Simulation analysis of prestressed tensioning whole processon direct constraint method
The accuracy simulation of the prestressed tensioning effect is the foundation of prestressed bridge design, construction and reinforcement. Direct constraint method was used in the application of prestressed tensioning whole process simulation analysis on the background of prestressed testing exper...
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Kaimin Liu 2018-06-16T14:55:35Z 2018-06-16T14:55:35Z 2017 Simulation analysis of prestressed tensioning whole processon direct constraint method / Kaimin Liu // Functional Materials. — 2017. — Т. 24, № 1. — С. 122-126. — Бібліогр.: 10 назв. — англ. 1027-5495 DOI: https://doi.org/10.15407/fm24.01.122 https://nasplib.isofts.kiev.ua/handle/123456789/136655 The accuracy simulation of the prestressed tensioning effect is the foundation of prestressed bridge design, construction and reinforcement. Direct constraint method was used in the application of prestressed tensioning whole process simulation analysis on the background of prestressed testing experiment. Its aim was to achieve the real simulation of interaction between prestressed tendon and concrete in the tensioning whole process. Three-dimensional solid elements were adopted to simulate pre-stressed reinforcement unit and concrete unit. Bilinear Coulomb friction was adopted as the friction form between prestressed tendon and concrete. Direct constraint method that has the characteristics of good stability and fast convergence speed was used to calculate the effective stress of prestressed tendon at each tension stage. The loss of one-way stress was also calculated. The effective prestressed values by simulation on direct constraints method can be well with the measured values and the theoretical values on Code for Design of Highway Reinforced Concrete and Prestressed Concrete Bridges and Culverts. The method has theoretical basis on accurately simulating the actual stress in different stages of the prestressed tendon. It can be helpful for bridge design and reinforcement. Методом прямого ограничения проведено моделирование процесса предварительного натяжения на основании экспериментов по тестированию предварительного напряженных систем. В качестве модельного объекта рассмотрено взаимодействие между предварительно напряженой арматурой и бетоном. Для имитации армирующих блоков и блоков бетона был адаптирован трехмерный метод упругого твердого тела. В качестве модели, описывающей силы трения, возникающие между предварительно напряженной арматурой и бетоном, рассматривается модель кулоновского трения. Для вычисления эффективных напряжений армирующей матрицы на разных этапах натяжения был использован метод прямого ограничения, обладающий хорошей стабильностью и высокой скоростью сходимости. Показано, что значения эффективных преднапряжений, полученные путем моделирования методом прямого ограничения, находятся в качественном согласии с экспериментальными и теоретическими значениями. Методом прямого обмеження проведено моделювання процесу попереднього натягнення на підставі експериментів по тестуванню попередньо напружених систем. В якості модельного об’єкту розглянуто взаємодію між переднапруженою арматурою і бетоном. Для імітації блоків, що армують та блоків бетону був адаптований тривимірний метод пружного твердого тіла. В якості моделі, яка описує сили тертя, що виникають між попередньо напруженою арматурою і бетоном, розглядається модель кулоновського тертя. Для обчислення ефективних напружень матриці, що армує, на різних етапах натягу був використаний метод прямого обмеження, що володіє гарною стабільністю та високою швидкістю збіжності. Показано, що значення ефективних переднапружень отриманих шляхом моделювання методом прямого обмеження, знаходяться в якісній згоді з експериментальними та теоретичними значеннями. en НТК «Інститут монокристалів» НАН України Functional Materials Modeling and simulation Simulation analysis of prestressed tensioning whole processon direct constraint method Моделювання натягу в попередньо напружених системах Article published earlier |
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| title |
Simulation analysis of prestressed tensioning whole processon direct constraint method |
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Simulation analysis of prestressed tensioning whole processon direct constraint method Kaimin Liu Modeling and simulation |
| title_short |
Simulation analysis of prestressed tensioning whole processon direct constraint method |
| title_full |
Simulation analysis of prestressed tensioning whole processon direct constraint method |
| title_fullStr |
Simulation analysis of prestressed tensioning whole processon direct constraint method |
| title_full_unstemmed |
Simulation analysis of prestressed tensioning whole processon direct constraint method |
| title_sort |
simulation analysis of prestressed tensioning whole processon direct constraint method |
| author |
Kaimin Liu |
| author_facet |
Kaimin Liu |
| topic |
Modeling and simulation |
| topic_facet |
Modeling and simulation |
| publishDate |
2017 |
| language |
English |
| container_title |
Functional Materials |
| publisher |
НТК «Інститут монокристалів» НАН України |
| format |
Article |
| title_alt |
Моделювання натягу в попередньо напружених системах |
| description |
The accuracy simulation of the prestressed tensioning effect is the foundation of prestressed bridge design, construction and reinforcement. Direct constraint method was used in the application of prestressed tensioning whole process simulation analysis on the background of prestressed testing experiment. Its aim was to achieve the real simulation of interaction between prestressed tendon and concrete in the tensioning whole process. Three-dimensional solid elements were adopted to simulate pre-stressed reinforcement unit and concrete unit. Bilinear Coulomb friction was adopted as the friction form between prestressed tendon and concrete. Direct constraint method that has the characteristics of good stability and fast convergence speed was used to calculate the effective stress of prestressed tendon at each tension stage. The loss of one-way stress was also calculated. The effective prestressed values by simulation on direct constraints method can be well with the measured values and the theoretical values on Code for Design of Highway Reinforced Concrete and Prestressed Concrete Bridges and Culverts. The method has theoretical basis on accurately simulating the actual stress in different stages of the prestressed tendon. It can be helpful for bridge design and reinforcement.
Методом прямого ограничения проведено моделирование процесса предварительного
натяжения на основании экспериментов по тестированию предварительного напряженных
систем. В качестве модельного объекта рассмотрено взаимодействие между предварительно
напряженой арматурой и бетоном. Для имитации армирующих блоков и блоков бетона был
адаптирован трехмерный метод упругого твердого тела. В качестве модели, описывающей
силы трения, возникающие между предварительно напряженной арматурой и бетоном,
рассматривается модель кулоновского трения. Для вычисления эффективных напряжений
армирующей матрицы на разных этапах натяжения был использован метод прямого
ограничения, обладающий хорошей стабильностью и высокой скоростью сходимости.
Показано, что значения эффективных преднапряжений, полученные путем моделирования
методом прямого ограничения, находятся в качественном согласии с экспериментальными
и теоретическими значениями.
Методом прямого обмеження проведено моделювання процесу попереднього натягнення
на підставі експериментів по тестуванню попередньо напружених систем. В якості модельного
об’єкту розглянуто взаємодію між переднапруженою арматурою і бетоном. Для імітації
блоків, що армують та блоків бетону був адаптований тривимірний метод пружного твердого
тіла. В якості моделі, яка описує сили тертя, що виникають між попередньо напруженою
арматурою і бетоном, розглядається модель кулоновського тертя. Для обчислення ефективних
напружень матриці, що армує, на різних етапах натягу був використаний метод прямого
обмеження, що володіє гарною стабільністю та високою швидкістю збіжності. Показано,
що значення ефективних переднапружень отриманих шляхом моделювання методом
прямого обмеження, знаходяться в якісній згоді з експериментальними та теоретичними
значеннями.
|
| issn |
1027-5495 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/136655 |
| citation_txt |
Simulation analysis of prestressed tensioning whole processon direct constraint method / Kaimin Liu // Functional Materials. — 2017. — Т. 24, № 1. — С. 122-126. — Бібліогр.: 10 назв. — англ. |
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AT kaiminliu simulationanalysisofprestressedtensioningwholeprocessondirectconstraintmethod AT kaiminliu modelûvannânatâguvpoperednʹonapruženihsistemah |
| first_indexed |
2025-11-26T17:43:56Z |
| last_indexed |
2025-11-26T17:43:56Z |
| _version_ |
1850766144039813120 |
| fulltext |
122 Functional materials, 24, 1, 2017
ISSN 1027-5495. Functional Materials, 24, No.1 (2017), p.122-126
doi:https://doi.org/10.15407/fm24.01.122 © 2017 — STC “Institute for Single Crystals”
Simulation analysis of prestressed tensioning
whole process on direct constraint method
Kaimin Liu
School of Civil, Environmental Engineering & Architecture, Hubei
University of Technology, Wuhan, Hubei 430068, China
Received December 7, 2016
The accuracy simulation of the prestressed tensioning effect is the foundation of prestressed
bridge design, construction and reinforcement. Direct constraint method was used in the ap-
plication of prestressed tensioning whole process simulation analysis on the background of pre-
stressed testing experiment. Its aim was to achieve the real simulation of interaction between
prestressed tendon and concrete in the tensioning whole process. Three-dimensional solid ele-
ments were adopted to simulate pre-stressed reinforcement unit and concrete unit. Bilinear
Coulomb friction was adopted as the friction form between prestressed tendon and concrete. Di-
rect constraint method that has the characteristics of good stability and fast convergence speed
was used to calculate the effective stress of prestressed tendon at each tension stage. The loss
of one-way stress was also calculated. The effective prestressed values by simulation on direct
constraints method can be well with the measured values and the theoretical values on Code for
Design of Highway Reinforced Concrete and Prestressed Concrete Bridges and Culverts. The
method has theoretical basis on accurately simulating the actual stress in different stages of the
prestressed tendon. It can be helpful for bridge design and reinforcement.
Keywords-Direct constraint method; Finite element simulation; Tensioning whole process;
Effective prestress; Prestressed tendon
Методом прямого ограничения проведено моделирование процесса предварительного
натяжения на основании экспериментов по тестированию предварительного напряженных
систем. В качестве модельного объекта рассмотрено взаимодействие между предварительно
напряженой арматурой и бетоном. Для имитации армирующих блоков и блоков бетона был
адаптирован трехмерный метод упругого твердого тела. В качестве модели, описывающей
силы трения, возникающие между предварительно напряженной арматурой и бетоном,
рассматривается модель кулоновского трения. Для вычисления эффективных напряжений
армирующей матрицы на разных этапах натяжения был использован метод прямого
ограничения, обладающий хорошей стабильностью и высокой скоростью сходимости.
Показано, что значения эффективных преднапряжений, полученные путем моделирования
методом прямого ограничения, находятся в качественном согласии с экспериментальными
и теоретическими значениями.
Моделювання натягу в попередньо напружених системах. Каймінь Лю.
Методом прямого обмеження проведено моделювання процесу попереднього натягнення
на підставі експериментів по тестуванню попередньо напружених систем. В якості модельного
об’єкту розглянуто взаємодію між переднапруженою арматурою і бетоном. Для імітації
блоків, що армують та блоків бетону був адаптований тривимірний метод пружного твердого
тіла. В якості моделі, яка описує сили тертя, що виникають між попередньо напруженою
арматурою і бетоном, розглядається модель кулоновського тертя. Для обчислення ефективних
напружень матриці, що армує, на різних етапах натягу був використаний метод прямого
обмеження, що володіє гарною стабільністю та високою швидкістю збіжності. Показано,
що значення ефективних переднапружень отриманих шляхом моделювання методом
прямого обмеження, знаходяться в якісній згоді з експериментальними та теоретичними
значеннями.
Functional materials, 24, 1, 2017 123
Kaimin Liu / Simulation analysis of prestressed tensioning ...
1. Introduction
Accurate simulation of prestressed tension
effects is the basis for the rational design of
prestressed concrete bridge. Old bridge rein-
forcement, fill-tensioned of prestress or supple-
ment of external prestress and other special
circumstances require more detailed and effec-
tive structural tension simulation. But the ac-
curate numerical analysis is very difficult. It is
often used as a boundary or an initial condition
applied to the calculation model, such as the
common methods of the equivalent load meth-
od, the cooling method and the initial strain
method [1-4]. Because of the common node or
coupling between prestressed tendon unit and
concrete unit, the above methods cannot simu-
late the interaction between prestressed tendon
and concrete. It also cannot accurately analyze
the stress development of tendon in tension
and loading stages.
The application of contact friction analy-
sis is the basis for the more accurate analysis.
However, the problems of convergence and nu-
merical stability on the friction model need to
be solved. The finite element analysis software
MSC.MARC is one of the common analysis
programs in nonlinear problems. It provides
a variety of contact friction models. But it has
not been applied for engineering analysis on
tensioning prestressed tendon with high stress
and large displacement. In this paper, based
on the application of MSC.MARC analysis soft-
ware and the 3-D solid element simulation of
prestressed reinforcement unit and concrete
unit, the friction model was established. The
simulation analysis of slip contact in the whole
tension stage was carried out by two engineer-
ing projects.
2. Coulomb bilinear models on contact
analysis
Prestressed tendon unit and concrete unit
adopted the solid unit. They were defined as the
deformable contact by CONTACT and specified
for TOUCHING contact form by CONTACT
TABLE in MSC.MARC software. The friction
form between concrete and prestressed ten-
don was defined as Coulomb bilinear friction.
Coulomb bilinear friction model assumes that
viscous friction and sliding friction are respec-
tively corresponding to the reversible (elastic)
and irreversible (plastic) relative displacement.
It uses a sliding surface representation φ, as
shown in Figure. 1 [5-6].
φ µ= f ft n- (1)
Where: ft means shear stress. fn means nor-
mal reaction force. µ means the friction coeffi-
cient of prestressed tendon and pipeline wall.
The viscous limit distance δ adopts the default
value in the model, which is 0.0025 times of the
average unit scale of deformable contact bod-
ies.
∆ut < <δ φ, 0，Viscous friction
∆ut > >δ φ, 0，Sliding friction
Contact analysis function in MSC.MARC
provides a contact algorithm on direct control,
as shown in Fig. 2.
Node P of contact unit E is in contact with
the surface of the target unit T. When the both
are in contact, the degree of freedom of point P
in the A-B-C-D surface direction can be elimi-
nated. It only has tangential motion along the
A-B-C-D surface. By the method of eliminating
point P freedom, two units are made together,
as shown in Formula 2 [7-8].
t
t T
E
T
E
T
K
K
u
u
f
f
E'é
ëê
ù
ûú
é
ë
ê
ê
ê é
ëê
ù
ûú
ù
û
ú
ú
ú
ì
í
ïï
îïï
ü
ý
ïï
þïï
=
ì
í
ïï
0
0
îîïï
ü
ý
ïï
þïï
(2)
Where: u is the displacement increment and
f is the residual force vector.
Fig. 2. Contact constraint
Fig. 1. Bilinear friction model
124 Functional materials, 24, 1, 2017
Kaimin Liu / Simulation analysis of prestressed tensioning ...
3. �inite element model �inite element model
A. Prestressed simply supported beam
with rectangular section
Geometric parameters of prestressed sim-
ply supported beam with rectangular section
are shown in Fig. 3.
Concrete strength is C50, and the elastic
modulus is 34.5GPa. Prestressed tendon chooses
the low relaxation steel strand with the elastic
modulus of 196.0GPa. The cross section size is
30mm × 30mm, and consistent with the dimen-
sion of the cross section of the original model.
Friction coefficient μ between prestressed ten-
don and pipeline wall is 0.25. Friction influence
coefficient κ of local deviation of per meter pipe
is 0.0015. Prestressed tendon adopts the para-
bolic curve style. The parabolic equation can be
expressed as Equation 3.
y f
x
l
e= ×
æ
è
ççç
ö
ø
÷÷÷÷ -
2
2
1 (3)
Where: f is strand vector high. e1 is the verti-
cal distance from the axis to the end of strand.
Unit models of prestressed tendon and con-
crete was respectively established. Prestressed
elements were embedded into the concrete ele-
ment and made the nodes on the fixed end of
prestressed tendon and the near concrete nodes
coupling, as the anchor end. A rigid surface on
tension side at the tendon end was created
and bonded with prestressed tendon. It was
controlled by one node that will transfer the
tension force to prestressed tendon. Force was
exerted on the concrete of tension end and the
value was the same with that of control node,
but the direction was opposite. While concrete
nodes subjected the reaction was coupled to pre-
vent stress concentration. Prestressed tendon
and concrete was defined as two groups with
different deformation body. The friction coeffi-
cient between them was defined as 0.25 in Code
for Design of Highway Reinforced Concrete and
Prestressed Concrete Bridge and Culverts (JTG
D62-2004) [9]. Friction type was Coulomb bilin-
ear friction. The finite element model is shown
in Fig. 4.
B. Prestressed simply supported beam
with T shaped section
Material properties of prestressed simply
supported beam with T shaped section are same
as that of beam with rectangular section. Equiv-
alent cross section size of prestressed tendon
is 40mm × 42mm. It consists of three straight
line segments and two arc segments. The ac-
tual measuring point arrangement is shown in
Fig. 5. Each prestressed beams arranged five
measurement points. The effective one-way
stress of shaded part in two prestressed beam
were tested. Two prestressed beam are respec-
tively embedded corrugated metal pipe and cor-
rugated plastic pipe. Mold resistance coefficient
of corrugated metal pipe and corrugated plastic
pipe is measured.
Corrugated metal pipe: μ=0.24 κ=0.0020
Corrugated plastic pipe: μ=0.16 κ=0.0014 [10]
The finite element model is shown in Fig.6.
4. Analysis o�� the resultsAnalysis o�� the results
A. Prestressed simply supported beam
with rectangular section
Tensile force of prestressed tendon in the
model was 1200kN. Tension simulation process
was divided into 100 load steps. Tensile force
of each load step was 12kN and the total time
was 1s.
Fig. 3. Prestressed tendon layout of rectangular
section beam (mm)
Figure 4. Finite element model of prestressed
beam with rectangular section
Fig. 5. Prestressed tendon layout of beam with
T-shaped section (mm)
Fig. 6. Finite element model of prestressed eam
with T-shaped section
Functional materials, 24, 1, 2017 125
Kaimin Liu / Simulation analysis of prestressed tensioning ...
When the tensile force reached 1200kN, the
effective frictional stress by MSC.MARC simu-
lation and JTG D62-2004 is shown in Fig. 7.
When prestressed tendon was stretched by
one-end, it can be seen from Fig. 7 that the ef-
fective tensile stress by MSC.MARC simulation
and JTG D62-2004 was similar. But the simu-
lation tension value is smaller than that of JTG
D62-2004.
Prestress loss value of mid-span unit
changed with the load in Fig. 8.
It can be seen from Fig. 8 that effective stress
of mid-span unit by MSC.MARC simulation
and JTG D62-2004 was similar. When the load
reached 960kN, the simulated values and theo-
retical values are 995.23MPa and 1018.05MPa
respectively. At this point, the both maximum
deviation was 2.24%. When the tension stage
was completed, the largest elongation of pre-
stressed tendon was 13.02mm.
B. Prestressed simply supported beam
with T shaped section
Tensile force of prestressed tendon in the
model was 2287 kN. Prestressed tendon was
stretched by two-end. Tension simulation pro-
cess was divided into 100 load steps. Tensile
force of each load step was 22.87kN and the to-
tal time was 1s.
1) Metal bellow
Effective stress of Prestressed tendon of
metal bellow by MSC.MARC simulation, JTG
D62-2004 and field measurement are shown in
Figure 9.
It can be seen from Figure 9. that the effec-
tive stress of metal bellows decreases gradu-
ally. Three curves of MSC.MARC simulation,
JTG D62-2004 and field measurement are sim-
ilar basically.
The deviation of measured prestressed val-
ues and JTG D62-2004 calculated prestressed
values on No. 3 measuring point were the max-
imum, 4.26%. The deviation of No. 2 measuring
point was the minimum, 2.62%.
The deviation of measured prestressed val-
ues and MSC.MARC simulated values on No.
1 measuring point were the maximum, 3.71%.
The deviation of No. 4 measuring point was the
minimum, 0.12%. When the tension stage was
completed, the largest elongation of prestressed
tendon was 127mm.
2) Plastic corrugated pipe
Effective stress of tendon of plastic corrugated
pipe by MSC.MARC simulation, JTG D62-2004
and field measurement are shown in Fig. 10.
It can be seen from Figure 10 that the ef-
fective frictional stress of plastic corrugated
pipe decreases gradually. Three curves of MSC.
MARC simulation, JTG D62-2004 and field
measurement are similar basically.
The deviation of measured prestressed val-
ues and JTG D62-2004 calculated values on
No. 3 measuring point was the maximum,
Fig. 7. Effective stress of prestressed tendon
Fig. 8. Effective stress of mid-span unit
Fig. 9. Effective stress of tendon of metal bellow
Figure 10. Effective stress of tendon of plastic
corrugated pipe
126 Functional materials, 24, 1, 2017
Kaimin Liu / Simulation analysis of prestressed tensioning ...
3.85%. The deviation of No. 4 measuring point
was the minimum, 1.86%.
The deviation of measured prestressed val-
ues and MSC.MARC simulated values on No.
1 measuring point was the maximum, 2.72%.
The deviation of No. 5 measuring point was the
minimum, 0.98%. When the tension stage was
completed, the largest elongation of prestressed
tendon was 151mm.
According to the above analysis, it can be
seen that the effective stress deviation of MSC.
MARC simulation, JTG D62-2004 and field
measurement is in 5%, which meets the engi-
neering accuracy requirement. However, the
drawback of this approach only considers the
effective stress from friction. It does not con-
sider the impact of per meter local variations of
channel on friction. In addition, using solid ele-
ment to simulate the prestressed tendon may
enlarge bending stiffness. But the both impacts
on the results are tiny, and need further study
in future.
5. Conclusions
In this paper, bilinear friction model of pre-
stressed tendon and concrete is established by
using the MSC.MARC software. It can analyze
the true stress of prestressed tendon in tension
and loading stage. Tension simulation results
show that the values of MSC.MARC simula-
tion, JTG D62-2004 and field measurement
are similar basically. The method is reasonable
with analysis of convergence speed and good
stability algorithm. It provides an effective
method of analysis for the bridge structural de-
sign, reinforcement and other engineering. For
prestressed concrete bridge, combined analy-
sis of prestressed tendon and concrete is still
in the exploratory stage. Simplified methods
widely used become slightly rough in old bridge
reinforcement analysis and other conditions,
because they need more precise conclusion.
Re��erences
1. Meng S.P., Wu C., Xiong J., Zhou Z.. Discussion
on the Nonlinear Finite Element Analysis of
Prestressed Concrete Complex Structures. In-
dustrial Construction. Vol.39, No.12, 2009: 1-4
2. Zhao Y., Zhao P., Li S.Y. Three-Dimensional Fi-
nite Element Analysis of Large Prestressed Con-
crete Box Flume Structure. Journal of Yangtze
River Scientific Research Institute. Vol.16 No.2,
1999: 17-20
3. Su J.W., Yao C.Q., Li G.Q., Zhou H.J. Equiva-
lent Load Method for Finite Element Analysis
of Prestressed Concrete Structures. J. of HUST.
(Urban Science Edition). Vol.20 No.2, 2003: 56-
60.
4. Zhou Z., Meng S.P., Wu J., Jiang J.F. Analysis
methods for the whole prestressing process of
hybridized space structure. Industrial Construc-
tion. Vol.38, No.9, 2008: 91-95.
5. MSC. Marc user’s Manual Volume A: Theory
and User Information. MSC Software Corpora-
tion, Version 2008: 480-482.
6. Wen X.H., Huang M.H., Zhan L.H. Finite Ele-
ment Study of the Giant Structure Modeling.
Modern Manufacturing Engineering. No.1,
2010:10-14.
7. Farahani K., Mofid M., Vafai A. A solution meth-
od for general contact-impact problems[J]. Com-
put. Methods Appl. Mech. Engrg. Vol.187, 2000:
69-77.
8. Du L.H., Deng L.J., Chen H.G., Ye J.Q. Direct
Constraint Procedure to Solve Contact Prob-
lems in Hydrostructures. J Tsinghua Univ (Sci
&Tech). Vol.43, No.11, 2003:1534-1537.
9. Industry standards of the People’s Republic of
China. Code for design of highway reinforced
concrete and prestressed concrete bridge and
culverts (JTG D62-2004), 115-116; 2004, Bei-
jing, China Communications Press.
10. Ye Z.H., Zhang G.C., Lu W. Test Study of
Along-Path Stress of Prestressing Strands of
Long Span PC Continuous Rigid-Frame Bridge.
Bridge Construction. N0.5, 2009:21-23+27.
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