a subsequent application of this command. A cable stay can be removed
entirely by the use of this command with a zero stressing force.
Stay elements are internally assumed connected to active nodal points.
Each end node of the stay element must be connected to at least a single
frame element. The formulation of the cable stay element allows small
displacements geometrical nonlinear analysis to be performed in which
case this option must be invoked in the input data through the STAY
ANALYSIS subcommand. Consequently, the stay element installation and
subsequent equilibrium solutions will be both performed in the deformed
configuration. Otherwise, the undeformed configuration will be considered.
STAY ANALYSIS
Syntax :
(UNDOCUMENTED)
STAY ANALYSIS
Geometry { [include] [exclude] [incremental] } \
Sag= { [include] [exclude] [incremental] }
where,
Geometry
= geometrical nonlinearity flag
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[exclude]
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ADDENDUM TO THE USER MANUAL
Sag
ABI
= sag nonlinearity flag
[exclude]
Explanation : The STAY ANALYSIS command is used to control the type of analysis to
be performed. The cable stay element formulation allows geometrical as
well as sag nonlinearities to be included independently in the solution. Small
displacement effects also known as geometrical nonlinearities considers the
cable stay elements geometry and equilibrium in the deformed
configuration. The ‘Geometry= include’ identifier must be specified to
activate this option. Similarly, the ‘Sag= include’ identifier must be
specified to activate the sag nonlinearity. The sag nonlinearities are
implicitly accounted for with the use of an equivalent cable stay modulus of
elasticity. The equivalent modulus of elasticity accounts for the change in
sag configuration in addition to the cable stay extension.
The use of the ‘exclude’ and ‘include’ options for both the GEOMETRY= ?
and the SAG= ? identifiers is provided to perform a unique type of analysis
for the whole input file. An ‘incremental’ option is introduced to provide
incremental control over the cable stay nonlinearities. When the
‘incremental’ option is used, either the geometrical or the sag nonlinearity
which are first initialized to true can be independently reset at every solution
phase of the input file. A detailed explanation and syntax of the SOLVE
command to account for these features is given next.
SOLVE
(UNDOCUMENTED)
Syntax :
SOLVE...
Geometry= { [include] [exclude] [incremental] } \
Sag= { [include] [exclude] [incremental] } F= ?
where,
Geometry
Sag
= geometrical nonlinearity flag
= sag nonlinearity flag
[previous]
F
= displacement increment scale factor
[previous]
[0.9]
Explanation : The SOLVE command is expanded to control the type of analysis to be
performed. The features and options of the SOLVE command remain
unchanged and are described in detail in the ABI manual. The cable stay
element formulation allows geometrical as well as sag nonlinearities to be
included or excluded independently in the solution. When the incremental
analysis is selected within the STAY ANALYSIS subcommand, the
geometrical and sag nonlinearities may be then switched on and off
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independently within the SOLVE command using the GEOMETRY= ? and
the SAG= ? identifiers respectively. The displacement increment scale
factor is used to scale the full displacement vector by the same value
specified with the F= ? identifier. A smaller F= ? value will improve on
convergence. A larger F= ? value will speed up the execution . A
compromising F= ? value should be used. The 0.9 default value have been
found adequate.
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ADDENDUM TO THE USER MANUAL
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APPENDIX A ADDENDUM - Comments on the Tabular Output
The following are comments on several of the data blocks in the tabular output of ADAPTABI
107.1 PRIMARY ELEMENTS
-------------------------------------------------For each element, this data block lists the moments at the ends I and J, together with the
shear and axial loading in the element. The actions listed are the integral of those acting on
the concrete section only.
Since the shear and axial loading within an element are assumed constant (actions are
concentrated at the nodes when modeling), only one value for shear and axial loading is
given.
The important item to note for this data block is that in ADAPT-ABI output the actions
listed are for the concrete section. This is explained in more detail next.
Refer to Fig.1. Part (a) which shows an element with a prestressing tendon. The actions at
node J of the element are shown as M, V and N (Actions are shown in the positive
direction. Unlike the direction shown for P, the member is generally in compression). The
actions on the face J of the member are broken to those due to the prestressing (p) and
those due to concrete (c). These are shown in part (b) of the figure.
Data block 107.1 in the pre-capture mode (ADAPT-ABI) lists the actions on the concrete
section. These are: Mc,Vc and Nc (refer to Fig. 1-b).
Data block 107.1 in the post-capture mode (ADAPT-Gen) lists M V and N (refer to Fig. 1a).
109.2 COMBINED ACTION AND FORCE OF ALL TENDONS
-----------------------------------------------------------------------------This data block lists the actions at the centroid of the concrete portion of each face of an
element due to the entire prestressing tendons contained within that element.
An element with three tendons is shown in Fig. 2-a. Let the forces in the tendons be P1, P2
and P3. The tendon forces will have a resultant, which is shown as force P in Fig. 2-(b).
The resultant force is reacted by an equal and opposite force on the concrete section. The
components of the reactive force on the concrete section are shown in Fig. 2-(c) at node J.
Obviously, the tendon force and the force on the concrete section will act in opposite
directions, but for consistency with the rest of the formulations, actions are shown as
vectors in the positive direction. The sign in front of the numerical value given in data
blocks determines the direction.
17
ADAPT
ADDENDUM TO THE USER MANUAL
ABI
110 TOTAL STATIC RESULTS FOR ELEMENTS
--------------------------------------------------------------This data block lists the resultant actions (moments, shear and axial loading) at the ends of
an element (nodes I and J) due to the combined forces of the concrete section and
prestressing. It simulates the free body diagram of an element from which the prestressing
tendons are not removed.
Consider Fig. 3-(a) which illustrates a beam resting freely on a frictionless bed. The beam
is prestressed with a centroidal tendon. Fig. 3(b) shows the free body diagram of a section
of this beam. The forces acting on the face of the element are:
•
•
Tension P on the prestressing tendon
Compression P on the concrete section
The sum of total forces on the section is (P-P) = 0. Data block 110 will list zero for this
condition.
18
ADAPT
ADDENDUM TO THE USER MANUAL
ABI
3. APPENDIX B ADDENDUM
3.1 ACI Committee 209 Recommendation (1992)
3.1.1
Strength and stiffness
The variation of compressive strength of concrete with time is obtained from the
following equation:
bg
fc' t =
b g
t
fc' 28
a + bt
(B.2.12)
where, a and b are constants, f’c (28) is the 28-day strength and t in days is the
age of concrete.
The initial modulus of elasticity is defined as:
bg
bg
E c t = 1.3518x1012 w 1.5 fc' t
(MPa)
(B.2.13)
where, w is the density of concrete in kilogram per cubic millimeter and f’c(t) is
the strength of the concrete in Newton per millimeter squared.
3.1.2
Creep strain
Creep strain of concrete and its variation with time is defined as:
vt =
tC
vu
tC + D
(B.2.14)
for which:
v u = Cr × γ cr
(B.2.15)
γ cr = γ la × γ λ × γ h × γ vs × γ s × γ ψ × γ α
(B.2.16)
where,
C
Cr
= creep factor;
= creep coefficient;
19
ADAPT
ADDENDUM TO THE USER MANUAL
and,
ABI
D
t
vu
γ cr
γh
γ la
γs
γ vs
γα
γλ
= creep factor;
= time in days after loading;
= ultimate shrinkage strain;
= creep correction factor;
= creep correction factor for the effect of member size;
= creep correction factor for the effect of loading age;
= creep correction factor for the effect of slump of concrete;
= creep correction factor for the effect of volume to surface ratio;
= creep correction factor for the effect of air content;
= creep correction factor for the effect of ambient relative humidity;
γψ
= creep correction factor for the effect of fine aggregate content.
The following describes each of the creep correction factors:
Creep correction factor for the effect of member size
γh
.
R|130
1.17
|
= S1.11
||1.04
|T1.14 - 0.023 × TH
TH ≤ 2 in
TH = 3 in
TH = 4 in , during the firs year after loading (B.2.17)
TH = 5 in
TH ≥ 6 in
γh
.
R|130
1.17
|
= S1.11
||1.04
|T1.10 - 0.017 × TH
TH ≤ 2 in
TH = 3 in
TH = 4 in , ultimate values
TH = 5 in
TH ≥ 6 in
(B.2.18)
where, TH is the average member thickness in inches.
Creep correction factor for the effect of loading age
γ la
R|125
. bt g
=S
. bt g
|T113
−0.118
la
−0.094
la
for moist cured concrete
for steam cured concrete
where, tla is loading age in days.
20
(B.2.19)
ADAPT
ADDENDUM TO THE USER MANUAL
ABI
Creep correction factor for the effect of slump of concrete
γ s = 0.82 + 0.067S
(B.2.20)
where, S is the observed slump in inches.
Creep correction factor for the effect of volume to surface ratio
γ vs = 2 3 1 + 113
. e -0.54VS
(B.2.21)
where, VS is the volume-surface ratio of the member in inches.
Creep correction factor for the effect of air content
γ α = 0.46 + 0.09 × AC ≥ 1.0
(B.2.22)
where, AC is the air content in percent.
Creep correction factor for the effect of ambient relative humidity
γ λ = 127
. − 0.0067 × HM, for HM > 40
(B.2.23)
where, HM is the relative humidity in percent.
Creep correction factor for the effect of fine aggregate content
γ ψ = 0.88 + 0.0024 × P
(B.2.24)
21
ADAPT
ADDENDUM TO THE USER MANUAL
ABI
where, P in percentage is the ratio of the fine aggregate to total aggregate by
weight.
3.1.3
Shrinkage strain
Shrinkage of concrete is obtained from the following equation:
b ε g = t t + F bε g
E
sh t
E
(B.2.25)
sh u
for which:
bε g
sh u
= Sr × γ sr
(B.2.26)
γ sr = γ λ × γ h × γ vs × γ s × γ ψ × γ c × γ α
(B.2.27)
where,
ratio;
E
F
Sr
t
γ sr
γc
γh
γs
γ vs
= shrinkage factor;
= shrinkage factor for the effect of curing type;
= shrinkage coefficient;
= time after the curing;
= shrinkage correction factor;
= shrinkage correction factor for the effect of cement type;
= shrinkage correction factor for the effect of member size;
= shrinkage correction factor for the effect of slump of concrete;
= shrinkage correction factor for the effect of volume to surface
γα
γλ
= shrinkage correction factor for the effect of air content;
= shrinkage correction factor for the effect of ambient relative
humidity
and,
γψ
= shrinkage correction factor for the effect of fine aggregate content;
bε g
= ultimate shrinkage strain.
sh u
The following describes each of the shrinkage correction factors:
22
ADAPT
ADDENDUM TO THE USER MANUAL
ABI
Shrinkage correction factor for the effect of ambient relative humidity
γλ =
. − 0.010 × HM
RS140
T3.00 - 0.030 × HM
for 40 ≤ HM ≤ 80
for 80 < HM ≤ 100
(B.2.28)
where, HM in percentage is the ambient relative humidity.
Shrinkage correction factor for the effect of member size
γh
γh
.
R|135
1.25
|
= S1.17
||1.08
|T1.23- 0.038 × TH
.
R|135
1.25
|
= S1.17
||1.08
|T1.17 - 0.029 × TH
TH ≤ 2 in
TH = 3 in
TH = 4 in , during the firs year after loading (B.2.29)
TH = 5 in
TH ≥ 6 in
TH ≤ 2 in
TH = 3 in
TH = 4 in , ultimate values
TH = 5 in
TH ≥ 6 in
(B.2.30)
where, TH is the average member thickness in inches.
Shrinkage correction factor for the effect of volume to surface ratio
γ vs = 12
. e -0.12VS
(B.2.31)
where, VS is the volume-surface ratio of the member in inches.
Shrinkage correction factor for the effect of slump of concrete
γ s = 0.89 + 0.041S
(B.2.32)
23
ADAPT
ADDENDUM TO THE USER MANUAL
ABI
where, S is the observed slump in inches.
Shrinkage correction factor for the effect of fine aggregate content
γψ =
RS0.30 + 0.014 × P
T0.90 + 0.002 × P
for P ≤ 50
for P > 50
(B.2.33)
where, P in percentage is the ratio of the fine aggregate to total aggregate by
weight.
Shrinkage correction factor for the effect of cement type
γ c = 0.75 + 16.8 × CC
(B.2.34)
where, CC is the cement content in pounds per cubic inch.
Shrinkage correction factor for the effect of air content
γ α = 0.95 + 0.008 × AC
(B.2.35)
where, AC is the air content in percent.
3.2 AASHTO Recommendations (1994)
3.2.1 Strength and stiffness
The variation of compressive strength of concrete with time is obtained from the
following equation:
bg
fc' t =
b g
t
fc' 28
a + bt
(B.2.36)
where, a and b are constants, f’c (28) is the 28-day strength and t in days is the
age of concrete.
24
ADAPT
ADDENDUM TO THE USER MANUAL
ABI
The initial elastic modulus of elasticity is defined as:
bg
bg
E c t = 0.043w 1.5 fc' t
(MPa)
(B.2.37)
where, w is the density of concrete in kilogram per cubic meter and f’c(t) is the
strength of the concrete in Newton per millimeter squared.
3.2.2
Creep strain
The creep coefficient is defined as:
H I
F
Cb t, t g = ck k G 1.58 −
H 120JK t
i
c
f
bt − t g
10 + b t − t g
0.6
−0.118
i
i
0.6
C cru
(B.2.38)
i
for which:
kf =
62
42 + fc'
(B.2.39)
. + 177
. e -0.0213b V/S g
18
kc =
2.587
26e 0.0142 b V/S g + t
45 + t
where,
C cru
c
H
kc
kf
t
ti
V/S
3.2.3
(B.2.40)
= ultimate creep coefficient
= creep correction factor
= ambient relative humidity in percent
= factor for the effect of the volume-to-surface ratio
= factor for the effect of concrete strength
= maturity of concrete in days
= age of concrete when the load is initially applied, ε cru is the
ultimate creep strain
= volume-to-surface
Shrinkage strain
Shrinkage of concrete is obtained from the following equation:
ε sh = k s k h
td
ε shu
td + F
(B.2.41)
where,
25
ADAPT
ADDENDUM TO THE USER MANUAL
F
= Curing correction factor,
= 35 for moist cure concrete
= 55 for steam cured concrete
kh
= Humidity correction factor
.
R|143
||1.29
1.14
|
= S1.00
||0.86
||0.43
T0
(B.2.42)
= correction factor for the effect volume to surface ratio and drying
time of concrete
ks
ks =
b g
1064 − 3.7 V / S
923
26e 0.0142b V/S g + t d
45 + t d
(B.2.43)
= drying time of concrete (days)
= ultimate shrinkage strain
td
ε
HM = 40
HM = 50
HM = 60
HM = 70
HM = 80
HM = 90
HM = 100
ABI
u
sh
3.3 Eurocode 2 Recommendations (2004)
3.3.1 Strength and stiffness
Compressive strength of concrete at an age t can be calculated using the following
equation:
LM FG 28 IJ OP
H t K PQ '
fc' t = e MN
fc 28
12
bg
s 1-
b g
(MPa)
(B.2.44)
where, t in days is the age of the concrete and s is a coefficient that is a function of
cement type:
s = 0.2 for Class R cement
= 0.25 for Class N cement
= 0.38 for Class S cement.
Modulus of elasticity is defined as:
26
ADAPT
ADDENDUM TO THE USER MANUAL
Ec
3.3.2
F f btgI
= 22000G
H 10 JK
'
c
ABI
0.3
(MPa)
(B.2.45)
Creep strain
Creep coefficient and its variation with time is defined as:
b g
b g
φ t, t 0 = φ 0 β c t, t 0
(B.2.46)
where,
t
t0
= maturity of concrete
= age of concrete when the load is initially applied.
= notional creep coefficient
φ0
b gbg
= φ RH β fcm β t 0
where,
φ RH = 1 +
F
GH
1 − RH 100
0.13 h 0
φ RH = 1 +
I
JK
1 − RH 100
α1 α 2
0.13 h 0
b g 16f.8
1
β bt g =
0.1+ t
for
fcm ≤ 35 MPa
(B.2.47)
for
fcm > 35 MPa
(B.2.48)
β fcm =
(B.2.49)
cm
0
and
(B.2.50)
0.2
0
L t - t OP
β b t, t g = M
Nβ + t - t Q
c
0
H
where
0.3
0
(B.2.51)
0
b
g
= 15
. 1 + b0.012 × RH g
β H = 15
. 1 + 0.012 × RH
18
h 0 + 250 ≤ 1500
βH
18
h 0 + 250α 3 ≤ 1500α 3
fcm ≤ 35
(B.2.52)
fcm ≥ 35 (B.2.12)
where
α1
L 35 O
=M P
Nf Q
cm
0 .7
α2
L 35 O
=M P
Nf Q
0.2
cm
27
α3
L 35 O
=M P
Nf Q
cm
0.5
(B.2.53)
ADAPT
3.3.3
ADDENDUM TO THE USER MANUAL
ABI
Shrinkage strain
Shrinkage of concrete is obtained from the following equation:
ε cs = ε cd + ε ca
(B.2.54)
where, ε cd is the drying shrinkage strain and ε ca is the autogenous shrinkage strain
Drying shrinkage strain is defined as:
bg
b g
ε cd t = β ds t, t s k h ε cd,0
(B.2.55)
where,
kh
and ,
.
R|100
|0.85
=S
||0.75
T0.70
h 0 = 100
h 0 = 200
h 0 = 300
h 0 = 500
t
b g bt − t gt+−0.04
β ds t, t s =
(B.2.56)
s
s
(B.2.57)
h 03
h0 is defined as:
h0 =
2AC
U
(B.2.58)
where, AC is the concrete cross section area and U is the perimeter exposed to drying.
b
g
ε cd,0 = 0.85 220 + 110 × α ds1 e −α
'
ds2 f c
10
× 10−6 × β RH
(B.2.59)
where β RH is defined as:
L F RH IJ OP
= 155
. M1 − G
MN H 100 K PQ
3
β RH
(B.2.60)
α ds1 and α ds2 are functions of cement type and RH is the relative humidity of the
environment.
28
ADAPT
ADDENDUM TO THE USER MANUAL
ABI
Cement class S:
α ds1 = 3
α ds2 = 0.13
s = 0.38
Cement class N:
α ds1 = 4
α ds2 = 0.12
s = 0.25
Cement class R:
α ds1 = 6
α ds2 = 0.11
s = 0.20
The autogenous shrinkage strain is as follows:
bg
bg b g
(B.2.61)
bg
b
(B.2.62)
ε ca t = β as t ε ca ∞
where,
g
ε ca ∞ = 2.5 fck − 10 × 10−6
bg
β as t = 1 − ee
−0.2t 0.5
j
(B.2.63)
3.4 British Code Recommendations
3.4.1 Creep strain
Creep coefficient and its variation with time is defined as:
bg
C t = Cr K L K m Kc Ke K jKs
(B.2.64)
where,
= Ultimate creep coefficient;
Cr
= depends on the relative humidity (Figure2.1);
KL
= depends on the hardening of the concrete at the age of loading (Figure
Km
2.2);
= depends on the composition of concrete (Figure 2.3);
Kc
= depends on the effective thickness of the member (Figure 2.4);
Ke
= defines the development of the time-dependent deformation with time
Kj
(Figure 2.5);and
= depends on the percent of reinforcement.
Ks
29
ADAPT
ADDENDUM TO THE USER MANUAL
R|1
| 1
=S
||1 + ρ EE
T
ABI
for plain concrete
for reinforced concrete
(B.2.65)
s
c
where ρ = steel ratio
= As/Ac
The values of the coefficients are taken from the following diagrams:
Figure 2.1. Coefficient KL (environmental thickness)
Figure 2.2. Coefficient Km (hardening at the age of loading)
30
ADAPT
ADDENDUM TO THE USER MANUAL
Figure 2.3. Coefficient Kc (composition of the concrete)
Figure 2.4. Coefficient Ke (effective thickness)
Figure 2.5. Coefficient Kj (variation as a function of time)
31
ABI
ADAPT
3.4.2
ADDENDUM TO THE USER MANUAL
ABI
Shrinkage strain
Shrinkage of concrete can be obtained using the following equation:
bg
ε t = S r K L K C K e K j KS
(B.2.66)
where,
Sr
= shrinkage coefficient;
= depends on the relative humidity (Figure 2.6);
KL
= depends on the composition of concrete (Figure 2.3);
Kc
= depends on the effective thickness of the member (Figure 2.7);
Ke
= defines the development of the time-dependent deformation with time
Kj
(Figure 2.5); and
= depends on the percent of reinforcement (Equation B.2.65).
Ks
Figure 2.6. Coefficient KL for shrinkage (environment)
32
ADAPT
ADDENDUM TO THE USER MANUAL
ABI
Figure 2.7. Coefficient Ke for shrinkage (effective thickness)
3.5
Hong Kong Code Recommendations
3.5.1
Creep strain
Creep coefficient and its variation with time is defined as:
bg
C t = Cr K L K m Kc Ke K jKs
(B.2.67)
where,
= Ultimate creep coefficient;
Cr
= depends on the relative humidity (Figure 2.1);
KL
= depends on the hardening of the concrete at the age of loading (Figure
Km
2.2);
= depends on the composition of concrete (Figure 2.3);
Kc
= depends on the effective thickness of the member (Figure 2.4);
Ke
= defines the development of the time-dependent deformation with time
Kj
(Figure 2.5);and
= depends on the percent of reinforcement (Equation B.2.65).
Ks
3.5.2
Shrinkage strain
Shrinkage of concrete can be obtained using the following equation:
33
ADAPT
ADDENDUM TO THE USER MANUAL
bg
ε t = C sS r K L K C K e K j KS
ABI
(B.2.68)
where,
= shrinkage coefficient for Hong Kong ;
= 4.0;
Sr
= shrinkage coefficient;
= depends on the relative humidity (Figure 2.6);
KL
= depends on the composition of concrete (Figure 2.3);
Kc
= depends on the effective thickness of the member (Figure 2.7);
Ke
= defines the development of the time-dependent deformation with time
Kj
(Figure 2.5); and
= depends on the percent of reinforcement (Equation B.2.65).
Ks
Cs
34