Study on the lateral response of the structures under seismic excitation (Adedeji
and Ige, 2011; Sasan and Mohammadsadegh, 2011) and/or
wind load (Majid et al., 2010) is one of the
interesting topic that is mentioned by most of the structural engineers. Recent
study are conducted to clear the ambiguous point of the lateral performance
of the spatial structures such as double layer cylindrical space truss (Jamshidi
et al., 2011), double layer lattice domes (Jamshidi
et al., 2012), metro tunnel (Bagherzadeh and
Ferdowsi, 2009). Avoiding of seismic evaluation of the special structure
in horizontal or vertical direction (Nezamabadi et al.,
2008) based on the lacking of an appropriate seismic provision and/or situating
in the low seismic region (Faisal et al., 2011)
during their design or construction enhanced the probability of retrofitting
in their service time which may need to spending too much money and complex
analysis (Amiri et al., 2008). Equivalent static
loading and dynamic analysis are the most comment methods that used in the seismic
analysis of civil engineering structures (Alsulayfani and
Saaed, 2009). But it is noticeable that time history analysis is time consuming,
spatially when the structural non-linear performance is considered (Majid
et al., 2010); so some of the researchers presented computer aid
(El-Kafrawy and Bagchi, 2007) or try to use some new
mathematical method such as wavelet method to mitigate its required time (Nadhim,
Steel bridge is regarded as anti-seismic structure that using of them is suggested
in the high seismic regions because few collapses of the steel bridge are reported
during the recent earthquake compare to the concrete bridges. There are a few
steel bridges with steel columns; however, the population of them will be increased
when steel bridges with concrete column are considered too, nevertheless, the
number of them is small compare to the concrete bridges. So there are little
data on their seismic performance of them during past earthquakes. Therefore,
considering the steel bridge as an anti-seismic system is regarded to the fact
that a few of them are exposed to seismic excitation rather than their high-capacity
Itani and Bruneau (2004). Some of the designers are
believed that the superstructure which is design for the out-of-plan gravity
load has adequate resistance against lateral loading; this believed is justified
for the concrete superstructure with heavy and stiff features. But slab-on-girder
steel bridges are maybe flexible in-plan (Itani and Bruneau,
Some damages are suffered by steel bridges during the past earthquake such
as Kobe (Bruneau and Dicleli, 1996; Shinozuka,
1995; Astaneh-Asl and McMullin, 1994) and show that
in some case, they will be more brittle than concrete superstructures (Carden
and Itani, 2004). For example, during the Petrolia earthquake, for the southbound
Van Duzen River Bridge, the end diaphragm is buckled and near the end of span,
the concrete covers are spall at the shear stud connection. Anchorage failure
of bearing at the abutment and bent cap is reported during Northridge earthquake,
buckling of the end diaphragm and failure of the connection in the end cross
frame and web stiffeners is observed and minimum damage of the column and pile
show that much of the displacement demand was accommodated in the superstructure
of each of these bridges. Failure of the concrete substructure, steel piers,
bearing and steel girder are typical damages which are observed during Kobes
earthquake. These observations indicted that, most of the steel bridges that
constructed in the seismic hazard zone didnt design base on the seismic
provision and induced the researcher to conduct the extensive study on the seismic
performance of this kind of highway bridges.
Saadeghvaziri and Yazdani-Motlagh (2008) conducted
some analytical study on the multi-span-simply-supported bridges and show their
variability even under low level of PGA.
Most of the bridge structures weight is regarded to the massive superstructure, so the main part of the inertia force during a seismic excitation is induced in the heavy slab deck. Transferring this lateral force to the support, involve some of the superstructure components. Detecting critical component in the load path can be used to improve seismic design and optimized cyclic behavior of the steel bridge structures. In this review, the seismic performance of the single span bridges, multi-span continues bridges and multi-span with simply supported bridges which are three common types of slab-on-girder steel bridges, are presented (Fig. 1).
Bearing force and sliding: As the damages of the slab-on-girder bridge
are reported during the past earthquake, some researchers started their study
to find the reason of these failures. Some study was concluded on the seismic
behavior of the single span; multi-span continues (Dicleli
and Bruneau, 1995c) and multi-span simply supported (Dicleli
and Bruneau, 1995b) steel highway bridges by focusing on the bearing force
and sliding of the girders. They state that the stiffness of the fix bearing
on the abutment severely affected on the period time of the two-span simply
supported bridges and consequently, on their seismic response but by increasing
the number of span, the influence of the fix bearing will be negligible (Fig.
If the single-span bridge is subjected under transverse excitation, Base on
the vectorial summation of the transverse force that induce by transverse reaction
and the longitudinal force which is created by the rational resistance of the
bearing, Dicleli and Bruneau (1995a) show that the critical
bearing is the farthest ones form the bridge centerline (Fig.
The ratio of the maximum bearing force (Br) to the mxAg (which
m is the seismic mass of the bridge and Ag is the pick ground acceleration)
becomes longer when the stiffness of the bearing increases. By increasing the
length of span, this mentioned ratio will be increased but it should be constant
for the bearing with zero rational stiffness. The Br is small in
the elastomeric bearing because of their long-period times.
||(a) Fixed bearing and (b) Rocker bearing (Padgett,
They also have shown that the bearing force for the bridge with 2 and 3 lanes
is the same if the bearings dont have any longitudinal stiffness but if
they have infinite longitudinal stiffness, the bearing force for the 2 lanes
bridge is 50% more than 3 lanes bridge. Failure of the bearing is acceptable
if they are stable and can slide freely once the anchors are damaged during
an earthquake (Bruneau and Dicleli, 1996).
For continues bridges, Dicleli and Bruneau (1995c)
show that the variation of the bearing force is similar to the single-span bridge
but the exiting difference between bearing force for the 2 and 3 lanes bridge
which has bearing with infinite longitudinal stiffness are less than single-span
bridges. And for the simply supported continues bridges that have the bearing
with infinite rotational stiffness, enhancing the length of the span up to 40
lead to the increasing of the TBFC (maximum transverse-bearing-force coefficient)
and TBFC will reduce when the length of span is more than 40 m. In this case
(continues bridges), the bearing force for the bridge which consists of 2 lanes
is more than the bridges with 3 lanes. It is noticeable that the bearing force
is negligible for the bearing with zero rotational stiffness and for this case
of the bearing, the number of the lane has not any effect on the bearing force.
In transverse direction, for the same ratio of the friction coefficient to
the peak ground acceleration, by increasing the peak ground acceleration and
the number of spans, the sliding displacement will be enhanced. On the other
hand, decreasing the above ratio resulted to increase of the sliding displacement.
Using of the wider bridge can reduce the sliding displacement. The sliding of
the narrow longer bridge is noticeable; therefore, in some case, their deck
maybe fell down if the seat width is not sufficient; Dicleli
and Bruneau (1995a) show that the tendency of a seismic excitation to cause
high sliding displacement related to the distribution of an earthquake content
which is a function of the velocity time history. Defining a bridge with more
spans for the constant total length, increase the sliding displacement. The
seismic performance of the continues bridge is severely affected by the magnitude
of the friction coefficient; it means that by using a bearing with the high
friction coefficients, the seismic capacity of the column will be improved.
Regarding to the bearing damage, 2 lanes continue bridge is more vulnerable
than 3 lanes ones (Dicleli and Bruneau, 1995c). Dicleli
and Bruneau (1996) proposed a methodology to evaluate the seismic performance
of slab-on-girder steel bridges.
Slab-on-girder steel bridges without diaphragm: Previously, for calculating
the effective stiffness of the bridges superstructure, the concrete deck
and girders are modeled as a beam with an equivalent effective section on the
column and/or foundation spring.
This theory is acceptable for the concrete bridges and some other bridges
but Zahrai and Bruneau (1998) show for the single span
simply supported bridge without diaphragm that contrary to the concrete slab
which act as a rigid body, steel girders deformed flexible in transverse direction
and its deformation is more noticeable near the bearing supports (Fig.
4). The distortion of the steel girder is severe near the bearing supports.
So traditional procedure isnt useful for calculating the time period and
therefore, appropriate method should be suggested.
Fundamental period: Zahrai and Bruneau (1998)
consider the transverse behaviour of the slab and girder as a beam on elastic
foundation and proposed Eq. 1 to calculate the lateral deflection
(Δr is the bottom flange which is simply supported on both ends:
Rs is the reaction of each girder due to the uniform lateral load applied to the deck; L is the span length:
where, kw is the web stiffness; E is module of the elasticity and
Ih is the bottom flange moment of inertia. So for calculating the
period of the systems Eq. 2-4 are used:
ng is the number of girders; Iw and hw is the web moment of inertia and high, respectively; m is the total mass of the bridge per unit length; Δh and ΔS are shown in Fig. 4.
Effect of the web stiffness: Most of the build-up girders have intermediate
web stiffeners which enhance the shear strength of the beam. Zahrai
and Bruneau (1998) consider the effect of the stiffed web by equivalent
thinner unstiffen web on the seismic response of steel bridges and they show
the high effect of the bearing stiffener on the period time of these structures.
Nonlinear response: As the lateral displacements of the heavy concrete
slab are large so for this kind of bridge without end diaphragm, the P-Δ
effect is more noticeable that may result to the insatiably of the system. Zahrai
and Bruneau (1998) show that via end-diaphragms even with small stiffness
the superstructure act as an unite body in the elastic range but by failure
of the end diaphragms, the seismic behavior change severely and the lateral
displacement increased and the P-Δ effect can remove the stability of the
bridge. So they continue their study to propose effective ductile end diaphragms.
Slab-on-girder steel bridges with ductile end diaphragm: Using of a
ductile end diaphragm over the abutment and piers are suggested by Bruneau
et al. (2002) as an appropriate strategy to improve the seismic performance
of the steel bridges structures. By conducting full-size testing (Zahrai
and Bruneau, 1999a) show that ductile end diaphragms can possess adequate
initial elastic stiffness, strength and high capacity of energy dissipation.
Base on the experimental result the average ductility of 8 to 10 is derived
for the tested end diaphragms (Fig. 5). Analysis show that
the effect of the intermediate diaphragm on the seismic performance when there
is not any end diaphragm is not considerable (Zahrai and
Fundamental period: The stick model is proposed to simplify
analytical development. This model consists of an end diaphragm, a piece of
two steel girder that surrounded the mentioned diaphragm with their bearing
stiffness, a stub of the concrete deck and an additional mass/spring system
that reflected the effect of longitudinal general mass and stiffness (Fig.
||(a) Hysteretic diagram for a specimen without end diaphragm
and (b) Hysteretic diagram for a specimen with EBF end diaphragm (Zahrai
and Bruneau, 1999a)
The most part of the girder stiffness is regarded to the bearing stiffeners,
so consider the longer stub-length of a girder doesnt have significant
influence on the results (Zahrai and Bruneau, 1999b).
As the general, end-diaphragm and substructure stiffness which are detected by K*, Kends and KSubs are connected together as a series spring model (Fig. 6), so the equal stiffness is derived by Eq. 5:
For the single span bridge, based on the high stiffness of the abutment, the third term of the denominator can be ignored. As the interaction of the ductile end diaphragm stiffness (KDD) and the girder stiffness (Kg) can be simulated by parallel spring, so Kendsis calculated by Eq. 6:
Finally, the lateral period time is calculated by Eq. 7:
Different kind of ductile end diaphragm: Zahrai
and Bruneau (1999b) demonstrate how Eccentrically Braced Frames (EBF), Shear
Panel System (SPS) and steel Triangular-plate Added Damping and Stiffness device
(TADAS) can be used as seismic resistance systems of single span bridges
substructures (Fig. 7). They also show that it can calibrate
to yield before reaching the strength of the abutments.
Carden and Itani (2004), conducted an experimental
test to find the efficiency of unbounded brace. The results show that they are
stable during transverse lading and limited the structural displacement more
than X bracing. The hysteric behavior of them is similar to the EBF, TADAS and
SPS end diaphragm but their displacement capacity is more than other diaphragms
Using of ductile end diaphragm as a retrofit strategy: Most of the exciting
stab-on-girder steel bridges are supported by stiffed vulnerable substructure
which expensive method may be required for their retrofitting. (Zahrai
and Bruneau, 1999b) show that the lateral transverse load transmitted from
the heavy superstructure to the pier and abutment will be mitigated by using
ductile end diaphragm.
||(a) Eccentrically braced frames (EBF), (b) Shear panel system
(SPS) and (c) Steel triangular-plate added damping and stiffness device
(TADAS) (Zahrai and Bruneau, 1999b)
By calibrating ductile end diaphragm to yield before reaching the ultimate
resistance of the substructure, they will act as a structural fuse (Fig.
Ductile end diaphragms which are studied by Zahrai and
Bruneau (1999b) can improve the seismic performance of steel bridges in
transverse direction and therefore, are useable for retrofitting of the slab-on-girder
steel bridge in transverse direction. Celik and Bruneau
(2009) proposed a new detail of the ductile end diaphragm by using of Buckling
Restrained Braces (BRBs) system which can use as a suitable strategy for retrofitting
of the steel bridge under bidirectional seismic loading (Fig.
Composite action: Transferring the lateral load from the concrete slab
deck to the bearing support through end diaphragm, highlight the effect of the
composite action at the end of spans. As the shear welding stud may fatigue
under tension, so for some slab-on-girder bridges, no shear connections are
designed in the negative moment. In this reign, the intermediate cross frame
which is located between contraflexure point and end diaphragm have a significant
action to transmit the transverse loading from top flange of the girder to the
bottom flange Itani and Bruneau (2004). Shamshad
et al. (2007) show that the limited-thick transverse slice model
cant capture the real lateral response of the bridge compare to the full
model because in the slice model, the second lateral load path consisting of
the steel girder, concrete slab and shear connector didnt consider (Fig.
Simplified model for transverse girder displacements at the bridge supports:
The efficiency of the end diaphragm is depended to the relative transverse displacement
between concrete slabs and bearing support due to the transverse load which
is applied at the bridge deck. Considering this deformation show that the transverse
stiffness of the girders is depended to the torsional stiffness of the girder
(modelled by a translation spring Kt), rotational stiffness of the
bearing (modelled by a torsional spring Kθb), flexural stiffness
of the bearing stiffeners (modelled by a beam element) and rotational stiffness
of the deck or connection between steel girder and concrete slab (modelled by
a torsional spring K0g) (Fig. 12). Carden
and Buckle (2007) are modelled two different girders at the end of the single-span
or continues bridge and a steel girder at the intermediate support; and then
calculates the capacity displacement of these girders.
By removing, the portion of the effective cross-section which is required to
carry gravity load (Fig. 13), Carden
and Buckle (2007) calculated the maximum moment capacity of the bottom which
is residual to carry lateral girder deformation and also the allowable girder
For the section between ends of the girder and intermediate cross frame, the
maximum stress will be taken place at the bottom flange if the transverse load
acts on the system (Carden and Buckle, 2007). Preventing
of the girder rotation under concrete slab by using of composite action, cause
distress to the shear stud and concrete deck.
To facilitate the rotation of the end of the steel girder, Carden
and Buckle (2007) proposed a length in each side of the support without
shear stud. By equalling the induced torque (Tf) at the top flange
to the ultimate torsional resistance of a row of shear stud (Tusr),
this mentioned length will be derived:
For the multi-span steel bridges, Carden and Buckle (2007)
show that removing the shear connector in the negative moment reign decrease
the transferred base shear to the substructure until 23% compared to the bridge
with full composite action. Additional bending stress will be induced in the
girder above the bent base on the non-composite action of the slab-on-girder
section which may lead to yield or buckle of the flange. For confirming of transition
of the transverse load to the end cross frame another element should be considered
(Carden and Garcia-Alvarez, 2002). Itani
and Bruneau (2004) found that design the top chord of the end diaphragm
to provide composite action in the negative zone give a favourite pass in transferring
lateral load from the deck to the bearing support.
Such an element is proposed by Carden and Itani (2006),
who show that by modifying the connection detail of the single angle concentrically
brace (Fig. 14), it can be used as a ductile end diaphragm
(Carden and Itani, 2006) and also show that using of
the buckling restrained braces can improve the hysteresis behaviour of the steel
bridges (Carden and Itani, 2006).
Bahrami and Buckle (2007) stated that contribution of
the torsional stiffness of the steel girders in the lateral load pass enhanced
the transferred shear force to the abutment and piers and it can be reviled
by using of decouple ductile end diaphragm. The shear transmitted to the substructure
by using such a decoupled end diaphragm (Fig. 15) is around
25% of the shear that transformed with conventional end diaphragm.
Recent studies show that absence of the end diaphragm slack the traditional procedure for calculating the period time because of the lacking of the adequate assumptive rigidity. This level of flexibility was enough to enhance the effect of P-Δ that may result to the insatiably of the system. Reported damage of the exciting slab-on-girder steel bridges show that most of them are supported by stiffed vulnerable substructure which, expensive method may be required for their retrofitting. Using of the structural fuse in the lateral load pass such as ductile end diaphragms which are calibrated to yield before reaching the ultimate resistance of the substructure, are proposed as an efficient retrofitting strategy. It also recommended that dont use shear connectors in the negative moment region to exclude of creating distress to the shear stud and concrete deck based on the prevention of the girder rotation. For confirming of transition of the transverse load to the end cross frame another element should be considered to provide composite action in the negative zone.