Single Span Suspension Bridge Research Articles

A simplified analysis method for long-span suspension bridges within the deck overlay retrofitting process from asphalt to UHPC

The steel-ultrahigh performance concrete (UHPC) lightweight composite deck (LWCD) is increasingly adopted by in-service steel bridges to address the fatigue cracking issue for orthotropic steel decks (OSDs) and the premature damage issue for asphalt overlays. While for in-service long-span suspension bridges that need to be retrofitted by LWCDs, the response of the UHPC layer in casting is complex. Within the UHPC casting process, the moment of the stiffening girder changes continuously as the self-weight of the stiffening girder changes in casting, and the change of moment will produce strains in the UHPC portion set earlier; in other words, the UHPC portion cast latter will produce strains in the UHPC portion cast earlier. If the resultant tensile strains are too high, the UHPC layer may crack within the casting process, which should be avoided. In this paper, a simplified analysis method, based on the linearized deflection theory, was proposed to rapidly obtain the response of long-span suspension bridges in retrofitting without significantly compromising the accuracy of the analysis results. A new solving method based on exponential functions was proposed, which is simpler than the commonly used hyperbolic function-based method. The proposed method was implemented as computer codes in Matlab and verified through two examples: a single-span suspension bridge and a three-span suspension bridge. The simplified analysis method was used to perform a detailed analysis for the Yichang Yangtze River Expressway Bridge (YYREB), a 960-m-long single-span suspension bridge in China, for which the existing asphalt overlay was replaced by an LWCD in 2021. In the analysis, three cast sequences were considered for the UHPC layer, i.e., from end to end, from mid-span to ends, and from ends to mid-span. It is revealed that the mid span-to-ends cast sequence produces the minimum tensile strain in UHPC, so the cracking risk of UHPC could be well controlled by using this casting method. Thus, the mid span-to-ends cast sequence was adopted by the YYREB within the deck overlay retrofitting process from asphalt to UHPC.

Analytic Solution to Longitudinal Deformation of Suspension Bridges under Live Loads

Live load of moving vehicles has a very important effect on the fatigue life of suspension bridges, which causes not only vertical deformation but also longitudinal deformation. In this study, a general analytical formulation for analyzing the quasistatic longitudinal displacement of suspension bridges under vertical live loads is developed, and the underlying deformation mechanism is revealed. First, the analytical vertical and longitudinal deformation equations for the single main cable subjected to live loads are formulated considering the geometric nonlinearity. Then, the relation of longitudinal displacements between the stiffening girder and the main cable for a single-span suspension bridge is established through analyzing the geometric configuration of deformed deck-suspender segment and imposing the null longitudinal force condition. The relation is further modified to incorporate the effect of central buckles (CBs). Compared with the finite-element (FE) prediction, the proposed analytical solution is quite accurate for both concentrated and distributed loads. It is found that the coupling of vertical and longitudinal displacement of main cables and the longitudinal constraint between the cables and girder, are responsible for the longitudinal displacement of the girder. The effects of sag-to-span ratio, CB, and inclined suspenders are studied. The longitudinal displacement of the girder can be reduced by about 20% when the sag-to-span ratio is varied from 1/9 to 1/11, and the CB with proper stiffness is more effective in reducing the longitudinal displacements. The proposed formulation can be conveniently applied for parameter optimization in the preliminary design stage so as to avoid tedious repetitive FE analysis.

DESIGN OF THE DOBRA CHANTI SUSPENSION BRIDGE IN DISTRICT TEHRI GARHWAL, UTTARAKHAND, INDIA

Since the Tehri dam was constructed on the River Bhagirathi in 2006, considerable productive land areas, many villages, including old Tehri town in Tehri-Garhwal district has been submerged. It has also disconnected the travel and transportation routes along the east slopes of the reservoir, making the local residents lose access to the New Tehri town, which is equipped with resident-friendly facilities including health and education institutions and markets. Accordingly, the Uttarakhand Government has proposed to build the Dobra-Chanti H.M.V. Suspension Bridge to meet the local demand for an easy intra-regional accessibility, especially between the left and right sides of the River Bhagirathi. The project consists of a single-span suspension bridge, an approach bridge at each end of the suspension bridge, and slope protection work on each side. The suspension bridge has a 440m-long stiffening truss girder, 57m-tall steel towers, locked coil cable systems including suspenders, and anchor blocks. The approach bridges are reinforced concrete bridges with T-shaped beams. And river side slopes installed on both banks are protected and stabilized through CC blocks, shotcrete, and anchor bolts. All cek dimension has met the requirement

Inspection, testing, assessment and rehabilitation of Daly's (Shakey) Bridge, Cork city

This paper describes the rehabilitation of Daly's (Shakey) Bridge, an existing single-span suspension bridge crossing the northern channel of the River Lee in Cork city. The bridge was opened in 1927 to replace an earlier ferry crossing at the same location. Daly's Bridge is included on the Record of Protected Structures and the National Inventory of Architectural Heritage. It remains the only suspension bridge in Cork city and is the only surviving bridge of its kind in Ireland. It is a significant contributor to the architectural heritage of the city. This paper describes the special inspections and structural assessments, site investigations and material testing, detailed design of repair works and particular aspects of construction and monitoring. The bridge is a well-known local landmark and its colloquial name ‘Shakey Bridge’ derives from the lively movement of the deck under pedestrian loading. A key aspect of the project included modelling and measurement of the dynamic response of the structure prior to and following repair works to confirm that the signature shake was retained. The project also incorporated approach upgrades and ancillary works, including new approach parapets, the repair of existing cast-iron railings, lighting, landscaping, surfacing and invasive species removal.

Analytical Solution for Horizontal Tension of Main Cable in Erection of Stiffening Girder

The horizontal tension of main cable is a key parameter to guarantee the safety of tower, form gravity stiffness and keep main cable shape correct during erection of stiffening girders. Instead of complicated Finite Element Modeling and iterative algorithms, simply analytical solutions of horizontal tension of main cable were deduced for two classical erection methods of stiffening girder based on the mathematical analogue and work-energy principle. Numerical method was also adopted to verify the analytical solutions on analysis of a single span suspension bridge. The results from analytical solution are found to be in good agreement with the numerical results. The theoretical results show that the presented analytical solutions can be easily applied in the calculation of the horizontal tension of main cable in any erection stage.

Analysis of modern three-span suspension bridges with stiff in bending cables

Suspension bridges are one of the most effective bridge structures used for large spans to overlap. Recently, not only the single-span bridges but also multi-span suspension bridges have been used. The main issue of design and analysis shall consider the excessive deformability induced by the interaction of flexible and kinematic displacement. Stabilization of suspension bridges could be ensured by various means. The most effective and up-to-date measure applied to reduce displacements of suspension bridges is the application of the so-called “rigid” cables with appropriate bending stiffness instead of conventional flexible cables. These retaining elements demonstrate high corrosion stability; their cross-sections are designed using conventional structural steel sections, factory and fabricated connections are simple and firm. The main advanced feature of these cables is that these elements along with the suspended stiffening girder stabilize the initial shape of the bridge effectively. It shall be noted that analysis methods applied for these innovative three-span suspension bridges with “rigid” cables are still under development. There are only few individual publications describing the behaviour of a single-span suspension bridge. The article describes the modern suspension three-span bridge and provides analytic expressions of internal forces and displacements calculated considering the erection sequence.

Huangpu Pearl River Bridge, China

The Huangpu Pearl River Bridge is a key project on the second ring highway of Guangzhou, which is the largest bridge in southern China. The total length of the bridge is 7049 m, including the northern approach bridge, northern channel bridge, central approach bridge, southern channel bridge and the southern approach bridges.The main bridge of the northern channel is a single pylon cable-stayed bridge with a main span of 383 m and steel box girder, which was constructed by balanced cantilever method. The main bridge of southern channel is a single span suspension bridge with a main span of 1108 m and steel box girder. This paper presents the tender design, the final design, the construction of the southern channel main bridge and the northern channel bridge including the foundation, pylon, main girder, main cable, main saddle and splay saddle.

Study on Wind Resistance Strategy and Stability Calculation of a Single-Span Suspension Bridge

A main span of 500m of rock tunnel anchor steel truss single span suspension bridge, Structure of the tower across the bridge, cross a large, soft, weak damping characteristics, and the bridge site at the complex terrain, the actual wind field is more disordered, so be checking the stability of the structure of the wind. Wind stability checking showed that the torsional flutter and torsional flutter separated flow is less than the critical velocity self-excited vibration of the main beam test wind speed, wind does not meet safety requirements. Therefore, an additional level of rigidity with the wind the cable, set the cross-slope index, increased truss width, the main cable using a single triangle boom, the use of space for the main cable, etc. to increase the stability of the bridge on wind resistance. After considering the construction of economic and structural terms, the final choice of the main cable space, the top cable from 1m, the main tower for the A-type tower program. The study on the stability of the same type of calculation of the bridge with the reference wind.

Mechanics Characteristics Study for Cable-Stayed-Suspension Bridges

As a composite structure, the cable-stayed-suspension bridge is characterized by relatively new structure, great overall stiffness and long-span capacity, which has been proposed for the design of some extra long-span bridges. In order to research further into the mechanics characteristics of this type of structural system, the proposed preliminary design of a cable-stayed-suspension bridge with a main span of 1800m is analyzed by means of finite element simulation method. The advantages on overall stiffness in the cable-stayed-suspension bridge are summarized in comparison with the three-span suspension bridge and the single-span suspension bridge. Then, the reasons for the fatigue of the longest suspension cables in the cable-stayed-suspension bridge are also discussed in this paper.

Railroad crossing of Nevel’skogo Strait from the mainland to Sakhalin Island — alternate scheme with a dead-end dike and navigation canal

Historically, two alternate schemes of a crossing of Nevel’skogo Strait have been considered for the Selikhin – Nysh Railroad between the mainland and Sakhalin Island, which is now under design: tunnel and bridge. Considering the high seismicity of the construction site, and the large stratum of slightly cohesive soils, which resides in the bottom of the strait, the extremely severe climatic conditions (significant wind action, large temperature gradients, loads due to ice floes drifting against bridge supports, and icing-over of span structures), as well as high current velocities in the easily scoured channel, which result in its deformation, it can additionally be presumed that construction of the crossing and, in particular, its operation will be rather difficult and expensive. In 2001, the JSC MIGG in conjunction with a branch of the JSC TsNIIS — NITs “Mosty” developed a new scheme for a railroad crossing of the strait [1], which will more reliable in service and less capital-intensive to construction as compared with the alternatives. The essence of this scheme consists in the fact that the Nevel’skogo Strait is completely spanned by a dead-end dike, and water flows and shipping are passed through a navigation canal cut into the scour-resistant bedrock of the eastern extremity of Cape Nevel’skogo. The canal is crossed by single-span suspension bridge, the length of which in this case will not be measured in kilometers, as in a competitive scheme, but in hundreds of meters. As compared with the bridge scheme, the dead-end dike is safer with respect to ice loads, and less sensitive to seismic effects. The supports of the suspension bridge areto be placed on a durable rock bed, will not come in contact with the water, and will not be subjected to either channel deformations, or ice effects. In contrast to the alternatives, this crossing scheme is characterized by maximum utilization of local construction materials and a minimum demand for imported materials (metal, cement, timber, etc.); this will satisfy in the best way possible the construction and economic conditions of the region, which is remote from industrially developed areas. Drilling-blasting, loading-transporting, and bottom-deepening operations, which have been rigorously mastered in domestic practice, will prevail in its construction. They can be rapidly deployed, and do not require the purchase of expensive foreign equipment, and also the importation of foreign specialists. The bridge, the cost of which will be approximately 20% of the total expenditures, and for the case in question, will not situated on a critical route, can be completely assembled even before the earth-and-rock work is completed. The rock sheared from the shaped depression of the canal will be placed in the dike, and the closeness of the waterway to Cape Nevel’skogo dictates a minimum of deepening work (in the sandy channel) involving its connection with the canal. This, of course, is also explained by the economy of the proposed scheme for a railroad crossing, which will require lower capital expenditures than the competitive schemes. As for the ecological aspects of the plan, the emotionally proposed alternate scheme for the crossing may be perceived as extremely radical. The hydraulic analyses and mathematical modeling that have been performed, however, have indicated that in terms of the degree of influence exerted on the environment and hydrological conditions of the strait, it does not differ appreciably from the bridge scheme, and is feasible for implementation from the standpoint of nature management. An expert council functioning on behalf of the Government of the Russian Federation considered all three schemes for a railroad crossing of the Nevel’skogo Strait (conclusion No. 4 from 10 February 2002), acknowledged them to be technically feasible, concurred with the fact that the cost of the crossing scheme with a dead-end dike and navigation canal may be lower as compared with the other schemes, and proposed to finalize the “Provisions for Investment” with Power Technology and Engineering Vol. 42, No. 3, 2008

Breaking the Mold: The Kentucky River High Bridge

This article describes the history of the Kentucky River High Bridge, the first modern cantilever bridge in the U.S. The bridge was chartered in the early 1850s and was originally designed by John A. Roebling as a single-span suspension bridge. The project, however, quickly mounted in costs and, because of a bankruptcy of the supporting railroad company, Roebling was left without funding. It was only after the Civil War during the Reconstruction period that the project finally received funding as a way to initiate more trade routes between the Southern and Northern states. Completed in 1877, the cantilever bridge was designed by Charles Shaler Smith, featuring a three-span continuous truss. The bridge serviced railway traffic until 1911 when it was replaced by a new bridge that could sustain heavier loads.

STOCHASTIC NON-LINEAR VIBRATIONS OF HIGHWAY SUSPENSION BRIDGE UNDER INERTIAL SPRUNG MOVING LOAD

The problem of vertical non-linear vibrations of a single-span suspension bridge due to a random stream of moving vehicles is considered. The inertia forces of car bodies and vehicle suspensions are taken into account because each vehicle is idealized by a set of viscoelastic oscillators. Vehicle arrivals at the bridge as well as the vehicle types and the masses of the truckloads are assumed to be random variables. The bridge model is defined as flat and geometrically non-linear. The numerical simulation method is developed to determine expected values and standard deviations of the bridge response. Solutions for the bridge deflections, the tension of cables and bending moments at the girder are presented and compared with results which have been calculated in simplified cases when a train of concentrated forces moving in the dynamic or static conditions idealizes vehicular traffic loads.

Vibration of Suspension Bridges under Moving Loads

The problem relates to the transient vibration of a single-span suspension bridge which is traversed by a constant force moving with constant velocity or a pulsating force moving with constant velocity. Damping is zero and there is no mass associated with the moving forces. Equations of motion are derived and solved. Solutions are obtained for the deflections and stresses of the truss and for the increase in horizontal component of cable tension. The theory is based on the deflection theory equations of suspension bridges. It is linearized by assuming that the increase in cable tension due to live load is small compared to the dead load cable tension. A numerical example illustrates the theory. The results of the example show large magnifications of stress (on the order of 2.70) when the moving pulsating force is driven at the frequency of the first symmetric mode. Also, in general, there is no appreciable dynamic effect associated with moving constant forces on long-span bridges. The dynamic effect of moving constant forces, however, becomes more pronounced on short-span bridges having a low frequency associated with the first asymmetric mode.