Composite bridge design (EN1994-2) Bridge modelling and structural analysis
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1 EUROCODES Bridges: Background and applications Dissemination of information for training Vienna, 4-6 October Composite bridge design (EN1994-2) Bridge modelling and structural analysis Laurence DAVAINE French Railways (SNCF) y ( ) Bridge Engineering Department (IGOA)
2 Contents Dissemination of information for training Vienna, 4-6 October Bridge modelling Geometry Effective width (shear lag effect) Modular ratios (concrete creep) Transversal distribution Cross-sectional mechanical properties 2. The global cracked analysis according to EN Determination of the cracked zones on internal supports Results from the global analysis
3 Twin-girder bridge modelling Dissemination of information for training Vienna, 4-6 October C3 G P2 y z x P1 C0 simply supported bar model (dz=0 for every support) half-bridge cross-section represented by its centre of gravity G (neutral fibre) structural steel alone, or composite, mechanical properties according to the construction phases of the bridge slab
4 Concrete slab thickness Dissemination of information for training Vienna, 4-6 October Actual slab Computed slab S actual = S computed (same area) µ actual = µ computed (same location of the slab gravity centre G c )
5 Shear lag in the concrete slab according to EN Dissemination of information for training Vienna, 4-6 October b eff xx,max xx Non-uniform transverse distribution of the longitudinal stresses 1b e 1 2b e 2 b 0 b m b m b mm b b b eff 0 i ei i b ei Le min ; bi 8 1 i except for end supports where Le i b ei
6 Shear lag in the concrete slab according to EN Dissemination of information for training Vienna, 4-6 October Equivalent span length L e Global analysis (calculation of internal forces and moments) : constant along each span (equal to the value at mid-span) Section analysis (calculation of stresses) : linearly variable along L i /4 surrounding the internal supports
7 Application to the twin-girder bridge example Dissemination of information for training Vienna, 4-6 October C0 P1 P2 C3 60 m 80 m 60 m L (m) 0.85x60 = x80 = x60 = 51 e 0.25 x (60+80) = x (60+80) = 35 L e (m) b e1 (m) b e2 (m) 1 2 b eff (m) In-span 1 and In-span Internal supports P1 and P End supports C0 and C but < < 6.0
8 Application to the twin-girder bridge example Dissemination of information for training Vienna, 4-6 October C0 P1 P2 C3 2 1 L /4 L 1 /2 L 2 /2 L 1 /2 1 L 1 /4 L 2 /4 L 2 /4 L /4 L /
9 Composite cross-sections mechanical properties Dissemination of information for training Vienna, 4-6 October Un-cracked behaviour (mid-span regions, M c,ed > 0) b eff G c Reinforcement neglected (in compression) y Gc y G G elastic neutral axis A A a A c n Ay A y A n y c G a Ga Gc y Ga G a y a a( G Ga) c c G Gc I I A y y I A y n Cracked behaviour (support regions, M c,ed < 0) b eff G s E a = E s = N/mm² (n = 1) ygs a s G G a elastic neutral axis A A A AyG AayGa AsyGs y 2 G I I ( ) 2 a Aa yg yga Is As yg ygs y Ga I s 0
10 Modular ratios (creep effect) Dissemination of information for training Vienna, 4-6 October Short-term modular ratio: Long-term modular ratio: t t t 0 n 0 E E a cm n n. 1 L 0 L t Creep coefficient according to EN with : f cm Ecm t = age of concrete at the considered time during the bridge life t 0 = age of concrete when the considered loading is applied to the bridge 0.3 t 0 = 1 day for shrinkage t 0 = mean value of age of concrete segments, in case of composites structures cast in several stages (permanent load) L depends on the load case : Permanent loads Shrinkage Imposed deformations 1.5
11 Creep coefficient according to Annex B in EN Dissemination of information for training Vienna, 4-6 October t t 0. t t. t t 0 c t t H (end of bridge life) RH.h H RH 1 0 RH cm f. t h 0.1 t 0 f cm 0 with : RH = 80 % (relative humidity in the bridge area) h 0 2A c u notional size (u is the concrete slab perimeter exposed to drying) 35 1 fcm fcm fcm
12 Application to the twin-girder bridge example Dissemination of information for training Vienna, 4-6 October Slab segments time (in day) t =0 t=66 t=80 t=110 Beginning of concreting Composite behaviour or not, according to the segment concreting order End of concreting Mean value of concrete age : t 0 = days 14 days Jacking Bridge equipments For shrinkage : 1,t0 t 0 = 1 day 0 y,t 4 0 t 0 = days 30 days n L,1 2,t0 t 0 = days n 3,t 0 L2 n L,2 n L,4 n L,3
13 Application to the twin-girder bridge example Dissemination of information for training Vienna, 4-6 October Short-term modular ratio Long-term modular ratio E For all load cases : n a E cm Load case L t 0 (days) t = 0 n L Concrete slab segment (selfweight) Settlement Shrinkage Bridge equipments
14 Transversal distribution between the two girders Dissemination of information for training Vienna, 4-6 October Influence line of the support reaction on girder id no. 1 1 a F e a 0 Bridge axle Girder no.1 (modeled) e/2 e/2 girder no. 2 R F1 a e 1 1 R 2 a F e
15 Application to the traffic load model LM1 Dissemination of information for training Vienna, 4-6 October Conventional traffic lanes positioning 1 m 0.5 m Lane no.1 Lane no.2 Lane no.3 Remaining area 3 m 3 m 3 m 2 m Bridge axle Girder no.1 (modeled) 3.5 m 3.5 m girder no. 2
16 Application to the traffic load model LM1 Dissemination of information for training Vienna, 4-6 October Tandem TS Bridge axle TS 1 per axle : 1.0 x 300 = 300 kn 1 TS 2 per axle : 1.0 x 200 = 200 kn TS 3 per axle : 1.0 x 100 = 100 kn 0 R1 0.5 m 1 m 2 m R2 Influence line of the support reaction on girder no. 1 Support reaction on each main girder : R 1 = kn R 2 = kn
17 Application to the traffic load model LM1 Dissemination of information for training Vienna, 4-6 October Uniform Design Load UDL Bridge axle Load on lane no.1 : 1.0 x 9 x 3 = 27 kn/ml 1 Load on lane no.2 : 1.0 x 2.5 x 3 = 7.5 kn/ml LANE 1 LANE 2 LANE 3 Load on lane no.3 : 1.0 x 2.5 x 3 = 7.5 kn/ml R1 R2 0 Influence Line 0.5 m 1 m 2 m Support reaction for each main girder : R 1 = kn/ml R 2 = 6.64 kn/ml
18 Application to the traffic load model LM1 Dissemination of information for training Vienna, 4-6 October Bending Moment (MN.m) for UDL and TS
19 Contents Dissemination of information for training Vienna, 4-6 October Bridge modelling Geometry Effective width (shear lag effect) Modular ratios (concrete creep) Transversal distribution Cross-sectional mechanical properties 2. The global cracked analysis according to EN Determination of the cracked zones on internal supports Results from the global analysis
20 Structural analysis of a composite bridge girder Dissemination of information for training Vienna, 4-6 October Uniform load q (N/m) Static system P Concrete cracking 1 Deformed shape Steel yielding 2 M Linear elastic global analysis (except for accidental loads) No bending redistribution is allowed Concrete cracking near internal support and steel yielding near mid-span are taken into account through simplified methods Plate buckling is neglected in the global analysis except if the effective p area of one of the panel is lower than half its gross area (A eff < 0.5 A gross ) M pl,rd M el,rd M at mid-span with P increasing Class 1
21 Global cracked analysis 1 Dissemination of information for training Vienna, 4-6 October Stress distribution c in the concrete slab for the characteristic SLS combination of actions assuming the concrete resists in every cross section (EI 1 ) In the zones where c < - 2 f ctm, the concrete is assumed to be cracked (and then neglected) for the bending stiffness distribution (EI 2 ) EI EI 1 1 EI 2 EI 1 = un-cracked composite second moment of area (structural steel + concrete slab in compression) EI 2 = cracked composite second moment of area (structural steel + reinforcement in tension)! This approach is not iterative (the cracked zones are determined only once).
22 Global cracked analysis 1 Dissemination of information for training Vienna, 4-6 October Simplified method is possible if : - no pre-stress -L min /L max > 0.6 EI (L 1 + L 2 ) A s L 1 L 2 EI 1 A c = 0 In the stiffness zones EI 2 : concrete in tension is neglected reinforcement are included
23 In-span steel yielding 2 Dissemination of information for training Vienna, 4-6 October Mid-span eventual yielding is taken into account if : Class 1 or 2 at mid span (and M Ed > M el,rd ) Class 3 or 4 on internal support L min /L max < 0.6 L max L min Class 1 or 2 Class 3 or 4 As L min /L max > 0.6 in the example, the redistribution due to yielding near mid-span is not taken into account.
24 Application to the twin-girder bridge example Dissemination of information for training Vienna, 4-6 October Concreting phases, Slab segments order: (N/mm²) ination 5 Stresses in co oncrete slab ( ic SLS comb Characteristi f ctm 6.4 N/mm 2-15 x = 35.0 m x = 76.0 m x = m x = m Cracked zone for P % 19.5 % Cracked zone for P % 20.0 %
25 Application to the twin-girder bridge example Dissemination of information for training Vienna, 4-6 October SLS and ULS bending moment distribution M Ed (= M a,ed + M c,ed ) 80 Characteristic SLS Fundamental ULS Bending mom ment (MN.m)
26 Application to the twin-girder bridge example Dissemination of information for training Vienna, 4-6 October SLS and ULS shear force distribution V Ed Characteristic SLS Fundamental ULS Shear force es (MN)
27 Application to the twin-girder bridge example Dissemination of information for training Vienna, 4-6 October ULS stresses (N/mm²) along the steel flanges, calculated without concrete resistance
28 Dissemination of information for training Vienna, 4-6 October Thank you for your kind attention!
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