International Journal of Civil Engineering and Technology (IJCIET) Volume 6, Issue 11, Nov 2015, pp. 156-163, Article ID: IJCIET_06_11_016 Available online at http://www.iaeme.com/ijciet/issues.asp?jtype=ijciet&vtype=6&itype=11 ISSN Print: 0976-6308 and ISSN Online: 0976-6316 IAEME Publication THE EFFECT OF LATERAL CONFIGURATION ON STATIC AND DYNAMIC BEHAVIOUR OF LONG SPAN CABLE SUPPORTED BRIDGES Prof. G. M. Savaliya Assistant Professor, Civil Engineering Department, Government Engineering College, Surat, Gujarat, India Prof. (Dr.) A. K. Desai Professor, Applied Mechanics Department, SVNIT, Surat, Gujarat, India Prof.(Dr.) S. A. Vasanwala Professor, Applied Mechanics Department, SVNIT, Surat, Gujarat, India ABSTRACT Long span bridge is the demand of every nation and it could be achieved with use of enhanced materials. With the development of the high strength materials and techniques for analysis of bridge, long span cable supported bridge are introduced. Generally, cable supported bridges comprise both suspension and cable-stayed bridge. Cable supported bridges are flexible in behavior. These flexible systems are susceptible to the dynamic effects of wind and earthquake loads. With increasing span of the bridge the flexibility of the bridge is increasing. Here, attempt is made to improve the rigidity of long span bridge and presented in this research paper. For enhancing the rigidity of the bridge in lateral and vertical directions, different configuration of the cables of long span cable supported bridges is considered in this study. To understand the response of the long span cable supported bridges, modal Time History analysis is carried out in SAP2000 software. The behavior of the cable supported bridges is studied with different configuration of cables in lateral direction. The behavioral response of the bridge is presented in form of a Time Period in lateral and vertical direction for structural members of the bridge. Key words: Cable-Stayed Bridge, Suspension Bridge, Cable-Stayed Suspension Hybrid Bridge, Cable-Stays Configuration, SAP2000, Modal Time History Analysis http://www.iaeme.com/ijciet/index.asp 156 editor@iaeme.com
The Effect of Lateral Configuration on Static and Dynamic Behaviour of Long Span Cable Supported Bridges Cite this Article: Prof. G. M. Savaliya, Prof. (Dr.) A. K. Desai and Prof.(Dr.) S. A. Vasanwala. The Effect of Lateral Configuration on Static and Dynamic Behaviour of Long Span Cable Supported Bridges, International Journal of Civil Engineering and Technology, 6(11), 2015, pp. 156-163. http://www.iaeme.com/ijciet/issues.asp?jtype=ijciet&vtype=6&itype=11 1. INTRODUCTION The requirement of bridges is increasing day by day with increasing the populations and their needs. To grant easy transportation in the urban areas long span bridges necessities are increasing day by day. In the twentieth century the development and research in the field of the bridge engineering is take place enormously to fulfill the need of the very long span bridges. With development of new material and techniques for analysis very long span cable supported structures came in to practice. In general for very long span bridges the high strength steel cables are used as a structural load resisting elements. Some aspects of cable supported bridges are illustrated here. 1.1. Cable-stayed bridge The cable-stays are directly connected to the bridge deck resulting in a much stiffer structure. A large number of closely spaced cable-stays support the bridge deck throughout its length, reducing the required depth and bending stiffness of the longitudinal girder to a minimum thereby allowing the construction of relatively longer spans. [2]The structural action is simple in concept; the cables carry the deck loads to the towers and from there to the foundation. The primary forces in the structure are tension in the cable-stays and axial compression in the towers and deck; the effect of bending and shear in deck is less influential. For cable-stayed bridge an iterative approach in which initially the post-tensioning cable forces in the DL configuration are determined by solving compatible conditions arising from flexibility matrix of the structure. In the cable-stayed bridge a cable-stays are making variable angles with horizontal axis, so the forces in the cable-stays are incompatible at different locations. So, the optimization procedure is utilized to minimize the crosssections of the cable system, on the basis of the maximum effects on stress and displacement variables evaluated on the live load configurations. 1.2. Suspension bridge A deck of suspension bridge is hanged by vertical hangers, which are connected to main suspension caternary cables. The main cable is continuous, over saddles at the pylons, or towers, from anchorage to anchorage. In a suspension bridge, a procedure to find the initial configuration under dead load is relatively simple as the main extremities are fixed at earth constraints. As an outcome, optimization techniques are frequently employed with the purpose to identify the structural behavior of the bridge with respect more complex external loads such as aeroelastic and seismic phenomena. However, most of the methodologies are typically concerned to evaluate optimum post-tensioning forces in the dead load (DL) configuration, without achieving the complete optimization of the geometry, the stiffness of the structural elements and thus the costs of construction. [1] The requirement of incredible long span bridges is increased day by day with increase in inhabitants and their needs. To achieve a very long span bridge, use of high strength material along with novel structural system is essential. In general to http://www.iaeme.com/ijciet/index.asp 157 editor@iaeme.com
Prof. G. M. Savaliya, Prof. (Dr.) A. K. Desai and Prof.(Dr.) S. A. Vasanwala achieve longer span bridges, cable-stayed and suspension systems are used, in which the cable-stayed bridge has better structural stiffness and suspension bridge has ability to offer longer span. Combination of above two structural systems could achieve a very long span cable-stayed suspension hybrid bridge. 1.3. Cable-stayed suspension hybrid bridge The cable-stayed suspension hybrid bridge is presented as an alternative to long span cable-stayed and suspension bridges. Hybrid cable-stayed suspension bridge is combination of cable-stayed bridge and suspension bridge as shown in Fig. 1. Figure 1 hybrid cable-stayed suspension bridge The idea for this innovative system was first introduced by Dischinger in 1949, Schlaich 1988; Gimsing 1988; Lin and Chow 1991.[1] There after a very little work is done on this system of combined bridge. 1.3.1. Advantages of Cable-stayed suspension hybrid bridge Advantages of combining both the systems were discussed below. By combining both the system of cable supported bridges following advantages could be achieve [3] 1. As compared to the suspension bridge with the same span length the partly suspension portion is replaced by cable-stayed portion and suspension portion can be shortened, so the tensional forces in the main caternary cables are greatly decreased. 2. Reduction of suspension portion in main span decrease in the construction costs of the main cables, massive anchors, difficulty to construct them in water, and therefore makes it possible to build in the soft soil foundation also. 3. As compared to cable-stayed bridges with the same span length, the cable-stayed portion is also greatly shortened. These results, the reduced height of tower, length of stays and the axial forces in the deck. 4. In addition to these, cantilevers during erection are also shorted and wind stability of the bridge under construction may therefore improve. Therefore Hybrid cable-stayed suspension bridge becomes an attractive alternative in the design of long span bridge systems. So, the long span cable supported bridges like cable-stayed bridge, suspension bridge and cable-stayed suspension hybrid bridge with different lateral configuration is considered in the current study. 1.3.2. Analysis of cable supported bridges Long span cable supported bridge highly are defined through large number of cable elements which lead to highly statically indeterminate structures. So, post tensioning forces in cables and cross sectional area of the cables can be considered as design variables, which must be determined to identify the bridge configuration under dead and live loading for economical structural steel quantity and optimum performance of http://www.iaeme.com/ijciet/index.asp 158 editor@iaeme.com
The Effect of Lateral Configuration on Static and Dynamic Behaviour of Long Span Cable Supported Bridges structural elements. The analysis of cable-stayed suspension hybrid bridge is a new area of research. The hybrid bridge is consists of the main cables, cable-stays and hangers in a bridge, which present better performances than conventional ones based on pure suspension and cable-stayed configurations. 2. BRIDGE CONFIGURATIONS The bridge configurations considered in the current study for cable-stayed bridge, suspension bridge and cable-stayed suspension hybrid bridge is explained here. The bridge configuration is based on bridge of the east channel of Lingding Strait in China [5] having central span = 1400 m, two side spans = 319 m and height of pylon=258.986 m. The behavior of bridge is studied for different cable configuration and thus pylon height is considered as a constant. Figure 2 Geometric configuration of cable-stayed suspension hybrid bridge (CSSHB) In current study as shown in Fig.2, the bridge having central span = 1400 m, two side spans = 312 m and pylon height = 258.986 m is studied with suspension to span ratio 0.5 means suspension portion length is 700m in centre of main span. Table 1 shows the material properties of different elements of bridge. Table 1 Cross-sectional properties of cable-stayed suspension hybrid bridge members [4] Members E (Mpa) A (m2) Jd (m4) Iy (m4) Iz (m4) M (Kg/m) Jm (Kg.m 2 /m ) Girder 2.1x10 5 1.761 3.939 193.2 8.33 26340 2.957x10 6 Tower C 3.3 x10 4 30 350 220 320 78000 5.7x10 5 Tower TB 3.3 x10 4 10 150 70 70 26000 4.7x10 5 Main Cable CS 2.0 x10 5 0.3167 - - - 2660.3 - Main Cable SS 2.0 x10 5 0.3547 - - - 2979 - Hanger Cable 2.0 x10 5 0.0064 - - - 50.2 - Stayed cables 2.0 x10 5 vary - - - vary - Where, E - Modulus of Elasticity; A - Cross section area; M - Mass per unit length; Jd - torsional constat; Iy-Lateral Bending moment of inertia; Iz-Vertical Bending moment of inertia; Jm mass moment of inertia per unit length Figure 3 presents cable-stays at different positions from the pylon to center of the span with the assigned cross sectional area in m 2. At the pylon the cable stays no is 0 and as the deck span is moving towards center of the main span the cable-stays no is increasing towards the 39, in graph shown below in the horizontal axis no of cablestays are presented and in vertical axis respective area of the cable-stays in m 2. Here, distance between two hanger cables λ is 17.941 m http://www.iaeme.com/ijciet/index.asp 159 editor@iaeme.com
Prof. G. M. Savaliya, Prof. (Dr.) A. K. Desai and Prof.(Dr.) S. A. Vasanwala Figure 3 Cable Area assigned to Stay Cables from pylon to center of span 2.1. Arrangements of stayed cable in cable-stayed bridge To study the effect of stay cable planes arrangement on dynamic strength, vertical configuration of cable-stays can be revised the same as in lateral directions inclined outward angles with vertical axis and inclined inward angels with vertical axis. The stay cables of bridges can be arranged to be vertical or inclined with vertical axis in lateral direction, which can be adjusted by lateral configuration of pylons top and its connection with cable-stays. In this research paper the significant stayed cable configuration of the cables are incorporated with special inclination of stayed cable with the vertical axis passes through the connection of deck and the cable stays. Here the considered configurations are generated by offering the inclined inclination angle. The cable configurations are generated by assigning offsets at the top of the cables-stays in pylon as 14m and respective inclination angles assigned is with the vertical axis passes through connection between the deck and cable- the vertical stays. The inclination is assigned in both directions inward direction from axis as well as outward direction also. In the below Figure 4 the cable-stays with angle profiles in inward and out ward direction generated by providing offset at top of the cable-stays with vertical axis is shown. Inward inclination θ= θ=0º outward inclinationn θ= Figure 4 the cable-stayss having vertical, inward and outward angles with vertical axis http://www.iaeme.com/ijciet/index.asp 160 editor@iaeme.com
The Effect of Lateral Configuration on Static and Dynamic Behaviour of Long Span Cable Supported Bridges Cable stays are provided with above vertical, inward and outward angle make with vertical axis passes through joints of deck and cable-stays. 3. LOAD ASSIGNMENTS Structural elements of bridge are assigned with load cases as shown in below Table 2. Table 2 loads assigned to the different members Type of the load Value of Assigned Load Element Assigned Dead Load 97.980 kn/m Deck SIDL 50.0 kn/m Deck Live Load 34.650 kn/m Deck 4. STATIC AND DYNAMIC BEHAVIOR Nonlinear static and dynamic analyses are carried out to determine the response of the cable-stayed bridge, suspension bridge and cable-stayed suspension hybrid bridge. Here, geometrical nonlinearity of the cable supported bridge is more influencing factor in analysis. The P-Delta effect can be a very important contributor to the stiffness for considering geometrical nonlinearity of cable structures. The lateral stiffness of cables is due almost entirely to tension, since they are very flexible when unstressed. It is important to use realistic values for the P-delta load combination, since the lateral stiffness of the cables is approximately proportional to the P-delta axial forces. Dynamic behavior of bridge can conclude by dynamic analysis. Hence, Modal analysis is carried out to recognize the dynamic behavior of bridge. In modal analysis each modal load case results in a set of modes. Each mode consists of a mode shape (normalized deflected shape) and a set of modal properties like Time periods and Frequencies of the structure. Results are presented for different length of suspension to main span ratio for cable-stayed suspension hybrid bridge. 4.1. Analysis results and discussions Static and dynamic analyses are carried out to determine the response of the structure for different types of loadings. Here, different cable layouts of the cable supported bridges are considered for the study. The effect of these considered layouts can be judge by the structures response to the applied load cases. Each mode consists of a mode shape (normalized deflected shape) and a set of modal properties like Time periods and Frequencies of the structure. 4.2. Result Parameters Considered For Parametric Study Result parameters considered to understand the dynamic response of the bridge is presented here. The geometrical parameter considered in this paper is effects of Cable stays configuration in lateral directions, which can be obtain by changing top orientation of the cables and form of pylon. Parameters considered for comparison of results in parametric study are as follows: 1. Time period of the bridge for different mode shapes in Lateral mode shapes, 2. Time period of the bridge for different mode shapes in Vertical Mode shapes, 3. Time period of the bridge for different mode shapes in longitudinal modes shapes with different cable-stayed configurations etc. http://www.iaeme.com/ijciet/index.asp 161 editor@iaeme.com
Prof. G. M. Savaliya, Prof. (Dr.) A. K. Desai and Prof.(Dr.) S. A. Vasanwala 4.3. Results considering cable-stayed configuration as geometrical Parameters of cable-stayed bridge Here, for the different cable layout configuration, the response of the structure in the form of time periods of different mode shapes is presented in below given tables. Table 2 Time period of the modes of the cable-stayed bridge with different cable layout configurations Layout Cable-stayed bridge Cable-Stayed suspension hybrid bridge Suspension Bridge Mode Shape Inward Vertical 0º Outward Inward Vertical 0º Outward Inward Vertical 0º Outward Lateral_1 11.56 12.38 14.14 12.42 13.15 14.59 12.00 12.79 14.41 Lateral_2 7.82 10.35 10.80 7.81 10.41 11.12 7.80 10.31 10.87 Pylon_1 7.93 11.21 13.39 7.97 11.24 13.43 7.97 11.24 13.45 Vertical_ 1 Vertical_ 2 4.71 4.74 4.77 7.28 7.05 7.28 7.28 5.20 7.28 4.08 4.13 4.19 4.82 4.87 4.89 5.03 4.04 5.09 Longi._1 5.09 5.13 5.19 5.40 5.48 5.47 4.81 4.81 4.82 5. CONCLUSIONS From the analysis carried out with the different three cable-stays configurations the follwing observations are found. The dynamic analysis of cable-stayed ridge, suspension bridge and cable-stayed suspension hybrid bridge (CSSHB) with suspension to main span ratio 0.5 (Sup/span=0. 5) is carried out to identify the behaviour of the bridge with the lateral configuration of cables. The following results are obtained from the analysis: 1. From the results of principal lateral bending mode time period of CSSHB (Sup/Span=0. 5) with the considered configuration of cables in lateral direction, It is found that the time period increases 9.87 % if the vertical configuration is replaced by outward inclination of 4.264. 2. The time period of bridge in lateral direction reduces effectively by provision of inward inclination to cables. From the figure it is found that by the provision of inward inclination of 4.264 the lateral bending time period is reduced 5.66%. 3. The pylon time period of the bridge reduces 29.10 %, if the inward inclination of 4.264 is provided instead of vertical configuration. The reduction in the time period is also due to the change in shape of the pylon to A shape. 4. From the Table, it finds that the pylon time period of CSSHB (Sup/Span=0. 5) increases by 16.31 % if vertical cables are replaced by outward inclination of 4.264. Here, for the provision of outward inclination to cables the shape of the pylon is also changed to inverted A shape and thus the stiffness of the bridge is reduced. The longitudinal and vertical mode shape time period not changing effectively with change in the lateral configuration of bridges. http://www.iaeme.com/ijciet/index.asp 162 editor@iaeme.com
The Effect of Lateral Configuration on Static and Dynamic Behaviour of Long Span Cable Supported Bridges REFERENCES [1] Gimsing, N. J.(1983), Cable-Supported Bridges Concept and Design, John Wiley & Sons, Inc., New York. [2] Podolny, W.(1986) Cable suspended Bridges,, John Wiley & Sons, Inc., New York. [3] Zhang Xin-jun(2006), Study of design parameters on flutter stability of cable stayed suspension hybrid bridges, Wind and Structures, Vol. 9, No. 4 pp. 331-344. [4] Zhang Xin-Jun(2007), Investigations on Mechaniscs performance of cablestayed suspension hybrid bridges, Wind and Structures, Vol. 10, No. 6 pp. 533-542. [5] XIAO, R. C., Research on design of cable-stayed suspension hybrid bridges, China civil engineering journal, 33(5), (2000), pp. 46-51. [6] Abdul Kareem Naji Abbood. A Comparative Technical and Economical Study To Different Options Location For Bridge and Its Approaches, International Journal of Civil Engineering and Technology, 4(6), 2013, pp. 214-229. [7] Dr. K.v. Ramana reddy. Aerodynamic Stability of A Cable Stayed Bridge, International Journal of Civil Engineering and Technology, 5(5), 2014, pp. 233-239. http://www.iaeme.com/ijciet/index.asp 163 editor@iaeme.com