Conventional Design Approach Structures : To resist earthquake through strength, ductility & energy absorption Excitations : Inelastic deformation of

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1 Earthquake Response of Seismically Isolated Bridges Suhasini Madhekar College of Engineering Pune Faculty Development Program on Fundamentals of Structural Dynamics and Application to 7 th Earthquake Engineering th to 12 th December 2015 Sanjay Ghodawat Group of Institutions Atigre, Kolhapur 1

2 Conventional Design Approach Structures : To resist earthquake through strength, ductility & energy absorption Excitations : Inelastic deformation of a structure by formation of plastic hinges Emphasis on increasing strength of structure to resist earthquake induced forces. Allow damages.. prevent collapse. Design forces considered << actual Earthquake forces. Δdesign << Δ actual. Permanent deformations through yielding 2

3 Bridges 0.2 T 1.2 sec.-close to the predominant periods of earthquake induced ground accelerations : Response (displacements, accelerations) is high. Uneconomical to design bridges to resist earthquake induced forces elastically. Bridge piers - Potential yielding allowed : consideration to stability of the bridge. Bridges: Extremely vulnerable to damage Relatively large deck mass supported by slender piers - Large displacements - large shear forces in the piers Effort of protection of bridges against earthquakes : Focus on minimising shear forces transmitted to piers. 3

4 Need of the Present Study.. CONVENTIONAL DUCTILITY DESIGN CONCEPT -not the best solution, as bridges have little or no redundancy. ULTIMATE DESIGN CONCEPT does not work as piers are found to fail in shear rather than flexure. STRENGTH increment increases cost. SEISMIC ISOLATION is the promising alternative -More emphasis on reducing earthquake forces Replacement of conventional bearings by isolation bearings. Control of structural vibrations.. By modifying stiffness, mass, damping or shape By providing passive or active counter forces. 4

5 Seismic Isolation : Reduce Input Earthquake energy with soft bearings. Suppress excessive displacement by Damping. Lengthens T of the structure-introduces flexibility in the horizontal plane» Increased displacement Control of vibrations through specially designed interface Introduce damping elements to control the excessive displacements Increases energy dissipation capability. Substructure and superstructure can be designed elastically. No permanent set. 5

6 Seismic Isolation: Bridges Replacing conventional bearings by special base isolation bearings. Deck Abutment Isolation system or bearings Rock line Pier 6

7 Modeling of Base isolated Bridges Mathematical formulation of geometry and behaviour characteristics of the prototype bridge structure. Discrete mathematical elements and their connections and interactions describe the prototype behaviour. Most bridge analysis models are displacement based. Design such that first few modes of vibrations are not Torsional / Breathing modes. 7

8 Lumped-Parameter Models Types of Models.. Bridge characteristics (m, k,ξ) are lumped at discrete locations Simple in their mathematical formulation. Require significant knowledge and experience to formulate equivalent force- deformation relationships Structural Component Models Based on idealized structural subsystems that are connected to resemble the geometry of the bridge prototype Response characterization is provided in the form of member end force- deformation relationships for each structural component Finite-Element Models Discretize the geometric domain of the bridge structure with a large number of small elements. 8

9 Assumptions in Modeling Bridge superstructure and piers assumed to remain in the elastic state during the earthquake excitation. The bridge deck is straight : supported by isolation systems. Both superstructure and substructure are modeled as lumped mass systems -Divided into number of small discrete segments. Segments connected by nodes. Two-DOFs Piers-Rigidly fixed at the foundation level-on firm soil or rock Stiffness contribution of non-structural elements neglected. Structure subjected to only horizontal ground motion. 9

10 Modeling of Bridges Model type l 1 y 1 x 1 2 i y i x i Abutment Isolation System Abutment Pier y N x N 10

11 Model type ll Deck Mass y 1 x 1 Same assumptions as model l-deck acts as a rigid mass. Deck displaces only in the Isolation S ystem direction of loading. y N x N Same eqns.of motion under two components of earthquake ground motion. 11

12 Model Type lll y 1 SDOF model. Deck mass Isolation system x 1 Both-Deck and pier are assumed as rigid body. Equations of motion under two horizontal components of earthquake ground motion are same those for SDOF system in two directions. 12

13 ISOLATION OF BRIDGES Bridges come under the category of lifeline structures. Disruption in the transportation network due to partial or total collapse of bridges after a major earthquake would seriously hamper the relief and rehabilitation operations. The traditional method of providing earthquake- The traditional method of providing earthquakeresistance in a structure is by increasing the strength as well as energy absorbing capacity (ductility) of the structural members. The development of ductility implies some damage, therefore, the current design method can be called failsafe approach, which would prevent collapse but not damage. 13

14 The following assumptions are made for the dynamic analysis of isolated bridge system under consideration: Bridge superstructure and piers are assumed to remain in the elastic state during the earthquake excitation. This is a reasonable assumption as the isolation attempts to reduce the earthquake forces in such a way that the structure remains within the elastic range. Force-deformation behaviour of the elastomeric bearings is considered to be linear. However, a comparison of the response of bridge with the linear and non-linear models is carried out separately. Piers of the bridge are fixed at the foundation level and effects of soil-structure interaction are ignored. The abutments of the bridge are assumed as rigid. 14

15 The bridge is founded on firm soil or rock and the earthquake excitation is perfectly correlated at all supports. The elastomeric isolation system is isotropic implying that it has the same properties in two orthogonal directions. In addition, the bearings provided at the piers and abutments have the same dynamic characteristics. The system is subjected to earthquake ground motion in two horizontal directions (referred as longitudinal and transverse direction of the bridge). The bridge deck and piers are modelled as a lumped mass system assumed to be divided into number of small discrete elements. At each node two horizontal dynamic degrees-offreedom (DOF) are considered as shown in Figure 8.1(b). 15

16 The stiffness of the elastomeric bearings is obtained by the following expression where m d is the mass of the bridge deck; Σk b is the sum of the horizontal stiffness of all the bearings provided for bridge isolation; and T b is the isolation time period of the bearings. The total viscous damping of the elastomeric bearings is expressed as T b = 2π cb = 2 where Σc b is total viscous damping of all the bearings; ξb is the damping ratio of the elastomeric bearings; and ωb = 2π/Tb is the isolation frequency of the bearings. 16 m ξ b d k b m d ω b

17 GOVERNING EQUATIONS OF MOTION The equations of motion are expressed as: [ M ]{& z } + [ C]{ z& } + [ K ]{ z} = [ M ]{ r}{ & z g } { } = { x1, x2,..., xn, y1, y2,..., y n z } T && xg {& z& g } = && y g where [M], [K] and [C] represents the mass, stiffness and damping matrices, respectively of the isolated bridge system; {z&} &, {z& } and {z} represent the structural acceleration, structural velocity and structural displacement vectors, respectively; {r} is the influence coefficient matrix. Solve equations by step-step-by method. 17

18 Dynamic Response of Pedestrian Bridges : Floor Vibration 18

19 Millennium Bridge, London 19

20 Case Study: Millennium Bridge Crosses River Thames, London, England 474 main span, 266 north span, 350 south span Superstructure supported by lateral supporting cables (7 sag) Bridge opened June 2000, closed 2 days later 20

21 Millennium Bridge Severe lateral resonance was noted (0.25g) Predominantly noted during 1 st mode of south span (0.8 Hz) and 1 st and 2 nd modes of main span (0.5 Hz and 0.9 Hz) Occurred only when heavily congested Phenomenon called Synchronous Lateral Excitation 21

22 Millennium Bridge Possible solutions Stiffen the bridge Too costly Affected aesthetic vision of the bridge Limit pedestrian traffic Not feasible Active damping Complicated Costly Unproven Passive damping 22

23 Passive Dampers 37 viscous dampers installed 19 TMDs installed Millennium Bridge 23

24 Millennium Bridge Results Provided 20% critical damping. Bridge was reopened February, Extensive research leads to eventual updating of design code. 24

25 Thank you.. 25