Reduction of inertial seismic forces in bridges by using ...€¦ · backwall. According to the Eurocode 8 - Part 2 [3], based on technical and economical criteria, checking of expansion

Reduction of inertial seismic forces in bridges by using the abutment backwall as a “yielding” stopper

S. Mitoulis & J. Tegos Department of Civil Engineering, Aristotle University of Thessaloniki, Greece

Abstract

The reduction of inertial seismic forces in long bridges, whose decks are mainly supported on piers through bearings, is a major challenge, given the fact that codes require seismic design of these systems using a behaviour factor q equal to 1. The objective of this paper is the investigation of the feasibility of reducing inertial forces through the development of appropriately configured and reinforced abutment backwalls, which play the role of “yielding” stoppers for seismic action in the longitudinal direction. The reduction of inertial forces contributes to a more economical design of piers, foundations, bearings and terminal joints of the bridge, without reducing the safety requirements. Keywords: bridge, pounding, backwall, earthquake resistant arm, kinetic energy, dissipation, viscous damper.

1 Introduction

The present paper applies to all the types of long bridges, either the conventional ones or not, whose deck is either, partially or totally, monolithically connected with the piers, or is “floating” on bearings, as also, in that case, to precast bridges. As it is already known, the design of long bridges has to satisfy both functional and earthquake resistant requirements, which are conflictful components of the same problem with reverse design demands. “Floating” systems deal with the problem of functional movements with the use of steel-reinforced elastomeric bearings, which allow the free movement of

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Earthquake Resistant Engineering Structures V 507

the deck of the bridge in the longitudinal direction. However, in floating bridges, the use of a behaviour factor q equal to 1 is required for the design of the longitudinal direction. The aforementioned requirements lead to economically burdensome solutions due to the increased dimensions of the piers and of the bearings, which have to be replaced at regular time intervals, and to robust foundations. Integral bridges, on the other hand, have major earthquake resistant advantages towards “floating” systems. Moreover they don’t require maintenance and replacement of expendable elements, such as bearings and expansion joints. This type of bridges takes advantage of the ability of reinforced concrete to dissipate part of the induced seismic energy by hysteretic behaviour. As a result, the seismic design forces are divided by the use of behaviour factor q equal to 3,5. However, the critical problem of integral bridges is the functional movement demand due to temperature rise and fall, creep and shrinkage. This study is performed using non-linear dynamic analysis [1], [2].

2 Suggested configuration of the abutment

The development of bridge engineering during the last years caused significant changes in the configuration of the abutment. The necessity to inspect the ends of the prestressed parts of the superstructure caused the widening of the seating beam towards the embankment behind the abutment and also the backwall’s positioning at the end of the seating beam, on which it is fixed, Figure 1. Up to the present day the backwall of the bridge is designed in order to resist the earth pressure of the embankment behind the abutment and to support the seating slabs of the deck. The requirement for the terminal expansion joints in bridges according to the regulations is in accordance with the aforementioned role of the backwall. According to the Eurocode 8 - Part 2 [3], based on technical and economical criteria, checking of expansion joints of the decks, by superposition

of 40% of the seismic plus 50% of the thermal displacement actions is sufficient. This implies that the code accepts pounding between the deck and the backwall for the design earthquake. Consequently, damages of the backwall and of the retaining wing-wall are expected. The current configuration of the abutment inspired the authors to use the segment of the abutment, which includes the extension of the seating beam and the backwall, in the seismic problem of bridges and to use the Γ shaped backwall with the seating beam as an earthquake resistant arm, which due to its elastoplastic behaviour can reduce the inertial forces as it resists by pounding to the free vibration of the deck causing reduction of the kinetic energy, [4]. It is implicit that the arm is not connected monolithically with the abutment’s wing-walls. During earthquake the resisting arm responses to the pounding, initially, as a unilateral elastic spring with or without viscous damping which determines the amount of the energy dissipated during pounding and not as a result of the installation of a viscoelastic damper, and after that as a unilateral elastoplastic impact element. This element could be characterized as a “yielding” stopper.


508 Earthquake Resistant Engineering Structures V

box girder

elastomeric bearing

abutment's backwall

footing

seating beamembankment behind

the abutment

0,75 to

1,20m

Figure 1: Conventional abutment.

3 Parameters of the analytical investigation The present paper is a part of a Research Project, which focuses both on analytical and experimental aspects. The experimental part is scheduled to take place on the Shaking Table of the Laboratory of Reinforced Concrete and Masonry Structures of A.U.TH. Using an appropriate program of non-linear time history dynamic analysis, which was developed for the needs of the investigation of the pounding effect, the influence, on the intended reduction of the inertial loads induced by the design earthquake, was examined. In particular the study focuses on the effect of: a) The width of the existing end joints at the beginning of the earthquake, b) The magnitude of the earthquake resistant properties of the arm, c) Seismicity and ground type, d) The stiffness of the bridge in the critical longitudinal direction and e) The improvement of the texture of the colliding surfaces.

3.1 The influence of the width of the existing end joints During earthquake the width of the end joints ∆ of the bridge, which is determined both from functional effects and from the length of the deck, can have any value varying from 0 to the maximum functional requirement of the shrinkage. For this reason 10 different cases of width values were examined, from 0 to 15cm, which also resulted in the detection of the value of the width for which no pounding is induced during earthquake.

3.2 The influence of the magnitude of the earthquake resistant properties of the arm

The earthquake resistant arm was considered to respond in an elastic and in an elastoplastic manner. Its contribution to the reduction of the inertial forces of the



bridge, mainly through the dissipation of the kinetic energy of the deck, depends on the magnitude of its three earthquake resistant properties meaning its stiffness Kimp, its strength Fy and its ductility µreq. For this reason four cases of arm’s stiffness were examined, which correspond to long and to shorter continuous decks of the bridges. These values are varying from 200000KN/m to 1700000KN/m, as seen in Figure 2. On the other side the strength of the earthquake resistant arm, as it is expected, defines the maximum pounding force of the deck, as also the displacement ductility demand of the arm. In correspondence with the aforementioned values of stiffness, equal number of values of the strength, varying from 5000KN to 30000KN, was examined.

width of theexpansion joint

backwall-earthquake resistant arm

Poun

ding

forc

e Fi

mp

K=Ec JII / δ11Displacement of the deck

"Fimp"

box girder

suggested reinforcement of theearthquake resistant arm

M,Fimp

width of the arm1,00-1,50m

width of the arm1,00-1,50m

Figure 2: Suggested development of the backwall as an earthquake resistant arm. (a) Moments due to pounding (b) Fimp-δ.

3.3 The influence of seismicity and ground type

The influence of these parameters is reflected on the corresponding design spectrum in which the accelerograms that are referred below and are used in the research are reduced. For this reason, the influence of these parameters is



investigated in common. Specifically, for the non-linear time history analysis natural strong motion records corresponding to recent earthquakes in Thessaloniki (1978), Corinth (1981), Kalamata (1986) and Athens (1999) were used. As far as the earthquake of Athens is concerned, both of the recorded ground motions were used, (Sepolia, KEDE). For the reduction of the aforementioned accelerograms to the corresponding elastic spectrum of EAK 2000 [5] spectral intensity factors S.I. suggested by Housner, were used. For the investigation two soft ground types and also two seismic zones, which correspond to most of the areas, were considered. In particular, the following combinations were examined: 1) The seismicity of Seismic Zone I, which corresponds to the design horizontal seismic acceleration of the ground Ao=0,16g, for two different ground types B(T1=0,15s , T2=0,60s) and C(T1=0,20s , T2=0,80s). 2) The seismicity of Seismic Zone II, which corresponds to the design horizontal seismic acceleration of the ground Ao=0,24g, for two different ground types B(T1=0,15s , T2=0,60s) and C(T1=0,20s , T2=0,80s).

3.4 The influence of the stiffness of the bridge in the critical longitudinal direction

The stiffness Kbase of the bridge in the critical longitudinal direction influences the displacements of the deck and consequently the magnitude of the forces which are induced by the pounding of the vibrated deck towards the earthquake resistant arm. Four representative cases of longitudinal stiffness have been studied, which correspond to the following cases: 1) Bridges with bearings of 160mm total thickness of the elastomer, 2) Bridges with bearings of 90mm total thickness of the elastomer, 3) Bridges with variable thickness of the elastomer of the bearings and 4) Bridges whose deck is monolithically connected to a number of the central piers.

3.5 The improvement of the texture of the contact area

The magnitude of the forces, which are induced by the pounding of the deck towards the earthquake resistant arm, depends on the geometry and the material of the surfaces in contact as also on the relative velocity of the colliding bodies. The improvement of the response of the bridge through the use of elastomer bearings-bumpers, installed in the forehead of the colliding bodies, was investigated. The bearings considered have a value of the modulus of elasticity E=3840KN/m2 and a value of shearing modulus G=1600KN/m2 and cover the total contact surface, which has an area of A=0,3x10,0=3,0m2. The total thickness of the elastomer of the bearings-bumpers is tbum=3,0cm.

4 Results: analysis of the results

Despite the great number of the analytical results of the investigation, which came up to 2000 examined bridge cases, which were studied parametrically, the



most interesting ones are presented below. The main results of this paper per examined parameter are the following:

4.1 The influence of the width of the existing functional joint

Functional joint is determined to be the existing joint at the beginning of the seismic event. The use of the aforementioned accelerograms resulted in the chart of Figure 3, which illustrates the influence of the width of the joint on the pounding load Fimp, which the earthquake resistant arm receives from the deck, and also on the displacement umax of the deck, due to longitudinal design earthquake. The earthquake resistant arm responses either in an elastic, continuous line, or in an elastoplastic manner, discontinuous line. For the case that the arm responses in an elastic manner it is noticed that the pounding force, for a narrow width of the joint, is increased, while the widening of the joint is resulting in the reduction of the force, [6]. It can also be seen that pounding effect is avoided for a value of the width of the joint equal to ∆=9cm.

0

1

2

3

4

5

6

7

8

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16Initial width of the expansion joint ∆(m)

Pounding ForceFimp (KNx104)

functional width of the expansion joint ∆=3,5cm

Max ductility demand µreq

Max seismic displacement of the deck umax (cm)

Response of the arm: elastic

elastoplastic

∆>9cm (No pounding)

Kimp(KN/m)| Fy(KN) | L (m) | Seismic Zone | Ground Type 600000 | 15000 | 200 | I | B

Figure 3: The influence of the width of the joint on the pounding force, on the ductility demand and on the displacement of the deck.

Generally, high values of the displacement of the deck lead to high values of the seismic actions of the piers while blocking of the free vibration of the deck through the activation of the arm, which reduces the kinetic energy of the deck, leads to the reduction of the displacement.



The results for the bridges of 400m and 600m length gave that the pounding force is expected to be higher, up to 40% and 70% respectively, than the force which is developed in the bridge of 200m, while pounding is avoided for widths of the joints 12cm and 13cm respectively. Similar charts, with the difference that the y-coordinate shows the displacement ductility demand µδreq of the arm, were extracted for the case that the arm responses in an elastoplastic manner, discontinuous line. As shown in Figure 3, the ductility demand of the earthquake resistant arm is easily accomplished. The same conclusion is effective for the bridges of 400m and 600m length, for which the ductility demand does not exceed the value 3 (µδreq ≤ 3), even if the value of the width of the joint is the most unfavourable as far as the ductility demand is concerned. By considering the elastoplastic behaviour of the arm, the displacement of the deck is up to 20% increased, in comparison with the consideration of the arm as an elastic stopper, owed to the widening of the joint which results from the permanent deformation of the arm during pounding. The increase of the displacement of the deck for the bridges of 400m and 600m lengths is 11%.

4.2 The influence of the magnitude of the earthquake resistant properties of the arm

The strength Fy, the stiffness Kimp and the ductility µreq of the earthquake resistant arm were studied parametrically in this paragraph, Figures 4-6. Figure 4 shows, for the cases that the arm responses in an elastic, continuous line, or in an elastoplastic manner, discontinuous line, the variation of the pounding force and the variation of the ductility demand respectively due to the increase of the stiffness of the arm in a bridge of 200m length. It can be derived that while the value of the stiffness is being increased from 200000 to 1700000KN/m the pounding force is being increased from 7800 to 27300KN. It can also be noticed that the ductility demand is easily accomplished. In the same figure the variation of the displacement of the deck is illustrated while the stiffness of the arm is increasing. It can be seen that the increase of the stiffness of the arm from 200000 to 1700000KN/m reduces the displacement of the deck by 40%, for the elastic behaviour of the arm, and up to 35%, for the elastoplastic behaviour, and consequently reduces the seismic actions of the piers and of their foundations up to the same percentages. Apart from the above investigation the simultaneous influence of two parameters has been studied in common. In Figure 5 the variation of the displacement of the deck is shown while the initial width of the arm as also the stiffness of the arm, which responses in an elastoplastic manner, are varying. This investigation was deemed to be necessary because the joints may have any width at the beginning of the seismic event. It is noted that the ductility demand of the arm is not varying significantly while the aforementioned parameters are changed, and is easily accomplished. However the displacement of the deck is significantly reduced while the stiffness and the strength of the considering arm is increased. The same figure shows that



the influence of the arm is significantly reduced for a value of the initial width of the joint greater than ∆≥ 6cm.

012345678

2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17Stiffness of the earthquake resistant arm Kimp (KN/m)x105




elastic response of arm elastoplastic response

Kimp(KN/m) | Fy(KN) | L (m) | Width ∆(m)|Seismic Zone |Ground Type (2,3,6,17)x105 |(5,10,15,30)x103 | 200 | 0.02 | I | B

Figure 4: The influence of the stiffness and of the strength of the arm.

0

2

4

6

8

10

12

14

16

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14Initial width of the expansion joint ∆ (m)

Max

duc

tility

dem

and

Max

disp

lace

men

tµr

eq

um

ax (m

) .

µreq

umaxKimp=200000 KN/m Fy= 5000KNKimp=300000 KN/m Fy=10000KN

functional width of the expansion joint

Kimp=600000 KN/m Fy=15000KNKimp=1700000KN/m Fy=30000KN

Figure 5: The influence of the width of the joint, of the stiffness and of the strength of the arm. The figure refers to seismic zone II, ground type C and to a bridge of 200m length.



0

2

4

6

8

10

12

14

16

50 100 150 200 250 300 350 400L (m)=

Max

duc

tility

dem

and

Max

disp

lace

men

tµr

eq

um

ax (m

)

3,5 7.01.75

Kimp=200000KN/m Fy= 5000KNKimp=300000KN/m Fy=10000KNKimp=600000KN/m Fy=15000KN

0,85∆(cm)=Length of the bridge L(m)

Initial functional width of the expansion joint ∆(cm)

µreq

umax

Kimp=1700000KN/m Fy=30000KN

Figure 6: The influence of the stiffness, of the strength of the arm and of the length of the bridge. Seismic zone II and ground type C were considered.

A relevant chart, Figure 6, came up for bridges with lengths of continuous deck varying from 50, 100, 200 to 400m. The difference in the last chart is that the functional width of the joint was used for each length. From chart 6 it is noticed that in bridges of short length the earthquake resistant arm is more effective because the arm is activated from the beginning of the earthquake due to the low value of the initial width of the joint. The same charts also show that the ductility demands are easily accomplished.

4.3 The influence of the seismicity and of the ground type

Figure 7 shows the variation of the pounding force for the case that the earthquake resistant arm responses in an elastic manner, continuous line, for four different values of the intensity factor S.I. that was estimated for a target design elastic spectrum which corresponds to: (a) ground type B and to seismic zone I, (b) ground type C and to seismic zone I, (c) ground type B and to seismic zone II and (d) ground type C and to seismic zone II. Specifically, the consideration of higher seismicity, by adopting a higher value of the design seismic ground acceleration Ao=0,24g instead of Ao=0,16g, leads to increased intensity factors and as a result to increased pounding force up to 40%. In a similar way the consideration of the soft ground type C instead of type B leads to a percentage increase of pounding force up to 25%. Figure 7 shows also that the displacement of the deck of the bridge of 200m is increased up to 28% while the seismic ground acceleration is being increased



from Ao=0,16g to Ao=0,24g. Also the consideration of the softer ground type C against B leads to an increase of the displacement of the deck up to 15%.

0

2

4

6

8

10

12

14

B , I C , I B , II C , IIGround Type , Seismic Zone (EAK 2000)




elastic response of arm elastoplastic response

Kimp(KN/m) | Fy(KN) | L (m) | Width ∆(m) 600000 | 15000 | 200 | 3.5

Figure 7: The influence of seismic zone and of ground type.

For the case that the earthquake resistant arm responses in an elastoplastic manner, discontinuous line, figure 7 shows that the ductility demand remains in low levels (µreq ≤ 4) even if the soft ground type and the high seismicity are considered. Relevant results, which are not presented here, show that the ductility demand is easily accomplished even for long bridges.

4.4 The influence of the stiffness of the bridge in the critical longitudinal direction

In §3.5 the influence of the stiffness Kbase of the bridge in the longitudinal direction was partially annotated. In the present paragraph flexible and stiff-integral systems of bridges are examined which correspond to values of the longitudinal stiffness of 80000, 150000, 340000 and 360000KN/m. Figure 8 illustrates the influence of the longitudinal stiffness of the bridge on the maximum pounding force considering that the earthquake resistant arm responses in an elastic manner. It is noticed that the pounding force of the deck towards the arm is up to 50% reduced, when the integral bridge is considered instead of the bridge with bearings of 160mm total thickness of the elastomer. The same figure illustrates, for bridges of 200m length, the variation of the displacement of the deck while the stiffness of the bridge in the longitudinal direction is being increased from 80000 to 360000KN/m. It is extracted that the displacement of the deck is reduced by 25%. The consideration that the earthquake resistant arm responses in an elastoplastic manner gives relevant results, with reduction of the displacement up to 40%.



0

12

34

56

7

50000 100000 150000 200000 250000 300000 350000 400000Stiffness in the longitudinal direction Kbase (KN/m)




Response of the arm: elastic

elastoplastic

Kimp(KN/m)| Fy(KN) | L (m) |Width ∆(m) | Seismic Zone | Ground Type 600000 | 15000 | 200 | 3.5 | I | B

Figure 8: The influence of the stiffness of the bridge in the longitudinal direction.

4.5 The improvement of the texture of the colliding surfaces

For the case that the earthquake resistant arm responses in an elastic manner the influence of the use of elastomeric bearings-bumpers, which are installed on the forehead of the colliding surfaces, was studied. Figure 9 illustrates the variation of the pounding force when elastomeric material is used as bumper, discontinuous line. It is noticed that the use of a soft bumper, which covers the total contact area between the arm and the deck, increases the pounding force. However, as it can be seen from the same figure, the use of the bumper reduces the displacement of the deck up to 40%, 15% and 5% in bridges of 200m, 400m and 600m lengths respectively. From this investigation it is concluded that the use of the elastomeric bumpers is more efficient in short bridges.

4.6 The influence of the use of viscous dampers

Apart from the consideration that the arm responses in an elastic manner or in an elastoplastic manner the influence of the use of viscous dampers, which connect the deck and the earthquake resistant arm, was investigated. The viscous damper functions bilaterally during earthquake and it dissipates energy through the work of the damping force FD=C.ua where, FD is the damping force, C is the damping coefficient, u is the relative velocity between the arm and the deck and a is the exponent of the velocity, [7]. The earthquake resistant arm is separated from the deck by a joint, whose width is estimated from the functional requirements of the deck, and it responses in an elastic manner when the seismic displacement of the deck is greater than the functional gap, which means that the deck pounds on the arm.



From Figure 10, which shows the influence of the coefficient C on the pounding force, continuous line, it is noticed that the force is effectively reduced, up to 45%, while the coefficient of the damping C is increased from 1000 KN-s/m to 5000KN-s/m. Also the displacement of the deck is reduced up to the same percentage.

0

2

4

6

8

10

200 400 600Length of the bridge L(m)



Bumper installed: no

yes

Kimp(KN/m)| Kbum(KN/m) | tbum (cm) | Width∆(m) |Seismic Zone| Ground Type 600000 | 380000 | 3 | functional | I | B

Figure 9: The influence of the use of an elastomeric bearing-bumper.

0

1

2

3

4

5

6

1000 2000 3000 4000 5000


Max seismic displacement of the deck umax

a exp=1 C var.

C=1500KN.s/m a exp var.

C(KN-s/m)= a exp = 0,02 0,05 0,10 0,50 1,00

Kimp(KN/m) | L (m) | Width ∆(m) | Seismic Zone | Ground Type 600000 | 200 | 3.5 | I | B

Figure 10: The influence of the coefficient of the damping C and of the a exponent of the velocity on the pounding force and on the displacement of the deck.



Apart from the coefficient C, the influence of the a exponent of the velocity on the magnitude of the pounding force and on the displacement of the deck was examined. Figure 10 also shows that the reduction of a exponent leads to a reduction of the pounding load up to 75%. Also the displacement of the deck in longitudinal direction is reduced up to 55% when the a exponent is reduced from 1 to 0,02. Relevant are the results for bridges of 400m and 600m length. The pounding forces are reduced up to 43% and 31% respectively. The displacements of the aforementioned bridges are reduced up to 33% and 25% respectively when the a exponent is reduced from 1 to 0,02. Consequently the contribution of the viscous damper to the dissipation of the seismic energy is significant.

5 Conclusions

In the present paper a properly developed and reinforced backwall, which is not monolithically connected to the wing-wall, was used as an earthquake resistant arm with the capability to dissipate part of the kinetic energy of the vibration of the deck during earthquake. The parametric analysis for the following parameters: (a) the width of the existing end joints at the beginning of the earthquake, (b) the earthquake resistant properties of the arm, (c) the length of the bridge, (d) the seismicity and the type of the ground, (e) the stiffness of the bridge in the critical longitudinal direction and (f) the texture of the colliding surfaces came to the following conclusions: 1) The increase of the stiffness of the earthquake resistant arm reduces significantly the deck displacements up to 40% which results in the reduction of the seismic actions of the piers. It is noticed that there is a sufficient margin for the increase of the stiffness without putting the stability of the abutment in risk due to favourable passive earthpressure of the embankment behind the abutment. 2) The efficiency of the suggested earthquake resistant arm is reduced when the width of the end joint at the beginning of the earthquake, which is proportional to the length of the bridge, is increased. However, the efficiency of the arm is advantageous even for bridges of 400m length. 3) The ductility demand of the arm, which responds in an elastoplastic manner, has a maximum value equal to µδreq=4 and can be easily accomplished, even in the demanding case of long bridges. 4) The consideration of higher seismicity, by adopting a higher value of the design ground acceleration, in combination with the amplification of the response due to the soft ground type leads, as expected, to higher displacements of the deck resulting in higher seismic actions of the piers and of their foundation. However, high values of the displacements give the possibility to the arm to dissipate greater amounts of the kinetic energy. 5) The use of an elastomeric bumper between the earthquake resistant arm and the deck of the bridge improves significantly the efficiency of the arm. 6) The use of viscous dampers, which dissipate part of the kinetic energy of the deck through the work of the damping force, which force is out of phase of the elastic resisting force, reduces significantly the displacement of the deck up to



75% and consequently reduces the seismic actions of the piers and their foundations. 7) The use of the backwall as a Γ shaped earthquake resistant arm allows the reduction of the width of the joint to functional values of the width, reducing at the same time the cost of the installed joints. This conclusion is mostly effective for “floating” bridges, in which the displacements determine the cost of the bearings. The development of the backwall of the abutment as an active Γ shaped earthquake resistant arm is beneficial for the earthquake resistance of the bridge. Further investigation will be performed in order to confirm the above conclusions.

References

[1] Ch. Athanasiadou, Seismic behavior of SDOF systems in contact, PhD. Dissertation A.U.TH. 1991.

[2] S.A. Anagnostopoulos, Pounding of buildings in series during earthquakes. Earthquake Engineering and Structural Dynamics, vol.16, 443-456, 1998.

[3] CEN 2003, Eurocode 8: Design of structures for earthquake resistance, Part 2: Bridges.

[4] S.A. Anagnostopoulos, Equivalent viscous damping for modeling inelastic impacts in earthquake pounding problems. Earthquake Engineering and Structural Dynamics, vol.33, 897-902, 2004.

[5] E.A.K. 2000, Greek Regulation for Earthquake Resistant Structures. [6] R. Jankowski, K. Wilde, Y. Fujino, Pounding of superstructure segments

in isolated elevated bridge during earthquakes. Earthquake Engineering and Structural Dynamics, vol.27, 487-502, (1998).

[7] M. Shinozuka, M.Q. Feng, J.M. Kim, F. Nagashima, H.K. Kim, Mitigation of seismic pounding effect on bridges using dynamic restrainers. SPIE's 7th Annual International Symposium on Smart Structures and Materials, Newport Beach, March 6-9, 2000.



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Reduction of inertial seismic forces in bridges by using ...€¦ · backwall. According to the Eurocode 8 - Part 2 [3], based on technical and economical criteria, checking of expansion