Steel Concrete Composite Railway Bridges with Continuous Decks

Transcription

1 Steel Concrete Composite Railway Bridges with Continuous Decks João Pedro Gamboia Fonseca Dissertation for Masters of Science in CIVIL ENGINEERING Jury President: José Manuel Matos Noronha da Câmara, PhD Supervisor: António José Luís dos Reis, PhD Vowel: Francisco Baptista Esteves Virtuoso, PhD May 2010

2 Abstract Nowadays, steel concrete composite structure railway bridges are extremely competitive solutions. It is this type of solution that constitutes the case study for this work. One has a double track railway bridge with composite two plate girder deck type, an extension of 220 m, a structural configuration of continuous decks and a typical span of 40 m in length. Besides the usual safety check, a complementary study is undertaken concerning two specific phenomena of these bridges type, which are the fatigue and the track-bridge interaction. The cracks process of initiation and propagation in structures - due to the action of cyclic loads - defines fatigue. In this work the analysis follows a simplified method indicated in European norms. The track-bridge interaction taking into account longitudinal stress distribution due to actions of temperature, traction, braking and vertical loads according to a non linear behavior law - consists in the making of a parametric study. The data is obtained from non linear behavior numerical models, solved with the finite elements method by the structural program SAP2000. The case study is analyzed in the same molds. The study results in the indication of design recommendations. Keywords: railway bridge; composite structure; fatigue; track- bridge interaction; parametric study INTRODUCTION In the design process of a bridge, designers decision process is dependent on factors such as span lengths, structural configurations, constructive methods, costs, and also aesthetics. The relevancy of these has no specific order. This means that no two projects are the same. More and more often steel-concrete composite structures are assuming themselves as the most competitive solutions concerning both road and railway bridges, leaving behind prestressed reinforced concrete that not so long ago was the preferred solution. Railway bridge projects carry within them the study of specific phenomena, characteristic to this bridge s type and that determines its design. The phenomena of fatigue and track-bridge interaction is going to be studied due to safety and comfort demands in railway bridges, out of many other reasons. This paper will carry on studying the referred phenomena, using a steel-concrete composite solution that will constitute the case study. 1

3 DESIGN BASICS Steel-concrete composite bridges represent an alternative to prestressed reinforced concrete bridges especially in railway bridges. They are particularly suited for spans ranging from 30 m to 80 m, when using standard composite solutions. The main advantages of composite structures are: reduced permanent loads with consequent savings to piers and foundations; simpler constructive methods (once the plate girders are set, they can provide for formwork support required to apply concrete); and faster execution times. The disadvantages are: higher initial costs due to the need of more qualified human resources; also demanding tighter control quality in execution, specifically in what concerns welding; and maintenance costs, despite that in present times we observe a decrease of these costs due to technology improvements in anticorrosion protection. The case study is a double track railway bridge with a composite two plate girder deck type. The bridge has 220 m of extension, a structural configuration of continuous decks and comprises 6 spans. The interior spans are 40 m long while the extremity ones are 30 m. The plate girders slenderness (span to depth ratio L h) varies between 14 and 18 in case of railway bridges with spans ranging from 30 to 80 m. Flanges are generally designed in order to be totally effective in Ultimate Limit States, which according to EN1993 corresponds to c t < 10ε. Webs are designed considering a slenderness h w t w varying from 70 to 200, so that one can mobilize the post buckling strength. The use of transverse stiffeners allows reduction of the web slenderness through a shear strength increase because of the higher value in τ cr. Transverse stiffeners spacing to adopt should be 1 to 1.5 times the girder depth. The case study s cross section is the one that follows: Figure 1: Cross section The structural steel adopted in the plate girders is the S355, while the concrete in the deck slab is a C40/50 grade, with steel reinforcement A500 grade. The dimensions of the cross section are: Deck slab is mm wide and 350 mm thick. Plate girders depth is 2600 mm. The upper flanges are 700 mm wide and 70 mm thick at the support sections and 50 mm thick at mid span. 2

4 The lower flanges are 1000 mm wide and 90 mm thick at the support sections and 70 mm thick at mid span sections. The web is 25 mm thick at support sections and 16 mm at mid span, the transition has a thickness of 20 mm. The transverse stiffeners are made of steel plates, asymmetrically placed, except the ones at the support sections, and they are all spaced of 4000 mm. The spacing to web height ratio is 1.64, thus resulting in a web normalized slenderness equals to FATIGUE One of the main causes of excessive deterioration in steel-concrete composite bridges is the cracking resulting from structural materials fatigue and/or corrosion and not from insufficient strength; though much of this deterioration, when it occurs, can be attributed to the lack of maintenance. But choices can be made at design process stages, to prevent and avoid this kind of issue. These choices have great impact to extend bridge serviceability life. One must remember that a bridge has to assure not only the adequate strength but also its durability and good service behavior during design life. The main features of a fatigue analysis are explained later on, according to the EN s regulations. In the present, one of the main concerns is to design the minimum essential number of connections because they are trouble zones where the stresses concentrate. Despite the lower number of connections we can achieve today, the fatigue strength is much higher; prestressed bolted connections are an example. Because bridges often undergo significant number of heavy load cycles, materials fatigue will precede fracture most of the time. This is why the fatigue is much more important to control. One thing must be clear, the fatigue cracking that may occur usually doesn t compromise the structural integrity, for redundancy and ductility. Only in particular cases where there isn t structural redundancy nor enough ductility, fatigue cracking can cause structural collapse. Fatigue Analysis The elements fatigue analysis can be undertaken with two different approaches. - Fracture Mechanics: that studies the cracking evolution from the appearing till fracture so that we can assess material fracture strength. - Damage Accumulation: whose application field is more generic than the one from Fracture Mechanics, and is based in use of fatigue strength curves. For design purposes, the fatigue analysis involves the Damage Accumulation method, as the Fracture Mechanics based analysis is much more complex and does not provide a better solution. 3

5 However, according to the EN, the fatigue analysis can be carried out through a simplified method called Damage Equivalent Stress Method, this fatigue check uses the characteristics values for Load Model 71 including the dynamic factor Φ 2 according to EN Damage Accumulation Method The Damage Accumulation Method is used in specific loading models or situations where no loading model, according to EN1991, exists, or whenever a more realistic model is required. This method applies to any material that a fatigue strength curve can depict. It consists of accumulated damage determination, caused by direct stress ranges (Δσ) or shear stress ranges (Δτ) that affect the structural element throughout the structure s design life. Accumulated damage (D) represents element cracking state which is the ratio between the number of cycles that already affected the element (n i ) and the number of cycles required to cause element rupture (N i ). The number of cycles which lead to element s rupture is obtained through material fatigue strength curves. This method s safety check is accomplished guaranteeing that the accumulated damage is lower than the unit: 1 (1) Fatigue Strength Curves Fatigue strength curves, also called S-N curves or Wohler curves represent the relationship between nominal stress range (S i ) and the number of cycles (N i ) which lead to fatigue rupture of particular structural detail category. These curves are determined from full scale fatigue test data whose results are statistically treated using linear regression and are displayed in a logarithmic scale chart. The test takes the geometric and structural imperfections into account; these imperfections result from production and execution, an example is the residual stresses effect originated by welding procedure. Fatigue strength curves apply to any grade of structural steel, within the scope of structures that operate under normal atmospheric conditions and have enough protection against corrosion. Figure 2: Fatigue Strength Curves for Direct Stress Ranges Figure 3: Fatigue Strength Curves for Shear Stress Ranges 4

6 Detail Category Detail category is the numeric designation assigned to particular details and for specific stress range direction, in order to know which fatigue strength curve matches. Detail category indicates the fatigue strength reference value (Δσ c ) in N/mm 2. Reference fatigue strength corresponds to stress range (Δσ c ) under which no fatigue damage occurs for a specific detail category considering a number of cycles equal to In case of the existence of several construction details, the category chosen is the one featuring the lower detail category. Stress ranges are determined based in an elastic analysis that excludes stress concentration effects because these have already been taken into account when the S-N curves were elaborated. Partial Factor for Fatigue Strength There are two safety philosophy approaches prescribed in the EN , the Damage Tolerant Method and the Safe Life Method. Damage Tolerant Method should provide an acceptable level of structural reliability, guaranteeing satisfactory performance throughout the structure s design life, considering it necessary to contemplate an inspection and maintenance plan in order to detect and repair the fatigue damage. This method applies to cases where the occurrence of fatigue damage is possible but also load redistribution along the structural elements components is, meaning that structural redundancy exists. Safe Life Method should provide an acceptable level of structural reliability, guaranteeing satisfactory performance throughout the structure s design life, considering no need to contemplate regular inspections concerning fatigue damage. This method applies to cases where the local formation of cracks in certain components can rapidly lead to structural element or structure collapse, meaning it compromises the structural integrity. Damage Equivalent Stress Method This simplified fatigue analysis method consists of determining damage equivalent stress range Δσ E2 or Δτ E2 and checking with a reference stress range Δσ c or Δτ c defined for cycles. Damage equivalent stress range simulates the stress range which is capable of producing the same damage to the one provoked by real train traffic throughout the design life. The damage equivalent stress range is given by: Δσ E λ Δσ (2) Where λ is the damage equivalence factor as defined in EN1993-2, that depends on the bridge structural behavior, bridge type, design life and loading; Φ is the dynamic factor as defined in EN1991-2; Δσ 71 is the stress range the Load Model 71 causes, considering the most adverse positioning. The safety check expression is: 5

7 γ F λ Δσ Δσ (3) γ M Where Δσ c is the reference stress range defined for cycles; γ Ff is the partial factor for fatigue loading, the EN recommends a value equal to 1.00; γ Mf is the partial factor for fatigue strength and depends on the approach chosen, whether Damage Tolerant Method or Safe Life Method. Safety Check Placing of the Load Model 71 in the bridge involves knowing which position is the worst, thus being necessary to get the influence line for the bending moment. After this, Δσ Ed can be calculated. (4) Δσ c value is retrieved from the EN , table 8.4: Weld attachments and stiffeners. The constructional detail comes from detail 7) Vertical stiffeners welded to a beam or plate girder, which means a detail category equal to 80 (Δσ c = 80 MPa) The safety check is the one that follows: γ F λ Δσ Δσ 1,0 0,565 1,0 102, ,92 59,26 (5) γ M 1,35 TRACK BRIDGE INTERACTION Long welded rails have been used for the last 40 years because of technology improvements in fields such as high strength steels, welding techniques and track maintenance; this allowed for substantial speed increase. An important subject in railway bridges is the interaction of long welded rails with the structure. The longitudinal stress distribution, according to a non linear force-displacement behavior of sleepers plus ballast, represents the track-bridge interaction phenomenon. So it is of utmost importance to endeavor studies on this matter, analyzing rail stresses in order to prevent track failure and displacements of both rail and bridge so that one can prevent ballast deconsolidation and rail instability. Whenever the continuity of long welded rails has to be disrupted, track rail expansion devices have to be placed. However the use of rail expansion devices has to be carefully planned, as these devices are expensive concerning acquisition and maintenance, as well as affecting passenger comfort. The analysis methodology for track-bridge interaction is defined in European regulations. 6

8 Non Linear Behavior The sleepers plus ballast system is responsible for the track-bridge interaction, as already mentioned, which consists of the relative longitudinal displacement resistance of the sleeper due to the ballast layer towards the deck. The ruling behavior law is non linear, dependent on the loading state of the track and presented per unit of rail length as defined in EN The force-displacement relationship is elastic-perfectly plastic, thus comprising 2 distinct parts. The first is linear elastic until system yielding is reached, afterwards the plasticity level governs; this level corresponds to the second part of behavior law. The following picture illustrates the non linear behavior and the table distinguishes the parameters according to the loading state of the track. Track k [KN/m] u 0 [mm] Loaded 60 2 Unloaded 20 2 Table -1: Behavior parameters Figure 4: Non Linear behavior Actions Actions considered for analysis purposes result from traction and braking effects, temperature effects and vertical loads effects. Rheological effects of shrinkage and creep can usually be neglected because of maintenance and long term ballast rearrangement. Traction and braking effects are taken into account through longitudinal forces resulting from the most unfavorable placing of train traffic. When the bridge has two or more tracks, it s necessary to consider the simultaneous actions of traction and braking for no more than two tracks. Characteristic values are defined in EN Temperature effects result from uniform temperature variation. If rail expansion devices don t exist, it is only necessary to account the temperature effects in the structure because the uniform temperature variation in the rail does not originate relative displacements among track and structure. In this case stresses produced represent additional ones, meaning they increment stress values. Whenever rail expansion devices exist, the temperature on both track and structure should be considered where the stresses produced represent total stresses. Uniform temperature variations to be considered are defined in the EN Vertical loads effects consider vertical train traffic action, which generate displacements due to structure s deformability. These actions are combined using linear superposition, according to EN

9 Design Criteria Stresses in rail for ballasted track must comply with values of 72 N/mm 2 in compression and 92 N/mm 2 in tension. These limits are valid for rail track complying with: UIC60 rail with tensile strength of at least 900N/mm 2, straight track or track radius 1500 m, ballasted tracks with concrete sleepers with maximum spacing of 65 cm and a ballast layer of at least 30 cm. Due to traction and braking effects, the relative displacement between track and bridge should not exceed 4 mm for long welded rails without rail expansion devices and 30 mm for long welded rails with rail expansion devices. The absolute displacement of the deck should not exceed 5 mm. Due to vertical effects, absolute displacement of the deck should not exceed 8 mm. Parametric Study Track-bridge interaction will now be presented for several structural configurations: simply supported deck; continuous decks with pinned support at one end and roller on the remaining ones; continuous decks with pinned support at the middle and roller on the remaining ones; and continuous decks with pinned support at one end, rail expansion device at the opposite end and rollers on the remaining supports. Simply supported deck: Continuous decks with pinned support at one end and roller on the remaining ones: Continuous decks with pinned support at the middle and roller on the remaining ones: 8

10 Continuous decks with pinned support at one end, rail expansion device at the opposite end and rollers on the remaining supports: NOTE: For each structural configuration the first chart corresponds to rail stresses due to the combined action of traction, braking, temperature and vertical load; the second chart corresponds to displacements due to traction and braking; the third chart corresponds to displacement due to vertical loads. Design Considerations This study showed that for steel-concrete composite structures, the maximum expansion length of a single deck carrying continuous welded rails without rail expansion devices of 90 m, indicated in the regulations, is conservative. It s possible to raise this value up to 100 m, according to the parametric study undertaken. So if the pinned bearing is considered in the middle, it s is possible to achieve 200 m of maximum expansion length. In cases where stresses or displacements exceed the limit values, it is necessary to adopt rail expansion devices. Therefore the maximum expansion lengths achievable for standard devices are 450 m considering a pinned bearing at one end and a rail expansion device at the other, therefore 900 m can be achieved considering that a pinned bearing is located in the middle and rail expansion devices located on both ends of the bridge. It is important to refer that the bridge design must adapt to the track design and not the other way round. As a result the designer must achieve the bridge design that suits best with the use of whichever structural configuration required. CONCLUSIONS Material s fatigue is a fundamental subject in railway bridge design. Bridge singularities, particularly connections, have to ensure enough fatigue strength. It s not tolerable for the structure to undergo major repair operations during design life. So the adopted safety philosophy must safeguard the adequate functioning of bridge with regards to cyclic solicitations. In a wider scope, since the phenomenon affects steel-concrete, steel and prestressed reinforced concrete bridges track-bridge interaction constitutes another relevant subject. It represents a Serviceability Limit State for the bridge and an Ultimate Limit State for the rails. Facing large extension bridges and different structural configurations, designers eventually need to adopt rail expansion devices to cope with the interaction issues. Therefore numeric 9

11 models assume themselves as fundamental tools to conduct the analysis and hence to comply with the regulations. REFERENCES [1] EN1991-2, Eurocode 1: Actions on structures - Part 2: Traffic loads on bridges. CEN, [2] EN1993-2, Eurocode 3 : Design of steel structures - Part 2: Steel Bridges. CEN, [3] UIC Code 774-3R, Interaction voie/ouvrages d'art. Recommendations pour les calculs. Union International des Chemins de Fer, [4] A. J. Reis, "Steel concrete composite bridges: options and design issues," in 7th International Conference on Steel Bridges, Guimarães, [5] P. Schmitt, D. Martin, and P. Ramondec, "Track-bridge interaction SNCF experience," in Track-Bridge Interaction on High-Speed Railways, Porto, [6] A. J. Reis, N. T. Lopes, and D. Ribeiro, "Track-structure interaction in long railway bridges," in Track-Bridge Interaction on High-Speed Railways, Porto, [7] H. Figueiredo, "Dinâmica de Pontes Mistas Aço-Betão em linhas Ferroviárias de Alta Velocidade," FEUP, [8] EN1994-2, Eurocode 4 - Design of composite steel and concrete structures - Part 2: General rules and rules for bridges. CEN, [9] EN , Eurocode 3 - Design of steel structures - Part 1-5: Plated structural elements. CEN, [10] EN , Eurocode 3: Design of steel structures - Part 1.9: Fatigue. CEN,