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ANSYS CivilFEM Bridge Webinar
e er . arre , . . . ., . .
2009 CAE Associates
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ANSYS + CivilFEM
Challenges of Bridge Engineers today: Increase Construction efficiency
Design and Build to Save Material Costs
Extend the life of existin brid es
Better Empower a shrinking engineering workforce
Develop more accurate representation of the structural response:
Nonlinear analysis and incremental construction are ANSYS/CivilFEM strengths
eve op au oma e ana yses o save es gn me
Perform what if and design optimization tasks to create more effectiveuse of construction materials
2
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CAE Associates CivilFEM / ANSYS Partner
The worlds biggest and most sophisticated users of engineeringsimulation choose CAE Associates for consulting services, training andsoftware. e.g. ABB, AREVA, Bechtel-Houston, GE (Nuclear, Energy, Aviation, GRC),Seimens, UTC (Pratt & Whitney, Otis, Sikorsky), AECOM, Westinghouse, Parsons.
nce e company s ncep on n , we ave spec a ze n prov ng
solutions to engineering problems using FEA and CFD technology.
3
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What is CivilFEM?
- , - - -traditional ANSYS developed by ANSYSs Spain distributorINGECIBER
AASHTO LRFDBr id eD es i n S eci f ic at i ons
N /CivilSYS FEM
55
2.5
40
5
15
15
5
8060
50
60
5
5
5
2.5
5
2.5
60
CANADA
50
40
30
(Western USA)
TropicofCancer
5
2.5
2.5
MXICO
AAccel eration Coeffic ient
SeismicZone
1
2
3
4> 0.29
> 0.19 and < 0.29
_> 0.09 and < 0.19
_
< 0.09
_
4
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INGECIBER- CivilFEM Developer / ANSYS Partner
Ingeciber S.A. is a CAE company and ANSYS Channel Partner
CAE Software
In ecibers Qualit Assurance S stem is ISO 9001 certified.
ANSYS, Inc. and Ingeciber, S.A. have a long standing OEMAgreement and established a strategic alliance for FEA solutionsin the construction industry. Some worldwide Customers:
5
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ANSYS Today
>10,000TotalCustomers
>6,000TotalCustomers
>2,000TotalCustomers,
>140,000UniversitySeats >200ChannelPartners >75IndustryPartners
, >70,000UniversitySeats >20ChannelPartners >80IndustryPartners
,
6
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ANSYS + CivilFEM
purpose structural analysis features of ANSYS (ISO-9001)with high-end civil engineering-specific structural analysiscapabilities of CivilFEM (ISO-9001).
7
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Current CivilFEM Distributors
8
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CAE Associates, Inc.
One of fi rst 4 ANSYSChannel Partners
Since 1985
9
.
Since 1981
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CAE Associates CivilFEM / ANSYS Partner
, One of the original ANSYS Channel partners
Custom Training of ANSYS and CivilFEM
10
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Sampling of CAE Consulting Services
NIST Structural Fire Response and ProbableCollapse Sequence of the World Trade CenterTowers Investigation
Steam Generator Replacement in Nuclear
on a nmen u ngs
Pre-stressed Concrete Pipe Simulation Concrete Dam simulation to meet
orps o ng neers cens ng
11
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CAE Associates Senior Technical Staff
Nicholas M. Veikos, Ph.D., President
Peter R. Barrett, M.S.C.E., P.E., Vice President
Michael Bak, Ph.D., Project Manager
a r c unn ng am, . . . ., ro ec anager
Steven Hale, M.S.M.E., Project Manager
James Kosloski M.S.M.E. Pro ect Mana er
Hsin-Hua Tsuei, Ph.D., CFD Manager
Jonathan Masters, Ph.D., Project Manager
George Bauer, M.S.M.E., Project Manager
Eric Stamper, M.S.M.E., Project Manager
, . . . .,Lawrence L. Durocher, Ph.D., Director
12
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ANSYS Strengths
Nonlinear Stress Analysis Contact
Plasticity
Creep
arge e ect on - e ta ects
Element Birth and Death
Full Element Library (over 200)
eams, pes e s
2D and 3D Solids
Springs, Contact, etc Dynamic Analysis
Response Spectrum
Nonlinear Transient Dynamics
Thermal-Stress Analysis
Indirect and direct coupled field simulations
13
Solvers, meshing, Postprocessing, Graphics
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CivilFEM Strengths
Entire suite of ANSYS capabilities including nonlinear analysis
and dynamics u - n a er a o e s an o e ec ng
Industry Specific CivilFEM Modules
Nonlinear Bridge Simulation Pre-stressed Concrete
14
Nuclear Applications
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CivilFEM & ANSYS
15
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CivilFEM Help
Examples Manuals
Advanced Workshops
Training Courses
16
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Bridges andon near t es
Overview
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Quote from Bridge Designer
"ANSYS has always been a powerful tool in the resolution of advanced
, , , . ,with the addition of CivilFEM, it has become a decisive instrument in the
entire design and project of bridges such as our "Viaducto del Sil, en
Ponferrada (Len, Spain)".
In the analysis of large bridges you must take into account a lot of
structural features; different materials, types of section, construction
process,... CivilFEM Preprocessor is a definitive help to give ANSYS all the
n orma on nee s.
Later, CivilFEM Postprocessor allows you to check your model under several
International Codes and, both quickly and safely, confirming that the
solution proposed for the bridge is valid.
This whole process eventually concludes in a highly accurate answer to our
clients' requests, with considerable savings in the amount of time spent in
developing the whole project and with a decisive saving of costs in theconstructed bridge.
Kind regards,
Jorge Prez Armio
18
A.T.P. Ingeniera, S.L.
www.atp-ingenieria.es
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Bridge Module Main Features
Utilities for generating common bridge sections andlayout design
Bridge layout modelling (in plan and elevation view)
Geometric and finite element model eneration witheither Beams or Shells or 3d Solid elementsincluding wizards for
Suspension bridges
Arch bridges
Cable-Stayed bridges
Load Generation Overloads
Moving loads (vehicles editor)
Utility for Automated Prestressed force input
User loadsAutomatic Load combinations
Simulation of construction process
19
Concrete Creep and Shrinkage
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Section Definition
20
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Slab Section Definition
RS
BTOP
BMTTOP
Rectangular section Trapezoidal section with flangesB
DEPTH DEPTH
BBOT
TBOT
TF
BTOP
BBOTDEPTH
TTOP
TS
TBOT BBOT
BM2
BM1
BTOP
DEPTH
TTOP
TM
PS
Trapezoidal section Polygonal section with two bends
BM2R
BTOPRBTOPL
BM2L TTOPR
axis
Polygonal Asymmetric with two bends Note: The upper line (deck) is always
BBOTR
BM1RBM1L
BBOTL
DEPTHL
TBOTL
TML
TBOTR
TMR DEPTHR
PA
21
Bridge Section Types
horizontal. The slope must be laterdefined with the sections bank.
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Slab Section Definition
tiections aredefined bydimensions
22
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Slab Section Definition
Global size Cell dimensions
Mesh divisions are defined
Supports are defined (3d Model)
Holes
Flange
23
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Box Section Definition
Box Section definition window:
Main dimensionsare entered here.
shape hasbeen created,
the eometrwill be refinedusing step-by-step
modification.
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Box Section Definition
CellSymmetry
WebFlange
25
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Box Section Definition
Crown
26
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Box Section Definition
Box Section window:
Global
Edit Mesh Divisions
Web div
o om
div
27
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Box Section Definition
It is im ortant to note that all the cross sections defined must have thesame number of divisions (the same number of sub-elements). If not, theprogram will not be able to generate a swept mesh of the bridgeautomatically.
1
2
12
3
to mesh the bridge because
the two cross section defined
do not have the same number
3
4
4
of divisions
28
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Box Section Definition - Script
! Defines a cross section in a box cross-section bridge.
! Main Menu > CIVIL Preprocessor > Bridges Prep > Bridge Sections > Box
!~BRSBOX, NSEC, MAT, NCEL, DEPTH, WDTCEL, THTOP, THBOT, THWEB, LFL
~BRSBOX, 1, 1, 1, 2.5, 6.00, 0.25, 0.2, 0.5, 2.5
~BRSMDF,1,NAME,,,Section 3
! Main Menu > CIVIL Preprocessor > Bridges Prep > Bridge Sections > Modify
!~BRSMDF,ICSEC, Lab1, Lab2, Lab3, VALUE, IDX1, IDX2, IDX3~BRSMDF, 1, BOX, KSYM, , -1
!
A=0.75/SQRT(2.50**2+0.75**2)
~BRSMDF,1,BOX,WEB,SLOPE,-A,0,0,0
~BRSMDF,1,BOX,WEB,RATS,0.25,0,1,0
~ , , , , , . , , ,
~BRSMDF,1,BOX,WEB,RATB,0.12,0,1,0
~BRSMDF,1,BOX,WEB,SLPB,0.75,0,1,0
~BRSMDF,1,BOX,WEB,RATB,0.2,0,3,0
~ , , , , , . , , ,
~BRSMDF,1,BOX,FLANGE,THICK,0.15,0,0,0
~BRSMDF,1,BOX,WEB,RATS,1 ,1,1,0
~BRSMDF,1,BOX,WEB,SLPS,0.1,1,1,0
29
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Layout Definition
Define Angle units (only for the layout)
Definition of the mileage points that represent the structure
Typically read from a file
~BRINIP,1,0,0,0,0,0 ! Defines the MP and Ansys direction
! from which the bridge model is generated
~BRADDPL,99.5,153.5 ! bridge layout in plan view
~BRADDEL,99.5,153.5 ! bridge layout in elevation view
~BRSKTCH,5 ! Plots the bridge axis (MPs path)
! Example
~BRINIP,1,
~BRADDPL, 90,120, 0, 0
~BRADDPL, ,170, 0,-200
~BRADDEL, 90,170, 0, 0
Definition of plan and elevation layout
30
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Layout in Plan View
, , , , ,
MP: initial and final mileage point
ANG: angle with respect to previous
.
31
L t i Pl Vi
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Layout in Plan View
Plan view parameter definition
Case 1: Straight stretch, If a radio is infinite the field is not introduced, or
the value zero is introduced.
Case 2: Circumference, If Ri = Rf Null:0
32
spiral spline ), If Ri Rf
L t i El ti Vi
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Layout in Elevation View
~ , , , ,
MP: initial and final mileage
II, IF: Slopes in % of then a
And final MP of the stretch
ANG: angle respect to theprevious stretch
33
L t i El ti Vi
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Layout in Elevation View
Elevation view parameter definition
If II = IF the stretch, in elevation view, is a
34
.
Plot Sketch
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Plot Sketch
35
Solid Model
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~BRDEF, MP, Nsec, Yoffs, Zoffs, Bank, Trans, Skew, Solid
Solid Model
For the correct generation of the solid model and the finite element modelof the structure, it is necessary to define a series of attributes. These
Cross section number that will be assigned to the different mileage points(MPs) forming the bridge.
points with the cross section plain (Yoffs, Zoffs), referred to the cross sectioncoordinate system
Bank: Possibility of defining the banks along the bridge.
yMP,s line
z
Zoffs
YoffsBank (Rotation's center P)
P
36
Bridge definition
Solid Model
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Solid Model
section with respect to the road axis.
o ow or so sect on: s capa ty a ows t e user to e ne o ow or
solid sections for a particular mileage point. Therefore, the user mayconsider hollow sections or solid section at particular points of the
, . -
Hollow section(Solid=0 or blank Solid sectionAccording to original contour (Solid0)
37
Cross sections at supports
Solid Model
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Solid Model
38
Model Generation
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Model Generation
This utility generates the complete geometrical model ofthe structure as well as the finite element model from thecross sections definition (location, offsets, banks, etc)
It is generated from the defined sections
It utilizes the previously defined layout It generates the finite element model of either beams, shells
or - r c s au oma ca y
39
Bridge Wizards
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Bridge Wizards
Concrete (with a CivilFEM bridge section)
Steel (with a CivilFEM steel 3D pattern)
Cable Stayed Bridgesw a v r ge sec on
Arch Bridges(with a CivilFEM bridge section)
Beam model
Shell model
40
Bridge Wizards
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Bridge Wizards
Concrete Suspension Bridgesw a v r ge sec on
(with a CivilFEM steel 3D pattern)
ener c uspens on r ges(with a CivilFEM generic cross section)
Mixed section, two types of section: Concrete slab over I-section steel beams
41
Suspension Bridge Generators
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Suspension Bridge Generators
Concrete Suspension Bridges
42
Supported Bridge Example
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Suppo ted dge a p e
Supported Bridges :
Same parameters as suspension bridges are used, but only bridge deck will begenerated.
ConcreteSteel
43
Loads Definition
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,are automatically generated such that can easily beincorporated into load combinations Load types :
Mobile (vehicles, pedestrian, etc.)
Surface loads (structural, traffic, snow, etc.)
Prestressing, in any direction.
Self weight
The loads enerate LoadStates LS that are rou ed in families and
LS 1
later become combinations.
LS 2Vehicle
Load
Family 19 Combination 19
44
Loads Definition: Families
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,topology.
All the load steps belonging to a family are combined
The combined family can be later introduced as astarting point in load combinations.
family
45
Loads Generation (Traffic Loads)
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( )
Vehicles: Ri id truck or flexible train, ada table to the ath
User friendly path definition: road surface and road axis are automaticallydetected by the program
46
Loads Definition: Vehicles
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Start End
Bridge deckFirst Last
ve ic eposition
position
It is possible to define when the vehicle movement starts and ends,relative to the bridge geometry.
47
Loads Generation (Prestressing Cables)
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points using splines)
Introduce the tensile force at specific locations in the tendons path
u u u
P'1 P'N
P
P
PP
P1
2
k+2
k+1
NPk
OP
Rz
MRz
MR Kfz
T1
1
3D spline generationx
RMRy
x
c.d.g.R
y
Kfx
Kfy
T2
2
48
Transmision of the cable actions to the model
3D Tendon Geometry Editor
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of all tendons of a structure. The geometry may be shown and editedeither graphically or by coordinates.
Tool Bar
Elevation
ObjectTree
View
Info/EditWindow
49
Plan View
Prestressed Forces, Moments & Stresses
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Stresses in the support and in the middle of span.
50
Combinations with Variable Coefficients
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point P?
P
51
Combinations with Variable Coefficients
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Combinations with variable coefficients (favorable/unfavorable)
Actions in different directions (wind, earthquakes, )
Combinations according to codes logic
52
Combinations with Variable Coefficients
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ost
most
1 e2
Permanent actions G
dint
hem
ition
tedinth
ositio
n
irtuallan
irtua
lla
Bor
der
Bor
der
Bor
der Self weight
Dead load of 20 kN/mRoad traffic actions (Qk)
0kNl
ocat
orablepo
200kNl
oc
a
vorable
Vehicles (Double-axis)2x300 kN in virtual lane 12x200 kN in virtual lane 2
2x30
unfa
2x
un n orm y s r u e oa s
9.0 kN/m2 in virtual lane 12.5 kN/m2 in virtual lane 2
2
Target:
.
53
Minimum MZ
Combinations with Variable Coefficients
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.
Permanent actions Variable actions
kQkG QG
the coefficients to apply foreach target and element.
Safety factorSafety factorfor variable actions:
Q = 0 if it is favorable
for permanent actions:
G = 1.00 if it is favorable
Q = 1.00 if it is unfavorableG = 1.35 if it is unfavorable
54
Combinations with Variable Coefficients
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. Each combination rule has its own Start States
A combination rule may have any number of Start States (up to ax u , ,
The result of the combination is called a combined result Combination rules can be nested
That means that the combined result of the combination i can be a startstate for the combinations i+1, i+2, , n, and combined results of
combination i+1 may be a start state for combinations i+2, i+3, , n
...QQGGE Windk,Wind0,WindQ,Livek,LiveQ,Deadk,DeadG,Gravityk,GravityG,
55
Combination RuleCombined result Start State
Combinations with Variable Coefficients
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56
Combinations with Variable Coefficients
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Before starting with calculations, you must define all the combination rules and
targets.
Combination number
Type of combinationNumber of Start States included in
57
Combinations with Variable Coefficients
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Maximum coefficient Minimum coefficient
If a default value is introduced, it will bea lied to the rest of Start States.
58
Code Checking Results
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.011637
.039639
.067641
.095642
.123644
.151646
.179647
PHASE 1:
AXIAL +BENDING CHECKING
.
.235651
.263652
X
Y
Z
59
CivilFEM Creep and Shrinkage
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Time dependent deformation without external loads, due to the concretehardening.
Time dependent deformation under the influence of stress
of stresses, the reaction forces and the pre-stressing forces that act on thestructure.
60
CivilFEM Creep and Shrinkage
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)()()( ttt shcrelt (t, )o Strain due to creep only appearsafter loading the structure
(t, ) CREEPoCRStrain due to shrinkageappears at the initial time
Elastic s train is produced, instantanously,at the moment the load is applied
(t)e
(t)SH
ELASTIC
SHRINKAGE
t,o t
2
F(t)
0
61
Strain components
t,o
CivilFEM Creep and Shrinkage
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Linearity: the creep deformation is proportional to the stresses
(t, )
(t,0)
(t, )1
CR
CR
(0)CR
( )1CR
*
*
(t, )2CR
( )2CR
*
),(),(28,
0 t
Et
c
ccr
t, 1 2
Creep variation w ith ti me and w ith th e load application age
The validity of this assumption is experimentally confirmed for initialstresses below 40% of the strength of concrete.
62
CivilFEM Creep and Shrinkage
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(t, )CR
(t, )1CRI
(t, )2CR
II
CR
(t, )CR
CR
Principle of superposition: thedeformation due to creep attime t caused b a stress
t, 1 2t,
o o
increment applied at time is
independent from any stressincrement that takes place,1 ,2
T I II
(t, )CR (t, )CR
Therefore, the deformations
1 t,
F FT I
CR CR CR
1 t,
CR CRT I
CR CRT I
CRII
t,1 2
o
o
t,1 2
o
Superposition princi ple
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CivilFEM Creep and Shrinkage
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CivilFEM Creep and Shrinkage
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Shrinkage in CivilFEM is computed from the shrinkage strain curvesdefined in the concrete material properties.
Curves can be defined by the user point-by-point.
r n age s ra ns w e compu e n a ma er a s w e s r n ageoption activated.
They are introduced in the model by temperature increments and calculated.
Since shrinkage strains are related to thermal strains, temperatureincrements must not be applied to elements that are associated to materialswith the shrinka e o tion activated.
65
CivilFEM Creep and Shrinkage
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- ,defined with command TIME, must coincide with active time of CivilFEMdefined with command ~ACTTIME.
All the structural elements of ANSYS support the modeling of concreteshrinkage with CivilFEM. Exceptions:
SHELL91, SHELL181, SOLID191
SHELL99 and SOLID46 elements can only be used with KEYOPT(2) = 0 or 1
66
CivilFEM Creep and Shrinkage
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- -
In the step by step method the time is divided into a series of intervals. In eachintervals the equilibrium and compatibility conditions of the structure aresatisfied. Strain is computed as follows:
t
cc
crel dE
t
Ett
028,
)(),(
)(
1)()(
The solution procedure of CivilFEM employs a non linear calculation withautomatic time discretization: the time steps, corresponding to load steps andsubsteps, are chosen to follow the evolution of loads and model geometry.
k
i
i
c
ik
ic
k tE
tt
tEt
1 28,
)(),(
)(
1)(
67
CivilFEM Creep and Shrinkage
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coefficients defined in the material properties and from the stressincrements produced during the steps of time discretization:
i
o
i t,
o
),(
k
ik tttt
ttt
68
1 28,
i cE
CivilFEM Creep and Shrinkage
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(subroutine UserCreep is programmed for this case, which uses an implicittime integration algorithm).
It is also possible to take into account an aging coefficient. In this case creepstrains are computed as follows:
k
iik
ikk
kcr ttttttttt 1
1 )(),(),()(),()(
t1 is the time of the application of the first load
If the value of the aging coefficient is not specified, the program uses:
cc 1 28,28,
5.0
5.0
1),(
i
iik
t
ttt
Like in case of shrinkage, for a correct evaluation of time-dependentproperties, ANSYS time defined with command TIME, must coincide with
69
act ve t me o v e ne w t comman ~ .
CivilFEM Creep Effective Modulus Method
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takes into account the additional strain caused by phenomenon of creep
The effective modulus is calculated b the followin ex ression:
1
,.t
EEtEx
xeffcr
28Ex
The concrete age at the moment of the load application is calculated as thedifference between the load application time, TAppLoad and the materialactivation time, Tact.
TActTAppLoad
70
CivilFEM Creep Effective Modulus Method
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s s mp e me o nee s on y one oa s ep or eac me o esolved, so this method is much faster than the step by step method.
Under this method, the creep strain only depends on the current state of
stresses thats why its independent of the previous load history. Thismethod provides accurate results for concrete stresses almost constant inme.
This method is based on the substitution of the material elasticity modulusby an effective modulus so it isnt possible to determine the creep strainindependent to the elastic strain so the final elastic strain will be thecombination of these.
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CivilFEM Creep and Shrinkage
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Step by step method:
Beam: LINK180, BEAM188, BEAM189
e :
2D Solid: PLANE182, PLANE183
3D Solid: SOLID185, SOLID186, SOLID187
ec ve mo u es me o :
All the ANSYS structural elements.
Element types that are supported in CivilFEM to model concreteShrinkage:
All the ANSYS structural elements except:
All pipe elements.
SHELL 91, SHELL 181, SOLID 191. It can only be used on SHELL 99 and SOLID 46 elements if KEYOPT (2)=0 or 1.
72
Creep and Shrinkage Time Stepping
~CFMP,1,LIB,CONCRETE,EC2,C16/20 ! Concrete
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~ , , , ,, reep y ep y ep e o
~CFMP,1,CONCR,KEYCT,,0
~CFMP,1,CONCR,KSHRINK,,1 ,0,0,0 ! by temperatures
~CFMP,1,CONCR,AGESRINI,,10 ,0,0,0 ! concrete age when shrinkage
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
TIME,10 $ ~ACTTIME,10 ! 10 Days
RATE,ON
NSUBST,1SOLVE
, ,
TIME,15 $ ~ACTTIME,15 ! 15 Days
SOLVE
NSUBST,10,
TIME 25 ~ACTTIME 25 ! 25 Da sSOLVE
TIME,90 $ ~ACTTIME,90 ! 90 Days
SOLVE
TIME,365 $ ~ACTTIME,365 ! 365 Days
SOLVE
TIME,1000 $ ~ACTTIME,1000 ! 1000 DaysSOLVE
TIME,10000 $ ~ACTTIME,10000 ! 10000 Days
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NON- INCREMENTAL ANALYSIS:
Construction Sequence (Curing) Analysis
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NON INCREMENTAL ANALYSIS:
Concrete
tee
,until concrete has gained resistance.
ANALY I :
First the steel beam is placed and then the concrete, without resistance, will
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e poure on e s ee s ruc ure.
Cable Stayed Bridge Wizard
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Y Y
X
Y
Z
XZ Z
MN
MX
X
Y
Z
75
Cable Stayed Bridge Wizard
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Cable Stayed Bridge Wizard
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~CPDEF,1,3 ! 3 Phases
! Phase 1Geometry
~ , , ,
~CPSTDEF,1,SS,6,14,,0
~CPSTDEF,1,SS,1,6 ~CPSTDEF,1,TENDON,1,10 Phases
40 m 40 m50 m
~CPSTDEF,1,TENDON,11,30,,0
! Phase 2
~CPSTDEF,2,TIME,12 ! 12 days
~CPSTDEF,2,SS,1,11 Cross Sections
50 m 30 m50 m
Phase 1 Phase 2 Phase 3
Section 1
~CPSTDEF,2,TENDON,1,20
~CPSTDEF,2,TENDON,21,30,,0
! Phase 3
~CPSTDEF,3,TIME,24 ! 24 days 8 m 8 m12 m 12 m 8 m 8 m12 m 12 m10 m 10 m15 m 15 m
Section 2 Section 2 Section 2 Section 2Section 1
Linear transition
Section 1
Linear transition
Section 1
Linear transition
Section 2
~CPSTDEF,3,SS,1,14
~CPSTDEF,3,TENDON,1,30
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Postprocess Results
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-.161E+ 08
-.985E+ 07
-.361E+ 07
.263 E+ 07
.887E+ 07
.151 E+ 08
+
PHASE 1:BENDING MOMENT MZ -.228E+ 08
-.152E+ 08PHASE 2:
X
Y
Z
.401E+ 08
.
.276E+ 08
.338E+ 08
-.
.765E+ 07
.152E+ 08
.229E+ 08
.305E+ 08
.381E+ 08
.457E+ 08
X
Y
Z
-.220E+ 08
-.143E+ 08
-.665E+ 07
.101 E+ 07
.867 E+ 07
.163E+08
PHASE 3:BENDING MOMENT MZ
Y
.240E+ 08
.316E+08
.393 E+ 08
.470E+ 08
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XZ
Case Study: Sil River Bridge
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Case Study: Sil River Bridge
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Case Study: Sil River Bridge
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