Technical Aspects of Cables Stayed Bridges - Coursework Example

TECHNICAL ASPECTS OF CABLES STAYED BRIDGES By Presented to Table of Contents Table of Figures 3 Executive Summary 4 Introduction 5 Configuration of Cable Stay Bridges 6 Cables 7 Girders 8 Conclusion 8 Bibliography 9 Appendix 1.0: Figures 11 Table of Figures Figure 1: The Idea of a simple cable-stayed bridge 11 Figure 2: Inclined Stay Cable 11 Figure 3: Initial cable press-stress calculation process 12 Figure 4: Dynamic Response of a stay cable in a real cable-stayed bridge. 12 Executive Summary Cable stayed bridges are some of the modern bridges in the world consisting of a strong continuous girder (beam) with one or more towers and pillars in the middle. They have become very popular since the Stromsund Bridge in Sweden was completed in 1955. In simple terms, cable-stayed bridges carry mainly vertical loads that act on the girder. Immediate support for the girder is provided by the stay cables so that the bridge can extend over a long distance. Basically, the structure of a cable-stayed bridge is such that, it is made up of a series of overlapping triangles, made up of the tower, the pylon, the girder and the cables, which are usually under axial forces, and are usually considered flexural and efficient. The cables are always under tension whereas the girder and the pylon, under compression. This reports looks at the history of cable stay bridges, examines the configuration and design structure, technical requirements, offers a description of various bridge structures and an analysis of the bridge structures. The report concludes by offering recommendations for stay-cable design, installation and testing. Introduction A first glance at cable-stayed bridges raises some interesting questions from both the public, bridge engineers-who find them technically challenging and innovative-and architects as well. These bridges-cable stayed bridges-have evolved since the Stromsund Bridge in Sweden was completed, into one of the most used bridge design type for a long-span of bridges (Tang 2000). The idea of cable-stayed bridges is very simple. A bridge usually has vertical loads that exert pressure on a girder as illustrated in Figure 1. The stay cables are used to offer transitional support for girders so that it can withstand the pressure exerted by the vertical loads while enabling it to span long distance (Svensson 2012). Basically, the structure of a cable-stayed bridge is such that, it is made up of a series of overlapping triangles, made up of the tower, the pylon, the girder and the cables, which are usually under axial forces, and are usually considered flexural and efficient. The cables are always under tension whereas the girder and the pylon, under compression (Dayaratnam 2000). Overtime, cable-stayed bridges have become very popular in bridge engineering; there are more than seven hundred cable-stay bridges in the world today. With advancement in technology and architectural design, the length of cable-stay bridges has significantly increased over the years. For instance, the first major cable-stay bridge built in 1955, the Stromsund Bridge in Sweden, spanned 183m; in the 1970’s, the Neuenkamp bridge in Germany spanned 350m and was considered the longest then until the 1980s when another bridge, the Alex Fraser-Annacis Island bridge spanned 465m was completed (W. Denney Pate & W. Jay Rohleder, Jr., P.E. 2008). This was however surpassed in 1994 by the Normandie bridge that spanned 856m. Today, the longest span cable-stay bridge is the Russky Bridge, in Vladivostok, Russia, spanning 1,104m, completed in 2012 (Svensson 2012). Configuration of Cable Stay Bridges The concept of cable-stayed bridges as illustrated in Figure 1. was that cable suspension was to be used to replace piers as intermediary support for girder, so that it could withstand the vertical load over a long span or distance (Morgenthal & Yamasaki 2010). As a result, the first cable-stayed bridges spaced stay cables far apart based on the maximum girder strength. The result was stiff girders that were supposed to resist global forces as well as span larger spacing between stay cables. Using an elasticity supported girder, it is easy to simulate how cable-stayed bridges would behavior in the real-world environment. Consider the bending of the girder under a given load as being made of a global and local component. The local bending moment between the stay cables is in proportion to the square of the spacing. Therefore, the approximate global bending moment of an girder-elastically supported-is in which I is the moment of the girder’s inertia, a, a coefficient that is dependent on the load p, and k an elastic constant that is derived from the stiffness of the stay cables. The global bending moment decreases with a decrease in the girder stiffness (I) (Dayaratnam 2000). It is therefore important to analyze and evaluate the ideal cable forces for the final bridge under its own self-weight following the procedure outlined in Figure 2. The stay cables are used for carrying loads on the bridge girder and remains the same, the total quantity of the cables required, therefore, is, in practical sense, same and is independent of the spacing of the stay cables or the number of stay cables. However, smaller cable spacing results in smaller local bending moment of the girder. Reducing the local bending moment makes the girder more flexible, which in turn, attracts less global moment. A problem of buckling stability arises when girders are more flexible (Su et al. 2011). Due to the need of replacing cables now and again, it is desirable to reducing the spacing between stay cables; this can allow for easy dismantling, detensioning, and replacement of stay cables under reduced loads. It is very important to note that, various cable configurations exist including Harp, Fan and Radial. Cable configurations have very major effects especially when it comes to long span bridges (Morgenthal & Yamasaki 2010). Cables These are the most important elements of cable-stayed bridges, since they are the ones responsible for carrying girder load and to transfer that load to the back-stay cable anchorage and the tower. In the design of cable-stayed bridges, the stay cables are usually inclined to determine the stiffness of the cables, as illustrated in Figure 2. Mostly, stay cables are tensioned to approximately 40% of their strength in a permanent maximum load condition. It is important to properly consider the effectiveness of stay cables especially during construction since at times, their tension might be very low (Y. Xi & Kuang 2000). A recommended safety factor for stay cables is usually about 2.2 which results in a considerable stress of about 45%, which is recommended for GUTS, Guaranteed Ultimate Tensile Strength. According to Svensson (2012), the recommended stress for stay cables must put into consideration several factors including the anchorage strength of assemblage at the cables weakest point with regards to the cables fatigue behavior and capacity. Cable anchorage is a very important aspect of a stay cables. Previously, for anchorage, the Hi-Am socket has been used for cable anchorage and its performance has been excellent. Bonded sockets have also been used to anchor strand cables and have also performed excellently. Recently, engineers have employed the use of unbounded anchorage in which all stands are anchored in position by only two wedges. All these anchorage type meet the design requirements as have been confirmed by various tests such as cable stiffness and boundary conditions tests. Consider the graph in Figure 4. it shows the results obtained while determining the exclusive cable force based on first Eigen frequencies (J. H. G. Macdonald & Fletcher 2003). Girders A well designed and fabricated deck-orthotropic-is a considerable solution for cable-stayed bridges. Increasing labor and development costs have, however, rendered orthotropic decks commercially less attractive. This has led engineers to consider using concrete and as such, a reasonable number of concrete cable-stayed bridges have since been built. Significant developments have occurred, in particular, precast construction and cast-in-place construction (Fish 2011). Today, lightweight and high strength concrete are used for the construction of girders used in building cable-stayed bridges, especially, in high seismic areas. With advancements in technology, girders are now constructed by combing concrete and steel, despite steel being expensive. These types of girders are referred to as composite decks. These composite decks made of steel girder, by shear studs, significantly reduces the quantity of steel of the girder. This results in an improved performance of the deck slab as a result of the compressive stress in the concrete deck. The Annacis Island Bridge is an example of a cable-stayed bridge completed using composite concrete-steel deck girders (W. Denney Pate & W. Jay Rohleder, Jr., P.E. 2008). Conclusion The technology of cable-stayed bridges is continually evolving as new materials, designs and configurations are tested. Based on various studies and evaluations of already completed cable-stayed bridges, engineers have learnt that torsional rigidity of a cell box girder that is closed boosts the structural response to wind loading at the time of construction and eradicates the requirement of attachments for temporary stabilizations. Reducing the spacing between stay cables can allow for easy dismantling, detensioning, and replacement of stay cables under reduced loads. Use of continuous strands cable-stayed system with wedge anchors at the deck level only, makes it easy for stays to be accessed inside the box girder superstructure for construction, maintenance and future inspections. Additionally, cable-stayed bridges are not only economical in the construction of spans of up to 1,500 feet and more, but, their configurations also offer elegance and beauty that considers communities’ interests in the creation of landmark bridges. Bibliography Dayaratnam, P., 2000. Cable Stayed, Supported And Suspension Bridges, Hyderguda, India: University Press. Fish, R., 2011. Stress Ribbon and Cable-supported Pedestrian Bridges. In J. Strasky, ed. The Institution of Civil Engineers Bridge Engineering. London: ICE Publishing, p. 227. J. H. G. Macdonald, P.A.I. & Fletcher, M.S., 2003. Vortex-induced vibrations of the Second Severn Crossing cable-stayed bridge: full-scale and wind tunnel measurements. In Institution of Civil Engineers Structures & Buildings. London: Oxford University Press, pp. 332–333. Morgenthal, G. & Yamasaki, Y., 2010. Behaviour of very long cable-stayed bridges during erection. In The Institution of Civil Engineers Bridge Engineering. London: ICE Publishing, pp. 213–224. Su, C., Chen, Zhaoshuan & Chen, Zhihui, 2011. Reliability of construction control of cable-stayed bridges. In The ICE - Bridge Engineering. London: ICE Publishing, pp. 15 – 22. Svensson, H., 2012. Cable-Stayed Bridges, London: John Wiley & Sons. Tang, M., 2000. Cable-Stayed Bridges. In W.-F. Chen & L. Duan, eds. Bridge Engineering Handbook. Boca Raton: CRC Press. W. Denney Pate, P.E. & W. Jay Rohleder, Jr., P.E., S.E., 2008. Evolution of Cable Stayed Bridge Technology payday loan storeonline pay day loanseasy payday loanspayday loans massachusettslow interest payday loans. Structure. Available at: http://www.structuremag.org/article.aspx?articleid=768. Y. Xi & Kuang, J.S., 2000. An energy approach for geometrically non-linear analysis of cable-stayed bridges. In The ICE - Structures and Buildings. London: ICE Publishing, pp. 227 – 237. Appendix 1.0: Figures Figure 1: The Idea of a simple cable-stayed bridge Figure 2: Inclined Stay Cable Figure 3: Initial cable press-stress calculation process Figure 4: Dynamic Response of a stay cable in a real cable-stayed bridge. Read More