J. Cent. South Univ. Technol. (2010) 17: 648-652
DOI: 10.1007/s11771-010-0535-z 
Improved methods for decreasing stresses of concrete slab of
large-span through tied-arch composite bridge
ZHOU De(周德), YE Mei-xin(叶梅新), LUO Ru-deng(罗如登)
School of Civil Engineering and Architecture, Central South University, Changsha 410075, China
? Central South University Press and Springer-Verlag Berlin Heidelberg 2010
Abstract: Mechanical behavior of concrete slab of large-span through tied-arch composite bridge was investigated by finite element analysis (FEA). Improved methods to decrease concrete stresses were discussed based on comparisons of different deck schemes, construction sequences and measures, and ratios of reinforcement. The results show that the mechanical behavior of concrete slab gets worse with the increase of composite regions between steel beams and concrete slab. The deck scheme with the minimum composite region is recommended on condition that both strength and stiffness of the bridge meet design demands under service loads. Adopting in-situ-place construction method, concrete is suggested to be cast after removing the full-supported frameworks under the bridge. Thus, the axial tensile force of concrete slab caused by the first stage dead load is eliminated. Preloading the bridge before concrete casting and removing the load after the concrete reaching its design strength, the stresses of concrete slab caused by the second stage dead load and live load are further reduced or even eliminated. At last, with a high ratio of reinforcement more than 3%, the concrete stresses decrease obviously.
Key words: composite bridge; concrete slab; tension; through tied-arch; large span; finite element method
1 Introduction
Through tied-arch composite bridge is a new-type structure for high-speed railway in China. This kind of structure has advantages such as large stiffness, low noises, low building height and good comprehensive benefits [1-5]. It is an attractive solution especially for 60-200 m long bridge near city or across expressways and railways where expectations and demands for appearance are usually high.
With the increase in span of the bridge, the mechanical behavior of the concrete slab gets severe. Previous studies show that the stresses of the concrete slab surpass its allowable value when the bridge span is larger than 100 m [6-7]. Concrete cracking is inevitable in this case. This not only reduces the stiffness of the bridge but also affects the durability and service life of the bridge.
Some researchers have worked on methods for decreasing concrete stresses. CHEN et al [7] suggested setting gaps on concrete deck slab. So, the axial tensile force of concrete slab is eliminated. But, this method decreased the bridge stiffness especially the lateral stiffness and resulted in inconvenience for repair simultaneously. LEBET and NAVARRO [8-9] and RAMM and EIZ [10] adopted concrete pre-stressing method. This method is available in short term, but doubtful due to losses of pre-stress by the long-term behavior of concrete. RYU et al [11-12], LAM et al [13] and YE et al [14] studied the application of prefabricated slabs. However, they mainly focused on simple composite beams and continuous composite beams, in which the concrete tensile stresses were caused by bending moments. This is different from the situation of through tied-arch composite bridge where the stresses of the concrete slab are caused by both axial forces and bending moments. Moreover, the bridges mentioned in these studies had spans less than 100 m.
In this study, the mechanical behavior of concrete slab of through tied-arch composite bridge with large span over 100 m was investigated by finite element analysis (FEA) and model test. New improved methods to decrease concrete stresses were discussed based on comparisons of different deck schemes, construction sequences and measures, and ratios of reinforcement.
2 Engineering background
Tingsi River Bridge (TRB) is located in Chibi City of Hubei Province, China, across the Beijing-Zhuhai expressway. It is an essential part on Wuhan-Guangzhou double-track passenger special railway. With a design speed of 350 km/h, the bridge is also the first through tied-arch composite bridge on high-speed railway in China.
As shown in Fig.1, TRB has a span of 140 m and an overall width of 18 m. The rise of the arch is 30 m high and the rise-to-span ratio is 1/4.76. The bridge is made of two rectangular hollow arches that carry the load of the carriageway through the hangers. The line type of the arch axis is quadratic parabola. There are 15 hangers with an adjacent distance of 8 m on each side of the bridge. The steel grid-beam system of the deck consists of 4 longitudinal beams and 19 transverse beams. The distance layout of the transverse beams along the bridge is 2×7+14×8+2×7 m. Being made of grade C50, the concrete slab is 13.4 m in width and 0.3 m in thickness. The steel beams and concrete slab are tied together by column headed shear studs of 22 mm in diameter.
The dimensions of the main steel box beams are shown as follows. The arch cross-section is 4.5 m high at abutment and 3.0 m high at apex. The heights of the mid cross-sections adopt indoor wiring interpolation. The cross-section of the collar beam is 3.5 m high. Both cross-sections of arch rib and collar beam have the same width of 2.0 m.
3 Finite element modeling
3.1 FEM model of TRB
A general-purpose finite element software package ANSYS was used to model the whole bridge for elastic analysis. Different element types, such as beam 189 for arch ribs，beam 44 for steel floor beams and hangers and shell 63 for concrete slab, were adopted to simulate the structure. Constraint equations were used to considerate the off-centre among steel beams and concrete slab. The slip between steel and concrete slab was ignored at the interface. Boundary conditions were imposed according to the actual situation [15]. As a result, 21 302 nodes and 18 282 elements were recognized on the whole model of TRB, as shown in Fig.2.
3.2 Materials and loads
The modulus of steel is Es=2.1×105 MPa. Not considering the concrete creep, giving that the age of concrete slab is four months, the elastic modulus of concrete slab is Ec=3.50×104 MPa. The main static loads are shown as follows.
(1) First stage dead load: The deadweights of steel beams and concrete slab.
(2) Second stage dead load: Uniformly distributed load of 1.38 t/m2 including line facility, pavement, handrail, protective layer of bridge deck, non-ballasted track and other additional equipments.
(3) Double-line live load: The load of the train converted to uniformly distributed load of 2.23 t/m2 which acted on the regions about 3 m wide along both of the track center lines.
4 Results and analysis
4.1 Composite deck schemes
The mechanical behavior of the concrete slab is closely related to the deck composite styles. With differences in composite regions, three deck schemes were investigated.
(1) Scheme 1: It is a half-composite deck scheme. The longitudinal beams and concrete slab are tied together, and the transverse beams only have the parts between the longitudinal beams to keep the same composition with the concrete slab, as shown in Fig.3(a).
(2) Scheme 2: It is a full-composite deck scheme where both the longitudinal and transverse beams are tied together with the concrete slab, as shown in Fig.3(b).
(3) Scheme 3: It is an integral-composite deck scheme. The concrete slab is tied together not only with the longitudinal and transverse beams but also with the collar beams, as shown in Fig.3(c).
Fig.4 illustrates the axial forces of the concrete slabs in different schemes under double-line live load. It is shown that the value of the axial tensile force of the concrete slab for Scheme 1 is the smallest among the three schemes. And the value for Scheme 2 is about 25% higher than that for Scheme 1. Scheme 3 has the largest axial tensile force of the concrete slab, about 45% higher than that of Scheme 1. This can be explained by the
Fig.1 General view of TRB
Fig.2 Finite element model of TRB
Fig.3 View of deck schemes: (a) Half-composite deck; (b) Full- composite deck; (c) Integral-composite deck
Fig.4 Comparison of axial force of concrete slab
following reasons. The horizontal thrust from the arch springing is endured by collar beams, longitudinal beams and concrete slab. With the increase of composite regions between them, the distribution of the horizontal thrust for the concrete slab increases and the distributions for the collar beams and longitudinal beams decrease correspondingly.
Fig.5 illustrates the longitudinal stresses of the concrete slab along the slab center line and the track center line (there are two track center lines on the concrete slab) under double-line live load. This further
Fig.5 Concrete longitudinal stresses: (a) Along slab center line; (b) Along track center line
confirms that the mechanical behavior of the concrete slab gets worse with the increase of the composite regions. Consequently, Scheme 1 is recommended on condition that the stiffness and strength of the bridge meet the design demands under service loads.
4.2 Comparison of construction sequences
Owing to large traffic flow under the bridge, in-situ place method of construction was adopted in TRB. Temporary steel frameworks were set up under the bridge after constructing the main piers and temporary piers. Then, collar beams, longitudinal and transverse beams, arch ribs and hangers were assembled, respectively. There were two sequences of construction for concrete casting as follows.
(1) Construction sequence 1: This sequence is to cast concrete first and then remove the temporary steel frameworks on condition that the concrete reaches its design strength.
(2) Construction sequence 2: This sequence is to remove the temporary steel frameworks first and then cast concrete.
Fig.6 shows the concrete longitudinal stresses along the slab center line and the longitudinal edge in different construction sequences under the first stage dead load. It can be seen that the mechanical behaviors of concrete slab in the two construction sequences are obvious different. The concrete stress in Construction sequence 1 is about 1.50 MPa more than that in Construction sequence 2. The reason is that the concrete slab in Construction sequence 1 bears not only the tensile axial forces originating from the arch springing, but also the bending moments caused by gravity. But, the concrete slab in Construction sequence 2 only endures bending moments caused by its own deadweight after removing the mould plates. It is a fact that the concrete has no force resistance and no composite action between the steel beams and the concrete slab during concrete casting. So, the axial tensile forces originating from the arch springing in Construction sequence 2 are all distributed by the collar beams and the longitudinal beams. There is no distribution for the concrete slab.
Fig.6 Concrete longitudinal stresses under the first stage dead load: (a) Along slab center line; (b) Along slab longitudinal edge
According to the analysis above, it is clear that the concrete is suggested to be cast after removing the temporary frameworks under the bridge. Thus, the axial tensile force of the concrete slab caused by gravity is eliminated completely.
4.3 Construction measure of preloading
Before reaching its design strength, the concrete slab is just a load supported by the steel floor beams in the Construction sequence 2 mentioned above. The stress of the concrete slab is also obviously less than that in Construction sequence 1. This gives us a clue to reduce the concrete stress further. If preloads are applied to the bridge before concrete casting and removed after the concrete reaching its design strength, the tensile stresses of the concrete slab may decrease further.
Fig.7 shows the concrete longitudinal stresses along the slab center line and longitudinal edge under the second stage dead load. The preload is equal to the second stage dead load in these figures. It is clear that the concrete stress with preload is about 1.0 MPa less than that without preload. Adopting preload before concrete casting, the stress sum of the top surface and the bottom surface at the same location is close to zero. This indicates that the concrete stress is mainly caused by bending moments. There is little axial force in the concrete slab.
Fig.7 Concrete longitudinal stresses under the second dead load: (a) Along slab center line; (b) Along slab longitudinal edge
It is possible that the concrete stresses caused by live load can be reduced if the preload is more than the second stage dead load. However, this measure also results in much distribution of the axial force for the collar beams and longitudinal beams. Their sections must be large enough.
4.4 Ratios of reinforcement
It is a fact that the load distributed to the steel bars in the reinforced concrete slab gets larger with the increase of the ratio of reinforcement under vertical load. And the distribution to the concrete is quite opposite. So, it is available to adopt a high ratio of reinforcement to improve the mechanical behavior of the concrete slab. Two cases were studied as follows.
Case 1: No steel bar existed in the concrete slab.
Case 2: A 3.4% ratio of reinforcement was adopted for the concrete slab.
The stresses of the concrete slab in both cases were obtained by FEA. Fig.8 shows the longitudinal stresses of the top surface along the slab center line under the dead and live load together. It is shown that the concrete stress in Case 1 is about 25%-30% higher than that in Case 2. With a high ratio of reinforcement, the stresses of the concrete slab decrease obviously. This indicates that the crack width is effectively controlled with a ratio of reinforcement above 3.0%.
Fig.8 Longitudinal stresses of top surface along slab center line under both dead and live loads
5 Conclusions
(1) The concrete slab of through tied-arch composite bridge mainly bears axial tensile force originating from the arch springing and bending moments under vertical loads. With the increase in bridge span, the tensile problem of the concrete slab gets severe.
(2) Compared with the half-composite deck scheme, the axial force of the concrete slab in full-composite deck scheme is about 25% higher and that of the integral- composite deck scheme is about 45% higher under the same vertical loads. The concrete slab distributes more axial tensile force originating from the arch springing with the increase of the steel-concrete composite regions.
(3) The axial tensile force of the concrete slab caused by gravity is eliminated in the construction sequence where concrete is cast after removing the temporary frameworks under the bridge. In the case that preloads are applied to the bridge before concrete casting and removed after the concrete reaching its design strength, the tensile stresses of the concrete slab caused by the second stage dead load and live load decrease further.
(4) The concrete stress decreases obviously and the crack width is also effectively controlled with a high ratio of reinforcement above 3.0%.
References
[1] NAKAMURA S, MOMIYAMA Y, HOSAKA T, HOMMA K. New technologies of steel-concrete composite bridges [J]. Journal of Constructional Steel Research, 2002, 58(1): 99-130.
[2] HAENSEL J. Composite bridge design: The reanimation of steel bridge construction [J]. Journal of Constructional Steel Research, 1998, 46(1/3): 54-55.
[3] JACQUES B. Design development of steel-concrete composite bridges in France [J]. Journal of Constructional Steel Research, 2000, 55(1/3): 229-243.
[4] ZHANG Ye-zhi. Comparison of bridge structures of railway through truss composite bridges [J]. Journal of the China Railway Society, 2005, 27(5): 107-110. (in Chinese)
[5] GAO Jing-qing. Deck system of double-track through steel truss girder and composite girder [J]. Railway Standard Design, 2005(5): 73-75. (in Chinese)
[6] ZHOU De, YE Mei-xin. Composite deck structure of large span through tied-arch bridge on high-speed railway [J]. Journal of Central South University: Science and Technology, 2009, 40(1): 256-262. (in Chinese)
[7] CHEN Lie, LI Xiao-zhen, LIU De-jun. Composite deck system of through tied-arch bridge on high-speed railway [J]. China Railway Science, 2007, 28(5): 37-42. (in Chinese)
[8] LEBET J P, NAVARRO M G. Influence of concrete cracking on composite bridge behaviour [C]// Proceedings of the 5th International Conference on Composite: Construction in Steel and Concrete V. New York: ASCE, 2006: 77-86.
[9] NAVARRO M G, LEBET J P. Concrete cracking in composite bridges: Tests, models and design proposals [J]. Structural Engineering International, 2001, 11(3): 184-190.
[10] RAMM W, ELZ S. Behaviour and cracking of slabs as part of composite beams in regions with negative bending moments [C]// Proceedings of an Engineering Foundation Conference: Composite Construction in Steel and Concrete III. New York: ASCE, 1997: 871-886.
[11] RYU H K, CHANG S P, KIM Y J, KIM B S. Crack control of a steel and concrete composite plate girder with prefabricated slabs under hogging moments [J]. Engineering Structures, 2005, 27(11): 1613- 1624.
[12] RYU H K, KIM Y J, CHANG S P. Crack control of a continuous composite two-girder bridge with prefabricated slabs under static and fatigue loads [J]. Engineering Structures, 2007, 29(6): 851-864.
[13] LAM D, ELLIOTT K S, NETHERCOT D A. Parametric study on composite steel beams with precast concrete hollow core floor slab [J]. Journal of Constructional Steel Research, 2000, 54(2): 283-304.
[14] YE Mei-xin, HUANG Qiong, WU Qin-qin. Analysis of steel-concrete composite structure with overlap slab of Xingguang bridge [J]. Journal of Central South University of Technology, 2007, 14(1): 120-124.
[15] ZIENKIEWICZ O C, TAYLOR R L. Finite element method [M]. Oxford: Butterworth-Heinemann, 2000: 276-304.
Foundation item: Project(2005k002-c-2) supported by the Science and Technology Development Program of Railways Department, China
Received date: 2009-09-31; Accepted date: 2010-02-14
Corresponding author: ZHOU De, PhD; Tel: +86-13974807317; E-mail: jody.zd@qq.com
(Edited by YANG Bing)
