Seismic Analysis on Girder Falling Damage and Unseating Prevention Design

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Journal of Information & Computational Science 10:12 (2013) 3667–3676 August 10,2013
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Seismic Analysis on Girder Falling Damage and
Unseating Prevention Design
Chunping Tang
,Liangliang Zhang
,Jingyun Hang
Ayad Thabit Saeed
College of Civil Engineering,Chongqing University,Chongqing 400045,China
Chongqing Technology and Business Institute,Chongqing 400052,China
T.Y.Lin International Egineering Consulting Co.,Ltd,Chongqing 401121,China
Girder falling is a serious seismic damage of bridge,which causes traffic disruption directly.In this paper
unseating-prevention philosophy of beam bridges are proposed by analyzing the process and causes of
girder falling according to structural characters of bridges and investigation on girder falling.The
design load of unseating-prevention device was theoretically deduced based on sudden loading principle
of dynamics.and puts forward calculation method of the maximum slip length and supporting width of
cap beam and unseating-prevention device to prevent damage of fallen girder.
Keywords:Earthquake;Fallen Girder;Seismic Analysis;Unseating-Prevention Device
1 Introduction
In recent years,big earthquakes constantly happened all over the world.In China,earthquakes
in Tangshan and Wenchuan caused great damages of life and properties.M8.0 earthquake in
Wenchuan on May 12,2008 resulted in transverse and longitudinal displacement of main beams
in most simply supported girder bridges or even fallen girders,interrupting the traffic and mak-
ing earthquake relief more difficult.According to San Fernando earthquake in America in 1971,
Tangshan earthquake in China in 1976,Loma Prieta earthquake in America in 1989,Northridge
earthquake in America in 1994,Kobe earthquake in Japan in 1995 and Taiwan Chi Chi Earth-
quake in 1999,multi-span simply supported girder bridges can easily cause fallen girder during
earthquakes.Fallen girder is one of the serious seismic damages of simply supported girder bridges
proved by many earthquakes.Table 1 shows some cases of fallen girder in Wenchuan earthquake
Bridge as a transport hub is an important lifeline project.Once it is damaged or interrupted
during earthquake,a series of sub-disasters will subsequently occur which causes important losses

Corresponding author.
Email (Chunping Tang).
1548–7741/Copyright ©2013 Binary Information Press
3668 C.Tang et al./Journal of Information & Computational Science 10:12 (2013) 3667{3676
Table 1:Some examples of bridge unseating in Wenchuan earthquake
Name of bridge Type
Seismic damage
Miaoziping Bridge
Simply supported T-beam (con-
tinuous bridge deck)
550 m
one span of the bridge fallen girder
Baihua Bridge Continuous curved girder bridge 520 m One side of spanning fallen girder
causes the whole collapse
Beichuan Shisuoyi
Simply supported girder bridge 1120 m
Transverse direction fallen girder of
No.5 span
Gaoyuan Bridge
Simply supported girder bridge 425 m
Fallen girder of the No.2 span on
the side of Gaoyuan
Nanba New Bridge
in Pingwu County
Simply-supported hollow slab
oblique bridge
1020 m
Longitudinally fallen girder of
middle-span main beam and trans-
verse fallen girder of side-span
of life and properties.Anti-seismic capacity is vital to urban earthquake relief.Fallen girder is the
most serious damage to bridges which directly causes traffic disruption.The ones during Tangshan
(1976) and Wenchuan (2008) earthquakes attracted wide attention of boffins,in relief times.With
accumulating experience in seismic damage to bridges and development in anti-seismic design,
it is an effective way to take anti-seismic measures to reduce damages to structures during big
earthquakes.A collapse-proof system consisting of adequate seat length,seismic restrainers and
unseating prevention device effectively lightens collision of structures during earthquakes and
prevents seismic collapse.and meets the principle of “unbroken in small earthquakes,repairable
in medium earthquakes and non-collapsed in big earthquakes” [2].
2 Analysis of Seismic Damage
Analysis of seismic damage to bridges and its causes offers theoretical bases for anti-seismic design
and effective anti-seismic measures.According to a great deal of analysis of seismic damage [3],
there are four factors contributing to seismic damage of bridges,as shown in Fig.1.In Fig.1,
seismic intensity unexpectedly exceeds standards of anti-seismic design.Location of bridge is
unfavorable to seismic resistance,which causes failures or deformation of foundation.Mistakes
in structural design and construction are referred as human factors.
2.1 Displacement of Main Beam But No Fallen Girder
Displacement of main beam is relatively common in meizoseismal area.It mainly includes longi-
tudinal displacement,transverse displacement and plane revolution,etc.As girders are directly
supported on the pier and they are connected by rubber support,basically without transverse
restraint,relative displacement occurs when transverse seismic force exceeds frictional force or
shear capacity of support.In Fig.2,No.3 pier top girder of G213 National Road Baishuixi
Bridge is transversally shifted to 48 cm,which may cause transversal fallen girder [4][5].Shou-
C.Tang et al./Journal of Information & Computational Science 10:12 (2013) 3667{3676 3669
Seismic damage of bridges
Bridge structureHuman factors
Site conditionsEarthquake intensity
Fig.1:Factors of bridge seismic damage
jiang Bridge near G213 National Road of Xuankou Town,over the Minjiang River,is a simply
supported girder structure and its seismic damage is mainly longitudinal displacement.Girder
on the side span may fall [6].Seismic damage to Shoujiang Bridge is shown in Fig.3.
Fig.2:Transversal displacement
Fig.3:Longitudinal displacement
2.2 Damage of Pier Block
Displacement of the main beam affects longitudinal and transversal pier blocks and damages
them.Its damage is shown in Fig.4.
But in earthquakes,due to setting of blocks,risks of transversal fallen girders are controlled.
Large amounts of bridge blocks are damaged at different degrees.Two sides of bent cap of the
3670 C.Tang et al./Journal of Information & Computational Science 10:12 (2013) 3667{3676
Fig.4:Damage of blocks
Minjiang River Bridge in Miaoziping are broken and damaged;small blocks on pad stones of bent
cap support are crushed and sheared.Blocks on the right side of Chediguan Bridge are crushed
and broken and transversal displacement occurs in the girder.Crack of these blocks is commonly
on the joint of block and bent cap.Cracks mainly include horizontal crack on the top of block,
oblique crack in the corner and vertical crack at the edge of bent cap.
Damage to anti-seismic blocks of bridges is caused by the followings:in earthquakes,in case of
transversal relative motion of girder and block,the block is hit and joint of block and bent cap is
strongly sheared;due to small-sized block and insufficient reinforcement,the strength of the joint
of block and bent cap is insufficient.Such a block is able to prevent transversal fallen girder to
some extent,but the block itself is seriously damaged.
2.3 Seismic Damage of Fallen Girder
Fallen girder is one of the most serious seismic damages to bridges,an extreme representation of
displacement of main beam.In earthquake,over-displacement of joints without restraints results
in that longitudinally relative displacement exceeds the length of support.It generally causes
fallen girders,especially in high-pier and multi-span bridges.The fall of girder on the top of pile
pier caused by soil displacement is the most common type of seismic damage.The fault layer is
greatly affected,such as many bridges in Kobe earthquake in Japan and Chi Chi earthquake in
Taiwan [7],as shown in Fig.5 and Fig.6.
Fig.5:Girder falling for Nishinomiya bridg,Kobe earthquake
C.Tang et al./Journal of Information & Computational Science 10:12 (2013) 3667{3676 3671
Fig.6:Girder falling for Shih-Wuibridge,Chi-Chi earthquake
Miaoziping Minjiang River Bridge is 1.8 kmaway fromthe upper reaches of Zipingpu Reservoir.
After Wenchuan earthquake on May 12,2008,many cracks were found on web and top plates
inside the box girder as well as on web and top plates outside the box girder.No.1 T-beam
falls,the pier was severely deformed longitudinally and transversely,foundation of bridge was
seriously damaged,support and expansion joint were seriously damaged through examination of
the bridge.Fig.7 shows the fall of girder of Duwen Highway Miaoziping Bridge.
Baihua Bridge was completed in 2004,total length of 496 m t,8 m in width and 30.3 m in
maximum pier height.The upper structure is divided into 6 links.The span combination is
(425+525+150+325+520+220) m.The lower part is double-column pier,light abut-
ment and pile foundation.The bridge was seriously damaged during Wenchuan earthquake,on
May 12,2008.It is very close to seismogenic faults and only 2 km away from Yingxiu Town,
the epicenter.Strong shock is the direct factor of collapse of No.5 link [8].Post-seismic Baihua
Bridge is shown in Fig.8.
There are various seismic damages to bridges.Usually,they result from many factors.In
case of big earthquake,sudden alteration of landform causes damage to bridge structure.It
is damaged due to sand liquefaction,foundation failure,large-scale or non-uniform settlement of
abutment foundation,unstable abutment and pier.Also,it could be damaged to bridge structure:
unreasonable structure,large single-span of bridge,insufficient reinforcement and inadequate
connection of bridge floor.The damage occurs in different degrees as internal force or displacement
of some part of bridge driven by seismic inertia force exceeds the limit of strength of structure
Fig.7:Damages of miao zi ping bridge
3672 C.Tang et al./Journal of Information & Computational Science 10:12 (2013) 3667{3676
Fig.8:Damages of Baihua bridge
and materials.
3 Unseating-prevention Design
3.1 Unseating-prevention Design Idea
Unseating-prevention design should reasonably deal with relation of pier,main beam,support,
bent cap supporting width and collapse-proof structure.If the design of support and collapse-
proof system is relatively “strong”,the pier will bear large inertia force of main beam so that
it will be obviously damaged or collapsed.If the design of support and collapse-proof system is
relatively “weak”,the pier will not be seriously damaged but the girder may fall.Fallen girder
and collapsed pier will cause traffic disruption,the aim of being non-collapsed in big earthquake
is not achieved.Most girders adopt laminated rubber bearing.The girder is directly seated on
the support.Hence connection of the upper and lower parts is relatively weak.Longitudinally
fallen girder will occur.It is vital to take measures to prevent fallen girders.
3.2 Supporting Width
The basic way to prevent fallen girder of the upper part is to make the lap length on the ex-
pansion joint support long enough.Several researches were carried out in America,Japan and
other countries to standardize supporting width.Seismic damage shows that fallen girder of
simply-supported girder bridge and early damage of weak support,are directly caused by pier
displacement relative to main beam.Considering relatively regular bridge and synchronous in-
put of seismic wave was carried out to simplify the calculation,maximum relative displacement
is studied through single-pier model in Fig.9.Only the mass of main beam is considered and
mechanical features of support after damage are described in Coulomb Friction Theory [9].The
maximum relative displacement S
is defined as follows:
= S
In the formula,S
represents the maximum displacement of main beam,S
is the
maximum displacement of top pier (bent cap), is a parameter, = 1:0 means slip of support
C.Tang et al./Journal of Information & Computational Science 10:12 (2013) 3667{3676 3673
max S
Supporting rigidity is small
(a) α=1.0 (b) α=0
Fig.9:Definition of maximum relative displacement spectra between bridge pier and girder
and  = 0 means no slip of support.
In case of slip of support,the main beam and bent cap have maximum relative displacement.
In case of no slip,through calculation,general cycle of pier-beam system is relatively long (above
3 s),seismic force is very small and response is controlled by displacement.If the maximum
relative displacement of pier-beam system is the maximum response displacement of main beam,
safely,it means the rigidity of support is far less than that of pier.
Through research on relative displacement of pier in S
chart,factors of fallen girder are pre-
liminarily determined:seismic motion near the fault,site condition,structural seismic cycle and
rigidity of support after damage.Adequate seat length shall be increased to economically and
effectively prevent fallen girder.In Guidelines for Seismic Design of Highway Bridges (JTG/T
B02-01—2008) in China,the adequate seat length is specified as follows:the end of simply-
supported girder shall be at a distance from the edge of the pier or bent cap.Its minimum value
a (cm) is 70+0.5 L,where L is calculated span of girder and m is the unit.AASHTO of America
also specifies the minimum demand for the adequate seat length,as shown in Formula (2).
a = 0:2 +0:0017L +0:067H
1 +
In the formula,L represents calculated span (m) of the girder;H is average height (m) of two
neighboring connected piers;S is skew angle of support.
Compared with existing international standards,standards in Japan specify a higher value of
the minimum supporting width,which is used in practical design.
3.3 Design of Unseating-prevention Device
(1) Design value of unseating-prevention device load H
In earthquakes,collapse of main beam is a complex dynamic phenomenon.Before the main
beam collapses,force on the connection cable is negligible [10].If t = 0,one end of girder falls.
The load R
is added on the cable until the bridge is restored.The representation formula is as
3674 C.Tang et al./Journal of Information & Computational Science 10:12 (2013) 3667{3676
P(t) =
0;t < 0
;t > 0
The displacement formula of SDOF system in static status initially with the force of any
dynamic load P(t) is as follows:
y(t) =

p() sin!(t )d (4)
Substituting formula (3) into formula (4),we obtain the dynamic displacement formula (formula
5).If t > 0:
y(t) =

sin!(t )d =
(1 cos!t) (5)
In formula (5),m is the mass of girder connected to the Cable;!is self-resonant frequency.
Static displacement 
of Cable caused by equivalent static load H
is as follows:

According to the reciprocal principle of power,the following is achieved:

= R
y(t) (7)
Substituting (5) and (6) into (7) we get H
= R
(1 cos!t),from which we deduce
the following:
= R
(1 cos!t) (8)
Then the maximum value of H
is [H
Actually,seismic force on unseating prevention device is not as ideal as the above sudden
loading.When the girder falls,it has initial velocity.To ensure certain safety coefficient of
unseating-prevention device,according to “Document on Seismic-resistant Design of Road Bridges
of Japan Road Association” and other foreign standards and literature,it is suggested that the
design load of unseating-prevention device to be calculated as follows:H
= 1:5R
(2) Design value of amount of movement S
To prevent fallen girder caused by over-large relative displacement of the upper and lower parts,
adequate seat length S
shall be increased.The adequate seat length is the distance fromthe end
of girder to the supporting edge of lower part,to prevent the upper part from falling from the top
of pier when over-large relative displacement of the upper and lower parts occurs.The minimum
value is S
= 70 + u
,and the maximum is S
= 50 + l.In the formula,unit of S
is cm;
is the maximum relative displacement (cm) of the upper and lower parts in large earthquake
(L2-magnitude);l is the calculated span (m) of girder.The long span shall be calculated if the
neighboring spans are different.
C.Tang et al./Journal of Information & Computational Science 10:12 (2013) 3667{3676 3675
To ensure unseating-prevention device is unaffected by the force of bridge in normal use and
girder take off the seat is allowed in unexpected large earthquake,it aims at preventing the fall
of girder.The gap S
since collapse-proof device starts to work is calculated as follows:
= C
In the formula:C
is design coefficient,commonly set to 0.75.If supporting is damaged or
repair and maintenance are difficult,C
< 0:75.S
is the supporting length of girder.
(3) Design of seismic restrainer
Seismic restrainers are installed among girders or piers to effectively control structural displace-
ment in earthquakes [11].In sequence,seismic restrainers are divided into first device and second
device.The first device starts to work at the beginning of earthquake and generally relies on
strength of materials to resist the seismic force.It is mainly for resistance to pier displacement
caused by earthquake with corresponding intensity.The second device is the final defensive line
to prevent the fall of girder in the upper part in case strong earthquake occurs when the first
device is damaged,as shown in Fig.10.
Second device
Second device
Second device
First device
First device
First device
(a) Work normally (c) Second device to constrain movement(b) First device relented
Fig.10:Mechanisms of unseating restrainers
4 Conclusions
(1) Common seismic damages to bridges are the slip of support,large displacement of girder,
damage of anti-seismic block,and fallen girder.Most bridges adopt plate rubber supports,with
the girder directly seated on the support.Hence,connection of the upper and lower parts is
relatively weak and girder falling easily occurs.It is vital to take measures to prevent the fall of
(2) According to structural features of bridges and investigation of the fallen girders,most are
longitudinally fallen girders.Hence it is an effective way to control the width of bent cap.
(3) Unseating-prevention design shall reasonably deal with pier,main beam,support,bent cap
supporting width and collapse-proof structure.Limitation of maximum slip length and sufficient
supporting width and installation of collapse-proof device are able to prevent the fall of girder and
meet anti-seismic design principle of being unbroken in small earthquakes,repairable in medium
earthquakes and non-collapsed in large earthquakes.
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