[机械模具数控自动化专业毕业设计外文文献及翻译]【期刊】索斜拉桥建模-外文文献

Advances in Bridge Engineering, March 24 - 25, 2006 161 MODELING OF CABLE STAYED BRIDGE Shilpa S. Kulkarni1, R.K. Ingle2 and P.N. Godbole3 1. M.Tech Scholar (Structural Dynamics and Earthquake Engineering), 2. Professor and 3.Visiting Professor, Department of Applied Mechanics, Visvesvaraya National Institute of Technology, Nagpur ABSTRACT Behavior of cable stayed bridge is of great importance as the influence of moving loads, seismic and wind forces, on these structures mainly dependent on its characteristic. Major structural component of cable stayed bridges are deck, tower (pylons), cables and abutments/piers. The structure is of nonlinear nature and highly indeterminate. The dynamic analysis demands various elements of cable stayed bridge be modeled properly so as to represent the actual behavior of structures as closely as possible. In this paper various aspects of modeling of cable stayed bridge using SAP2000 are discussed. Also this paper discussed the effect of various parameter and their variation on design of cable stayed bridge. Further vibration analysis has been performed to obtain natural frequencies and the results are presented. INTRODUCTION A typical cable stayed bridge consists of continuous girder with one or more towers erected in the middle of the span. From these towers, cables stretch down diagonally and support the girder. Cable stayed bridge can be distinguished by the number of spans, number of towers, girder type, number of cables and types of cables etc. Concrete cable stayed bridges possess a high degree of vertical rigidity, a relatively small deflection and their damping effect is such that there are relatively small vibrations. The main advantage can be summarized as below i. The horizontal component of inclined cable forces, causing compression in deck combined with bending due to vertical loading favors a deck system design using monolithic and/or precast concrete. ii. The amount of steel used for cables is comparatively less. An optimum solution can be achieved by correct choice of height of tower and diameter of cables. iii. The erection of cables as well as reinforced concrete deck is comparatively easy. Construction with free cantilevering system is very suitable. Due to small amount of steel and ease of erection, this system is highly recommended with regard to the cost. Shilpa S. Kulkarni, R.K. Ingle and P.N. Godbole 162 Cable Stayed Bridge presents a three dimensional structural system consisting of various structural components such as Stiffening girder, Cable system, Tower and Foundation. The stiffening girder is supported by cables which are anchored at the pylon. These pylons are placed on main piers so that the cable forces can be transferred down to the foundation system. In this paper it is proposed to study the effect of variation in parameter such as change in height of pylon, use of one and different cable diameter, various end boundary conditions etc. all these studies are carried out using the cable stayed bridge at Krishnarajapuram, Bangalore-Chennai National Highway, Bangalore. STRUCTURAL IDEALIZATION The cable-stayed bridge included in this study consists of deck supported by two longitudinal girders connected with transverse cross girders. The members of pylon, longitudinal girder and cross girder are modeled using 3-D frame element. The cables are modeled using cable element and 4 noded shell element used to model the deck slab. Mathematical modeling of Cable Stayed Road Over Bridge at Krishnarajapuram, Bangalore-Chennai National Highway in SAP2000 is shown in Fig. 1 SALIENT FEATURES OF THE BRIDGE The total length of the bridge is 230m out of which the length of the cable-stayed portion is nearly 142m. Asymmetrical span arrangement used with span chosen 93.03m and 48.7m. The transverse cable arrangement is of double plane vertical type and the longitudinal cable arrangement is of semi-harp type. In indeterminate structure like cable-stayed bridges, cables are the predominant structural members. In this bridge, High fatigues resistant BBR-DINA cables (a bundle of 7mm diameter wires) have been used. These cables are bundle of parallel wires encased Figure 1 Cable-stayed bridge (a) 3D view (b) Pylon (a) (b) Advances in Bridge Engineering, March 24 - 25, 2006 163 in high-density polyethylene sheathing and anchored in socket filled with special DINA- hardener-resin compound, which provides excellent high fatigue resistance. The ultimate tensile strength of these HT wire is upto 1570 N/mm2 The deck girder is a reinforced concrete section of 23.4m overall width catering for 4-lane traffic. Along the length of the bridge, the overall depth of the girder is 2.81m and width 1.76m. Cross girders at every cable attachment having depth 1.707m, width 0.4m and thickness of deck slab is 0.5m. The grade of concrete for deck and pylon is M 45. The entire bridge deck in the cable-stayed portion is constructed in several equal segments of length 9.768m by cantilever construction method in conjunction with the erection of stay cables in a clearly defined sequence. A H frame pylon of solid section is provided with an overall height of about 60m. The cross-section dimension of each leg varies from 4.6m x 3.2m at base to 2.6m x 3.2m at top. The column top beam- 2m x 1m and column bottom Beam- 1.5m x 1m. PARAMETRIC INVESTIGATION Effect of Variation in Cable In this section it is propose to study the effect of use of single cable diameter various diameter cables. The various cable areas used are given in Table 1 Table 1 Cable Area for Parametric Study Cable no. Cable area(mm2) Cable no. Cable area(mm2) Cable no. Cable area (mm2) 1 3695 6 7389 11 4849 2 4849 7 7158 12 5311 3 5311 8 8313 13 4849 4 6234 9 9005 14 30480 5 6696 10 3695 The result of the above are compared with single cable area of 7702 mm2 The results for key location compared in Table 2 Shilpa S. Kulkarni, R.K. Ingle and P.N. Godbole 164 Table 2 Comparison of Results for Variation in Cable Areas Sr. no. Element Forces Uniform Cable area Different Cable area 1 Cable Axial (kN) 3000 2078 Axial (kN) 1558 1209 Shear (kN) 5426 4851 2 Longitudinal Beam Moment (kN-m) 77266 29187 68368 26035 Axial (kN) 41374 41215 Shear (V2)(kN) 1937 2709 Moment (M3)(kN-m) 45142 65132 Shear (V3)(kN) 2349 1882 3 Pylon Moment (M2)(kN-m) 77078 53926 Figure 2 (a) and (b) Comparison of Bending Moment Diagram (b) Different cable area (a) Uniform cable area Advances in Bridge Engineering, March 24 - 25, 2006 165 It can be seen that using different cable areas, cable tension decreases and moment (M3) in pylon deceases. It can also be seen that use of uniform cable area gives predominantly sagging moment. Effect of variation in pylon height The pylon height may be decided by the location of bridge. Here it is proposed to study the effect on the structural response by varying the height to 35.4m, 45.4m and 55.4m. Cable stayed bridge at Krishnarajapuram; Bangalore is having height 45.4m. The comparison of results presented in Table 3 Table 3 Comparison of Results for Varying Pylon Height Pylon Height (m) Sr. no. Element Forces 55.4 45.4 35.4 1 Cable Axial (kN) 1701 2078 2770 Axial (kN) 892 1209 1552 Shear (kN) 4563 4851 5298 2 Longitudinal Beam Moment (kN-m) 64886 68368 73875 Axial (kN) 43135 41215 38725 Shear (V2)(kN) 2861 2709 3268 Moment (M3)(kN-m) 69268 65132 65937 Shear (V3)(kN) 1301 1882 2966 3 Pylon Moment (M2)(kN-m) 47248 53926 62337 It can be assured that as the height of the pylon increases, the cable tension decreases, beam forces decreases however there increase in pylon forces. Effect due to various boundary conditions This study results obtained by using different deck end support condition along with various girder pylon attachment are compared. The support conditions are, both end of the longitudinal girder are hinged, one end hinge and other end roller, both end roller etc. with these support condition, it is also proposed to see the impact of connection of deck with pylon. Hence three types of connections are considered here for study i.e. no connection, rigid connection and hinge connection. The results are presented in Table 4-6. Shilpa S. Kulkarni, R.K. Ingle and P.N. Godbole 166 Table 4 Comparison of Results for Various Deck Pylon Connections when both Girder Ends on Support Hinge Deck and Pylon connection Sr. no. Element Forces No Rigid Hinge 1 Cable Axial (kN) 3987 1194 2435 Axial (kN) 4162 3171 3798 Shear (kN) 4677 4901 4814 2 Longitudinal Beam Moment (kN-m) 65937 68984 67842 Axial (kN) 49338 37609 42637 Shear (V2)(kN) 1426 1256 5557 Moment (M3)(kN-m) 31906 27479 139551 Shear (V3)(kN) 1808 2104 1812 3 Pylon Moment (M2)(kN-m) 51009 63138 51164 Table 5 Comparison of Results for Various Deck Pylon Connections when one End of Longitudinal Girder is Hinge and Other Roller Deck and Pylon connection Sr. no. Element Forces No Rigid Hinge 1 Cable Axial (kN) 3992 1196 2439 Axial (kN) 1636 21.13 1510 Shear (kN) 4684 4914 4821 2 Longitudinal Beam Moment (kN-m) 66073 26245 67963 Axial (kN) 49287 37528 42575 Shear (V2)(kN) 1428 1261 5563 Moment (M3)(kN-m) 31929 27602 139668 Shear (V3)(kN) 1820 2089 1823 3 Pylon Moment (M2)(kN-m) 51454 62414 51559 Advances in Bridge Engineering, March 24 - 25, 2006 167 Table 6 Comparison of Results for Various Deck Pylon Connections when Rollers at Both Ends of Longitudinal Girder Deck and Pylon connection Sr. no. Element Forces No Rigid Hinge 1 Cable Axial (kN) 3948 1198 2388 Axial (kN) 708 664 711 Shear (kN) 4818 4919 4969 2 Longitudinal Beam Moment (kN-m) 68055 69279 70159 Axial (kN) 50139 37579 43524 Shear (V2)(kN) 1433 1262 5573 Moment (M3)(kN-m) 32042 27617 139895 Shear (V3)(kN) 176 2022 3.53 3 Pylon Moment (M2)(kN-m) 19217 59654 21554 Referring to the results it can be seen that cables are unaffected due to the support condition. The longitudinal girder show less moment when pylon and deck are rigidly connected. The pylon column moment is drastically reduced when there is no or hinged connection between deck and pylon. Effect of parametric variation on dynamics of cable stayed bridge The results with parametric variation are compared in Table 7. Table 7 Comparison of Time Periods in Seconds for Successive Mode Shapes Deck Support connection Cable Area Height of Pylon(m) H-H H-R R-R Deck-Pylon connection Deck-Pylon connection Deck-Pylon connection Modeno. SingleDifferent (ht of Pylon45.4m) 35.4 55.4 NoRigidHinge NoRigidHinge NoRigidHinge 1 1.40 1.29 1.37 1.27 1.30 1.28 1.29 1.30 1.28 1.30 1.30 1.30 1.30 2 1.12 1.08 1.11 1.26 1.09 1.06 1.08 1.11 1.07 1.11 1.14 1.07 1.12 3 0.95 0.95 0.75 1.07 0.91 0.83 0.88 0.95 0.95 0.95 1.02 0.97 0.97 4 0.63 0.70 0.71 0.70 0.82 0.67 0.71 0.82 0.67 0.79 0.84 0.87 0.81 5 0.54 0.60 0.58 0.62 0.75 0.53 0.64 0.79 0.53 0.68 0.81 0.66 0.68 6 0.52 0.57 0.57 0.61 0.62 0.49 0.59 0.65 0.49 0.59 0.69 0.53 0.59 7 0.50 0.52 0.52 0.57 0.52 0.45 0.52 0.61 0.46 0.52 0.62 0.49 0.52 8 0.41 0.42 0.41 0.53 0.42 0.38 0.40 0.52 0.39 0.42 0.52 0.46 0.41 9 0.39 0.40 0.36 0.52 0.40 0.37 0.40 0.42 0.38 0.40 0.42 0.37 0.39 Shilpa S. Kulkarni, R.K. Ingle and P.N. Godbole 168 The first predominant modes are shown in figure 3. It can be that the time period of the first mode is not affected very much while the time periods of subsequent modes show a reasonable variation. Mode shapes CONCLUSION The main objective of the paper has been to demonstrate the use of SAP2000 software in the analysis of cable stayed bridge. SAP2000 is user friendly software in which modeling and parametric studies can be carried out easily. Work is in progress to study the effect of nonlinearity, influence of moving loads, seismic and wind effect on the structure. REFERENCES 1. Caicedo J.M., Turan G., Dyke S.J., Bergman L.A., Comparison of Modeling Technique for Dynamic Analysis of a Cable-Stayed Bridge, Washington University,