Overview of Seismic issues for bridge

Transcription

1 EUROCODES Bridges: Background and applications Dissemination of information for training Vienna, 4-6 October Overview of Seismic issues for bridge design (EN1998) Basil Kolias DENCO SA Athens

2 Overview of the presentation Indian Concrete Institute Workshop on Eurocode 8 - New Delhi, September Dissemination of information for training Vienna, 4-6 October Example of ductile piers Special example of seismic design of a bridge with concrete deck rigidly connected to piers designed for ductile behaviour 2. Example of limited ductile piers Seismic design of the general example: Bridge on high piers designed for limited ductile behaviour 3. Example of seismic isolation Seismic design of the general example: Bridge on squat piers designed with seismic isolation

3 1 Example of ductile piers Indian Concrete Institute Workshop on Eurocode 8 - New Delhi, September Dissemination of information for training Vienna, 4-6 October Bridge description 3 span voided slab bridge (overpass), with spans 23.0m, 35.0m and 23.0m. Total length of 82.50m. Piers: single cylindrical columns D=1.20m, rigidly connected to the deck. Pier heights 8.0m for M1 and 8.5m for M2. Simply supported to abutments through a pair of sliding bearings. Foundation of piers and abutments through piles.

4 Example of ductile piers Indian Concrete Institute Workshop on Eurocode 8 - New Delhi, September Dissemination of information for training Vienna, 4-6 October Longitudinal section A1 M1 M2 A2

5 Example of ductile piers Indian Concrete Institute Workshop on Eurocode 8 - New Delhi, September Dissemination of information for training Vienna, 4-6 October Plan view A1 M1 M2 A2

6 Example of ductile piers Indian Concrete Institute Workshop on Eurocode 8 - New Delhi, September Dissemination of information for training Vienna, 4-6 October Cross section of deck d = 1.65m Pier cross section D = 1.20m

7 Linear Analysis Methods Indian Concrete Institute Workshop on Eurocode 8 - New Delhi, September Dissemination of information for training Vienna, 4-6 October Equivalent Linear Analysis: Elastic force analysis with forces from unlimited elastic response divided by the global behaviour factor = q. design spectrum = elastic spectrum / q (except for very low periods T < T B ) Response spectrum analysis: Multi-mode spectrum analysis Reference method Fundamental mode analysis Equivalent static ti load analysis With several models of varying simplification

8 Linear Analysis Methods Indian Concrete Institute Workshop on Eurocode 8 - New Delhi, September Dissemination of information for training Vienna, 4-6 October Basic prerequisite: Stiffness of Ductile Elements (piers): secant stiffness at the theoretical yield, based on bilinear fit of the actual curve M y Yield of first bar Secant stiffness = M y / φ y φ y M y = M Rd Guidance for estimation of stiffness in Annex C

9 Linear Analysis Methods Indian Concrete Institute Workshop on Eurocode 8 - New Delhi, September Dissemination of information for training Vienna, 4-6 October Stiffness of concrete deck Bending stiffness: uncracked stiffness both for prestresed and non-prestressed decks Torsional stiffness: open sections or slabs: may be ignored prestressed box sections: 50% of uncracked reinforced box sections: 30% of uncracked

10 Linear Analysis Methods Indian Concrete Institute Workshop on Eurocode 8 - New Delhi, September Dissemination of information for training Vienna, 4-6 October Ductility Classes Limited Ductile Behaviour: q 1.50 (behaviour factor) minμ Φ = 7 (curvature ductility) Ductile Behaviour: 1.50 < q 3.50 minμ Φ = 13 μ Φ

11 Ductility Classes Indian Concrete Institute Workshop on Eurocode 8 - New Delhi, September Dissemination of information for training Vienna, 4-6 October Force Behaviour Limited ductile Ductile Displacement

12 Behaviour factors Indian Concrete Institute Workshop on Eurocode 8 - New Delhi, September Dissemination of information for training Vienna, 4-6 October Type of Ductile Members Reinforced concrete piers: Seismic Behaviour Limited Ductile Ductile Vertical piers in bending λ(α s ) Inclined struts in bending λ(α s ) Steel Piers: Vertical piers in bending Inclined struts in bending Piers with normal bracing Piers with eccentric bracing Abutments rigidly connected to the deck: In general Locked-in structures (see (9). (10)) Arches Shear ratio α s = L s /h. For α s 3 λ s = 1, for 1 α s < 3 λ s α s /3

13 Regular / Irregular bridges Indian Concrete Institute Workshop on Eurocode 8 - New Delhi, September Dissemination of information for training Vienna, 4-6 October Criterion based on the variation of local required force reduction factors r i of the ductile members i : r i = qm Ed,i /M Rd,I =,, q x Seismic moment / Section resistance A bridge is considered regular when the irregularity index: ρ ir =max(r i )/min(r i ) ρ 0 = 2 Piers contributing less than 20% of the average force per pier are not considered

14 Regular / Irregular bridges Indian Concrete Institute Workshop on Eurocode 8 - New Delhi, September Dissemination of information for training Vienna, 4-6 October For regular bridges: equivalent elastic analysis is allowed with the q-values specified, without checking of local ductility demands ds Irregular bridges are: either designed with reduced behaviour factor: q r = q ρ o / ρ ir or verified by non linear static (pushover) or or verified by non-linear static (pushover) or dynamic (time history) analysis

15 Design Seismic Action to EN 1998 Indian Concrete Institute Workshop on Eurocode 8 - New Delhi, September Dissemination of information for training Vienna, 4-6 October Two types of elastic response spectra: Types: 1 and 2. 5 types of soil: A, B, C, D, E. (+ S1,S2) 4 period ranges: short < T B < constant acceleration < T C < const. velocity < T D < const. displacement. Design spectrum = elastic spectrum / q. 3 importance classes: Class III II I γ I = Reflect reliability differentiation

16 Seismic action: Elastic response spectra S e (T) Indian Concrete Institute Workshop on Eurocode 8 - New Delhi, September Dissemination of information for training Vienna, 4-6 October Ground motion: Dependence on ground type (A, B, C, D, E) max. values: A g = a g S, v g = a g ST C /(2π) π),, d g = a g ST C T D Response spectrum: Acceleration S e (T) as a function of T a T g : P.G.A. 0 T TB : SeT ag S 1 2,5 1 S: soil factor T B η(ξ) =1 1, ξ = T B T T C T a S 2, 5 : S : e g T T C T T D : S e T a g S 2, 5 T TCT TD T 4s : Se T ag S 2, 5 2 T C D S e (T) / α g S η Regions corresponding to constant: acceleration velocity displacement (1/Τ) (1/Τ 2 ) qββ Τ Β Τ C Τ D Τ

17 Seismic action Indian Concrete Institute Workshop on Eurocode 8 - New Delhi, September Dissemination of information for training Vienna, 4-6 October Response spectrum type 1 Ground type C: Characteristic periods T B =0 20s T C =0.60s and T D =2.50s. Soil factor S=1.15. Seismic i zone Z1: Reference peak ground acceleration a gr = 0.16g Importance factor γ I = 1.0 Lower bound factor β = s, Seismic i actions in horizontal directions a g = γ Ι. a gr = g=0.16g Behaviour factors ( 4.1.6(3) of EN ) : q x =3.5 (α s =3.3>3, λ(α s )=1.0) and q y =3.5 (α s =6.7>3, λ(α s )=1.0)

18 Methods of analysis Indian Concrete Institute Workshop on Eurocode 8 - New Delhi, September Dissemination of information for training Vienna, 4-6 October Multi mode spectrum response analysis - Combination of modes with CQC rule. - Combination of responses in 3 directions through the rule specified in Eq. (4.20)-(4.22) 22) of EN ( rule). 30 modes considered, Σ(modal masses)>90% Program: SOPHISTIK Fundamental mode method In the longitudinal direction (hand calculation for comparison/check)

19 Deck weights and other actions Indian Concrete Institute Workshop on Eurocode 8 - New Delhi, September Dissemination of information for training Vienna, 4-6 October Self weight (G): (6.89m m m m). 25kN/m3 = 14903kN 2. Additional dead (G 2 ): q G2 = 43.65kN/m = sidewalks safety barriers road pavement 2. 25kN/m m kN/m + 7.5m. (23kN/m m) 3. Effective seismic live load (L E ): (20% of uniformly distributed traffic load) q LE = 0.2 x 45.2 kn/m = 9.04kN/m 4. Temperature action (T)*: o C / -45 o C 5. Creep & Shrinkage (CS)*: Total strain: -32.0x10-5 * Actions 4, 5 applicable only for bearing displacements Deck seismic weight: W E =14903kN+( )kN/m x 82.5m = 19250kN

20 Fundamental mode method Indian Concrete Institute Workshop on Eurocode 8 - New Delhi, September Dissemination of information for training Vienna, 4-6 October Horizontal Stiffness in longitudinal direction For cylindrical column of diameter 1.2m, J un = π /64 = m 4 Assumed effective stiffness of piers J eff /J un = 0.40 (to be checked later). Concrete grade C30/37 with E cm = 33GPa Assuming both ends of the piers fixed, the horizontal stiffness of each pier in longitudinal direction is: K 1 =12EJ eff /H 3 = MPa. ( m 4 )/(8.0m) 3 = 31.5MN/m KK 0 2 = 12EJ eff /H 3 = MPa. ( m 4 )/(8.5m) 3 = 26.3MN/m Total horizontal stiffness: K = = 57.8MN/m Total seismic weight: W E = 19250kN (see loads) Fundamental period: T m = 2 π = 2 π K (19250kN/9.81m/s 57800kN/m 2 ) = 1.16s

21 Fundamental mode method Indian Concrete Institute Workshop on Eurocode 8 - New Delhi, September Dissemination of information for training Vienna, 4-6 October Spectral acceleration in longitudinal direction: S e = a g S(β /q)(t /T) =0.16g C (2.5/3.5)(0.60/1.16) ) = 0.068g Total seismic shear force in piers: V E = S e W E /g = 0.068g kN/g = 1309kN Distribution to piers M1 and M2 proportional to their stiffness: V 1 = (31.5/57.8). 1309kN = 713kN V 2 = = 596kN Seismic moments My): (full fixity of pier columns assumed at top and bottom) M y1 V 1. H 1 /2 = 713kN. 8.0m/2 = 2852kNm M y2 V 2. H 2 /2 = 596kN. 8.5m/2 = 2533kNm

22 Multimode response spectrum analysis Indian Concrete Institute Workshop on Eurocode 8 - New Delhi, September Dissemination of information for training Vienna, 4-6 October st mode (T=1.75s) (rotational MMy =3%) 2 nd mode (T=1.43s) (transverse MMy=95%) 3 rd mode (T=1.20s) (longitudinal MMx = 99%) 4 th mode (T=0.32s) (vertical MMz= 9%)

23 Comparison in longidudinal direction Indian Concrete Institute Workshop on Eurocode 8 - New Delhi, September Dissemination of information for training Vienna, 4-6 October Fundamental mode analysis Multimode response spectrum analysis Effective period T eff 1.16s 1.20s for longitudinal (3 rd mode) direction Seismic shear, V z M1 713kN 662kN M2 596kN 556kN Seismic moment, M y M1 2852kNm kNm M2 2533kNm kNm (values at top and bottom)

24 Required Longitudinal Reinforcement in Piers Indian Concrete Institute Workshop on Eurocode 8 - New Delhi, September Dissemination of information for training Vienna, 4-6 October Pier concrete C30/37, f ck =30MPa, E c =33000MPa Reinforcing steel S500, f yk =500MPa Diameter D=1.20m Cover to center of reinforcement c=8.2cm Required reinforcement in bottom section of Pier M1 Combination N M y M z A s kn knm knm cm 2 maxm y + M z minm y + M z maxm z + M y minm z + M y Final reinforcement: 25Φ32 (201.0cm 2 ) M RD = 4779kNm

25 Verification of Longitudinal Reinforcement in Piers Indian Concrete Institute Workshop on Eurocode 8 - New Delhi, September Dissemination of information for training Vienna, 4-6 October Moment Axial force interaction diagram for the bottom section of Pier M Section with 25Φ32 N (KN) M (KNm) Design combinations

26 Required Longitudinal Reinforcement in Piers Indian Concrete Institute Workshop on Eurocode 8 - New Delhi, September Dissemination of information for training Vienna, 4-6 October Pier concrete C30/37, f ck =30MPa, E c =33000MPa Reinforcing steel S500, f yk =500MPa Diameter D=1.20m Cover to center of reinforcement c=8.2cm Required reinforcement in bottom section of Pier M2 Combination N M y M z A s kn knm knm cm 2 maxm y + M z minm y + M z maxm z + M y minm z + M y Final reinforcement: 21Φ32 (168.8cm 2 ) M RD = 4366kNm

27 Verification of Longitudinal Reinforcement in Piers Indian Concrete Institute Workshop on Eurocode 8 - New Delhi, September Dissemination of information for training Vienna, 4-6 October Moment Axial force interaction diagram for the bottom section of Pier M Section with 21Φ N (KN) Design combinations M (KNm)

28 Verification of sections Indian Concrete Institute Workshop on Eurocode 8 - New Delhi, September Dissemination of information for training Vienna, 4-6 October Ductile Behaviour: Flexural resistance of plastic hinge regions with design seismic effects A Ed (only in piers). A Ed A Rd All other regions and non-ductile failure modes (shear of elements & joints and soil) are checked with capacity design effects A Cd. For non-ductile failure modes: A Cd A Rd /γ Bd γ Bd 1.25 (depending on A Cd ) Local ductility (μ Φ ) ensured by special detailing rules (confinement, restraining of compressed bars etc), i.e. without direct assessment of μ Φ.

29 Capacity Design Effects Indian Concrete Institute Workshop on Eurocode 8 - New Delhi, September Dissemination of information for training Vienna, 4-6 October A Cd Cd correspond to the section forces under permanent loads and a seismic action creating the assumed pattern of plastic hinges, where the flexural over-strength: M o = γ o M Rd has developed with: γ o = 1.35 and γ Bd =1.0 However when A Cd = qa A Cd qa qa Ed qa Ed then 1.0 γ Bd 1.25 Simplifications for A Cd satisfying the equilibrium conditions are allowed. Guidance is given in normative Annex G

30 Shear verification of piers (Capacity effects) Indian Concrete Institute Workshop on Eurocode 8 - New Delhi, September Dissemination of information for training Vienna, 4-6 October Over strength moment M o = γ o. M Rd Over strength factor γ o = 1.35 is increased due to η k = 0.22 > 0.1 according to (4) of to: γ o = [1+2. ( ) 2 ] = = 1.39, Over strength moments: M o1 = = 6643kNm M o2 = = 6069kNm o2 Longitudinal direction (seismic actions in negative direction) Capacity shear forces (over strength moments in both ends): V C1 = 2M o1 /H 1 = 2x6643/8.0 = 1661kN V C2 = 2M o2 /H 2 = 2x6069/8.5 = 1428kN

31 Shear verification of piers (Capacity effects) Indian Concrete Institute Workshop on Eurocode 8 - New Delhi, September Dissemination of information for training Vienna, 4-6 October Capacity design in transverse direction M o1 =6643kNm V C1=1476kN V C2 =1251kN M o2 =6069kNm M E1 =3061kNm V E1 =680.3kN M E2 =2184kNm V E2 =450.2kN The base shear on each pier is calculated by V Ci =(M o /M Ei ). V Ei according to simplifications of Annex G of EN Design for shear Design shear force V C1 = 1661kN and V C2 = 1428kN. γ Bd = 1.0 For circular section effective depth: d e = /π = 0.93m, Internal lever arm: z = d e = m = 0.84m V Rd,s = (A sw /s). z. f. ywd cotθ / γ Bd, cotθ = 1 Pier M1: A sw /s = 1661kN / (0.84m. 50kN/cm 2 /1.15) = 45.5cm 2 /m Pier M2: A sw /s = 1428kN / (0.84m. 50kN/cm 2 /1.15) = 39.1cm 2 /m

32 Confinement reinforcement Indian Concrete Institute Workshop on Eurocode 8 - New Delhi, September Dissemination of information for training Vienna, 4-6 October Typical arrangements Closed hoops Hoops + crossties Overlapping hoops

33 Mechanical confinement ratio ω wd Indian Concrete Institute Workshop on Eurocode 8 - New Delhi, September Dissemination of information for training Vienna, 4-6 October ω wd = ρ w f sd /f cd Geometric reinforcement ratio ρ w Rectangular Circular ρ w = A sw /(s L b) 4A sp /(s L D w ) Requirement max ω ω A f c yd w, req ληk 0,13 ( ρl Acc fcd 0,01) 2 ω ; ω ω max 14 1,4 ω ; ω wd,r w,req 3 w, min wd.c w,req Seismic Behaviour ω w,min Ductile 0,37 0,18 Limited ductile 0,28 0,12 w,min

34 Special detailing rules: Confinement reinforcement Indian Concrete Institute Workshop on Eurocode 8 - New Delhi, September Dissemination of information for training Vienna, 4-6 October Confinement reinforcement according to of EN Normalized axial force: η k = N Ed /A c. f ck = 7600kN / 1.13m 2. 30MPa = 0.22 > 0.08 Confinement of compression zone is required For ductile behaviour: λ = 037and 0.37 ω w,min = Longitudinal reinforcement ratio: - Pier M1: ρ L =201.0cm 2 /11300cm 2 = Pier M2: ρ =168.8cm 2 2 L /11300cm = Distance to spiral centerline c=5.8cm (D sp =1.084m) A cc =0.923m 2 Required mechanical reinforcement ratio ω w,req : - Pier M1: ω w,req = (A c /A cc ). λ. η k (f yd /f cd )(ρ L -0.01) = (1.13/0.923) (500/1.15)/( /1.5). ( ) 01) = Pier M2: ω w,req = 0.116

35 Confinement Reinforcement Indian Concrete Institute Workshop on Eurocode 8 - New Delhi, September Dissemination of information for training Vienna, 4-6 October For circular spirals Mechanical reinforcement ratio (for worst case: pier M1) ω wd,c = max(1.4. ω w,req ; ω w,min ) = max( ; 0.18) = 0.18 Required volumetric ratio of confining reinforcement ρ w = ω wd,c. (f cd /f yd ) = ( /1.5)/(500/1.15) = Required confining reinforcement A sp /s L = ρ w. D sp /4 = m/4 = m 2 /m = 19.0cm 2 /m Req. spacing for Φ16 spirals s L req = 2.01/19.0= 0.106m Allowed max spacing Allowed max. spacing s L allowed = min(6. 3.2cm; 108.4cm/5) = min(19.2cm; 21.7cm) = 19.2cm > 10.6cm

36 Buckling of longitudinal bars Indian Concrete Institute Workshop on Eurocode 8 - New Delhi, September Dissemination of information for training Vienna, 4-6 October Avoidance of buckling of longitudinal bars according to of EN For steel S500 the ratio f tk /f yk = 1.15 δ =2.5. (f tk /f yk ) = = Maximum required spacing of spirals s req L = δ d L = cm = 16.4cm

37 Transverse reinforcement of piers Indian Concrete Institute Workshop on Eurocode 8 - New Delhi, September Dissemination of information for training Vienna, 4-6 October Comparison of requirements for Φ16 spiral Requirement Confinement Buckling of bars Shear design A t /s L (cm 2 /m) 2x19.0=38 - M1: 45.5 M2: 39.1 maxs L (cm) The transverse reinforcement is governed by the shear design. Reinforcement selected for both piers is one spiral of Φ16/8.5 (47.3cm 2 /m)

38 Calculation of capacity effects Indian Concrete Institute Workshop on Eurocode 8 - New Delhi, September Dissemination of information for training Vienna, 4-6 October General procedure: combination G + Mo-G (acc. to G1 of Annex G of EN ) Alternative: G + Mo on continuous deck articulated to piers Permanent Load G G G M G1 M G2 + M G1 (1) (2) M G2 M G1 M G2 ΔAc: Over strength G M O1 -M G1 M O2 -M G2 M O1 M O2 M G1 M G2 M O1 -M G1 M O2 -M G2 M O1 M O2 - M G1 M G2 M O1 -M G1 M O2 -M G2 M O1 M O2 M G1 M G2 general procedure alternative procedure

39 Calculation of capacity effects Indian Concrete Institute Workshop on Eurocode 8 - New Delhi, September Dissemination of information for training Vienna, 4-6 October G loading Overstrength M o (+x direction) G M o1 =6643kNm M o2 =6069kNm Capacity effects G + M o (+x direction) M (knm) M (knm) M (knm) V (kn) (+) V (kn) (-) (-) V (kn) (+) (-) 4311 (+) 1661 (+) 1428 (+) 1661 (+) 1428 alternative procedure is applied Reversed signs for x direction

40 Verification of deck section for capacity effects Indian Concrete Institute Workshop on Eurocode 8 - New Delhi, September Dissemination of information for training Vienna, 4-6 October Deck section, reinforcement and tendons Top layer: 46Φ Φ16 (210.8cm 2 ) 4 groups of 3 tendons of type DYWIDAG 6815 (area of 2250mm 2 each) Bottom layer: 2x33Φ16 (182.9cm 2 ) Combination / location M y (knm) N (kn) Pier M1 left side (+x) Pier M1 right side (+x) Pier M2 left side (+x) Pier M2 right side (+x) Pier M1 left side (-x) Pier M1 right side (-x) Pier M2 left side (-x) Pier M2 right side (-x) Moment Axial force interaction diagram for deck section N (KN) Design combinations M (KNm)

41 Capacity effects on pier foundation Indian Concrete Institute Workshop on Eurocode 8 - New Delhi, September Dissemination of information for training Vienna, 4-6 October Longitudinal direction (pier M1 foundation for +x direction) N=7371kN V z =1661kN M y =6643kNm Y X Transverse direction (pier M1 foundation for +/- direction) V y =1476kN M z =6643kNm N=7371kN V z =730kN M y =124kNm M y

42 Displacements in linear analysis Indian Concrete Institute Workshop on Eurocode 8 - New Delhi, September Dissemination of information for training Vienna, 4-6 October Control of Displacements Assessment of seismic i displacement d E d E = d d Ee. d Ee = result of elastic analysis. = damping correction factor for ξ η 0.05 ξ d = displacement ductility as follows: when T T 0 =1.25T C : d = q when T<T 0 : d = (q-1)t 0 /T+ 1 5q - 4

43 Displacements in linear analysis Indian Concrete Institute Workshop on Eurocode 8 - New Delhi, September Dissemination of information for training Vienna, 4-6 October Provision of adequate structure clearance for the total seismic design displacements: d Ed = d E + d G + ψ 2 d T with ψ 2 = 0.5 d G due to permanent and quasi-permanent actions G (mainly shrinkage + creep). d T due to thermal actions. Roadway joint displacements: d Ed = 0.4d E + d G + ψ 2 d T

44 Roadway joints over abutments Indian Concrete Institute Workshop on Eurocode 8 - New Delhi, September Dissemination of information for training Vienna, 4-6 October Roadway joint: d Ed,J = 0.4d E + d G + ψ 2 d T, where ψ 2 = 0.5 Structure clearance: d Ed = d E + d G + ψ 2 d T Displacements (mm) d G Shrinkage +Creep d T Temper. variation d E Earth quake d Ed,J Roadway joint d Ed clearance Longit opening +18,7 +10,7 +76,0 +54,5 +100,7 udinal closure 0-8,5-76,0-34,7-80,3 Transverse ,99 44,00 109,99 Roadway yjoint type: T120 Capacity in longitudinal direction: 60mm Capacity in transverse direction: 50mm

45 Roadway joints over abutments Indian Concrete Institute Workshop on Eurocode 8 - New Delhi, September Dissemination of information for training Vienna, 4-6 October Detailing of back-wall for predictable (controlled) damage. ( (5), EN )) Clearance of roadway joint Approach slab Structure clearance

46 Minimum overlapping length Indian Concrete Institute Workshop on Eurocode 8 - New Delhi, September Dissemination of information for training Vienna, 4-6 October Minimum overlapping (seating) length at moveable joint (according to of EN ) l m = 0.50m > 0.40m d m/s g = a g S T C T D = m/s s 2.50s = 0.068m 068m L g = 400m (Ground type C) L eff = 82.50/2 = 41.25m No proximity to fault Consequently d eg = (2. d g /L g )L eff = ( /400) = 0.014m < 2d g d es = 0.101m (deck effective seismic displacement) l ov l ov = l m + d eg + d es = = = 0.615m Available seating length: 1.25m > l ov

47 Conclusions for design concept Indian Concrete Institute Workshop on Eurocode 8 - New Delhi, September Dissemination of information for training Vienna, 4-6 October Optimal cost effectiveness of a ductile system is achieved when all ductile elements (piers) have dimensions that lead to a seismic demand that is critical for the main reinforcement of all critical sections and exceeds the minimum i (e.g:ρ min = 1%) This is difficult to achieve when the piers resisting the earthquake: - have substantial height differences, or - have section larger than required. In such cases it may be economical to use: - limited ductile behaviour for low a gr values - flexible connection to the deck (seismic isolation)

48 2 Example of limited ductile piers Indian Concrete Institute Workshop on Eurocode 8 - New Delhi, September Dissemination of information for training Vienna, 4-6 October Seismic design of the general example: Bridge on high piers designed for limited ductile behaviour Bridge description Composite steel & concrete c deck Three spans: 60m+80m+60m Pier dimensions: Height 40 m, External/internal diameter 4.0 m/3.2 m Pier head: 4.0 m width x 1.5 m height

49 Bridge elevation and arrangement of bearings Indian Concrete Institute Workshop on Eurocode 8 - New Delhi, September Dissemination of information for training Vienna, 4-6 October Articulated connection Articulated connection Sliding Longitudinal, Articulated Transverse Y C0R P1R P2R C3R X C0L P1L P2L C3L

50 Example of limited ductile piers Indian Concrete Institute Workshop on Eurocode 8 - New Delhi, September Dissemination of information for training Vienna, 4-6 October Design Concept Due to the high pier flexibility: Hinged connection of the deck to both piers both piers resist earthquake without excessive restraints High fundamental period Low spectral acceleration No need of high ductility or seismic isolation q = 1.5 (limited ductility)

51 Design seismic action Indian Concrete Institute Workshop on Eurocode 8 - New Delhi, September Dissemination of information for training Vienna, 4-6 October Soil type B Importance factor γ I = 1.00 Reference peak ground acceleration: a Gr = g Soil factor: S = 1.20, a Gr S = 0.36g Limited elastic behaviour is selected q = 1.50 Lower spectral boundary β = 0.2

52 Design seismic spectrum Indian Concrete Institute Workshop on Eurocode 8 - New Delhi, September 2009 ction 52 Dissemination of information for training Vienna, 4-6 October Ag=0.3, Ground Type: B Soil Factor: 1.2 T b =0.15sec, T c =0.5sec, 05sec T d =2.0sec, 20sec β= Acc celeration (g) Period (sec)

53 Seismic analysis Indian Concrete Institute Workshop on Eurocode 8 - New Delhi, September Dissemination of information for training Vienna, 4-6 October Quasi permanent traffic load for the seismic design situation (4.1.2 (4): For bridges with severe traffic ψ 21 2,1 Q k1 k,1 with ψ 21 2,1 = 0.20 Q k1 is the characteristic load of UDL system of k,1 y Model 1.For the 4 lanes of the deck: 3 m x m x m x m x 2.5 Q k,1 = 47.0 kn/m ψ 2,1 Q k,1 = 9.4 kn/m

54 Seismic analysis Indian Concrete Institute Workshop on Eurocode 8 - New Delhi, September Dissemination of information for training Vienna, 4-6 October Structural Model Z Y X

55 Seismic analysis Indian Concrete Institute Workshop on Eurocode 8 - New Delhi, September Dissemination of information for training Vienna, 4-6 October A beam finite element model of the bridge is used with program SAP Each composite steel concrete beam and cross beam is modeled as a beam element. The effective width of the main beams is assumed equal to the total geometric width. The bending stiffness about the vertical axis of the two main beam sections is modified so that the sum of the stiffnesses is equal to the relevant stiffness of the entire composite deck.

56 Seismic analysis Indian Concrete Institute Workshop on Eurocode 8 - New Delhi, September Dissemination of information for training Vienna, 4-6 October Effective Pier Stiffness (1) of EN defines the stiffness of the ductile elements (piers) to correspond to the secant stiffness at the theoretical yield point. This value depends on the axial force and on the final reinforcement of the element. It is estimated from the moment-curvature and dthe moment Jeff/Jgross ratio curves of the piers for the estimated final reinforcement ρ = 1.5% and the seismic axial force, as Jeff/Jgross 0.30

57 Seismic analysis Indian Concrete Institute Workshop on Eurocode 8 - New Delhi, September Dissemination of information for training Vienna, 4-6 October Moment (k knm) Bottom Section Top Section ρ=1.5% N= 15000kN N= 20000kN 0.00E E E E E E E 03 Curvature Moment-Curvature M-Φ curve of Pier Section for ρ = 1.5%

58 Seismic analysis Indian Concrete Institute Workshop on Eurocode 8 - New Delhi, September Dissemination of information for training Vienna, 4-6 October Nm) Moment (k Bottom Section Top Section N= 15000kN N= 20000kN ρ=1.5% J/Jgross Moment (ΕΙ) eff /(EI) Curve of Pier Section for ρ = 15% 1.5% (ΕΙ) eff /(EI) = (M/Φ)/(ΕΙ)

59 Seismic analysis Indian Concrete Institute Workshop on Eurocode 8 - New Delhi, September Dissemination of information for training Vienna, 4-6 October Eigenmodes Response Sectrum Analysis The first 30 eigenmodes of the structure were calculated and considered in the response spectrum analysis. The sum of modal masses of these modes amounts to: 97.1% in the X and 97.2% in the Y direction respectively. Combination of modal responses was carried out using the CQC rule. Following table shows the characteristics of the first 10 eigenmodes.

60 Seismic analysis Indian Concrete Institute Workshop on Eurocode 8 - New Delhi, September Dissemination of information for training Vienna, 4-6 October No First 10 eigenmodes Period Modal Mass % Sec X Y Z % 0.0% 0.0% % 76.8% 0.0% % 0.0% 0.0% % 0.0% 00% 0.0% 12% 1.2% % 0.5% 0.0% % 8.4% 0.0% % 0.0% 0.0% % 0.0% 0.0% % 0.0% 21% 2.1% 00% 0.0% % 0.0% 0.0%

61 Seismic analysis Indian Concrete Institute Workshop on Eurocode 8 - New Delhi, September Dissemination of information for training Vienna, 4-6 October st Mode - Longitudinal Period 5.02 sec c (Mass Participation Factor Ux:93%)

62 Seismic analysis Indian Concrete Institute Workshop on Eurocode 8 - New Delhi, September Dissemination of information for training Vienna, 4-6 October nd Mode -Traqnsverse Period 3.84 sec (Mass Participation Factor Uy:77%)

63 Seismic analysis Indian Concrete Institute Workshop on Eurocode 8 - New Delhi, September Dissemination of information for training Vienna, 4-6 October rd Mode - Rotation Period 1.49 sec

64 Seismic analysis Indian Concrete Institute Workshop on Eurocode 8 - New Delhi, September Dissemination of information for training Vienna, 4-6 October th Mode - Vertical Period 0.42sec (Mass Participation Factor Uz:63%)

65 Seismic analysis Indian Concrete Institute Workshop on Eurocode 8 - New Delhi, September Dissemination of information for training Vienna, 4-6 October Max bending moment distribution along pier P1

66 2 nd order effects for the seismic analysis Indian Concrete Institute Workshop on Eurocode 8 - New Delhi, September Dissemination of information for training Vienna, 4-6 October Geometric Imperfections of Piers According to 5.2 of EN :2005: i l l0 ei i 2 3 Imperfection Eccentricities Direction l 0 (m) e i (m) X Y

67 2 nd order effects for the seismic analysis Indian Concrete Institute Workshop on Eurocode 8 - New Delhi, September Dissemination of information for training Vienna, 4-6 October The first and second order effect of imperfection eccentricities e i,ii including creep for φ = 2.0 ll 1 e imp, e imp(1 ) v 1 where v=n B /N Ed N B : buckling load according to 5.8 of EN Direction e i ν = Ν Β /Ν ED e i,ii /e i e i,ii x y

68 2 nd order effects for the seismic analysis Indian Concrete Institute Workshop on Eurocode 8 - New Delhi, September Dissemination of information for training Vienna, 4-6 October Second order effects due to seismic first order effects Two alternative approaches: 1. To 5.8 of EN (nominal stiffness method) Use of nominal stiffness method (5.8.7) for (EI) eff = 0.30 (EI) Moment magnification factor: MF = 1+[β/((N B /N Ed )-1)] N 2 2 B = π (EI) eff /(β 1 L 0 ) β 1 =1 Longitudinal direction MF = Transversal direction MF = 1.034

69 2 nd order effects for the seismic analysis Indian Concrete Institute Workshop on Eurocode 8 - New Delhi, September Dissemination of information for training Vienna, 4-6 October nd order effects due to seismic 1st order effects 2. To 5.4 of EN (followed in the example) Increase of bending moments at the plastic hinge section ΔM = 05(1 0.5 (1+q)d Ed N Ed d Ed : seismic displacement of pier top 2 nd Order Effects on Pier Base Moments icombination EN EN Ex+0.3Εy+2 nd Ord My Ey+0.3Εx+2 nd Ord Mx The Eff. Stiffness method of EN may be unsafe for 1.5 < q 3.5

70 Verification of piers Indian Concrete Institute Workshop on Eurocode 8 - New Delhi, September Dissemination of information for training Vienna, 4-6 October Flexure and axial force for pier base section Design action effects: N Ed = kn M Ey = knm M Ex = 9833 knm A s,req = 678 cm 2 External perimeter 62Φ28 (381 cm 2 ) Internal perimeter 49Φ28 (301 cm 2 ) ρ 1.5% See design interaction diagram next page

71 Verification of piers Indian Concrete Institute Workshop on Eurocode 8 - New Delhi, September Dissemination of information for training Vienna, 4-6 October ρ=1.5% ρ=1.0% N) Axial Force (k Moment (knm) Design Interaction Diagram of Pier Base Section

72 Verification of piers Indian Concrete Institute Workshop on Eurocode 8 - New Delhi, September Dissemination of information for training Vienna, 4-6 October Shear verification Design shear: V x,d = 1887 V y,d = Vd Vx, d Vy, d 1908kN 1/3 V [ C k (100 f ) k ] b d Rd, c Rd, c l ck 1 cp w CRd, c 0.12 c rs 21.8 de r (EN1998-2:2005, (2)) N Ed 332 k k cp 3.32 A 4.52 d 3150 c V 2670kN Rd,c vrd, c kN V No shear reinforcement required Bd d

73 Verification of piers Indian Concrete Institute Workshop on Eurocode 8 - New Delhi, September Dissemination of information for training Vienna, 4-6 October Ductility requirements Confining reinforcement To of EN for limited ductile max(1.4 ;0.12) max( ;0.12) 0.12 wd, c w, req A f c yd wreq, 0.28k 0.13 ( l 0.01) Acc fcd ( ) w fcd w f yd w D A cc sp A s l sp 16 / 11 No buckling of reinforcement s L < 5d bl = 14 cm

74 3 Example of seismic isolation Indian Concrete Institute Workshop on Eurocode 8 - New Delhi, September Dissemination of information for training Vienna, 4-6 October Bridge Elevation: Typical deck cross-section: section: Layout based on general example bridge Three spans (60m+80m+60m) Composite steel & concrete deck

75 Pier Layout Indian Concrete Institute Workshop on Eurocode 8 - New Delhi, September Dissemination of information for training Vienna, 4-6 October Longitudinal section: Transverse section: Section A-A: Section B-B: B Section C-C: Short piers h=10m Short piers h=10m Rectangular cross-section 5.0m x 2.5m Enlarged pier head 9.0m x 2.5m to support bearings

76 Bridges with Seismic Isolation Indian Concrete Institute Workshop on Eurocode 8 - New Delhi, September Dissemination of information for training Vienna, 4-6 October Effect of period shift from T in to T eff a d Period schift a d dag a2 Tπ 2 Displacement spectrum Acceleration spectrum T in T C T eff T D

77 Bridges with Seismic Isolation Indian Concrete Institute Workshop on Eurocode 8 - New Delhi, September Dissemination of information for training Vienna, 4-6 October Effect of increasing damping (ξ eff ) d ξ in =0.05 ξ in ξ eff Increasing ξ in to ξ eff reduces displacements but not necessarily forces d η ξeff d 0,05 T eff η 0,10 0,05 ξ eff 0,4

78 Layout of Seismic Isolation Indian Concrete Institute Workshop on Eurocode 8 - New Delhi, September Dissemination of information for training Vienna, 4-6 October Plan: Y C0_ L P1_ L P2_ L C3_ L X C0_R P1_R P2_R C3_R 8 bearings of type Triple Friction Pendulum System (Triple FPS) 2 bearings at each abutment 0.9m x 0.9m x 0.4m 2 bearings at each pier 1.2m x 1.2m x 0.4m Allow displacements in all horizontal directions with non-linear frictional force-displacement law

79 Triple FPS bearings Indian Concrete Institute Workshop on Eurocode 8 - New Delhi, September Dissemination of information for training Vienna, 4-6 October Photo of Triple Pendulum TM Bearing Schematic Cross Section Concaves and Slider Assembly Concaves and Slider Components

80 Triple FPS bearings Indian Concrete Institute Workshop on Eurocode 8 - New Delhi, September Dissemination of information for training Vienna, 4-6 October Section: h 4 Stainless steel concave sliding surfaces & articulated slider Special low-friction sliding material low horizontal stiffness (increased flexibility) high vertical stiffness and load bearing capacity Protective seal Plan:

81 Triple FPS Force-Displ. relation Indian Concrete Institute Workshop on Eurocode 8 - New Delhi, September Dissemination of information for training Vienna, 4-6 October (b) (c) (a) Adaptive behaviour (a) minor events: high stiffness, improved recentering (b) design earthquake: softening, intermediate damping (c) extreme events: stiffening, increased damping

82 General Loads Indian Concrete Institute Workshop on Eurocode 8 - New Delhi, September Dissemination of information for training Vienna, 4-6 October Permanent loads: (from general example) Total support Self weight Minimum Maximum Time Total with Total with variation loads in after equipment equipment minimum maximum due to creep MN (both construction load load equipment equipment & shrinkage beams) C P P C Sum of reactions % of quasi-permanent traffic load: Lane Number 1: Lane Number 2: Lane Number 3: Residual area: α q q 1,k = 3 m x 9 kn/m 2 = 27.0 kn/m α q q 2,k =3 m x 2.5 kn/m 2 = 7.5 kn/m α q q 3,k =3 m x 2.5 kn/m 2 = 7.5 kn/m α q q r,k =2 m x 2.5 kn/m 2 = 5.0 kn/m Total load = 47.0 kn/m 3. 50% of thermal action: +25 o C / -35 o C

83 Seismic Action Design Spectra Indian Concrete Institute Workshop on Eurocode 8 - New Delhi, September Dissemination of information for training Vienna, 4-6 October S e (T) (g) a g S β 0 a g Sη Constant velocity branch (1/T) β 0 a g Sη(T C /T) Constant displacement branch (1/T 2 ) β 2 0 a g Sη(T C T D /T ) T B T C T D T(s) Elastic response spectrum EN , EN and Average importance: γ Ι =1.00 High Seismicity Zone: a gr =0.40g a g =a gr x γ I =0.40g Ground Type B: S=1.20, T B =0.15s, T C =0.5s, T D =2.5s Horizontal spectrum: spectral amplification β 0 =2.5 Vertical spectrum: β 0 =3.0, S=1.00, a vg =0.9a g, T B =0.05s, T C =0.15s, T D =1.0s

84 Seismic Action Ground Motions Indian Concrete Institute Workshop on Eurocode 8 - New Delhi, September Dissemination of information for training Vienna, 4-6 October Ground Motions: 2 horizontal & 1 vertical components Semi-artificial accelerograms from modified records Consistency with design spectrum: EN , 3.2.3(6): ion (g) Spec ctral accelerati Average SRSS spectrum of ensemble of earthquakes 1.3 x Elastic spectrum Damping 5% Period (sec)

85 Triple FPS - Equivalent bilinear model Indian Concrete Institute Workshop on Eurocode 8 - New Delhi, September Dissemination of information for training Vienna, 4-6 October F F 0 =0.061W d: F = W x [ (F o /W) + d / R ] EN1998-2, (2) 5(2) μ d =F o /W = effective friction coefficient = ± 16% R = effective pendulum length = 1.83m D y =effective yield displacement = 0.005m005 F = shear force d = displacement

86 Design properties of isolators Indian Concrete Institute Workshop on Eurocode 8 - New Delhi, September Dissemination of information for training Vienna, 4-6 October Design properties of the isolating system Nominal design properties p (NDP) assessed by prototype tests, confirming the range accepted by the Designer. Variation of design properties due to external factors (aging, temperature, contamination, cummulative travel/wear) Design is required for: Upper Bound design properties (UBDP). Lower Bound design properties (LBDP). Bounds of Design Properties result either from tests or from modification λ-factors (Annexes J & JJ).

87 Isolator design properties Indian Concrete Institute Workshop on Eurocode 8 - New Delhi, September Dissemination of information for training Vienna, 4-6 October Effective pendulum length: R=1.83m Yield displacement: D y =0.2 =0.005m Force at zero displacement F 0 /W: Upper bound design properties (UBDP) and Lower bound design properties (LBDP) in accordance with EN , Nominal value range: F 0 /W = ± 16% = ~ LBDP: (F 0 /W) min = mindp nom = UBDP: According to EN Annexes J and JJ Minimum isolator temperature for seismic design: T min,b =ψ 2 T min +ΔΤ 1 = 0.5 x (-20 o C) o C = -5.0 o C where ψ 2 =0.5 is the combination factor for thermal actions, T min =-20 o C the minimum shade air temperature at the site, ΔΤ 1 =+5.0 o C for composite deck. λ max factors: max f1 - ageing: λ max,f1 =1.1 (Table JJ.1, for normal environment, unlubricated PTFE, protective seal)

88 Isolator design properties Indian Concrete Institute Workshop on Eurocode 8 - New Delhi, September Dissemination of information for training Vienna, 4-6 October f2 - temperature: λ max,f2 =1.15(TableJJ.2forT min,b =-10.0 o C, unlubricated PTFE) f3 - contamination λ max,f3 =1.1 (Table JJ.3 for unlubricated PTFE and sliding surface facing both upwards and downwards) f4 cumulative travel λ max,f4 =1.0 (Table JJ.4 for unlubricated PTFE and cumulative travel 1.0 km) Combination factor ψ fi : ψ fi =0.70 for Importance class II (Table J.2) Combination value of λ max factors: λ U,fi =1+(λ max,fi -1)ψ fi (J.5) f1 - ageing: λ U,f1 = 1 + ( 1.1-1) x 0.7 = 1.07 f2 - temperature: λ U,f2 = 1 + ( ) x 0.7 = f3 - contamination λ U,f3 = 1 + (1.1 1) x 0.7 = 1.07 f4 cumulative travel λ U,f4 = 1 + (1.0 1) x 0.7 = 1.0 Effective UBDP: UBDP = maxdp nom λ U,f1 λ U,f2 λ U,f3 λ U,f4 (J.4) (F 0 /W) max = x 1.07 x x 1.07 x 1.0 = 0.09

89 Fundamental mode spectrum analysis Indian Concrete Institute Workshop on Eurocode 8 - New Delhi, September Dissemination of information for training Vienna, 4-6 October Estimation of d max = d cd from dynamic equilibrium Assume d cd,a From static ti F-d relation : F max F max K eff = F max /d cd,a Effective period and damping M D,i Teff 2π ξ eff 2 K eff 2π K effd cd Displacement spectrum 1 ΣE 2 d 005 0,05 a005 0,05 ) d ξeff η d 0,05 η ( T 2 π 0,10 0,05 ξ eff 0,4 d cd,a K eff ξ =0.05 ξ = ξ eff d cd,r Iterations for d cd,r = d ξeff = d cd,a T C T eff T D

90 Fundamental Mode analysis (LBDP) Indian Concrete Institute Workshop on Eurocode 8 - New Delhi, September Dissemination of information for training Vienna, 4-6 October Fundamental mode analysis (EN1998-2, 7.5.4) Seismic weight: W= 36751kN (see loads) Assume value for design displacement: Assume d cd =0.15m Effective Stiffness of Isolation System (ignore piers): K eff =F/d cd =Wx[(F 0 /W) + d cd /R]/d cd = 36751kN x [ m/1.83m] / 0.15m = K eff = kn/m Effective period of Isolation System: eq. (7.6) T eff 2π m K K eff 2π (36751kN/9.81m/s 32578kN/m 2 ) 2.13s Dissipated energy per cycle: EN1998-2, (4) E D =4xWx(F 0 /W) x (d cd -D y ) = 4 x 36751kN x (0.051) x (0.15m-0.005m) E D = knm

91 Fundamental Mode analysis (LBDP) Indian Concrete Institute Workshop on Eurocode 8 - New Delhi, September Dissemination of information for training Vienna, 4-6 October Effective damping: eq. (7.5), (7.9) ξ eff = ΣE D,i /[2xπxK eff xd cd2 ] = kNm / [2 x π x 32578kN/m x (0.15m) 2 ] = η eff = [0.10 / ( ξ eff )] 0.5 = Calculate design displacement d cd (EN Table 7.1) d cd =(0.625/π 2 )xa g xsxη eff xt eff xt C = (0.625/π 2 ) x (0.40 x 9.81m/s 2 ) x 1.20 x x 2.13s x 0.50s = 0.188m Check assumed displacement Assumed displacement 0.15m Calculated displacement 0.188m Do another iterationti

92 Fundamental Mode analysis (LBDP) Indian Concrete Institute Workshop on Eurocode 8 - New Delhi, September Dissemination of information for training Vienna, 4-6 October Assume value for design displacement: Assume d cd =0.22m Effective Stiffness of Isolation System (ignore piers): K eff =F/d cd =Wx[(F 0 /W) + d cd /R]/d cd = 36751kN x [ m/1.83m] / 0.22m = K eff = kn/m Effective period of Isolation System: eq. (7.6) T m K (36751kN / 9.81m / s 28602kN / m eff eff Dissipated energy per cycle: EN1998-2, (4) 5(4) E D =4xWx(F 0 /W) x (d cd -D y )= 4 x 36751kN x (0.051) x (0.22m-0.005m) E D = knm ) s

93 Fundamental Mode analysis (LBDP) Indian Concrete Institute Workshop on Eurocode 8 - New Delhi, September Dissemination of information for training Vienna, 4-6 October Effective damping: eq. (7.5), (7.9) ξ eff = ΣE D,i /[2xπxK eff xd cd2 ] = kNm / [2 x π x 28602kN/m x (0.22m) 2 ] = η eff = [0.10 / ( ξ eff )] 0.5 = Calculate design displ. d cd (EN Table 7.1) d cd =(0.625/π 2 ) x a g x S x η eff x T eff x T C = (0.625/π 2 ) x (0.40 x 9.81m/s 2 ) x 1.20 x x 2.27s x 0.5s = 0.22m Check assumed displacement Assumed displacement 0.22m Calculated displacement 0.22m Convergence achieved Spectral acceleration S e (EN Table 7.1) S e =2.5x(T C /T eff )x η eff xa g x S = 2.5 x (0.5s/2.27s) x x 0.40g x 1.20 = 0.172g Isolation system shear force (EN eq. 7.10) V d =K eff xd cd = kn/m x 0.22m = 6292kN

94 Fundamental Mode analysis (UBDP) Indian Concrete Institute Workshop on Eurocode 8 - New Delhi, September Dissemination of information for training Vienna, 4-6 October Fundamental mode analysis: Summary of results Seismic weight: W= 36751kN (see loads) Design displacement d cd =0.14m Effective stiffness K eff = kn/m Effective period T eff = 1.84s Dissipated energy per cycle E D = knm Effective damping ξ eff = 0.331, η eff = Spectral acceleration S e= 0.166g Isolation system shear force V d = 6096kN Pier shear forces for averaged vertical load Abutments C0, C3: V d = 570kN Piers P1, P2: V d = 2480kN

95 Comparison with non-isolated bridge Indian Concrete Institute Workshop on Eurocode 8 - New Delhi, September Dissemination of information for training Vienna, 4-6 October Non-isolated bridge with fixed bearings at pier top Period: longitudinal T x = 0.33s, transverse T y = 0.17s Behaviour factor q (EN1998-2, Table 4.1): q=3.5xλ(α s ), where α s =L s /h the shear ratio Long. q x =3.5x1.0=3.5, Transverse: q y =3.5x0.82= 2.87 Spectral acceleration in constant acceleration branch of spectrum S e =2.5Sa g /q Longitudinal: S e = 2.5x1.2x0.40g/3.5 = 0.34gV=12495kN Transverse: S e = 2.5x1.2x0.40g/2.87 = 0.42gV=15435kN Isolated bridge with UBDP Spectral acceleration S e = 0.166g V= 6096kN Reduction of forces with respect to non-isolated: - at 49% in longitudinal direction - at 40% in transverse direction