Finite Element Simulation of Cantilever Construction Structure

Transcription

1 Finite Element Simulation of Cantilever Construction Structure Baofeng Pan 1, Gang Li 2 Abstract In order to realize the control ultimate goal, it is necessary to predict and control the deformation and stress state in the segmental construction process. To know about the structure behavior, geometric and internal force, it needs to simulate the entire construction process according to each construction stage, and to determine the ideal state of the stress and distortion of each stage of the construction process. Keyword construction control, segmental construction, continuous beam, finite element simulation, cantilever construction C I. INTRODUCTION HINA s highway and railway develop rapidly recent years. With more and more long-span bridges needed to span great river or bay, the prestressed concrete (PC) continuous beam has been widely used. There are many methods to construct the PC continuous beam bridge. And cantilever method is widely used. With the cantilever construction individual spans are counterweighted about their substructure support. Reference [1] shows construction of segment bridge superstructures is a complex process. That s because the cantilever method is related to the physical means of constructing the foundations, bridge substructure, and its especially its superstructure, the structural resistance of the bridge changes with each construction stage, load conditions, time-dependent materials behavior and environmental influences. These complex interactions, especially the internal forces and displacements of the structure, need to be considered in the construction calculation simulation and for developing the flow of work tasks in the construction schedule. To ensure the construction quality and safety, the control of the construction stages is indispensable. The most basic requirements, of the construction control, is to ensure the structure safety when constructing, and make sure the linear and internal force complying with the design requirements when the continuous beam completed. The construction control of segmentation PC continuous beam is to adjust the calculation model according to the observed real parameters of the structure during the construction, and to simulate the construction stage. On the basis of construction monitoring 1 Associate Professor is with Institute of Road Engineering, the Faculty of Infrastructure Engineering, Dalian University of Technology, Dalian , P. R. China, pbfeng@yahoo.cn 2 M. S. is with Institute of Road Engineering, the Faculty of Infrastructure Engineering, Dalian University of Technology, Dalian , P. R. China. ligang519@163.com results of the finished segments, it has to analyze the error and adjust the vertical mold elevation for the next section. So the relative mistake of the two sides of the closure segment is within the limit of the specified value, and the linear and internal force state of the continuous beam corresponds to the design requirements. II. CANTILEVER CONSTRUCTION PROCEDURE Cantilever method is an erection method in which individual beam segments are sequentially erected at the tip of the self-supporting superstructure. Posttensioning with longitudinal prestressing tendons is employed to hold the segments in the cantilever arms together and to provide the needed moment resistance to withstand dead loads and live loads. Fig. 1 shows the cantilever construction procedure of the PC continuous beam: 1) Cantilever construction starts from the main pier B, 2) Side-span closes and temporary bearings of B removed, 3) The cantilever construction of the main pier C carried out, 4) Side span closed and temporary bearings of C removed, 5) Mid closure 5 finished and the three-span continuous beam structure founded [2]. In practical engineering, cantilever construction of B and C often start simultaneously. The structure is stable and load symmetrically in the construction stage. It is convenient to adjust structural internal force. But it has to pay attention to that when the side span closed and the temporary bearing of B is not yet removed, it will produce second moment when the prestress tendons are tensioned. A B Fig. 1 T structure-single cantilever-construction III. DIMENSIONS OF SEGMENTAL BEAM Concrete segmental bridges were built as early as 1925(Plougastel Bridge). Since then, prestressed concrete bridges, both pretensioned and posttensioned, have seen a rapid development. In most cases, posttensioning is employed, i.e., C D 181

2 the prestressing tendons are stressed with hydraulic jacks after the concrete has been placed and gained a minimum strength. Concrete segmental construction bridges utilize box girder superstructures. These superstructures consist of bottom slabs, webs, which can be inclined and straight, and a cantilevering top slab to provide maximum deck width. Concrete box girders have multiple advantages, e. g., their versatility in alignment, width, and depth, high torsional and bending stiffness of the closed cross section, and an aesthetically pleasing geometric appearance. A continuous beam is has a total length of m between the abutments and is divided into three spans, mid span of 48.0 m and two side spans of 32.6 m measured center to center. The cross section of the bridge is a single-cell box girder with cantilevering flanges and straight webs and a variable depth that reduces from 3.50 m at the pier table to 2.50 m at mid-span and side-span in a quasi-parabolic curve of the box girder soffit. The top slab is m wide and the bottom is 6.4m wide. The box girder s roof slab is 35cm thick, its web is 48cm~90cm thick and the thickness of bottom slab is 40cm~60cm. The beam has a transverse slope of 2% for drainage. As shown in Fig. 2 and Fig.3 [3] - [6]. Fig. 3 Girders cross-sectional (Unit: cm) The continuous girder is three-dimensional prestress structure. The box girder adopts high strength concrete C50. The closure segment is 1.5m long. There are totally 31 segments, 23 cast-in-placed by balanced cantilever and 8 cast-in-placed by stents. Fig. 2 Continuous beam section (Unit: cm) IV. SIMULATION OF THE SEGMENTAL CONSTRUCTION STAGE The calculation and analysis software select MIDAS Civil. Midas Civil is bridge field general structure analysis and design system, has the intuitive interface, and a cutting-edge computer display technology. Midas Civil integration of the static analysis, dynamic analysis, geometry nonlinear analysis, buckling analysis, moving load analysis, analysis, analysis of suspension bridge PSC bridge, the hydration heat analysis function analysis and design. Complete bridge girder elevation survey data indicate that finite element software MIDAS/civil has kind guidance to confirm segment construction. MIDAS CIVIL has high efficient automatic model assistant function. As long as input cross-section shape parameters, material parameters, prestressed parameters and other basic data, the model can be set up quickly. Before the truss program analyses the structure, it has first to discretize the structure and establish the structure calculation scheme. The structure s discretization is important to the structure analysis. The computational model must accurately reflect the constitution and load features. [4]At the condition of computational accuracy, it s better to reduce nodes and lessen calculation model. 1) Concrete has a complex behavior time-dependent. So the construction of segmental beams often shows unexpected deflections. It is difficult to accurately calibrate these deflections in site. In order to reduce its influences, concrete time-dependent behavior is defined as time load in the model. When establishing the model, the MIDAS CIVIL will calculate the time property of concrete, including strength development curve, creep coefficient and shrinkage coefficient, according to each unit material age. 2) Sorting the basic data of the continuous beam, including concrete elastic modulus, box girder section size, steel strand distribution, and put these data input to the calculation software. Table Ⅰ shows the basic parameters of the longitudinal steel strand. TABLE Ⅰ LONGITUDINAL PRESTRESSING TENDONS MAIN PARAMETERS Item Value Model 9(12)-15.2 Metallic bellow inner diameter(mm) Modulus of elasticity(mpa) Anchor stress under control(mpa) 1265 coefficient of relaxation 1.0 Warp coefficient of per meter duct Coefficient of friction resistance 0.25 Anchorage deformation, reinforced retraction and joint compression value (mm) 6 2) Based on the finite element method, the continuous beam is simplified as the plane truss structure and the cantilever 182

3 segments are discreted as beam elements. The beam is divided into 46 beam elements and 49 nodes. As shown in Fig.4. 4) As shown in Fig. 5, the hanging basket function is simplified as concentrated load. The load is put on the end of the built cantilever, including z direction perpendicular load and y direction bending moment, M = P e. Fig. 4 Mesh of continuous beam hinge joint of the main pier is changed to one-way hinge joint. And the continuous beam is founded [7]. 6) Fig. 6 shows the main process of cantilever construction. Table Ⅱ shows the continuous beam construction stage division situation. Fig. 5 Form traveler load diagram 5) The structure stress system has to transfer at the cantilever construction process. Before side pan closes, the main pier forms the "T" type static structure with the superstructure and the constraint condition between them is consolidation constraints. When the side span closes and the consolidation constraint is removed, the structure system changes. Then the constraint condition between the main pier and the superstructure is transformed to bilateral hinge joint and the constraint condition of the side support is simulated as one-way hinge joint. After the mid-span closes, the bilateral Fig. 6 Construction process simulation: a) Advancing form traveler to the next segment, b) Placing reinforcement ducts, tendons and concrete, c) Posttensioning tendons. TABLE Ⅱ CONTINUOUS BEAM CONSTRUCTION STAGES DIVISION construction stage construction content construction stage construction content 1 0# casting 13~28 construction stage 9~12 cycling for 3#~6# segment construction 2 0# curing 29 side cast-in-site segment constructing 3 0# tensioning 30 side closure segment formwork erecting 4 1# formwork erecting 31 side closure segment casting 5 1# casting 32 side closure segment curing 6 1# curing 33 side closure segment tensioning 7 1# tensioning 34 temporary bearings removing 8 form traveler preloading 35 mid closure segment formwork erecting 9 2# formwork erecting 36 mid closure segment casting 10 2# casting 37 mid closure segment curing 11 2# curing 38 mid closure segment tensioning 12 2# tensioning 39 creep and shrinkage(3 years) 183

4 V. CALCULATION RESULTS By calculating and considering the permanent load effect, pre-stressed effect, shrinkage effect, creep effect, temperature effect, temporary load effect and the construction load effect of each segment, the internal force and displacement value of the left and right cross section of each segment can be got. In the construction control process, the calculated results can be the ideal state of the continuous beam and used to predict the next segment s pre-camber and determine the mould elevation. The calculated results can also determinate the structure stress state and stability to judge whether the structure is safe in construction process [8]-[10]. 5.1 Internal force calculation results Stress considerations are of importance in segmental bridge construction. In the cantilever construction process, the stress foot of the beam is maximum. Furthermore, time-dependent material properties like strength of the newly cast concrete, as well as shrinkage, creep, and relaxation influence the structural system resistance. Resulting stresses in the unfinished bridge structure during construction can even exceed the final stresses during service. The case is dangerous. So it has to take measures to see the stress there in real time. Here we make use of vibration wire strain sensor, buried in concrete, to reveal the stress level according to strain value. Fig.7 shows the vibration wire strain sensor. Fig. 8 shows the data acquisition instrument. Fig. 7 The vibration wire strain sensor Fig. 8 The data acquisition instrument Fig. 9 ~ Fig. 12 show the internal force calculation results of construction structural in main stages. Seen from the internal force diagram, the stress control section is chosen at the root. Fig. 9 The bending movement after 6# segment tensioned Fig. 10 The bending movement after side span closed and tensioned Fig. 11 The bending movement after mid span closed and tensioned 5.2 The calculation results of pre-camber In the cantilever construction, the most key issue need to be resolved is linear control. The linear, deviated from design Fig. 12 The bending movement after 3 years linear, will lead to the final connection difficulty and the inner force state deteriorated. In order to accomplish a high-quality bridge project, the linear control must be effectively in the cantilever construction. 184

5 Reference [11] established a linear adaptive control system to ensure the quality of the cantilever construction linear control. The system consists of three parts, namely model modification subsystem, theoretical calculation subsystem and monitoring control subsystem. The simulation model of the structure can provide precamber for each segment. The precamber is used to confirm segment mould elevation. Fig.13 shows the calculated precamber. S1 S2 Precamber (m) N7 N8 N9 N10 N11 N12 N13 N14 N15 N16 N17 N18 N19 N20 N21 N22 N23 N24 N25 N26 N27 N28 N29 N30 N31 N32 N33 N34 N35 N36 N37 N38 N39 N40 N41 N42 N43 N44 N45 N46 N47 N48 N49 N50 N51 N52 N53 Node number Fig. 13 The calculated precamber The mould elevation is calculated as follows: H i L =H i D +f i Y +f G Where H i L is the mould elevation of segment i, H i D is the design elevation of segment i, f i Y is the calculated precamber, f G is form traveler deformation, got from form traveler loading test data analysis. It must specify, the calculated result shown in Fig.13 is just applied to preliminary construction stages. That s because along with the construction progress some calculation parameters in calculation model have to adopt test value and the result is varying. Fig. 14 shows the measured value after the mid-span connected. Elevation (m) Left measured value Right measured value Caculated value Beam section Numbers Fig. 14 The comparison of the left and right elevation control points measured value of the continuous beam From Fig.14 we can see when the cotinuous beam closed, the error, between the real elevation values and the calculated values, is generally in the distribution of (-3mm, 13mm), which is within the specified range (-5mm, 15mm). The error between the left side and the right side of the beam is generally in the distribution of (-7mm, 10mm), which is within the specified range (-10mm, 10mm). So through 3 years creep and shrinkage effect of concrete, the actual linear will be close to the design linear. VI. CONCLUSION In this paper, key technology issues, concerning how to simulate the construction stages of a PC continuous beam, have been outlined. The continuous beam has successfully closed. In the whole construction process, the stress value calculated by finite element model is consistent with the measured value. When the closure segment is constructed, the biggest elevation deviation is 10mm which meets the specification requirement. As analyses show, to obtain real behavior of concrete bridges, segmental construction stage analysis must consider time-dependent behavior of concrete, because construction period continue along time and loads may change during this period and after [12]. By monitoring the construction of each segment of the continuous beam and modifying the related parameters, the expected goal is achieved. That indicate the construction control program is feasible. 185

6 From the monitoring results we can know that the construction monitoring work is successful, and that of course is based on the right structure simulation calculation. The experience of continuous beam structure modeling mentioned in the paper can be used for the other similar project. ACKNOWLEDGMENT Thanks the sponsors of this international conference to provide us a precious academic platform. REFERENCES [1] G. Lucko, J. M. Garzade, Constructability considerations for balanced cantilever construction. Practice Periodical on Structural Design and Construction, Practice Periodical on Structural Design and Construction, vol. 8, n 1, pp , Feb [2] A. G. Bishara, N. G. Papakonstantinou, Analysis of cast-in-place concrete segmental cantilever bridges, J. Struct. Eng., vol 16(5), pp , [3] R. Malm, H. Sundquist, Time-dependent analyses of segmentally constructed balanced cantilever bridges, Engineering Structures, vol 32, n 4, pp , Apr [4] Y. Xu, Y. J. Wang, Z. J. Wan, Prestressed Concrete Continuous Bridges Design, Bei Jing: China Communications Press, 1th Ed. 2000, pp [5] B. F. Pan, G. Li, Monitoring and control technology in cantilever construction of continuous beam bridge, 2011 Inter. Conf. on Consumer Electronics, Communications and Networks, Xian Ning, 2011, pp [6] S. Jung, J. Ghaboussi, C. Marulanda, Field calibration of time-dependent behavior in segmental bridges using self-learning simulation, Engineering Structures, vol. 29, is. 10, pp , Oct [7] J. Y. Song, Simulation and analysis of construction process of Juancheng Yellow River Highway Bridge, Harbin Gongye Daxue Xuebao/Journal of Harbin Institute of Technology, vol. 42, n SUPPL.1, pp , Apr [8] H. Jiang, X. D. Guo, H. L. Yang, Research on space simulation methods for high-pier long-span pre-stressed continuous rigid frame bridges, Advanced Materials Research, vol , pp , [9] Y.F. Duan, Y.L. Xu, Q.G. Fei, et al, Advanced finite element model of Tsing Ma Bridge for structural health monitoring, International Journal of Structural Stability and Dynamics, vol. 11, no. 2, pp , Apr [10] J. M. Ko, Y. Q. Ni, Technology developments in structural health monitoring of large-scale bridges, Engineering Structure, vol 27, Is. 12, pp , Oct [11] Q. Wang, Y. B. He, Linear Adaptive Control in the Cantilever Construction of Long-span PC Continuous Beam Bridge, in 2th Inter. Conf. on Information Science and Engineering, Hang Zhou, 2010, pp [12] S. Ates, Numerical modeling of continuous concrete box girder bridges considering construction stages, Applied Mathematical Modeling, vol35, is.8, pp , Aug