Design of Steel-Concrete Composite Bridges to Eurocodes Ioannis Vayas and Aristidis Iliopoulos Design of Steel-Concrete Composite Bridges to Eurocodes Design of Steel-Concrete Composite Bridges to Eurocodes Ioannis Vayas and Aristidis Iliopoulos A SPON PRESS BOOK CRC Press Taylor & Francis Group 6000 Broken Sound Parkway NW, Suite 300 Boca Raton, FL 33487-2742 © 2014 by Taylor & Francis Group, LLC CRC Press is an imprint of Taylor & Francis Group, an Informa business No claim to original U.S Government works Version Date: 20130809 International Standard Book Number-13: 978-1-4665-5745-1 (eBook - PDF) This book contains information obtained from authentic and highly regarded sources Reasonable efforts have been made to publish reliable data and information, but the author and publisher cannot assume responsibility for the validity of all materials or the consequences of their use The authors and publishers have attempted to trace the copyright holders of all material reproduced in this 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the CCC, a separate system of payment has been arranged Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation without intent to infringe Visit the Taylor & Francis Web site at http://www.taylorandfrancis.com and the CRC Press Web site at http://www.crcpress.com To my father Dinos Ioannis Vayas To my mother Maria Aristidis Iliopoulos Contents Foreword Preface Acknowledgments Authors xvii xix xxi xxiii Introduction 1.1 1.2 General List of symbols 2 Types of steel–concrete composite bridges 2.1 2.2 2.3 2.4 13 General 13 Composite bridges: The concept 14 Highway bridges 16 2.3.1 Plate-girder bridges with in situ concrete deck slab 16 2.3.2 Plate-girder bridges with semiprecast concrete deck slab 18 2.3.3 Plate-girder bridges with fully precast concrete deck slab 22 2.3.4 Plate-girder bridges with composite slab deck with proile steel sheeting 23 2.3.5 Plate-girder bridges with partially prefabricated composite beams 26 2.3.6 Double-girder bridges 27 2.3.6.1 Ladder deck bridges 29 2.3.7 Bridges with closed box girders 31 2.3.8 Open-box bridges 34 2.3.9 Arch bridges 40 2.3.10 Cable-stayed bridges 43 2.3.11 Suspension bridges 46 Railway bridges 47 2.4.1 General 47 2.4.2 Half-through bridges 48 2.4.3 Plate-girder bridges 49 2.4.4 Box-girder bridges 50 2.4.5 Filler-beam bridges 51 2.4.6 Pipe-girder bridges 51 vii viii Contents 2.4.7 Arch bridges 51 2.4.8 Lattice girder bridges 52 2.5 Construction forms 52 2.5.1 General 52 2.5.2 Simply supported bridges 53 2.5.3 Continuous bridges 53 2.5.4 Frame bridges 54 2.5.5 Integral and semi-integral bridges 55 2.6 Erection methods 57 2.6.1 General 57 2.6.2 Lifting by cranes 57 2.6.3 Launching 57 2.6.4 Shifting 59 2.6.5 Hoisting 59 2.6.6 Segmental construction 59 2.7 Concreting sequence 59 2.8 Execution 61 2.9 Innovation in composite bridge engineering 62 References 63 Design codes 67 3.1 Eurocodes 67 3.1.1 General 67 3.1.2 EN 1990: Basis of structural design 69 3.1.3 EN 1991: Actions on structures 70 3.1.4 EN 1998: Design of structures for earthquake resistance 70 3.1.5 EN 1994: Design of composite steel and concrete structures 70 3.1.6 EN 1993: Design of steel structures 70 3.1.7 EN 1992: Design of concrete structures 71 3.2 National annexes 71 References 71 Actions 4.1 4.2 Classiication of actions 73 4.1.1 Permanent actions 73 4.1.2 Variable actions 73 4.1.3 Accidental actions 73 4.1.4 Seismic actions 74 4.1.5 Speciic permanent actions and effects in composite bridges 74 4.1.6 Creep and shrinkage 75 4.1.7 Actions during construction 75 Trafic loads on road bridges 75 4.2.1 Division of the carriageway into notional lanes 75 4.2.2 Vertical loads on the carriageway 76 4.2.2.1 Load model (LM1) 76 4.2.2.2 Load model (LM2) 78 73 Contents 4.3 4.4 4.5 4.6 4.7 ix 4.2.2.3 Load model (LM3) 79 4.2.2.4 Load model (LM4) 79 4.2.3 Vertical loads on footways and cycle tracks 80 4.2.4 Horizontal forces 80 4.2.4.1 Braking and acceleration forces 80 4.2.4.2 Centrifugal forces 81 4.2.5 Groups of trafic loads on road bridges 83 Actions for accidental design situations 83 4.3.1 Collision forces from vehicles moving under the bridge 83 4.3.1.1 Collision of vehicles with the sofit of the bridge, for example, when tracks are higher than the clear height of the bridge 83 4.3.1.2 Collision of vehicles on piers 83 4.3.2 Actions from vehicles moving on the bridge 83 4.3.2.1 Vehicles on footways or cycle tracks up to the position of the safety barriers 83 4.3.2.2 Collision forces on kerbs 85 4.3.2.3 Collision forces on safety barriers 86 4.3.2.4 Collision forces on unprotected structural members 87 Actions on pedestrian parapets and railings 87 Load models for abutments and walls in contact with earth 88 4.5.1 Vertical loads 88 4.5.2 Horizontal loads 88 Trafic loads on railway bridges 89 4.6.1 General 89 4.6.2 Vertical loads 89 4.6.2.1 Load model 71 89 4.6.2.2 Load models SW/0 and SW/2 90 4.6.2.3 Load model “unloaded train” 91 4.6.2.4 Eccentricity of vertical loads (load models 71 and SW/0) 91 4.6.2.5 Longitudinal distribution of concentrated loads by the rail and longitudinal and transverse distribution by the sleepers and ballast 91 4.6.2.6 Transverse distribution of actions by the sleepers and ballast 91 4.6.3 Dynamic effects (including resonance) 92 4.6.4 Horizontal forces 95 4.6.4.1 Centrifugal forces 95 4.6.4.2 Nosing force 99 4.6.4.3 Actions due to traction or braking 100 4.6.5 Consideration of the structural interaction between track and superstructure 100 4.6.6 Other actions and design situations 102 4.6.7 Groups of loads 102 Temperature 103 4.7.1 General 103 Structural bearings, dampers, and expansion joints 537 REMARK 13.5 In many bridges, bearings are equipped with indicator devices for the measurement of translations Such devices consist of a measuring scale and a pointer that are mounted on a well-visible area of the bearing The support plans are followed by the bearings’ schedules that ensure that bearings are designed and constructed so that under the inluence of all possible actions, unfavorable effects of the bearing on the structure are avoided Therefore, a bearing schedule contains a detailed list of forces and movements of the bearings for each action Other performance characteristics can be included Such documents are given to the bearing producers to design the bearings according to the rules in EN 1337 EN 1993-2 gives a typical bearing schedule in Annex A similar to that of Table 13.1 In the bearing schedule, the number of the bearing is included in order to be located in the layout of the support plan The bearing type is also given (e.g., elastomeric C 2) One can see that the bridge’s temperature reference T0 is also provided Together with the bearing schedules, bearing installation drawings should be prepared In these drawings, the installation procedure is explained so that a stress-free construction process is feasible EXAMPLE 13.1 The twin-girder bridge of Example 13.1 is supported by simple low-damping elastomeric bearings The bridge is continuous with two spans of 25 m each (Figure 13.15) The bridge is located in a seismic area with peak ground acceleration 0.10 g The characteristic values of the response spectrum are TB = 0.15 s, TC = 0.50 s, and TD = 2.0 s The importance factor of the bridge is γΙ = 1.0, and the behavior factor for elastomeric bearings is q = 1.0 The thickness of the surface is 50 mm Soil factor S = 1.0 The bearing dimensions are to be speciied and veriied Actions on the bridge The actions to be considered and the relevant load cases are described in Table 13.2 Trafic loads are represented by LM1 (see Section 4.2.2) Uniform distributed loading (UDL) and tandem system (TS) trafic loads are considered separately since they are introduced with different coeficients in the groups of trafic loads (see Table 4.7) For maximum support forces at the internal supports, trafic loads are imposed on the entire bridge deck, while for maximum forces at end supports, on one span only (Figure 13.16) Braking forces are determined in accordance with Section 4.2.4 as follows: • For bearings at internal supports Equation 4.3: Qlkm = 0.6 ◊1◊2 ◊300 + 0.1◊1◊9 ◊3 ◊50 = 495 kN and 180 kN ≤ 495 kN ≤ 900 kN • For bearings at end supports Equation 4.3: Qlke = 0.6 ◊1◊2 ◊300 + 0.1◊1◊9 ◊3 ◊25 = 427.5 kN and 180 kN ≤ 427.5 kN ≤ 900 kN 538 Design of steel–concrete composite bridges to Eurocodes Table 13.1 Typical bearing schedule Bearing no Type Bearing schedule no Reference temperature T0 (°C) Uncertainty ∆T0 (°C): ± y x z Permanent Self-weight Dead load Creep–shrinkage Variable Trafic Braking/acceleration Centrifugal Nosing Footpath Wind 10 Temperature 11 Settlement Accidental 12 Derailment 13 Collision Seismic 14 Earthquake (ULS) 15 Earthquake (SLS) Max/Min V w Max/Min Hx vx Max/Min Hy vy Max/Min Mz θz Max/Min Mx θx Max/Min My θy kN mm kN mm kN mm kN mm kN mm kN mm kN mm kN mm kN mm kN-m mrad kN-m mrad kN-m mrad kN-m mrad kN-m mrad kN-m mrad kN-m mrad kN-m mrad kN-m mrad kN mm kN mm kN mm kN mm kN mm kN mm kN mm kN mm kN mm kN mm kN mm kN mm kN mm kN mm kN mm kN mm kN mm kN mm kN mm kN mm kN mm kN mm kN mm kN mm kN-m mrad kN-m mrad kN-m mrad kN-m mrad kN-m mrad kN-m mrad kN-m mrad kN-m mrad kN-m mrad kN-m mrad kN-m mrad kN-m mrad kN-m mrad kN-m mrad kN-m mrad kN-m mrad kN-m mrad kN-m mrad kN-m mrad kN-m mrad kN-m mrad kN-m mrad kN-m mrad kN-m mrad kN mm kN mm kN mm kN mm kN mm kN mm kN-m mrad kN-m mrad kN-m mrad kN-m mrad kN-m mrad kN-m mrad kN mm kN mm kN mm kN mm kN mm kN mm kN-m mrad kN-m mrad kN-m mrad kN-m mrad kN-m mrad kN-m mrad Structural bearings, dampers, and expansion joints 539 Table 13.1 (continued) Typical bearing schedule Max/Min Max/Min Max/Min Max/Min Max/Min Max/Min V w Hx vx Hy vy Mz θz Mx θx My θy kN mm kN mm kN mm kN mm kN mm kN mm kN mm kN mm kN mm kN mm kN mm kN mm kN mm kN mm kN mm kN mm kN mm kN mm kN-m mrad kN-m mrad kN-m mrad kN-m mrad kN-m mrad kN-m mrad kN-m mrad kN-m mrad kN-m mrad kN-m mrad kN-m mrad kN-m mrad kN-m mrad kN-m mrad kN-m mrad kN-m mrad kN-m mrad kN-m mrad Combinations y z x ➳➵ ➸➺ Pl 300 × 40 Pl 1200 × 15 Pl 500 × 40 3.4 m 7.0 m Cross section 25 m 25 m System 3.4 m Figure 13.15 Continuous bridge of Example 13.1 These forces are uniformly distributed along the main girders Each main girder is assigned a longitudinal force 495/(2 · 50) = 4.95 kN/m over the entire bridge length for the irst case and 427.5/(2 · 25) = 8.55 kN/m over one span for the second case Wind forces equal to 3.6 kN/m are considered over the entire bridge length in the transverse direction They are shared between the two main girders Dimensions and mechanical properties of elastomeric bearings Type B elastomeric bearings (Figure 13.2) are selected in accordance with preliminary calculations The bearings not have any holes Their dimensions are given in Table 13.3 The bearings are represented by means of springs acting in longitudinal and transverse directions The spring constant is determined in accordance with Equation 13.14 For the internal bearings, it Total nominal thickness of the elastomer, Figure 13.6: Te = Tb − (n + 1) · ts = 60 mm Plan area: A = 45 · 50 = 2250 cm2 0.09 ◊2250 ◊100 = 3375 kN/m Spring constant, Equation 13.14: K x = K y = Similarly for the end bearings, it is K x = Ky = 2000 kN/m 540 Design of steel–concrete composite bridges to Eurocodes Table 13.2 Actions for dimensioning of bearings LC Symbol G LM1 middle LM1 frequent middle Qlkm LM1 end LM1 frequent end Qlke ∆TN,con (see Section 4.7.2) ∆TN,exp (see Section 4.7.2) ∆TM,heat (see Section 4.7.3) ∆TM,cool (see Section 4.7.3) W S C Ex Ey 10 11 12 13 14 15 16 Description Self-weight of superstructure LM1, unfavorable for middle bearings Frequent LM1, unfavorable for middle bearings Braking/acceleration force, unfavorable for middle bearings LM1, unfavorable for end bearings frequent LM1, unfavorable for end bearings Breaking/acceleration force, unfavorable for end bearings Uniform temperature contraction for bearings 45°C Uniform temperature expansion for bearings 55°C Temperature difference (heating), top warmer 15°C Temperature difference (cooling), top colder 18°C Wind in transverse direction Shrinkage at time ∞ Creep at time ∞ Earthquake in x (longitudinal) direction Earthquake in y (transverse) direction LM1 UDL + For the internal support 1.0 UDL LM1 – + 1.0 For the end supports Figure 13.16 Inluence lines and position of LM for the support reactions at internal and end supports Global analysis and combination of actions For global analysis, the bridge is represented by a grillage The longitudinal beam elements represent the main composite girders, and the transverse beams the concrete slab Cracked analysis is made considering cracked cross-sectional properties at a length 15% of the span adjacent to the internal support The bearings are introduced as springs acting in longitudinal (x) and transverse directions (y), while displacements are blocked in the vertical z direction (see Remark 13.2) Global analysis provides reactions, displacements, and rotations at supports for all load cases considered These are appropriately combined to form ULS combinations For trafic loads, groups of loads are considered in accordance with Table 4.7 In the speciic case, groups 1a and are considered gr1a includes the characteristic values of LM gr2 includes the frequent values Structural bearings, dampers, and expansion joints 541 Table 13.3 Dimensions of elastomeric bearings in millimeters (see Figure 13.6) Internal support End support a b Tb n ti ts e 450 250 500 400 84 63 5 11 2.5 2.5 of LM set equal to kN/m2 over the entire deck and the characteristic values of the braking/ acceleration forces Accordingly, the following groups of trafic loads are considered: gr1a: TS + UDL (load cases or 5) gr2: (TS + UDL) frequent + breaking/acceleration (load cases + or + 7) Subsequently, ULS load combinations in accordance with Table 5.6 are formed The load combinations considered for the speciic bridge are given in Table 13.4 Analysis results for the bearings at internal supports for two combinations are illustrated indicatively in Table 13.5 Veriication of bearings The bearing veriications shall be performed for all combinations In the following, veriications for the bearings at internal supports for the load combination in accordance with Table 13.4 will be illustrated Forces, rotations, and displacements are presented in Table 13.5, line Length of steel plates, Figure 13.6: a′ = 450 − 10 = 440 mm Width of steel plates, Figure 13.6: b′ = 500 − 10 = 490 mm Area: A = a · b = 45 · 50 = 2250 cm2 Area of steel plates: A1 = 44 · 49 = 2156 cm2 Table 13.4 Combinations of actions for bearing design Line No of combination 3 10–17 18–25 26–27 Combination 1.35 · (G + Csec) + Ssec +1.35 · gr1a + 1.5 · 0.6 ·W 1.35 · (G + Csec) + Ssec +1.35 · gr1a + 1.5 · 0.6 ·T T is ∆TN,con or ∆TN,exp or ∆TM,heat or ∆TM,cool or ∆TM,heat + 0.35 · ∆TN,exp or ∆TM,cool + 0.35 · ∆TN,con or 0.75 · ∆TM,heat + ∆TN,exp or 0.75 · ∆TM,cool + ∆TN,con 1.35 · (G + Csec) + Ssec + 1.35 · gr2 + 1.5 · 0.6·T For T, see line 1.35 · (G + Csec) + Ssec + 1.35 · (0.75 ·TS + 0.4 · UDL + 0.4 · qfk* ) + 1.5 ·T For T, see line 1.35 · (G + Csec) + Ssec + 1.35 · (0.75 ·TS + 0.4 · UDL + 0.4 · qfk* ) ± 1.5 ·W (loaded bridge) 542 Design of steel–concrete composite bridges to Eurocodes Table 13.5 Support reactions, rotations, and displacements for internal bearings No of combination Pz (kN) Px (kN) Py (kN) aa,d (mrad) ab,d (mrad) vx,d (mm) vy,d (mm) 26 5959 4775 ≈0 ≈0 37.9 63.8 4.88 3.9 0.25 0.184 ≈0 ≈0 9.29 15.6 Note: For illustration purposes, values for load combination and 26 are given However, in practice, all combinations shall be examined Shape factor, Equation 13.4: S = 44 ◊49 =10.54 ◊1.1◊( 44 + 49) Ê 0.929 ˆ Reduced area, Equation 13.3: A r = 2156 ◊Á1 = 2115 cm2 49 ˜ Ë 44 ¯ a Check of distortion 1.5 ◊5959 Distortion due to compression, Equation 13.2: ec,d = = 4.46 0.09 ◊2115 ◊10.54 2 Shear deformation: v xy ,d = + 0.929 = 0.929 cm Total thickness of the elastomeric layers, Figure 13.6: Tq = Te = 6.0 cm 0.929 Distortional deformation, Equation 13.5: eq,d = = 0.15 6.0 ( 442 ◊4.88 + 492 ◊0.25) ◊10 -3 Distortion due to angular rotation, Equation 13.6: ea ,d = = 0.83 ◊5 ◊1◊12 Total design distortion, Equation 13.1: εt,d = 1.0 · (4.46 + 0.15 + 0.83) = 5.44 < with KL = and εq,d = 0.15 < 1.0 (suficient) b Check of the tension of the steel plates 1.3 ◊5959 ◊2 ◊1.1◊1◊1 ◊10 = 3.4 mm > mm Equation 13.7: required t s = 2115 ◊23.5 ts = mm > 3.4 mm (suficient) c Limitation of rotation 5959 ◊5 ◊1.1 Ê 1 ˆ 44 ◊4.88 + 49 ◊0.25 = ◊Á + = 0.38 ≥ Equation 13.8: ˜ 2156 200 ¯ ◊103 Ë5 ◊0.09 ◊10.54 0.076 (sufficient ) d Check of stability 5959 ◊44 ◊0.09 ◊10.54 = 2.82 < = 4.64 (sufficient ) 2115 ◊6 e Safety against slip Equation 13.10: Fz,Gmin = Fz,d,min = 2231 kN 2231 = 0.99 kN/cm2 = 9.9 MPa 2250 1.5 ◊0.6 = 0.19 Friction coeficient, Equation 13.13: me = 0.1 + 9.9 Mean compression stress: sm = Shear force, Equation 13.11: Fxy ,d = 02 + 37.92 = 37.9 kN £ 0.19 ◊2231= 423.89 kN Equation 13.12: FZ ,G 2231 = ◊10 =10.5 MPa ≥ MPa (sufficient ) Ar 2115 Structural bearings, dampers, and expansion joints 543 Seismic design The masses for seismic analysis correspond to the self-weight of the bridge (G) plus ψ2,1 = 0.2 of the Qk,1 = · 300 = 600 kN trafic load (see Table 4.18) The total weight in the seismic situation is accordingly equal to 7496 + 0.2 · 600 = 7616 kN Trafic loads are placed over lane to account for possible eccentricities For seismic analysis, minimum and maximum values Gb,min = 1.0 · Gb and Gb,max = 1.5 · Gb (Gb = 1.1 · G) are used for the shear modulus of the elastomer The spring constants for the internal bearings are then Kmin = 3712.5 kN/m and Kmax = 5568.75 kN/m, and similarly, 2200 kN/m and 3300 kN/m for the end bearings Multimodal response spectrum analysis is performed The resulting fundamental modes of vibration correspond to translations in longitudinal and transverse directions The fundamental periods are almost equal in both directions since translations are due to the lexibility of the bearings only, which is equal in both directions The participating mass factors for both modes amount to almost 100% Consequently, the fundamental mode method may also be applied (Table 4.19) This is done in the following for illustration purposes The overall stiffness of the system equals to the sum of stiffness of the bearings (four end, two middle bearings) Therefore, Kmax,tot = 24,337.5 kN/m, and Kmin,tot = 16,225 kN/m The fundamental periods are determined from Table 4.19 For Kmax,tot , it is T = ◊p ◊ 7616/ 9.81 =1.12 s, and similarly, T = 1.37 s for Kmin,tot 24337.5 The corresponding base shears with TC ≤ T ≤ TD, Equation 4.24c, are 2.5 0.5 ˆ Ê ◊ ◊ ◊ Vb = 7616 ◊Á0.11 = 850 kN 1.0 1.12 ˜ Ë ¯ for Kmax, and similarly, Vb = 694.9 kN for Kmin The deck and bearing translations, equal in the two directions, are determined from u = (850/24337.5) · 1000 = 34.9 mm for Kmax, and similarly, u = 42.8 mm for Kmin It may be conirmed that upper values lead to maximum forces, and lower values to maximum displacements The horizontal forces of bearings for Kmax are at internal supports Fx = Fy = 5568.75 · 34.9/103 = 194.3 kN and at end supports Fx = Fy = 3300 · 34.9/103 = 115.2 kN It may be conirmed that the base shear is Vb = · 194.3 + · 115.2 ≈ 850 kN Table 13.6 provides the design values of internal bearings in the seismic situation The bearing veriication procedures for internal bearings for the seismic situation are similar as for the basic ULS combinations The most critical are the safety against slip for Kmax and bearing distortion for Kmin that are illustrated subsequently Table 13.6 Forces, rotations, and displacements for internal bearings in the seismic situation Calculation with Pz (kN) Px (kN) Py (kN) aa,d (mrad) ab,d (mrad) vx,d (mm) vy,d (mm) Kmax Kmin 2331 2331 194 159 194 159 ≈0 ≈0 ≈0 ≈0 34.9 42.8 34.9 42.8 544 Design of steel–concrete composite bridges to Eurocodes • Safety against slip for Kmax Ê 3.49 3.49 ˆ Reduced area, Equation 13.3: A r = 2156 ◊Á1 =1831.4 cm2 44 49 ˜ Ë ¯ Shear force: Fxy ,d = 1942 +1942 = 274.4 kN 2331 =1 kN/cm2 =10 MPa 2250 1.5 ◊0.6 = 0.19 Friction coeficient, Equation 13.13: me = 0.1+ 10 Equation 13.11: Fxy ,d = 274.4 kN < 0.19 ◊2331= 442.89 kN (sufficient ) Mean compression stress: sm = Fz ,G 2331 = ◊10 =12.7 MPa ≥ MPa (sufficient ) 1831.4 Ar • Bearing distortion for Kmin Ê 4.28 4.28 ˆ =1758 cm2 Reduced area, Equation 13.3: A r = 2156 ◊Á1 44 49 ˜ Ë ¯ 1.5 ◊2331 =1.91 Distortion due to compression, Equation 13.2: ec,d = (1.1◊0.09) ◊1758 ◊10.54 Shear distortion: v xy ,d = v 2x ,d + v 2y ,d = 4.282 + 4.282 = 6.05 cm Distortional deformation, (sufficient, see Remark 13.3) Equation 13.5: eq,d = 1.5 ◊6.05 = 1.51< (sufficient, see Remark 13.3) 442 ◊0 + 492 ◊0 =0 ◊5 ◊1.12 Total design distortion, Equation 13.1: εt,d = 1.0 · (1.91 + 1.51 + 0) = 3.42 < (suficient) with KL = Distortion due to angular rotation, Equation 13.6: ea ,d = REMARK 13.6 In Example 13.1: • The stiffness of the piers and the foundations were not taken into account It was assumed that Kpier, Kfoundation ≫ Kbearing (see also Remark 13.4) A more detailed 3D model can be chosen • The veriications for the bearings were based on the results of the most adverse combination of action effects Due to the simplicity of the bridge and the mild climate conditions, this can be described as an acceptable approach In a different case, the increased temperature of Equation 13.25 according to the recommendations of the National Annex should be applied, alternatively Equation 13.26 13.9 FLUID VISCOUS DAMPERS These dampers behave like safety belts, developing low resistance at slow loading velocities and high resistance at high loading velocities (Figure 13.17a) Consequently, displacements are not restrained at service conditions due to temperature changes, creep, or shrinkage, but the dampers “block” and restrain deformations at higher velocities like during an Structural bearings, dampers, and expansion joints F Fmax F Restoring force 545 d Temperature, creep, and shrinkage Earthquake dbd ED v ≈1 mm/s (a) Loading velocity (b) Figure 13.17 (a) Response of hydraulic viscous dampers for various loading velocities and (b) response to cyclic loading Orifices (a) Conne ➘➽➹➾➷ ➽➾ ➬➪ ck Piston ➮➹➼➘ous fluid Damp➪➶ Conne ➘➽➹➾➷ ➽➾ substru➘➽ure El➻➼➽➾➚➪➶➹➘ ➴➪➻➶➹➷g (b) Figure 13.18 (a) Schematic representation of a luid damper and (b) combination of dampers with elastomeric bearings earthquake, sudden breaking, or acceleration Damping is produced by the displacement of a piston moving in a cylinder illed with oil, silicon, or similar materials (Figure 13.18a) Small oriices allow the low of oil for low loading velocities, while at higher speeds, the oriices prevent the free low and damp the movement Dampers are called in EN 1998-2 shock transmission units The reaction (or damping) force is a function of the loading speed in accordance with Equation 13.28 and is illustrated in Figure 13.17a for a sinusoidal motion: F = C ◊va (13.28) where C is a device-speciic viscous damping coeficient [kN · s/m] v is the loading velocity [m/s] a is a device-speciic damping exponent (usually 0.2–0.25) Such dampers are used in combination with bearings Their application is associated with nonlinear time history analysis since they cannot be modeled in the frame of a spectrum analysis (see Figure 13.18b) 13.10 FRICTION DEVICES Friction devices exploit the energy dissipation with development of friction The restoring force for lat sliding surfaces is equal to F = md ◊N Ed ◊sign(dɺ bd) (13.29) 546 Design of steel–concrete composite bridges to Eurocodes F ÐÑ❮ F Ò = μd NEd F0 d d bd ED (a) d ❒❮ Rb F F ➱✃❐ NE d F0 K ❰ Ï ÐÑ❮/R b F0 d d ❒❮ ED (b) Figure 13.19 (a) Response of friction devices with lat and (b) spherical sliding surfaces while the dissipated energy by E d = ◊md ◊N Ed ◊dbd (13.30) where μd is the dynamic friction coeficient N Ed is the applied vertical force dbd is the maximal design device displacement · sign(dbd) is the sign of the velocity vector It may be seen that such devices (Figure 13.19) have zero stiffness and no restoring capability so that they must be complemented by additional devices Other devices with curved sliding surfaces such as friction pendulum devices have been developed that have restoring capabilities and improved stiffness properties (Figure 13.19b) The restoring force is given by F= N Ed ◊dbd + md ◊N Ed ◊sign(dɺ bd) Rd (13.31) where Rb is the radius of the spherical surface and all other symbols as in Equation 13.29 The dissipated energy is the same as for lat sliding surfaces and is given by Equation 13.30 13.11 EXPANSION JOINTS As already explained, horizontal deformations of the superstructure arise due to temperature, creep, shrinkage, earthquakes, trafic, etc These deformations are associated with signiicant uncertainties and accurate calculations are obviously not feasible Expansion Structural bearings, dampers, and expansion joints ểễếệìỉ Epoỗố ịễổì ỏỉịệị Elổệỉỏễị Laệễịõ ọõệễ Central plate Asphalt 547 Bỉõệ ồỉõễ sealing t ĩìíễị òễ veling mortar 170 ~250 mm Deck plate àØá×ÙÚâ ãÚä Resin adhesive Rubber sealing sheet B Ú Ú L ExäÚÙỉ×ØÙ äØ×ÙƯ Figure 13.20 Highway expansion joint joints are lexible links that connect independent parts of a road bridge at piers and the abutments They are capable of absorbing the aforementioned deformations, and in case of failure, they can be easily replaced A typical cross section of an expansion joint is shown in Figure 13.20 [13.1] The joint is made of natural or synthetic rubber with steel plates embedded in it (reinforced elastomer) The dimensions of the joint BxLxt depend on the required design movement For small-span bridges, longitudinal deformations usually range between ±20 and ∼40 mm with BxLxt ≈ (250 ∼ 400) × 2000 × (30 ∼ 50) For long-span applications, the required deformations may exceed ±300 mm and BxLxt ≥ 1000 × 2000 × 80 The expansion joint in Figure 13.20 is ixed through chemical anchors in the deck plate Expansion joints should • Not increase the degree of the bridge’s static indeterminacy by restraining degrees of freedoms at supports • Be waterproof • Produce low noise when vehicles are passing over them Expansion joints should be manufactured and designed according to the regulations of the European Technical Approval (ETA) [13.8] Such a document speciies the design guidelines of the expansion joint that are compatible with the requirements of the Eurocodes 548 Design of steel–concrete composite bridges to Eurocodes Alternative types of expansion joints are described in EN 1993-2 [13.7] for the use in steel bridges and they are as follows: • Buried expansion joint The surfacing is continuous over the joint gap and the expansion joint is not lush with the running surface The joint consists of waterprooing membranes or an elastomeric pad and is formed in situ • Flexible expansion joint This is an in situ poured joint that is lush with the running surface The joint gap is covered with steel plates that support the surfacing materials (aggregates or binder) • Nosing expansion joint It has lips or edges made of concrete, resin mortar, or elastomeric The gap between the edges is illed by a prefabricated lexible proile The components of the joints are not lush with the running surface • Mat expansion joint The movements of the structure are absorbed by a lexible prefabricated elastic strip The strip is ixed by bolts to the structure (see Figure 13.20) The joints’ components are lush with the running surface • Cantilever expansion joint Cantilever symmetrical and nonsymmetrical elements (such as comb or sawtooth plates) are anchored on one side of the deck joint gap and interpenetrated to span the deck joint gap The elements are lush with the running surface • Supported expansion joint This joint consists of an element that is fixed by hinges on one side and sliding supports on the other side This element is flush with the running surface and spans the deck joint gap Movements are allowed through sliding on the non-fixed side of the hinged element • Modular expansion joint Steel beams encased in watertight materials bridge the joint gap in a way that a moveable joint is formed The beams are lush with the running surface More details are found in the “Guideline for European Technical Approval of Expansion Joints for Road Bridges” [13.8] An expansion joint schedule should be prepared so that the inal design is veriied by the manufacturer This schedule should contain the arrangement of the expansion joints in conjunction with the geometry of the bridge and a list of actions and imposed deformations Moreover, the designer should describe in detail the installation procedure REFERENCES [13.1] [13.2] [13.3] [13.4] [13.5] [13.6] AGOM International SRL: Metal rubber engineering, Bridge Expansion Joints, Italy Bridge design to Eurocodes, Worked examples, JRC scientiic and technical reports, EUR 25193 EN-2012 Caltrans: Bridge Bearings, Memo to designers 7-1 Caltrans, Eureka, CA, 1994 Eggert, H., Kauschke, W.: Lager im Bauwesen Ernst & Sohn, Berlin, Germany, 1995 EN 1337, CEN (European Committee for Standardization): Structural bearings, Parts to 11 CEN, 2000 to 2006 EN 1998-2, CEN (European Committee for Standardization): Design of structures for earthquake resistance, Part bridges, CEN 2005 Structural bearings, dampers, and expansion joints [13.7] [13.8] [13.9] [13.10] [13.11] [13.12] [13.13] [13.14] [13.15] 549 EN 1993-2, CEN (European Committee for Standardization): Design of steel structures—Part 2: Steel bridges, 2006 ETAG 032: Expansion Joints for Road Bridges EOTA, Albuquerque, NM Gumba, Bridge bearings, 2011 Kawaki Core-Tech Co Ltd.: Steel Bearings Lee, D J.: Bridge Bearings and Expansion Joints, 2nd edn E & FN Spon, London, U.K., 1994 Setra: Laminated elastomeric bearings, Technical Guide Setra, Neu-Ulm, Germany, 2007 Steel bridge bearing Selection and design guide AISC, Chicago, IL Steel Bridge Group: Guidance notes on best practice in steel bridge construction Attachment of bearings 2.08, 2010 Steel Bridge Group: Guidance notes on best practice in steel bridge construction Bridge bearings 3.03, 2010 Bridge and Structural Engineering Combining a theoretical background with engineering practice, Design of Steel-Concrete Composite Bridges to Eurocodes covers the conceptual and detailed design of composite bridges in accordance with the Eurocodes Bridge design is strongly based on prescriptive normative rules regarding loads and their combinations, safety factors, material properties, analysis methods, required veriications, and other issues that are included in the codes Composite bridges may be designed in accordance with the Eurocodes, which have recently been adopted across the European Union This book centers on the new design rules incorporated in the EN-versions of the Eurocodes The book addresses the design for a majority of composite bridge superstructures and guides readers through the selection of appropriate structural bridge systems It introduces the loads on bridges and their combinations, proposes software supported analysis models, and outlines the required veriications for sections and members at ultimate and serviceability limit states, including fatigue and plate buckling, as well as seismic design of the deck and the bearings It presents the main types of common composite bridges, discusses structural forms and systems, and describes preliminary design aids and erection methods It provides information on railway bridges, but through the design examples makes road bridges the focal point This text includes several design examples within the chapters, explores the structural details, summarizes the relevant design codes, discusses durability issues, presents the properties for structural materials, concentrates on modeling for global analysis, and lays down the rules for the shear connection It presents fatigue analysis and design, fatigue load models, detail categories, and fatigue veriications for structural steel, reinforcement, concrete, and shear connectors It also covers structural bearings and dampers, with an emphasis on reinforced elastomeric bearings The book is appropriate for structural engineering students, bridge designers or practicing engineers converting from other codes to Eurocodes an informa business www.crcpress.com 6000 Broken Sound Parkway, NW Suite 300, Boca Raton, FL 33487 711 Third Avenue New York, NY 10017 Park Square, Milton Park Abingdon, Oxon OX14 4RN, UK Cover image: Bridge in France painted by Jutta Legien-Vaya K15469 ISBN: 978-1-4665-5744-4 90000 781466 557444 w w w.crcpress.com