Comparative Study of Various Passive Control Devices For Seismic Control of

cable stayed bridge

Presented by:

Piyush Ram Soti Y7CE220

Objective:

Earthquake response of benchmark cable-stayed bridge with passive control systems is investigated.

The passive damping system consists of :- Viscous fluid damper (VFD) High damping rubber bearing(HDRB) , Lead-rubber bearing(LRB), Friction pendulum system (FPS) and Resilient-friction base isolator (R-FBI) Visco-elastic dampers and Elastoplastic dampers

A comparative performance study among these control systems for seismic response control of bridge is carried out by finding the various evaluation criteria under different parameters.

Introduction

Cable-stayed bridges, which are very popular nowadays, are susceptible to strong earthquake motions because of the associated low damping and high flexibility.

In order to decrease the seismic vibrations, different active, passive and hybrid control systems have been devised.

For direct comparison among the various control strategies for a particular type of structure, benchmark bridge has been taken and benchmark problems were created.

Therefore to compare the results of different control devices, a benchmark bridge has been taken.

Benchmark cable stayed bridge

The cable-stayed bridge used for this benchmark study is the Bill Emerson Memorial Bridge spanning the Mississippi River near Cape Girardeau, Missouri.

The bridge is composed of 2 towers, 128 cables. It has a total length of 1205.8 m.

The main span is 350.6 m in length, the side spans are 142.7 m in length, and the approach on the Illinois side is 570 m.

Methodology

The important responses to be considered in cable stayed bridges subjected to an earthquake in horizontal direction are:

a)force responses of towers. b)the displacement of the deck. c)the variations of forces in stays.

The bridge without control is assumed with 2 evaluation models:

a model where deck is restrained to the main piers with shock transmission devices.(Base shear and Overturning moment is high in this case)

a model where deck is not restrained to the main piers.

(displacement of the deck is very high)

Control Devices

Viscous Fluid Damper(VFD): It consists of a stainless steel piston and an

accumulator. It is filled with silicon oil and the piston may

contain a number of small orifices through which the fluid may pass from one side of the piston to the other.

A fluid viscous damper dissipates energy by pushing fluid through an orifice, producing a damping pressure, which creates a force.

These damping forces are 900out of phase with the

displacement driven forces in the structure and hence, the VFD reduces both stresses and

deflection in the structure.

High Damping Rubber Bearing(HDRB)

HDRB is one type of elastomeric bearing consisting of thin layers of high damping rubber and steel plates built in alternate layers.

The vertical stiffness of the bearing is several times the horizontal stiffness due to the presence of internal steel plates.

Horizontal stiffness of the bearing is controlled by the low shear modulus of elastomer while steel plates provide high vertical stiffness as well as prevent bulging of rubber.

HDRB

Lead Rubber Bearing(LRB)

This is another type of elastomeric bearings consisting of thin layers of low damping natural rubber and steel plates built in alternate layers .

Additional, a lead cylinder plug is firmly fitted in a hole at its centre to deform in pure shear.

The steel plates in the bearing forces the lead plug to deform in shear.

This bearing provides an elastic restoring force and also, by selection of the appropriate size of lead plug, produces required amount of damping.

Friction Pendulum System(FPS)

The FPS isolator has an articulated slider that moves on a stainless steel spherical surface.

As the slider moves over the spherical surface, it causes the supported mass to rise and provides the restoring force for the system.

The natural period of the FPS depends on the radius of curvature (rc) of the concave surface. The natural period vibration (Tb) of a rigid mass supported on FPS connections is determined from the pendulum equation.

The resisting force (f) provided by the FPS is given by: f= kb.xb + Fx ,

kb = the bearing stiffness provided by virtue of inward gravity action at the concave surface; xb =the device displacement and Fx =the frictional force.

Resilient Friction Base Isolators(R-FBI)

The R-FBI consists of a set of concentric layers of Teflon-coated plates in friction contact with each other with a central rubber core or peripheral rubber core .

It combines the beneficial effect of friction damping with that of the resiliency of rubber.

The RFBI provides isolation through the parallel actions of friction, damping and restoring force.

The resisting forces provided by the system can be given by:

Where, kb, cb and Fx are the stiffness, damping and frictional force of the R-FBI, respectively.

Visco Elastic Dampers

The visco-elastic dampers have steel sheets and BRC sheets laminated alternately resulting in a multiple number of layers.

BRC is a bitumen rubber compound.

This material has high adhesive strength and can adhere without any bonding agent.

It can induce large damping force due to shear deformations.

It is very stable, chemically inert and is resistant to any pollutants.

Elasto plastic dampers

Elasto-plastic Dampers, based on plastic deforming steel plates,

consist of X-shaped plates. These plates sustain many cycles of

stable yielding deformation, resulting in high levels of energy dissipation or damping.

Elastoplastic dampers like mild steel

and lead dampers are made of relatively low-cost elements, which absorb vibration through the hysteretic deformation of the material.

Evaluation criteria for uncontrolled bridge.

Earthquake El. Centro Mexico City Gebze

Peak deck displacement(m) 0.09758 0.02432 0.07192

Peak base shear (KN) 48782.3 11181.0 30847.7

Peak base moment(KNm) 1027060

198235 697787

Earthquake El. Centro Mexico City Gebze

Peak deck displacement(m) 0.36263 0.18410 0.77342

Peak base shear(KN) 22242.7 622.094 12480.0

Peak base moment(KNm) 398342 173582 603021

Configuration A: longitudinally constrained deck

Configuration B: longitudinally unconstrained deck

Numerical Study A set of numerical simulation is performed in MATLAB (2002) for the specified three

historical earthquakes. The three specified earthquakes are: (1) El Centro earthquake,1940, PGA=3.417 m/s2

(2)Mexico City earthquake ,1985, PGA= 1.4068 m/s2, and (3)Gebze earthquake ,1999 ,PGA= 2.5978 m/s2.

The model was tested with all the damping devices by keeping:

The optimum value of damping coefficient(cd) and velocity component(λ) was taken 3500 KN s/m and 1 respectively.

damping ratio of 15% for HDRB, 5% damping ratio and 0.1 normalized yield strength ratio for LRB. 0.05 frictional coefficient for FPS . 10% damping ratio and 0.04 frictional coefficient for R-FBI. The viscoelastic dampers with K=50000 kN/m, C=1000 and α=0.2 was used for the

equation. The values of the coefficients for elastoplastic dampers used are Fy=1000, k1=50 000 and

k2=10 to get the optimum result.

Results The variation of peak base shear, deck displacement and base moment with respect to

different passive dampers for different earthquakes is shown in bar charts.

Parameter Linear VFD HDRB LRB FPS R-FBI Elasto-viscous Elasto-plastic

Max. deck displacement(m)

0.1076 0.1803 0.1757 0.1711 0.1657 0.08675 0.13165

Max. Shear(KN) 20293.4 22000.8 21805.7 21561.8 21269.1 13673.3 16864.7

Max. Moment(KNm) 357416.8 392336.9 388228.7 385147.5 380012.2 257325 276699

Evaluation for deck displacement, base shear and base moment of El Centro Earthquake

Parameter Linear VFD HDRB LRB FPS R-FBI Elasto-viscous Elasto-plastic

Max. deck displacement(m)

0.065 0.0952 0.1065 0.0727 0.0779 0.0226 0.0392

Max. Shear(KN) 5556.9 6149.5 6306.1 5389.2 5691.1 7107.88 6017.17

Max. Moment(KNm) 98522.8 109029.2 111804.5 95549.3 100901.6 103372 114959

Evaluation for deck displacement, base shear and base moment of Mexico Earthquake

Parameter Linear VFD HDRB LRB FPS R-FBI Elasto-viscous Elasto-plastic

Max. deck displacement(m)

0.3133 0.6911 0.5124 0.5387 0.4969 0.07217 0.1782

Max. Shear(KN) 13542.1 11876.4 15362.1 15269.6 15084.5 12907.3 11270.7

Max. Moment(KNm) 282603.7 540087.1 533807.1 540784.9 518455.7 243474 271710

Evaluation for deck displacement, base shear and base moment of Gebze Earthquake

Conclusion

Despite being a flexible structure, significant seismic response (especially deck displacement) reduction of the bridge can be achieved by applying hybrid passive control system consisting of HDRB, LRB, FPS, R-FBI, VFD, Visco-Elastic damper and Elastoplastic damper in the benchmark cable-stayed bridge.

  The passive control system which supplied the best results was the one with viscoelastic

dampers. This system produced values of maximum moment and shear on the piers equal respectively to 25.1 and 28.0% of the values obtained for a uncontrolled bridge in configuration (a) and 42.7 and 61.5% of the values obtained for an uncontrolled bridge in configuration (b). The maximum displacement of the deck is 0.087 m, equal to 11.2% of the maximum deck displacement of the bridge in configuration (b).

  As in case of Mexico City Earthquake having less PGA, the shear and moment was best

controlled by Friction pendulum system(FPS).Thus it can be inferred that for Earthquakes with lower PGA values, FPS gives the best result and is more effective in controlling shear and moment.

  Among all the passive control devices, Viscoelastic damper is found to be better

THANK YOU