Department of Civil Engineering and Architecture

Transcription

1 Department of Civil Engineering and Architecture LONG-SPAN RAILWAY BRIDGE DESIGN: EVALUATION OF ALTERNATIVE STRUCTURAL FORMS, A CASE-STUDY OF A 70 M SINGLE-SPAN DOUBLE-TRACK BRIDGE PIKASILDELISTE RAUDTEESILDADE PROJEKTEERIMINE: ALTERNATIIVSETE KONSTRUKTSIOONILAHENDUSTE TEHNILINE ANALÜÜS 70 M SILDEAVA KORRAL MASTER S THESIS Student Student code Supervisor Kees Vanamölder 44394EATM Professor Juhan Idnurm Tallinn 207

2 AUTHOR S DECLARATION Hereby I declare that I have written this thesis independently. No academic degree has earlier been applied for based on this material. All works, major viewpoints and data of the other authors used in this thesis have been referenced Author:... /signature / Thesis is in accordance with terms and requirements Supervisor:... /signature/ Accepted for defence Chairman of theses defence commission:... /name and signature/

3 Preface Current MSc thesis has been carried out in cooperation with Republic of Estonia Technical Regulatory Authority and Ministry of Economic Affairs and Communications in order to analyse possible structural solutions for railway bridge of Rail Baltic over Pärnu river. I would like to express high gratitude to my supervisor professor Juhan Idnurm for supporting, consulting and advising me during thesis writing. I want to thank professor emeritus Siim Idnurm for teaching and introducing me to the exciting world of bridge and structural engineering. I appreciate highly my mentor and a great friend Vladimir Keiv for motivating me to study bridge engineering. Finally, I would like to thank everyone who have contributed to my pleasant time at Tallinn University of Technology during my master studies , including my fellowstudents from the university and colleagues from Sweco. 2

4 Table of contents Preface...2 Table of contents...3 Introduction Literature survey and current practice in design of long-span railway bridges Classic arch bridges Network arch bridges Cable-stayed bridges Suspension bridges Truss bridges Beam and cantilever bridges Case-study: technical characteristics and ground information Location of designed railway bridge Railway track geometry on the bridge Technical constraints for design and requirements of Rail Baltic Structural design of solutions for case-study railway bridge Structural materials Basics of structural design Loads Ultimate limit state Service limit state Structural dynamics Structural design and FEM analysis Basics of girder modelling Basics of arch modelling Basics of cables modelling Basics of truss modelling Supports and bridges layout Structural evaluation and description of bridge alternatives Deflections and displacements of structural elements Internal forces of structures

5 5.3 Conclusions of structural analysis Quantities of structural materials Life cycle cost evaluation Methodology and base-prices Conclusions and LCC comparison Aesthetics evaluation Methodology Conclusions Conclusions and further research Conclusions Main contributions Further research Summary Kokkuvõte Bibliography

6 Introduction Due to constant development and upgrading of railway infrastructure around the world, structural solutions for long-span railway bridges need to be applied around the world. Being a technically advanced solution and requiring high investments, decision-making about costeffective and rational structural form is important. Many long-span railway bridges were built during 9th or 20th century around the world. Despite long history, bridge engineering is in constant development by new construction materials, increased application of high strength concrete and steel and new developments for innovative structural solutions. For example, network arch bridge that is among the structures analysed in current study, was developed during the second half of 20th century but found wider use in last 20 years [Varennes 20]. Truss bridges have been widely used during 9th and 20th century, nowadays optimized structural forms have been developed. The aim of current study was to analyse and compare different structural forms for 70 m single-span railway bridge, taking into account modern structural solutions and materials available. For comparing the structural forms, following evaluation criterions have been defined: - Cost-effectiveness: life-cycle cost and construction price; - Aesthetics: architectural value of structural form of bridge. For estimation of described criterions, conceptual design, including structural analysis and optimization was carried out on 5 different structural forms for case-study bridge. 5

7 2 Literature survey and current practice in design of long-span railway bridges In current chapter, literature survey was carried out to determine common design and construction practices of railway bridges similar to 70 m span that is being analysed in current study. Bridges with double-track railway superstructure spanning up to 70 m are considered as exceptional solutions and should not be considered as economically reasonable solution in case possibility for intermediate supports exist. According to investigations conducted at Delft University of Technology, long-span solutions for double-track railway bridges solved with arch or cable-stayed structure showed to be in average times more expensive than typical continuous beam or truss bridge with intermediate supports. [TU Delft: ESDEP course] Optimal and possible span length for different bridge structure types can be observed from Figure 2.. These values are based on mechanical characteristics of existing building materials, excluding any possible new materials that could probably be available in the future. [Melaragno 2009] Suspension bridge Cable stay bridge Concrete/steel arch bridge Steel truss bridge Concrete/steel beam bridge Span lenght [m] Figure 2.. Optimal and possible range of span for different bridge structure types 6

8 As showed in Figure 2.2, all above described bridge types can be found amongst variety of road bridges in Sweden (Trafikverket) [Safi 202]. Suspension bridge Cable stay bridge Arch bridge Beam/truss bridge Number of bridges in analysed segment [pcs] Figure 2.2. Structural forms of road bridges in use in Sweden with span range m 2. Classic arch bridges Arch is a typical structure of bridge for spans between m. Philosophy of arch bridge lies in exertion of vertical loads into compression forces in the arch cross-section and transmitting them to ground support to be balanced by horizontal and vertical reaction component. Since for curved beams forming the arch, longitudinal forces are usually more economical to resist compared to bending, arch type structure, in case if optimally designed, can be more economical for long spans, compared to simple beam bridges. For abutments of arch bridge, solid ground conditions are required since both vertical and horizontal forces from the arch are transmitted to the ground by abutments. [Melaragno 998] 7

9 Arch bridges for long spans can be divided into two main categories based on configuration of hinges presented in Figure 2.3. Figure 2.3. Arch types divided according to number of hinges [Sundquist 2007] For zero-hinge arches, foundation needs to absorb both the horizontal force and clamping moment, therefore remarkably good ground conditions are required, preferably rock or other material with internal friction. Zero-hinge arches provide the most material-economical solution for arch. In case of poor ground conditions, two-hinge arch should be introduced. In Figure 2.4, different bridge deck configurations are presented. Bridge types 4) and 5) use deck plate as both tie and stiffening beam, as for bridge types ) and 2) expansion joint have been introduced to accommodate railway connection in the middle of the bridge. This solution can be called bow-string arch and can be used for two-hinge arch in order to reduce horizontal reaction forces on abutments. 8

10 Figure ] Different solutions of bridge deck configuration for arch bridges [Sundquist Span-to-rise ratio L/f is normally provided between 5 and 7 in order to introduce economically reasonable solution. [Sundquist 2007] Figure 2.5. Stäketbron in Sweden. Concrete arch bridge on Mälarbanan (Stockholm- Västerås railway). Span lenght 30 m. Opened for traffic in 200. Picture of author 9

11 Figure 2.6. Typical process for construction of concrete arch bridge with no intermediate supports. Arch is constructed step-by-step with supporting of pieces with cables, supported on vertical columns and anchored to soil [Осипов, Храпов, Бобриков 988] For conventional arch bridge both reinforced concrete and steel are considered as suitable options for arch material. Reinforced concrete, according to world practice, can be more suitable option when majority of internal forces are formed by bending moments. In case of longitudinal tension is considered as the dominating type of internal forces, steel arch would be more suitable. [Осипов, Храпов, Бобриков 988] In case of arch is installed on top of bridge deck, vertical hangers conventionally can be manufactured from steel since they work for longitudinal tension. 2.2 Network arch bridges Network arch is defined as a tied-arch bridge with inclined hangers that cross each other at least twice. The hangers always work under tension and chords for both tension and 0

12 bending. Arch is usually manufactured from steel. Lower bridge deck is typically a concrete slab. Example of network arch bridge is presented in Figure 2.7. [Varennes 20] Figure 2.7. Typical network arch bridge [Varennes 20] Figure 2. Network arch road bridge at Rannu-Jõesuu, Estonia. Span lenght 90 m, opened in Photo: AS Merko Ehitus. Network arch hangers can be wires or rods and they have strength for longitudinal tension, they are not meant for resisting bending moments. Hangers are typically tied to each other in order to prevent them from bumping into each other. Network arch bridge is considered to be structural form where components are loaded with more longitudinal tension and less bending moment compared to tied arch bridge. This

13 effect is especially remarkable in case if bridge is only partially loaded and not being under constant divided load for all length. This phenomena was characterised by calculations of Per Tveit in 980, presented in Figure 2.9. [Tveit 204] Figure 2.9. Influence lines for bending moments in the lower chords [Tveit 204] Hangers of network arch should be configured as shown in Figure 2.0. Angles α between arch axis and hangers should be equal. Figure 2.0. Geometry of fastening for hangers and arch [Brunn, Schanack 2003] 2

14 Figure 2.. Fehrmansundbrücke, Germany. Steel network arch bridge on railway line Lübeck-Puttgarden, longest span 248 m. On bridge deck single-track railway and + road is accommodated. Bridge was constructed Photo: Mario Schürholz In order to simplify constructability, arch structure for network arch bridge has typically circular shape. It could be manufactured from I-beams (shorter spans) or box steel beams (longer spans). Network arch as a first alternative can be constructed on site by erecting the arch and fastening the hangers with each other and finally constructing the lower bridge deck. Since network arch is considered to be light structure, compared to other bridge types, constructing it nearby and then lifting it on site with floating cranes (Brandanger bridge, Norway) or by sliding the bridge to right place. Mentioned alternative is illustrated in Figure 2.2. [Tveit 204] 3

15 Figure 2.2. Possible construction technology proposed by Per Tveit for Straubing bridge (span lenght 52 m), Germany, constructed in 98 [Tveit 204] 2.3 Cable-stayed bridges Cable-stayed bridge consist of vertical or longitudinally tilted pylons and cables that connect pylons to the bridge deck. Typically cable-stayed bridge consists of one medium span and two spans on sides that in most cases are approximately two times shorter than medium span. Beams that support the bridge deck can be trusses, plate-girders or box-girders. Cable-stayed 4

16 bridges are common solutions for covering long spans, also for railway bridges. Typical configurations of a cable-stayed bridges are presented in Figure 2.3. [Осипов, Храпов, Бобриков 988] Figure 2.3. Main structural types of cable-stayed bridges. Type ) harp configuration, type 2) fan configuration and type 3) asymmetrical system. For type 4) pylon has been tilted in longitudinal direction in order to equalize cable forces [Sundquist 2009, Idnurm 206] 5

17 Figure 2.4. Cable-stayed bridge over Po river, Milan-Bologna high-speed railway in Italy. Main span length is 92 m, the bridge was opened in Picture: Mario Petrangeli & Associati Cables are typically formed of steel ropes fixed with internal plastic cover. Several different configurations exist for configuration of cable and pylon supports. Main configurations are presented in Figure 2.4. [Idnurm 206] 6

18 Figure 2.5. Typical construction procedure of a cable-stayed bridge [Sundquist 2009] 7

19 Figure 2.6. Main configurations of cable fastenings and pylon supports for cable-stayed bridge. For a) and b) cables are fastened to bridge deck and are therefore supported for both sides. For c) cables are anchored to ground, pylon can be lighter in that case. For d) pylons are stiffly fastened with deck plate. For railway bridges typically solution a) or b) is applied [Idnurm 206] 2.4 Suspension bridges A suspension bridge is a type of bridge in which the deck (the load-bearing portion) is hung below suspension cables on vertical suspenders. Main load-bearing components are main cable, vertical hangers, pylons and bridge deck that also works as stiffening girder (See Figure 2.7). 8

20 Suspension bridges can be classified by number of spans, continuity of stiffening girders, types of suspenders and types of cable anchorage. Stiffening girders can be classified into two-hinge or continuous types. In order to provide equalised distribution of internal forces, for railway (or combined road-railway bridges) typically continual girder is preferred. [Kivi 2009]. Examples of suspension bridge classification can be found from Figures 2.8 and 2.9. Figure 2.7. Main components of suspension bridges and typical cable ground anchorage [Harazaki, Suzuki, Okukawa 2000] 9

21 (a) (b) Figure 2. Suspension bridge with continuous (a) and two-hinge (b) stiffening girders (a) (b) Figure 2.9. Suspension bridge with cable anchorage to stiffening girder with side-spans (a) and to externally anchored main cables (b) without side-spans. Typically suspension bridges are designed with one span in the middle and two side-spans with length 0.5 times the length of middle span. In case if the need for side-spans does not exist, suspension bridge can be designed also with single middle-span with main cables anchored to ground (Figure 2.8b). [Gimsing, Georgakis 202] Typically suspension bridges are in use in world practice for long-span solutions (300 m or more) with road or combined road-railway bridges. Longest spans of suspension bridges cover up to 2000 m in length. 20

22 World s practice lacks of good examples about railway dedicated suspension bridges. World s first railway suspension bridge was opened in 855 at Niagara Falls between USA and Canada (Figure 2.20). Good examples exist for very long-span road and railway combined bridges, bridges with span more than,0 km have been built (Figure 2.2). Figure Suspension bridge for single-track railway, opened in 855 with middle span length 25 m. The suspension bridge was replaced with arch bridge during 890s due to increased traffic loads. 2

23 Figure 2.2. Tsing Ma bridge in Hong Kong, carrying 6 lanes of road traffic and 2 railway tracks with middle span 377 m [Wikipedia] Typical erection technology for suspension bridge involves firstly launching main cables and fastening deck plate and hangers piece-by-piece to main cables and can be observed from Figure [Harazaki, Suzuki, Okukawa 2000] Figure Typical construction technology of a suspension bridge 22

24 2.5 Truss bridges Truss is a load-bearing element of a structure that is formed of elements that bear only longitudinal tension and compression, not bending moment, and are connected to each other with pinned joints. Truss was introduced to wider use for railway bridges during 9 th century. Main types of truss configuration can be found from Figure Figure Main truss types in use for bridges [Kulicki 2000] In world practice truss has appeared as reasonable structural type for covering spans between 25 and 300 m. Examples of truss bridges can be found from Figures 2.24, 2.25 and

25 Figure Steel truss single-track railway bridge in Estonia over Narva river with span 50 m that was opened for traffic in 947. Truss can be considered as double-intersection Warren type Figure Ekensbergsbron in Stockholm city, light rail Warren truss bridge over conventional railway with span 70 m that was manufactured during 20 [promostal.pl] 24

26 Figure Stockley bridge in London is a Warren truss railway bridge constructed in 204 [crossrail.co.uk] Warren truss has occurred as the most popular option for railway bridges during 980s and 990s due to high structural performance and aesthetics. Typically truss bridges are constructed similarly compared to network arch or tied arch bridges, i. e manufactured on ground and then lifted to place. [Kulicki 2000] 2.6 Beam and cantilever bridges Beam and slab bridges are not frequently used for covering long spans because usually high beam is needed for that case and that increases significantly structural height of a bridge. Span-to-structural depth ratio is usually considered to be about /20 in case of concrete bridges, so for example bridge with 70 m span would require at least 8,5 m height of beam and slab. [Melaragno 998] Therefore simple beam or continous beam bridges are not further analysed in current study. For beam cross-section, T-beams, box-girders or steel-concrete composite bridges can be used. Two mainly preferred girder systems for long-span bridges can be followed in Figure

27 Figure Possible cross-sections for long-span single-track railway beam or cantilever bridge box girder (left) and steel-concrete composite bridge (right) [Sundquist 2009] For long-span bridges, balanced cantilever bridges can be used that are common in world practice with span range m. Bridge piles support rigidly cantilevers that are usually formed of symmetrical beams, balancing vertical loads both sides of supports. Beams are connected to each other in the middle of a span with vertically stiff bearing in order to equalize internal forces of structure. [Sundquist 2009] Typical cantilever bridge layout can be seen in Figure 2.2 Figure 2.2 Typical cantilever bridge [Sundquist 2009] 26

28 Figure 2.29 Voroshilov cantilever road bridge, Russia. Longest span 60 m. Photo: Rostov-on-Don city municipality Typical construction method for cantilever bridge construction is presented in Figures 2.29 and Bridge is being constructed step-by-step by lifting segments into place. Figure Construction of Krasnopresnensk cantilever bridge from precast concrete elementsthat are lifted into place with a crane, Russia. Span 30 m [Осипов, Храпов, Бобриков 988] 27

29 Figure 2.3. Construction of cantilever road bridge at Ihaste, Estonia. Cast-in-situ technology is applied with movable form step-by-step. Photo: Estonian society of concrete engineering In order to compensate bending moment that is exerted to cantilevers in middle span, typical cantilever bridge should have in addition to middle span, side spans with length about 0,5 middle span. Structure of cantilever bridge is being designed with an assumption that selfweight of side span bridge deck and possible traffic load on side span compensates bending moments exerted to structure in middle span. Therefore bridge supports are not designed to resist great bending moments and properly designed side spans are required. In case if side spans were to be eliminated and supports to be designed to resist bending moments the described technical solution of a bridge would appear to become an integral beam bridge instead of cantilever bridge. Integral beam bridges have not shown to be technically optimal solution for span as long as 70 m. [Sundquist 2009] As the case-study railway bridge of current thesis does not require side spans and providing side spans would result with unreasonably long and probably economically not optimal solution, cantilever bridge is not further analysed in this study. 28

30 For case-study railway bridge, cantilever bridge requires to be analysed in further investigations in case of placement of supports into the river becomes possible or side spans appear to be necessary due to additional roads etc. 29

31 3 Case-study: technical characteristics and ground information In order to evaluate possible structural solutions for bridges in practical case, case-study was performed on the basis of designed Rail Baltic bridge over Pärnu river. Rail Baltic is designed as new railway line between Tallinn and Poland that would connect Baltic states with European railway network with 435 mm track gauge. Rail Baltic is double-track electrified railway line for mixed traffic with design speed of 240 km/h and with overall length around 700 km. In Estonia overall length of railway route is around 20 km and railway alignment follows Tallinn (Muuga/Ülemiste), Rapla, Pärnu and Ikla. Preliminary design of Rail Baltic will be finished during Detailed design will be carried out starting from 20 Construction works scheduled to begin in 209 and by 2026 new railway will be opened for traffic. For ground information of current study, Rail Baltic preliminary design was presented to author by agencies representing Estonian government in Rail Baltic project and consulting company 2 performing preliminary design. 3. Location of designed railway bridge According to approved railway alignment in preliminary design, Rail Baltic intersects Pärnu river, with a width of 50 m, inside Pärnu city. Due to environmental reasons locating bridge supports into the river is restricted, therefore bridge spanning around 70 m needs to be applied. Future Rail Baltic bridge is located 20 m East from existing railway and road bridge over Pärnu river. Location of bridge can be seen in Figures 3., 3.2, 3.3 and Appendix. Republic of Estonia Ministry of Economic Affairs and Communications; Republic of Estonia Technical Regulatory Authority. 2 Reaalprojekt OÜ 30

32 Figure 3.. location is highlighted. Route of Rail Baltic inside Pärnu city. With red circle case-study bridge Figure 3.2. Proposed location of case-study bridge, view from North-East side. Future Rail Baltic bridge will be located next to existing railway and road bridge. 3

33 Figure 3.3. Proposed location of case-study bridge, view from South-East side. 3.2 Railway track geometry on the bridge On the proposed bridge a double-track railway is located with a straight track section and a constant gradient 5. Following clearances have been taken into account for bridge design: - Vertical clearance above road at least 5,3 m; - Vertical river clearance 7,3 m or more. As a part of Pärnu station, railway track crossovers need to be placed on the bridge. That requires good accessibility and possibility for turnout installation to be taken into account in bridge design. Since, according to current design, turnouts are partly located on deformation joints that cannot be relocated on the future bridge, solution for turnouts on the bridge will probably need to be redesigned. Due to railway horizontal curve near Pärnu station, design speed of railway on the Pärnu river bridge is restricted to 20 km/h. 32

34 3.3 Technical constraints for design and requirements of Rail Baltic Near Pärnu river, two road bridges need to be located at: - Km+m that is solved with a slab frame bridge in current study, span length 8,0 m; - Km+m that during current study is solved with a two-span (20+24 m) continuous beam. Due to design restriction of one middle-span and two relatively short side spans, structural forms that require side-spans with at least 0,5 times the length of middle-span (cantilever bridge, typical solution of suspension or cable-stayed bridge) cannot be used or needs to be modified to meet the requirement of having only one span. Due to clearances, main load bearing structure cannot be accommodated under a bridge and therefore arch, truss etc need to be located above the bridge deck. For Rail Baltic, railway structural clearance GC is in use together with distance between parallel railway tracks 4,2 m that can be followed in Figure 3.4. [EVS-EN :203+A:207] 33

35 Figure 3.4. Typical cross-section of Rail Baltic structural clearance (GC 34

36 4 Structural design of solutions for case-study railway bridge In order to provide alternative bridge solutions on sufficient level that allows to compare them by multi-criteria analysis and to perform technical assessment, solutions were designed on a level of preliminary bridge design. Designed structures can be followed from appendixes 2, 3, 4, 5 and 6. Structural analysis were carried out using FEM (Finite element method) numerical analysis with software Bentley STAAD.Pro. Structure elements were dimensioned on the basis of ultimate limit state (ULS) and service limit state (SLS). Bridge structure optimisation and structural analysis were parts of overall technical evaluation that allowed to make conclusions about different technical characteristics of investigated bridge solutions. 4. Structural materials For structural analysis and technical evaluation, main structural materials were used that form the basis of structures load bearing capacity. List of structural materials and their properties is presented in Table

37 Type of material Steel S355 Reinforced concrete C35/45 Modul of elasticity E [MPa] 20*0³ 33,5 Poisson s ratio υ 0,3 0,2 Shear modulus G [MPa] 8*0³ 9,28*0³ Density ρ [kg/m³] Yield stress f.y [MPa] 335 Tensile strength f.u [MPa] 490 Compression strength f.ck [MPa] 35 Table 4.. List of structural materials properties used in current study [Rohusaar et al 204, Otsmaa 204] Reinforced concrete was modelled with FEM as monolitic material with modul of elasticity 60 MPa for longitudinal tension. Reinforcement rate was not considered during current study since it needs to be determined during following phases of design. 4.2 Basics of structural design 4.2. Loads Load models that were used as basis of structural design, are defined in standard EVS-EN 99-2/NA: Main load models for railway traffic on bridges are as follows: - Vertical traffic loads LM7, SW/0 and SW/2, presented in figures 4. and 4.2; - Centrifugal force, applied in case railway track on a bridge is located on a horizontal curve; - Traction and braking force; - Derailment forces. For vertical load definition, load models LM7 and SW/2 have been applied: 3 EVS-EN 99-2/NA:2007. Actions on structures. Part 2: Traffic loads on bridges. Estonian National Annex 36

38 Figure 4.. EN 99-2] Load model LM7 for static influence of conventional railway traffic [EVS- Figure 4.2. Application scheme of load model SW/0 for static influence of conventional railway traffic to continuous beam structure and SW/2 for influence of heavy railway traffic [EVS-EN 99-2] Load model qvk [kn/m] a [m] c [m] SW/0 SW/ ,0 25,0 5,3 7,0 Table 4.2. Normative load values of SW/0 and SW/2 models According to information that was available during this investigation for Rail Baltic, heavy railway traffic load model SW/2 needs to be taken into account for dimensioning of structures. SW/0 load model is not taken into consideration during current study since continous beams are not in use for designed structures, it is expected that SW/2 is source of higher loads that are governing compared to SW/0. Vertical load models need to be multiplied with coefficient of dynamics Φ3 [EVS-EN 99-2/NA:2007] as following: = 2,6 0,2 + 0,73 has been considered as double distance between lateral beams, that according to designed structures is 5 m. Therefore =,32 for all structures. 37

39 Braking and traction forces acting on a bridge deck can be estimated according to following rules: - Traction force: Qlak= 33 [kn/m] La,b [m] 000 [kn] for LM7, SW/0 and SW/2; - Braking force: Qlbk=20 [knm] La,b [m] 6000 [kn] for LM7 and SW/0 or Qlbk=35 [kn/m] La,b [m] for SW/2. In order to evaluate the effect of different load models through bending moment formation in the structure, a simple exercise has been carried out to compare load model effect on simple beam bridge with 70 m long span. As seen from Figure 4.3, in general cases LM7 could be a source of highest bending moment in structure. 0 x-coordinate of span [m] Bending moment [knm] LM7 SW/2 SW/2 SW/0 Figure 4.3. Calculated bending moments for 70 m single-span beam bridge. Different structure types, such as suspension, cable-stayed or arch bridge could be more sensitive to concentrated loads from load models SW/0 and SW/2. Also differences occur depending on load exertion position on bridge deck for example suspension bridges in general could be more sensitive to concentrated loads on one side of the span than loads exerted at mid-point of span. 38

40 Selfweight of designed structures are considered with their respective densities (see Table 4.) Ultimate limit state Ultimate limit state (ULS) is defined as a loading state where structure is working at its limit of load bearing capacity. Exceeding ULS would result in a collapse of the structure. Load factors can be found from EVS-EN 990:2002/A:2006. Generally for railway bridge design dead load factor =,35 and live load factor =,45. Therefore for ULS following equations apply for total load calculations: = + stands for dead load according to standard load models. stands for live load according to standard load models. For calculation of ULS, all normative load cases were analysed in combination with dead load in order to analyse structural stress and define necessary dimensions of structural elements. For material strength check in ULS, permissable stress in material can be calculated as following: For concrete compression: = For steel: = According to EVS-EN 993-2:2006 =,5 and =,5. Structures in current study have been dimensioned for ULS according to Eurocodes. Variety of checks have been carried out to provide necessary structure load bearing capacity. For example steel structures for bending and shear stresses, steel beams for buckling and 39

41 stability, reinforced concrete deformation, stresses, crack opening, reinforcement tension etc. For global design of compressed and/or bent steel structures classification of cross-sections has been taken into use for determining safe limits for minimum flange and wall width. According to Figure 4.4, steel elements have been dimensioned for class cross-sections [EVS-EN 993-2:2006/AC:2009]. Figure 4.4. Drawings for determining element width t and size c and factor α for crosssection classification [EVS-EN 993-2:2006/AC:2009]. Cross-sections for class need to be determined according to following equation [EVS-EN 993-2:2006/AC:2009]: In case if > 0,5, In case if 0,5, 40

42 = 235 Where yield strenght of steel For estimating stresses in elements that are simultaneously suffering bending moment and longitudinal tension, following equation was used for determining stresses [EVS-EN 993-2:2006/AC:2009]:, +,,, +3 Where, stress of longitudinal tension, stress of lateral tension shear stress Service limit state Service limit state (SLS) involves several requirements that need to be followed in order to provide acceptable working situation for the structure. In case if SLS is not followed, structure strength is not necessarily yet endangered, but structure working state is no longer providing visual aesthetics or reasonable maintenance, also structure reliability could be in danger. Service limit state is stated in Eurocode EVS-EN 990:2002/A:2006 and main requirements are following: - Vertical accelerations of bridge deck must be limited in order to maintain contact between rail and rolling stock wheel. For ballasted railway track acceleration is limited to 3,5 m/s² and for slab track 5,0 m/s². - Twist of bridge deck is limited in order to avoid risk of rolling stock derailment. For railway tracks with design speed 20 km/h or less bridge deck is allowed to be twisted up to,5. 4

43 - Deflection of every specific bridge span is limited in order to provide general stiffness of structure and to ensure required minimum vertical radius for passenger comfort. Required L/δ (span/deflection) ratios can be observed from Figure 4.4. L/δ ratio overall must not exceed 600. That results in maximum 283 mm deflection of bridge deck at any point for 70 m span. - Horizontal displacement of bridge deck upper level at span end is limited in order to provide sufficient working conditions for deformation joints. - Bridge deck horizontal rotation around its bearing at span edge is limited in order to maintain required level of railway track geometry. - Lateral deflection of bridge deck is limited in order to avoid additional forces in rail fastenings and rail longitudinal tension. Figure 4.4. Minimum span/deflection values stated in Eurocode for bridge with 3 or more spans. For single-span bridge L/δ should be multiplied with 0,7. [EVS-EN 990:2002/A:2006] During FEM simulation of current study, bridge deck deformations are observed and further discussed in chapter 5. It is assumed that bridge deck deflections only need to be calculated with traffic loads since deformations from selfweight are compensated during construction process and deflection of a bridge suffering only selfweight and no traffic loads is zero. 42

44 4.2.4 Structural dynamics According to Eurocodes [EVS-EN 99:2004+NA:2007] requirements whether a static only or also a dynamic analysis is needed, are presented on Figure 4.5. Figure :2004+NA:2007] Flow chart for determining whether a dynamic analysis is needed [EVS-EN 43

45 Where [Hz] actions [Hz] V maximum line speed at site [km/h]; L span length [m]; n0 first natural bending frequency of the bridge loaded by permanent actions nt first natural torsional frequency of the bridge loaded by permanent v maximum nominal speed [m/s] According to Eurocodes, dynamic analysis is not needed for case-study railway bridge. Therefore dynamic analysis are not included in this study and the results are valid only for bridges that do not require dynamic analysis. 4.3 Structural design and FEM analysis In order to analyse structural differences of bridges for load bearing capacity and to determine dimensions of structural elements, structural analysis with FEM software Bentley STAAD.Pro was carried out during this study. Bridge structures were analysed with traffic loads and self-weight according to EVS-EN 99-2/NA:2007. Ultimate limit state (ULS) was evaluated according to EVS-EN 990:2002/A:2006 and EVS-EN 993-2:2006 and therefore bridge structures were dimensioned with sufficient load bearing capacity. As a result of the study, major requirements that define structure dimensions for ULS and has the most effect on overall design of the bridge from ULS point of view are stresses in bridge elements (arch, pylons, cables and deck plate) due to tension, compression and bending. Service limit state (SLS) was determined according to requirements in EVS-EN 990:2002/A:2006, therefore bridges were dimensioned according to different requirements stated for SLS. As a result of the study, major requirement that defines structure dimensions for SLS and has the most effect on overall design of the bridge from SLS point of view is vertical deflection of bridge deck. Other requirements such as twisting of bridge deck or horizontal deflection of elements can easily be avoided with increase of dimensions and moment of 44

46 inertia for single specific element. Therefore these requirements have no effect on general structure of the bridge Basics of girder modelling Designed bridge deck is typically a box girder of reinforced concrete, carrying two tracks of ballasted or ballastless railway. Deck width has been selected according to required structural clearances of railway and fixed distance between track centrelines. Typical crosssection is presented in Figure 4.6. Figure 4.6. Typical bridge deck for designed alternatives. Girder has been modelled in STAAD.Pro as 4 parallel longitudinal beams consisting of following: - Two edge beams, forming edge of deckplate and fastening of cables and hangers; - Two main beams, forming together box gross-section, including walls, upper and lower flanges. For load distribution between girders, lateral beams were designed, typically with 0 m step between longitudinal girders. Typical girder modelled in STAAD.Pro is presented in Figure

47 Figure 4.7. Analysed deck plate in STAAD.Pro. Longitudinal girders are displayed red, lateral beams are painted blue and edge beams green. Deck plate was analysed as a beam element, working for bending, tension and compression Basics of arch modelling For arch bridge, reinforced concrete arch was taken into use and modelled in STAAD.Pro as beam element, working for bending, tension and compression. Box beams were used as arch with cross-section 2.0*2.5 m. Arch was formed from different straight beams that were connected to each other at hanger position. For network arch bridge, steel box beam is used as arch with dimensions 0.75*.0 m. Crosssections of steel and reinforced concrete arch are shown in Figure 4. 46

48 Figure 4. study Cross-sections of reinforced concrete (left) and steel arch analysed in current Basics of cables modelling Cables and hangers of all bridge types were modelled from steel with a condition that they can only bear longitudinal tension, not to resist bending moment or compression (truss element). Therefore realistic working conditions were possible to simulate Basics of truss modelling Truss was modelled similar to cables and hangers, they were programmed to bear only longitudinal forces: tension and compression. Box steel beams were used as members for truss bridge with selected cross-section 0.7*0.7 m for main horizontal rod and 0.5*0.5 m for diagonal rods Supports and bridges layout For analysis of bridge structures, bridges with 70 m long main span were considered separately from short-spans at North side of the bridge. For deck plate, simple beam instead of continuous beam was used (for arch bridge, continuous beam with intermediate supports to arch through hangers) in order to avoid interaction of long-span bridge structure with sidespan on North side of the bridge and therefore to avoid unequal force and displacement distribution in the main span. 47

49 Pylons were modelled with stiff fastening to ground as they could be reinforced in stiff connection with foundation. Layouts of alternative bridges, 2, 3, 4 and 5 are presented in Figure 4.9. With black, beams and truss members are presented. With red, cables and hangers are presented. FEM models made with Bentley STAAD.Pro can be found from Figure 4. 48

50 (a) (b) (c) (d) (e) Figure 4.9. Layouts of tied-arch bridge (alternative, a), network arch bridge (alternative 2, b), suspension bridge (alternative 3, c), cable-stayed bridge (alternative 4, d) and truss bridge (alternative 5, e). Tied-arch bridge deck is formed of continous beam, supported at ends and by arch. For other alternatives bridge deck is formed of simple beam 49

51 5 Structural evaluation and description of bridge alternatives 5. Deflections and displacements of structural elements Deflection of bridge deck under traffic loads is important parameter that should be followed during structural design of a railway bridge. Deflection is limited according to Eurocode service limit state requirements and therefore forms one of the main criterions for dimensioning of general bridge structural elements, such as arch, hangers, truss, deck plate etc. Deflection characterizes an overall bending stiffness of bridge structural form. During current study was estimated that deflection of structure selfweight could be compensated during construction and therefore only deflection from traffic loads needs to be taken into account. Deflection of bridge deck of compared structural forms can be followed from Figures 5., 5.2 and 5.3. Overall deformations can be followed from Figure Deflection of bridge deck [mm] Arch Network arch Suspension Cable stay Truss x-coordinate [m] Figure 5.. Bridge deck deflection caused by traffic load LM7. 50

52 50 Deflection of bridge deck [mm] Arch Network arch Suspension Cable stay Truss x-coordinate [m] Figure 5.2. the middle of span. Bridge deck deflection caused by traffic load SW/2 that has been located to 300 Deflection of bridge deck [mm] Arch Network arch Suspension Cable stay Truss x-coordinate [m] Figure 5.3. the edge of span. Bridge deck deflection caused by traffic load SW/2 that has been located to 5

53 a) b) c) d) e) Figure 5.4. Deformations caused by LM7 traffic load exaggerated 00 times for arch (a), network arch (b), suspension (c), cable-stayed (d) and truss bridge (e) 52

54 According to analysis of deflections of different structural forms of bridges, following conclusions can be formed: - Conventional arch bridge can be considered as a relatively stiff structure for loads that are located to middle of span. In case if load is located only to one side of the span, deflections occure higher due to low bending stiffness of bridge deck and displacement of arch; - Network arch bridge can be considered as relatively stiff structure that results in low deformations. Bridge deck deflection for equally distributed load is higher than for concentrated load in the middle of the span. High structural stiffness means that the structure should be dimensioned for ultimate limit state instead of service limit state; - Truss bridge can be considered as relatively stiff for loads that are exerted to one side of the span, but relatively flexible for loads that are equally distributed to the whole length of the span; - Suspension and cable-stayed bridges have the least stiffness for concentrated loads that are exerted to only one side of the span due to low bending stiffness of bridge deck and flexible structural form. High flexibility of structural form causes high dimensions of structural elements that need to be dimensioned according to service limit state and therefore have high amount of reserve for ultimate limit state. 5.2 Internal forces of structures In order to characterize distribution of loads in structure, peculiarities of every studied structural form are described in current chapter. As described in previous chapters, arch structures are dedicated to work under compressive internal forces and the amount of bending moment should be as small as possible. Internal bending moments for arch and network arch bridge are presented in Figure

55 Figure 5.5. Internal bending moments for conventional arch and network arch bridges formed by SW2 load model and selfweight As visible from Figure 5.5, arch is suffering higher amount of bending moments in case of classic arch bridge compared to network arch since hangers that are configured in diagonal direction compensate bending moment which therefore results in required lower bending stiffness of arch. Bending moment in deck plate is distributed more equally in case of classic arch bridge compared to network arch. Axial force diagrams of designed structures are presented in Figure

56 a) b) c) d) e) Figure 5.6. Deformations caused by SW2 traffic load and selfweight for arch (a), network arch (b), suspension (c), cable-stayed (d) and truss bridge (e). Tension is presented with red, compression with blue color 55

57 According to Figures , following conclusions can be made: - For classic arch bridge, load bearing capacity of the structure is formed mainly by bending of bridge deck and arch and compression of arch. For non-tied arch bridge, deck is working for tension only with longitudinal, but not with vertical traffic loads. Due to high compression forces in the arch, geotechnical conditions of ground ought to be sufficient for anchorage; - For network arch bridge, load bearing capacity of the structure is formed mainly by compression of arch and tension and bending of bridge deck; - For steel truss bridge, load bearing capacity of the structure is formed mainly by longitudinal tension and compression of rods and bending of bridge deck; - For suspension and cable-stayed bridges, structural load bearing capacity is formed by tension of cables, compression of pylons and bending of deck plate. Due to high tension in anchored cables, geotechnical conditions of ground ought to be sufficient for anchorage. 5.3 Conclusions of structural analysis In order to satisfy the criterions for ULS (ultimate limit state) and SLS (service limit state) structural design for different structural forms, bridge alternatives were designed and analysed. ULS was main criterion for global design of structure for network arch and truss bridges. Therefore these two structural forms are over-dimensioned for SLS. SLS was main criterion for global design of structure for suspension, arch and cable-stayed bridges. Due to high requirements for railway bridges SLS (including deflection), suspension and cable-stayed bridges need to have relatively massive structure with high longitudinal stiffness of cables. 56

58 6 Quantities of structural materials According to designed and optimised structures, quantities of structural materials have been calculated for designed bridge alternatives. More detailed list of quantities can be found in Appendix 7. Quantities of requiered reinforced concrete and structural steel are presented in Figures 6. and Volume of reinforced concrete [m³] Arch bridge Network arch bridge Suspension bridge Cable-stayed bridge Truss bridge Deck plate Substructure and pylons Arch and truss Figure 6.. Volume of reinforced concrete for bridge alternatives 2500 Volume of structural steel [m³] Arch bridge Network arch bridge Suspension bridge 2063 Cable-stayed bridge 083 Truss bridge Cables and hangers Arch and truss Figure 6.2. Volume of structural steel for bridge alternatives. 57

59 7 Life cycle cost evaluation In order to evaluate possible alternative structural solutions, life-cycle cost for designed alternatives was calculated. 7. Methodology and base-prices Life-cycle cost analysed in current study consists of following components: - Construction cost; - Maintenance cost. In order to simplify calculation, construction and maintenance costs were calculated with base-year 206. Construction cost was calculated according to structural quantities and unit prices. Unit price estimation by Estonian Road Administration statistics for year 206 tenders for bridge construction was used. In order to more accurately consider various structural peculiarities, recommendations from unbiased construction experts were included in order to estimate the unit prices. Overview and detailed construction price calculation results can be found in Appendix 7. Maintenance cost was estimated according to following basis: - Maintenance work list and intervals are partly based on Russian Federation requirements on railway bridges and culverts maintenance 4. Experience and practice of Estonian Road Administration (Maanteeamet) and Estonian Railways Ltd (AS Eesti Raudtee) for bridge maintenance has been taken into account. Therefore a typical maintenance worklist and intervals have been determined for a railway bridge located in Estonia. Detailed maintenance worklist can be found from Appendix - Base-prices of maintenance work were determined on basis of Estonian Road Administration tender statistics Инструкция по содержанию искусственных сооружений. МПС России. Москва: Транспорт

60 Maintenance cost was calculated with estimation of total bridge life cycle 70 years. For discounting maintenance prices, NPV (net present value) was used: = (+ ) Where i discount rate, as estimated 0,04 C206 cost of specific maintenance work during 206 [EUR], t number of years, counted from 206 when a specific maintenance work will be carried out N total number of maintenance procedures following same algorithm To implement annual increase in bridge maintenance prices, average coefficient of price change was calculated on the basis of analysis of construction price index during the years of Average increase in bridge maintenance was selected as im=,03. Similar coefficient (,04) is also recommended in Estonian Road Administration roadworks unit price prognosis 5. Unit prices for maintenance works for years have been calculated according to following formula: ( ) = (+ ) 5 Teetööde ühikhinnad ja nende prognoos aastani Tallinn: Tallinna Tehnikaülikool