SEISMIC DESIGN OF SINGLE SPAN STEEL GIRDER BRIDGES AND BRIDGES IN SEISMIC PERFORMANCE CATEGORY A

This paper studies the validity and accuracy of the seismic design force recommended by AASHTO for single span bridges. A parametric study for single steel girder bridges is presented, included the effect of span length and elastomeric bearing and lateral bracing (cross-frame) stiffness. The results of simplified AASHTO method are compared with response spectrum and time history analysis. Also studying the seismic design reqiurements for continuous steel girder bridges in seismic performance category (A), included the effect of span length, seismic zone, effect of elastomeric bearing and cross-frame stiffness and bridge skew on their seismic responses. It is concluded that the AASHTO simplified analysis method for single span bridges underestimates the seismically induced forces at supports and the proposed seismic design force of (2.5 multiplied by acceleration coefficient multiplied by tributary weight w(x)) has been recommended for single span bridges for seismic zone 3 and 4 and for soil type II. Also it is observed that the seismic design force for two span continuous bridges in performance category A is safe and conservative method to predict the shear forces transferred by connection elements to the substructures


INTRODUCTION
The recent edition of AASHTO specification (AASHTO, 2002) does not required any seismic analysis, regardless of seismic zone for single span bridges.However, AASHTO required that the connection between the superstructure to substructure shall be designed to resist a force equal to design acceleration coefficient (A) multiplied by the site coefficient (S) multiplied by the tributary weight at the abutment.
To study the validity and accuracy of the seismic design force recommended by AASHTO for single span bridges, a parametric study for single span steel-girder bridges is presented in this paper included the effect of span length and support stiffness (bearing and cross-frame stiffness) on seismic response of these bridges.

DESCRIPTION OF BRIDGES
A steel-girder bridge consisting of (0.24m) reinforced concrete slab built integrally with rolled steel beams spaced at (2 m) is studied.The carriage way is (10 m) and the slab has a (1 m) overhang on both sides of the deck.The span lengths of these bridges range between 20 and 60 m with increment of (10 m).The end of steel beam is placed on elastomeric bearing in the longitudinal direction and the steel girders are connected together by cross-frames as shown in Fig. (1).The bridges are designed according to the AASHTO requirements and the bearings are designed according to Iraqi loading.The properties of bridges are summarized in tables (1) and (2).
The slab is modeled with (2×2 m) shell elements and the girders are modeled by frame elements connected to the shell elements at each joint.The end of each girder is attached to a spring representing the elastomer's lateral stiffness in longitudinal direction and in transverse direction it is attached to a spring representing the lateral stiffness of end cross-frame.The value of stiffness for both elastomeric bearing and lateral bracing system is determined as explained in the following sections.The finite element model of the bridges is shown in Fig. (2).Modeling of the superstructure is consistent with recommendations of (Tarhini and Frederick, 1989) and ( Mabsout, et. al., 1997).SAP 2000 finite element program is used for analysis (Computer andStructures, SAP 2000, 1998).

STIFFNESS OF LATERAL BRACING SYSTEM
Diaphragms provide an important load path for the seismically induced load acting on slab steelgirder bridges.

Elastomeric Bearings Stiffness
The elastomeric bearings transmit the force from the superstructure to substructure.Spring is used to model the stiffness of elastomeric bearing (k e ) in the longitudinal direction.The value of bearing stiffness can be determined from the following equation (Mast et. al., 1996): where: G : shear modulus of elastomer.A : area of bearing.T : total thickness of rubber layers.

SEISMIC DESIGN FORCE FOR BRIDGE
The bridges are assumed to be located in Iraq (Baghdad city).The contour map in AASHTO is for United State.Depending on UBC code (Uniform Building Code), Baghdad is located in zone 3 and the AASHTO divided the region into contour lines with (A) range (A>0.29),therefore (A) for Baghdad is assumed to equal (0.3).
To study the validity and accuracy of seismic design force recommended by AASHTO for single span bridge, the bridge models are analyzed for three loading cases:  Multi mode response spectrum analysis (MMRS method): using the AASHTO'S design response spectrum curve for seismic zone of acceleration coefficient (A) equal to (0.3) and soil profile type II (Site coefficient (S)=1.2).  Simplified AASHTO method (AASHTO method) in this method the bridge models are subjected to load of (S A=1.2 0.3w(x) = 0.36w(x)) in two orthogonal directions. Time history analysis (TH method) in this method the bridges are assumed to excite by a real earthquake time history accelerogram.El Centro earthquake accelerogram of May 18, 1940 is used for time history analysis.The El Centro horizontal component (north-south component) is applied in the two horizontal directions (X, Y) and the ground acceleration data includes 1559 data points of equal time intervals of (0.02 sec) (Chopra, 1996).The numerical values of the data are in units of the gravitational acceleration (g).

Discussion of the Results
The variation of longitudinal periods against the span length for bridge models with different support conditions is shown in Fig. ( 6).Whereas, The longitudinal period decreases severely when the elastomeric bearing stiffness reached infinity (pin-x support).However, the periods of spring and pin-y condition coincide.This means that longitudinal vibration is unaffected by the lateral bracing stiffness (cross-frame stiffness).The longitudinal period for all cases increase as the span length increases.Fig. ( 7) shows the variation of transverse periods against span length for different support conditions.Comparing the transverse period for spring support and pin-y support condition, it can be concluded that the period decrease as the stiffness of cross-frame increases toward infinity (pin-y).The transverse period for pin-x support is closed to period for elastic support for span length upon (30 m) that means the increasing of elastomeric bearing to infinity for span length upon (30 m) does not affect the transverse period significantly.
Maximum longitudinal and transverse deck displacements due to MMRS method versus span length are plotted in Figs. ( 8) and ( 9), respectively.It is shown that the displacement increases as span length increases.The longitudinal displacement for bridges which are supported on elastomers is much higher that for bridges with pin-x support, because that the bridges with elastomers support are more flexible and have vibration periods higher than for pin-x support bridges by several times.
The response spectrum for El Centro ground motion with scale ratio of (3/4) and 5% damping ratio agrees well with the AASHTO design response spectrum for acceleration coefficient (A=0.3) and soil type II (S=1.2) as shown in Fig. ( 4), therefore, the (3/4) scaled El Centro accelerogram with 5% damping ratio is used for linear time history analysis.The response spectrum of El Centro ground motion is obtained and drawing by using SAP Nonlinear program.5) shows that the AASHTO design response spectrum have a constant acceleration of (2.5A) for soil type I and II for periods below than (0.43715 sec).The single span bridges which are studied have periods less than (0.43715 sec) of transverse vibration for all support stiffness and of longitudinal vibration with pin-x and pin x-y cases.The bridges are analyzed for seismic force of 2.5 A multiplied by tributary weight.10) shows the variation of longitudinal shear forces against span length for the three loading cases.In the longitudinal, the simplified AASHTO and time history forces are very close for all support conditions, but the MMRS method is yielding a higher force than (AASHTO) and (TH) methods.11) shows the variation of transverse shear forces versus span length with different support conditions for the three loading cases.In transverse direction, the simplified AASHTO method yields a higher force than time history force at 20m span length, but for span length beyond 20 m, the simplified AASHTO method yields a lower force demand for all support conditions and it become unsafe.While the MMRS method is yielding higher forces than (AASHTO) and (TH) methods.

INTRODUCTION
AASHTO specification does not consider seismic forces for design of structural components for bridges in low seismic zones such as SPC (A) [A<= 0.09] except for the connection between superstructures to substructures.AASHTO requires that the minimum connection force that must be transferred from superstructure to its supporting through the bearings is 20% of the weight that is effective in the restrained direction.

CASES STUDIED
Two span continuous steel girder bridges are studied.The same cross section properties that were used for single span bridges are adopted here.The span length of these bridges range between 20 and 60 m with increment of 10 m.The straight and skewed bridges with skew angles varying from 0 to 60 degrees are considered.The bridge is supported on elastomeric bearings in the longitudinal direction and cross-frames in the direction parallel to skew of the deck.The values of stiffness for both elastomeric bearings and cross-frames are determined as explained above.The elastomeric bearing and lateral bracing are designed due to Iraqi loading.The properties of elastomeric bearing and lateral bracing system for end support are summarized in table (3) and for central support are the twice of these for end support.Springs are used to model the elastomeric bearing stiffness and crossframe stiffness.For skewed bridge, the spring in the direction parallel to the skew that simulates the

Analysis of the Bridge Models
A parametric study is performed to study the validity of seismic design force recommended by AASHTO for bridges in SPC (A).The bridge models are analyzed by two methods:  Response spectrum analysis (dynamic analysis) using the AASHTO's design response spectrum curve with acceleration coefficient (A) equals to (0.05 & 0.09) and soil profile type II (site coefficient(S)=1.2) which are applied in two horizontal orthogonal directions X and Y.  Simplified AASHTO method (static analysis): according to his method a static load of [0.2 w(x)] is applied uniformly on the bridge model in two horizontal orthogonal directions X and Y.

Fig
Fig. (1) Cross section of the bridge Zahrai and Bruneau (1998) have shown that the intermediate cross-frames do not affect the seismic response of straight slab on girder bridges, in either the elastic or inelastic range also proposed a simplified model for bridge with only end cross-frames as shown in Fig. (3).The stiffness of lateral bracing system (k b ) at one end depends on the geometry of the bridge and the properties of the bearing stiffeners and diaphragm braces.K b can be calculated by the following equation (Zahrai and Bruneau, 1998): k b (1) The k b for each interior steel beam can be determined from the following formula: k b ( 2 ) The k b for exterior steel beam can be determined from the following formula: moment of inertia of the bearing web stiffener about the longitudinal axis of girder.ng : the number of girders.h w : the web height between top and bottom flanges.A b : cross sectional area of the brace.L b : length of brace.θ : slope angle of brace.

Fig. (
Fig.(5)  shows that the AASHTO design response spectrum have a constant acceleration of (2.5A) for soil type I and II for periods below than (0.43715 sec).The single span bridges which are studied have periods less than (0.43715 sec) of transverse vibration for all support stiffness and of longitudinal vibration with pin-x and pin x-y cases.The bridges are analyzed for seismic force of 2.5 A multiplied by tributary weight.

Fig
Fig. (4) Comparison of El Centro spectrum with AASHTO design spectrum for A=0.3

Fig. (
Fig. (11) shows the variation of transverse shear forces versus span length with different support conditions for the three loading cases.In transverse direction, the simplified AASHTO method yields a higher force than time history force at 20m span length, but for span length beyond 20 m, the simplified AASHTO method yields a lower force demand for all support conditions and it become unsafe.While the MMRS method is yielding higher forces than (AASHTO) and (TH) methods.

Fig
Fig. (6) Longitudinal period variation versus span length for a single span bridge with different support conditions.

Fig
Fig. (12) Finite element model of two span continuous bridge