Analytical and Field Experimental Studies on Hollow Core Slab

Analytical and Field Experimental Studies on Hollow Core Slab Beam
Bridges Strengthened by a U-section Steel and Concrete Composite
Anchorage System
By
Hui Jin
Taizhou University, School of Civil and Architecture, P.R.China, Associate Professor
Chang’an University, College of Highway, P.R.China , PhD Student
Hanwan Jiang
Research Institute of Highway, Ministry of Transport, P.R.China, Associate Research Professor
New Mexico State University, Civil Engineering Department, USA
Email: [email protected]
Ruinian Jiang
New Mexico State University, Civil Engineering Department, USA
Email: [email protected]
Jinquan Zhang
Research Institute of Highway, Ministry of Transport, P.R.China, Senior Research Professor
[email protected]
Submit for Presentation at the 94th Transportation Research Board Annual Meeting and
Publication in the Transportation Research Record
Washington D.C. , January, 2015
Date of Submission: August 1, 2014
1
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
Abstract:
This paper studies the mechanism of the “Single Slab Load Bearing” phenomenon of Hollow Core Slab Beam (HCSB)
Bridges that count for about 25% of the total bridges in China. The typical structure of HCSB bridges is to place prefabricated slab
beams side by side, and then connect adjacent slabs laterally with hinge joints. Finite element models were developed for HCSB
bridges with 13m, 16m, and 20m simple spans, the most commonly used lengths of this type of bridges. The traditional design of
HCSB bridges with small sized hinge joints covered by a 10 cm deck was found insufficient for the standard design trailer-100 load;
the maximum normal stress in hinge joints exceeded the specification limits, which caused the damage of the joints. With the failure
of hinge joints, the maximum normal stress in the deck reached 5.3MPa, which exceeded the design strength and caused wide
longitudinal cracking in the deck; as a result, the “Single Slab Load Bearing” phenomenon occurs. To solve this problem, the authors
proposed a new strengthening technique by installing a U-section Steel and Concrete Composite Anchorage System attached to the
bottom of hinge joints. The system can be installed without interruption to traffic. A 3-dimensional finite element analysis
demonstrated a significantly improved bridge performance after strengthening; the maximum stress in hinge joints decreased by
about 90%, and the maximum normal stress in slabs decreased by 44.7%. Furthermore, tensile stresses in the deck were completely
removed. A field load test on a HCSB bridge before and after rehabilitation verified the finite element results. Stresses and
deflections at the mid-span of slabs were measured under six load cases; both were found decreased by around 30% on average after
strengthening. A more uniform lateral load distribution factor curve was realized, indicating a better working performance of the
whole system. The study confirmed that the proposed method is practical and reliable for the rehabilitation of HCSB bridges.
Keyword： Bridge Engineering, Hollow Core Slab Beam bridge, Composite Anchorage System, “Single Slab Bearing”
Phenomenon, Strengthening
20
0 Introduction
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
Prefabricated concrete hollow core slabs have broad applications in civil engineering due to their structural
advantages including high cost-effectiveness, quick installation, and standardization. China has approximately
170,000 prefabricated concrete hollow core slab beam (HCSB) bridges, which accounts for about 25% of the total
bridges in the country. The typical structure of a prefabricated concrete hollow core slab bridge is shown in Fig.1,
in which the prefabricated slab beams are laid side by side to each other, and are then laterally connected by
cast-in-place hinge joints.
In the recent decades, the deterioration of the infrastructure has been aggravated by
aging and more intensified and heavier loading. According to the National Bridge Management Database of China,
9746 bridges were reported as unsafe in the nation in 2010. Among them, 44% were HCSB bridges [1]. The
failure of HCSB bridges often starts with the failure of the hinge joints, which causes insufficient lateral
connection between adjacent slabs [2]. As a result, the slabs bear more loading than designated and produce more
deformation. Deeper and uneven deformation of the slabs aggravates the damage of the joints. The load shared by
each slab beam increases with the loss of lateral connection. A slab will carry the entire load when the lateral
connection is completely lost due to damage of joints, which is called the “single slab load bearing”. This loading
condition causes serious problems to the bridges, even the collapses of beams. Aimed at solving this problem,
several methods are commonly applied including replacing the deck, applying transversal tendon post tensioning
at the bottom of the slabs, and pasting steel plates on the slabs[3-9]. Replacing the bridge deck with
doubly-reinforced concrete is effective and easy for construction, but the traffic has to be disrupted. Post
tensioning transversal tendon at the bottom of the slabs also has some technical limitations. Due to the damage
and drop of the grout concrete in the joints, a 1cm gap normally forms between slabs at the time of strengthening,
and the slab bottom is commonly rugged transversely with 1cm to 5cm elevation difference between the slabs. It
is hard to transfer the tension from the tendon to the slabs due to the gap and the rugged bottom surface. This may
also create tensile stress in the deck. And for the same reason, it is difficult to compactly paste steel plates on the
bottom of the slabs; the stress concentration at the joint locations cause the plates peel off from the slab surface
[10]. To eliminate the shortcomings of the above methods, the authors develop a new method by using a U-section
1
2
3
4
5
6
Steel and Concrete Composite Anchorage system to enhance the working performance of damaged slab bridges.
The new method is to bolt a specially designed reinforced U-Section steel on the bottom of the slabs across the
hinge joints, and then grout high strength mixture into the U-Section. Experimental results showed that the
performance of bridges can be profoundly improved by using this method without replacing the bridge deck; thus,
the whole construction can be done without interrupting traffic. A case study was conducted on the rehabilitation
project of the 2nd Shouchang River Bridge on 330 National Highway to illustrate the effectiveness of the method.
7
1 Mechanism of the “Single Slab Load Bearing” Phenomenon
8
9
10
11
12
13
14
15
16
“Single Slab Load Bearing” phenomenon means that a slab has lost lateral connections with the adjacent
slabs and carries the entire vehicle load by itself. It is caused by the damage of the hinge joints between the slabs.
Ideally, each slab is designed to carry a certain portion of the live load determined by designated load distribution
factors. However, the load share by an individual slab increases due to the failure of hinge joints caused by
various reasons including deficient design, increasing traffic loads or poor construction. As shown in Fig.1,
shallow and small-sized plain concrete hinge joints were widely used during the 1980’s and 1990’s in China,
which were not capable of providing sufficient connections between slabs. The joint design has been improved
since 2000 by adopting wider and deeper hinge joints with reinforcements connecting with slabs and decks, as
shown in Fig.2 [11].
17
18
Fig.1 Deficient design with a small hinge joint
19
20
21
22
23
24
25
26
27
28
29
Fig.2 Bridge cross section with improved deeper and reinforced hinge joints (unit: cm)
The mechanism of small shallow hinge joints is studied in order to better improve the performance of widely
existing HCSB bridges. The authors analyzed simply supported HCSB bridges with a span of 13m, 16m and 20m,
respectively, which are the most commonly used standard lengths. A typical cross-section of a HCSB bridge is
shown in Fig.2. The thickness of the deck is 10cm, the width of the pavement is 0.5m+11.4m+0.5m. C50 concrete
is used for slabs (nominal compressive strength is 32.4MPa, and nominal tensile strength is 2.65MPa) and C40 for
the deck (nominal compressive strength is 26.8MPa, nominal tensile strength is 2.40MPa). The stresses of the
bridge were calculated under both good and failed joint conditions with a load of trailer-100 (see Fig.3) centrally
placed and eccentrically placed on the deck. A finite element model (FEM) with undamaged joint condition is
shown in Fig.4 by using solid elements of ANSYS software. The calculated results are summarized in Table 1.
Trailer
1
2
Fig.3 Layout of the Trailer-100 load (axle loads in ton; dimensions in meter)
3
4
a)
Overview of the FEM model
b) the model for the bridge with undamaged hinge joints
5
6
c) the model for the bridge with damaged hinge joints
7
Fig. 4 Finite element models and analysis results
8
9
Table 1
Maximum Stresses in Selected Locations Under Centrally Loaded Trailer-100
Maximum Stresses in Different Locations
Span
Hinge Joint
Normal Stress at
Principal Tensile
Length
Integrity
Mid-span of Slabs
Stress in Hinge
()MPa
Joints (MPa)
Undamaged
3.95
Failed
13m
16m
20m
Shear Stress in the
Normal Stress in the
Deck (MPa)
Deck (MPa)
6.32
1.22
1.06
4.52
/
1.71
5.3
Undamaged
2.87
4.05
1.16
0.8
Failed
3.52
/
1.67
4.65
Undamaged
3.23
4.47
1.16
0.47
Failed
3.77
/
1.25
5.04
10
The following results are obtained from Table 1:
11
1) Under Trailer-100 centrally loaded, the maximum tensile stresses in the hinge joints reached 6.32MPa，
1
2
3
4
5
6
7
8
9
10
4.05MPa and 4.47MPa for 13m, 16m and 20m span length bridge respectively even under the undamaged
condition, all of which were larger than the nominal tensile strength of the concrete. Hence, longitudinal cracking
will occur along the hinge joints, which reduces the lateral connection between slabs.
2) After hinge joints completely loss its function, the deck takes the role of distributing the loads between
slabs. As a result, the maximum tensile stresses at the bottom of the deck reach 5.3MPa， 4.65MPa and 5.04MPa
for 13m, 16m and 20m spans, respectively. Typically, the deck of most HCSB bridges has a total thickness of
10cm with one layer of reinforcement 3cm under the surface. The 5MPa tensile stress will cause longitudinal
cracking in the deck. The cracks would further weaken the connection between the slabs, finally no loads are
distributed through the hinge joints and the deck, the “single slab load bearing” phenomenon occurs and slabs
carry much larger loads than their capacity and cause the failure of the bridge.
11
2 Introduction of U-section Steel and Concrete Composite Anchorage System
12
2.1StructuralDesignfortheStrengtheningProject
13
14
15
16
17
18
Aiming at solving the widely existing “single slab load bearing” problem in China, the authors developed a
U-section Steel and Concrete Composite Anchorage System that can be installed in the following steps. First, a
group of U shaped rebar is inserted into the bottom of slabs crossing the hinges, as shown in Figures.5 and 6.
Second, a U-section steel with rib stiffeners is bolted on the slabs to cover the U shaped bars, as shown in
Figures.5 and 7. Third, a high strength mixture is grouted into the U-section, and lastly, the openings are sealed at
each end. In this way, the newly attached composite system is strongly bound together.
19
20
Fig. 5
Design of U-section Steel and Concrete Composite Anchorage System
21
22
23
Fig. 6 Inserted Rebars
Fig. 7 U-Section Steel Anchored at the Bottom of the Slabs
24
25
26
This technique has the following advantages:
1) Improving the moment resistance of the bridge
A composite structure is formed by adding the U section to the existing slabs. The cross sections and stress
1
diagrams of a single beam before and after strengthening are illustrated in Fig.8.
b
x1
C=f cd bx
x1
x
f sd A s
2
3
4
Z1
Z2
M
Z1
M'
As
f sd A s
As
σ sd A b
h1
x
b
C=f cd bx
Ab
a). Before Strengthening
b). After Strengthening
Fig 8 Cross Sections and Stress Diagrams Before and After Strengthening
5
Capacity of the beam before strengthening ： M u  f sd As z1
6
Capacity of the beam after strengthening： M 'u  f sd As z '1  sb Ab z 2
7
Where M u is the flexural capacity before strengthening, M 'u is the flexural capacity after strengthening;
8
f sd is the design strength of the longitudinal reinforcing bars;  sb is the working stress of the steel plate; As
9
is the area of the longitudinal reinforcing bars; Ab is the section area of the steel plate; z1  h0 
x'
x'
, the lever arm after strengthening; z 2  h   h' , the distance
2
2
10
arm before strengthening; z '1  h0 
11
12
13
between the gravity center of the steel plate and the center of the compression zone.
2) Improving the stress state of the deck and hinge joints
The lateral internal forces in a hollow core slab are illustrated in Fig. 9 and analyzed below.
14
15
16
x
, the lever
2
a). Before Strengthening
b). After Strengthening
Fig 9 Diagrams for Lateral Internal Forces in a Hollow Core Slab Beam
17
18
19
20
21
22
Usually, we consider that hinge joints only transfer shear forces, leaving the deck to transfer the transversal
moment, as shown in Fig (9a). After strengthening, the newly added steel plate and grouted mixture undertake the
shear and moment jointly with the hinge joints and the deck. Hence, shear in the hinge joints is remarkably
reduced and there is the tensile stress in the deck is removed, which improves the serviceability of the deck, as
illustrated in Fig (9b). Therefore, cracking in the deck can be avoided accordingly.
Based on the equilibrium equations, the maximum tensile stress in the deck before strengthening
23
  6mmax / h 2 ; after strengthening, the tensile stress is removed and the compressive stress (negative) in the deck
24
'
'
  mmax
/( H 0 h) ; where mmax and mmax are the maximum transversal moments before and after strengthening,
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
h is the deck thickness, and H0 is the arm of the force couple.
3) Strengthening the lateral connections of the slabs
The new added composite system provides additional lateral connections between slabs, which can transfer
both shear and moment. In this way, the previous hinge connection is turned into rigid connection. Therefore the
vehicle loads can be laterally distributed more evenly among slabs, which improves the integrity of the the whole
bridge system.
2.2FiniteElementAnalysis A finite element analysis was conducted using ANSYS to analyze the effectiveness of the strengthening
method. 3D models have been built by choosing solid elements to simulate 13m, 16m and 20m span length
bridges, respectively. The comparison of the stresses under different conditions is shown in Fig 10. The hinge joint
in Fig.1 and the cross section of the bridge in Fig. 2 were used in the analysis.
a)Maximum Normal Stress at the Mid-span of the Slabs
c、Maximum Shear Stress in the Deck
Fig 9
b、Maximum Normal Stress in the Hinge joints
d、Maximum Lateral Normal Stress in the Deck
Comparison of Stresses under Different Conditions
The analysis results are summarized as follows:
1) After strengthening, the maximum mid-span normal tensile stress in the slab dropped from 4.52 MPa to 2.5
MPa (see Fig.9a, hinge joints damaged vs. post strengthening). The maximum tensile stress occurred in the
U-section steel plate with a value of 3.4MPa. The maximum tensile stress in the slab dropped 44.7%, 37.5%, and
44.3% for the 13m, 16m, and 20m bridge, respectively.
2) The maximum lateral stress in the hinge joints decreased significantly after strengthening, from 6.32 MPa
to 0.6 MPa (90.5%), 4.05 MPa to 0.46 MPa (88.6%), and 4.47 MPa to 0.8 MPa (82.1%) for the 13m, 16m, and
20m bridge, respectively (Fig.9b).
1
2
3
4
3) The maximum shear stresses in the deck were notably reduced after strengthening; the drop ranged from
13% to 42% (Fig.9c), which indicates a better lateral connection.
4) The tensile stress in the deck was removed after strengthening (Fig.9d), which greatly improved the stress
condition of the deck.
5
3 Experiments in a Bridge Rehabilitation Project
6
3.1Introductionoftherehabilitationproject
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
The study bridge is the 2nd Shouchang Bridge on G330 National Highway in the south of China. The bridge is
176-metre long with ten 16-metre simple spans, and 12-metre wide (0.5m+11.0m+0.5m). The cross section of the
bridge is composed of 11 prestressed hollow core slabs laterally connected with small sized hinge joints (Fig.1),
covered with a 10cm deck. The design load was Vehicle-20 and Trailer-100. The bridge was in service for about
10 years at the time of rehabilitation. The deck of the bridge had several long and wide longitudinal cracks (see
Fig.10), and water was observed seeping out through the hinge joints, which was a sign of failure of the joints
(Fig.11).
The main reasons for the damage of the bridge were: 1) There were a large number of over-weight vehicles
crossing the bridge constantly; 2) Small-sized hinge joints did not provide sufficient connections between slabs, so
the deck carried more loads than designed that caused the wide longitudinal cracks in the deck right along the
position of the hinge joints; 3) Poor lateral connections did not distribute the loads evenly among the slabs; as a
result, “single slab load bearing” occurred and slabs carried more loads than designed, making the slabs crack.
Fig. 10
Longitudinal Cracking in the Deck
Fig. 11 Cracking in the Hinge Joints
22
23
3.2RehabilitationDesignandConstruction
24
25
26
27
28
Since the purpose of the rehabilitation was to strengthen the transversal connections between slabs and
enhance the loading capacity of the bridge at the mid-span, a U-section Steel and Concrete Composite Anchorage
System was applied in the middle 10m of the slabs, that is, 60% of the span length (0.6L), symmetric to the
mid-span. The rehabilitation design is illustrated in Fig. 12.
Pavement
80
Hollow Corn Slab Beam
12
Bolts
N1Steel Plates
N3 Rebar
Bolts
High-strength Self-compacting Mortar
N5 Steel Plates
N4 Rebar
1
2
3
Fig. 12
Strengthening Design for the 2nd Shouchang Bridge
4
5
6
7
8
9
10
11
The construction process included: 1) Smoothening the surface of the slabs where the U-section plate was
going to be bonded and bolted; 2) Embedding the U-shaped rebar in the bottom of the slabs on both sides of the
hinge joints (see Fig.6); 3) Laying the rebars into the U-section steel plates; 4) Drilling holes in steel plates and
slabs for bolts; 5) Getting the binder ready; 6) Putting the U-section steel plates in place and presetting the
pressure grouting holes; 7) Sticking the U-section steel plates in places and assembling the bolts; 8) Curing; 9)
Grouting the self-compact high strength mixture into the U-section; and 10) Coating the surface of steel with
anticorrosive paint.
12
3.3FieldTesting
13
14
15
16
17
18
19
A static load test was performed on the second span of the bridge before and after rehabilitation to verify the
strengthening effectiveness A strain sensor and a deflectometer were placed at the bottom of each slab at
middle-span (Fig.13a). Two trucks were placed side by side laterally with a total of six location combinations
(cases); that is, loading at 1/4L, 1/2L, and 3/4L longitudinally with the trucks on the one side of the road, and on
the center of the road (Fig.13b, c, and d). The two trucks used before strengthening weighed 30.13 ton and 29.7
ton respectively, and the two used after strengthening weighted 32.7 ton and 30.04 ton, respectively. The ratios
of the testing to design loads ranged from 0.99 to 1.09.
20
21
a. Sensor Locations
b. Longitudinal Truck Locations
22
23
24
c. Laterally Offset Loading
Fig. 13
d. Laterally Centered Loading
Loading Cases and the Location of Sensors (Unit: cm)
1
3.4TestingResultsandComparisons
2
Strains measured before and after strengthening are summarized in Table 3 and illustrated in Fig. 13. It was
3
4
5
6
7
observed that the maximum strain dropped from 99.83μ (before strengthening) to 55μ (after strengthening) at
sensor location 1 in load case 2. Strains at all sensor locations and loading cases except location 1 in cases 4 and 5
decreased significantly after strengthening, with an average drop of 25.2%, and a maximum of 30.4%. All residual
strains were also reduced significantly after strengthening, indicating a more resilient structural system.
Table 3 Comparison of Strains at Mid-span Before and After Strengthening (Unit: μ)
Sensor’s
Measured
Location
Strain
Residual Strains When
Case 1
Case 2
Case 3
Unloaded for Offset Loading
Residual Strains When
Case 4
Case 5
Case 6
Cases
Unloaded for Centered
Loading Cases
Before Strengthening
68.00
99.83
39.17
4.17
13.14
17.56
19.08
15.78
After Strengthening
40.17
54.62
24.60
1.33
13.57
27.33
16.63
5.36
Before Strengthening
41.67
71.83
30.00
4.00
46.86
72.11
44.46
21.50
After Strengthening
30.00
50.33
20.15
0.33
32.43
58.00
29.13
9.39
Before Strengthening
6.83
11.83
7.50
1.00
25.00
34.00
28.15
19.50
After Strengthening
5.67
4.33
2.74
0.15
21.38
38.11
16.80
4.00
1
5
9
8
9
10
11
12
13
14
15
Fig. 13 Comparison of Strains Before and After sStrengthening
Deflections of all cases are listed in Table 3 and illustrated in Fig.14.
Deflections at sensor location 1 in cases 5 and 6 (under offset loading) slightly increased after strengthening,
indicating a larger load share of the side slabs. In all cases, deflections dropped 25.2% on average, with a
maximum 30.4%. In all cases, residual deflections decreased to zero when unloaded .
3) Fig. 14e shows the lateral load distribution factor curve under load case 2 (2/1L and offset loading) to
1
2
3
4
5
demonstrate the change of lateral load distribution after strengthening. It was observed that the curve became
much smoother after strengthening, which indicates a more uniform load distribution among slabs due to stronger
lateral connections.
Table 3 Comparison of Deflections at Mide-spanBefore and After Strenthening (Unit: cm)
Monitoring
Points
Residual Deflections When
Conditions
Case 1
Case 2
Case 3
Unloaded for Offset Loading
Residual Deflections When
Case 4
Case 5
Case 6
Cases
1
5
9
6
Unloaded for Centered
Loading Cases
Before Strengthening
0.30
0.39
0.24
0.17
0.09
0.10
0.05
0.00
After Strengthening
0.24
0.26
0.17
0.00
0.08
0.11
0.06
0.01
Before Strengthening
0.23
0.35
0.22
0.00
0.27
0.32
0.22
0.00
After Strengthening
0.17
0.20
0.13
0.00
0.23
0.25
0.16
0.00
Before Strengthening
0.05
0.08
0.03
0.02
0.17
0.20
0.11
0.00
After Strengthening
0.03
0.05
0.02
0.01
0.12
0.13
0.05
0.00
1
2
3
4
5
6
7
8
9
10
11
12
Fig. 14
Comparison of Deflections and Lateral Load Distribution Factors
4 Conclusions
This paper studied the mechanism of the “Single Slab Load Bearing” phenomenon of HCSB bridges and
proposed a new technique to strengthen this type of bridges by installing a U-section Steel and Concrete
Composite Anchorage System across the hinge joints. Through a finite element analysis and a field testing on a
HCSB bridge before and after strengthening, the conclusions are obtained:
1) A finite element analysis was performed on 13m, 16m, and 20m HCSB bridges respectively (commonly
used span lengths for HCSB bridges). The models included small sized hinge joints and a 10cm deck. A
standard design trailer was applied and the normal stresses in the hinge joints exceeded the specification
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
limits, which caused the damage of the joints. As a result of the failure of the hinge joints, the maximum
normal tensile stress in the deck reached 5.3MPa, which may cause wide longitudinal cracking in the
deck. The insufficient design of hinge joints is the reason of the “single slab load bearing” phenomenon,
even under standard design and construction conditions.
2) The results of the 3-dimensional finite element analyses demonstrated a significant improvement of the
stiffness and capacity of the bridges by installing a U-section Steel and Concrete Composite Anchorage
System. The maximum lateral tensile stress in the hinge joints decreased by about 90%, and the normal
maximum stress in slabs decreased by 44.7%. Furthermore, the tensile normal stress in the deck was
completely removed after strengthening.
3) The field load testing on a HCSB bridge before and after strengthening verified the finite element
analysis results, which confirmed that the proposed method is practical and reliable for the rehabilitation
of HCSB bridges.
References
[1] Research Institute of Highway, Ministry of Transport, P.R. China, Nation Investigation Report for Bridge
Durability Issues, July 2013;
[2] WANG, Yan-tong. Phenomenon of Single Beam Bearing in High-grade High ways Phenomenon of Single
Beam Bearing in High – grade High ways[J]. Technology of High way and Transport Aug. 2004 No. 4:
29-32.
[3] ZhANG, Yan.The Load Transverse Distribution of Research on The Deck Pavement Composite Layer
Reinforced Hollow Slad [D]. Chang’an University,Xi’an,China.2010.5
[4] WU,Ying-heng; ZHANG, Jun-ping. Research on force behavior influenced by deck pavement to the simply
supported hollow slab[J] ,Journal of Guangzhou University( Natural Science Edition), Feb.2011,Vol.10 No.1:
60-64.
[5] Jin,Hua; SunLigong. FEM Analysis of Plate Girder Bridge Transversely Strengthened by Pre-stress[J]. Journal
of Shijiazhuang Railway Institute ( Natural Science) Mar.2010,Vo. 23 No.1: 70-73.
[6] ZHANG,Yun-na. Study on strengthening assembly board bridges by imposing transverse external pre-stress[D].
Zhengzhou: Zhengzhou University2007.
[7] Pan, Zuanfeng. Study on transverse post-tensioning in assembly slab bridges[J]. Journal of southeast
University(Natural Science Edition) Nov.2010,Vol.40 No.6: 1264-1270.
[8] Du, Hongjing. Study on Structural Analysis Method of Assembly Hollow Slab Bridge with Transverse
Strengthening[D],Chang’an University,Xi’an,China.
[9] Huang, minshui; Zhu, hongping. Study on mechanism and reinforcement processing of “single slab
bearing”disease of hollow core slab beam bridge[J]. Huazhong Univ. ofSci.&tech.(natural Science
Edition),Feb.2008.Vol.36 No.2:118-121
[10] Jin, hui, Technology of transverse reinforcement hollow plate[R]. Taizhou university School of civil
engineering &architecture, August 2013
[11] Han, Xiangdong, Analyze, Comparison and Application on the Hinged Joints forms of Hollow Plank Girder
Bridge, Thesis for Master Degree, Chang’an University, June 2010;