**3. Description of the bridge**

The bridge is located at the Primary State Highway No.1, Seattle Freeway Ravenna Boulevard Overcrossing North Bound. Figure 1 shows an aerial view of the bridge. The North Bound Bridge is the first bridge from below shown in the picture. The bridge length is 1310 ft back to back of pavement seats and consists of twenty spans. Plan and elevation views are shown in Figure 2 and Figure 3.

**Figure 1.** Aerial view of the North Bound bridge

Nonlinear static analysis under monotonically increasing lateral loading is becoming an increasingly popular tool for seismic performance evaluation of existing and new structures. Pushover analysis can be viewed as a method for predicting seismic force and deformation demands, which accounts in an approximate manner for the redistribution of internal forces occurring within the inelastic range of structural behavior. It is expected to provide information on many response characteristics that cannot be obtained from an elastic static or dynamic analysis. Pushover analysis is based on the assumption that the response of the structure can be related to the response of an equivalent SDOF system. This implies that the response is controlled by a single mode, and that the shape of this mode remains constant through the time history response. These assumptions are likely to be reasonable if the structure response is not severely affected by higher mode effects, or the structure has only a single plastic mechanism that can be detected by an invariant load pattern. The use of at least two load patterns that are expected to bound inertia force distribution is recommended. For structures that vibrate primarily in the fundamental mode, pushover analysis will very likely provide good estimates of global as well as local inelastic deformation demands. It will also expose design weaknesses that may remain hidden in an elastic analysis. Such weaknesses include storey mechanisms, excessive deformation demands, strength irregularity, and overloads on potentially brittle elements, such as columns and connections. On the negative side, the most critical is the concern that the pushover analysis may detect only the first local mechanism that will form in an earthquake and may not expose other weaknesses that will be generated when the structure's dynamic characteristics change after the formation of the first local mechanism.

238 Engineering Seismology, Geotechnical and Structural Earthquake Engineering

The purpose of this research is to evaluate the displacement capacity of bents from a long span bridge. A three-dimensional nonlinear finite-element model of the bridge bents were devel‐ oped to determine the inelastic response by performing nonlinear pushover analysis. Modal pushover analyses were carried out in the transverse direction. Detailed data of performance was collected and interpreted to use as a baseline in a parametric study. Separate parametric study was carried out on a single column within this bridge in order to locate appropriate plastic hinge locations. These results were then transferred to individual bents, where multiple columns were modeled based on the results from the single column parametric study.

The bridge is located at the Primary State Highway No.1, Seattle Freeway Ravenna Boulevard Overcrossing North Bound. Figure 1 shows an aerial view of the bridge. The North Bound Bridge is the first bridge from below shown in the picture. The bridge length is 1310 ft back to back of pavement seats and consists of twenty spans. Plan and elevation views are shown in

**2. Objectives of the analysis**

**3. Description of the bridge**

Figure 2 and Figure 3.

**Figure 2.** Plan view of the North Bound Bridge

**Figure 3.** Elevation view of the North Bound Bridge

The superstructure is composed of pre-tensioned concrete beams. Each span includes twelve girders, and the general girder cross-section varies for each span. This complicates the calculation of the total mass of the superstructure. In order to simplify the procedure, indi‐ vidual span cross-sections were drawn in AutoCAD. The sections can be found is Figure 4 relating them to the spans they are assembled for. A table with calculated weight and length for each span can be found in the Appendix. Overlaid on top of the girders is a 5 in thick, approximately 60 ft wide reinforced concrete deck slab.

**Figure 5.** Cross-Beam Plan for Bents

**Figure 6.** Section Thru Cross-Beam

The columns are spaced at 18 ft centerline to centerline. Each column is hollow with an outer diameter of 48 in and a wall thickness of 5 in. Twelve evenly spaced No. 5 bars provide the longitudinal reinforcement within each column. The columns also include twelve No. 3 steel

Pushover Analysis of Long Span Bridge Bents

http://dx.doi.org/10.5772/52728

241

**Figure 4.** Superstructure Sections

There are a total of 19 bents in the bridge. Five are 6-column bents (#1-6), three are 7-column bents (#18-20) and ten are 4-column bents (#7-17). The cross-beam plans for the three types of bents are shown in Figure 5. Each bent has a unique elevation above the ground. Also, because of the curved shape of the bridge, each bent has a slight rotation in the vertical direction. Consequently, there is column height variation within each bent. The various column height values can be found in the Appendix.

At each bent, a 3x4.6 ft crossbeam transversely connects the columns. Figure 6 below shows the geometry and steel reinforcement. The length of the beams varies for each bent, which can be found in the Appendix. The steel reinforcement consists of nine No. 10 bars located at the top and at the bottom of each crossbeam. Two No. 5 bars are located at the side edges and run longitudinally along the crossbeam. For shear reinforcement, No. 5 stirrups are spaced evenly along each member.

**Figure 5.** Cross-Beam Plan for Bents

The superstructure is composed of pre-tensioned concrete beams. Each span includes twelve girders, and the general girder cross-section varies for each span. This complicates the calculation of the total mass of the superstructure. In order to simplify the procedure, indi‐ vidual span cross-sections were drawn in AutoCAD. The sections can be found is Figure 4 relating them to the spans they are assembled for. A table with calculated weight and length for each span can be found in the Appendix. Overlaid on top of the girders is a 5 in thick,

There are a total of 19 bents in the bridge. Five are 6-column bents (#1-6), three are 7-column bents (#18-20) and ten are 4-column bents (#7-17). The cross-beam plans for the three types of bents are shown in Figure 5. Each bent has a unique elevation above the ground. Also, because of the curved shape of the bridge, each bent has a slight rotation in the vertical direction. Consequently, there is column height variation within each bent. The various column height

At each bent, a 3x4.6 ft crossbeam transversely connects the columns. Figure 6 below shows the geometry and steel reinforcement. The length of the beams varies for each bent, which can be found in the Appendix. The steel reinforcement consists of nine No. 10 bars located at the top and at the bottom of each crossbeam. Two No. 5 bars are located at the side edges and run longitudinally along the crossbeam. For shear reinforcement, No. 5 stirrups are spaced evenly

approximately 60 ft wide reinforced concrete deck slab.

240 Engineering Seismology, Geotechnical and Structural Earthquake Engineering

**Figure 4.** Superstructure Sections

along each member.

values can be found in the Appendix.

**Figure 6.** Section Thru Cross-Beam

The columns are spaced at 18 ft centerline to centerline. Each column is hollow with an outer diameter of 48 in and a wall thickness of 5 in. Twelve evenly spaced No. 5 bars provide the longitudinal reinforcement within each column. The columns also include twelve No. 3 steel cables each post-tensioned initially to 61 kips. Transverse reinforcement is provided by No. 2 spiral hooping spaced at 6 in on center. Figure 7 shows the plan column section. The columns are extended approximately 27 ft into the ground to act as piles.

**Figure 7.** Plan Column Section

The columns and crossbeam were cast monolithically adding considerable rigidity to each bent. Figure 8 shows the elevation view of a typical bent. Further, the top 4 ft of each column is filled with class A concrete. This fill is further reinforced with sixteen No. 8 bars longitudi‐ nally, and No. 3 hoops spaced at 12 in transversely. In this section of the column, the hollow column is transversely reinforced with No. 2 spiral hooping spaced at 3 in over center. Figure 9 shows a typical pile.

**Figure 9.** Typical Pile

**4. Modeling of the bents**

represented in 3D in Figure 10.

A spine model of each bent is created in the finite element program SAP2000. Line elements can behave three-dimensionally in the form of beam, beam-column elements and springs. The superstructure is represented as a distributed dead load which represents the dead weight of the superstructure based on tributary length of related spans for each bent. A table in the Appendix provides the distributed load values used in the analysis for each bent. The soilstructure interaction is represented by springs. In order to capture nonlinear behavior of the columns, plastic hinges were defined at maximum moment points. The general model is

Pushover Analysis of Long Span Bridge Bents

http://dx.doi.org/10.5772/52728

**Figure 8.** Elevation View of Bents

**Figure 9.** Typical Pile

cables each post-tensioned initially to 61 kips. Transverse reinforcement is provided by No. 2 spiral hooping spaced at 6 in on center. Figure 7 shows the plan column section. The columns

The columns and crossbeam were cast monolithically adding considerable rigidity to each bent. Figure 8 shows the elevation view of a typical bent. Further, the top 4 ft of each column is filled with class A concrete. This fill is further reinforced with sixteen No. 8 bars longitudi‐ nally, and No. 3 hoops spaced at 12 in transversely. In this section of the column, the hollow column is transversely reinforced with No. 2 spiral hooping spaced at 3 in over center. Figure

are extended approximately 27 ft into the ground to act as piles.

242 Engineering Seismology, Geotechnical and Structural Earthquake Engineering

**Figure 7.** Plan Column Section

9 shows a typical pile.

**Figure 8.** Elevation View of Bents

#### **4. Modeling of the bents**

A spine model of each bent is created in the finite element program SAP2000. Line elements can behave three-dimensionally in the form of beam, beam-column elements and springs. The superstructure is represented as a distributed dead load which represents the dead weight of the superstructure based on tributary length of related spans for each bent. A table in the Appendix provides the distributed load values used in the analysis for each bent. The soilstructure interaction is represented by springs. In order to capture nonlinear behavior of the columns, plastic hinges were defined at maximum moment points. The general model is represented in 3D in Figure 10.

The cross-sections of the cap beam and the column were accurately modeled by using the subprogram offered in SAP2000 called Section Designer. Section Designer lets the user draw the shape of the cross-section and also include the steel reinforcement. Figure 11 shows the

The columns were considered fixed in the cap beam. Nonlinear springs along the pile shafts were used to model the resistance provided by the surrounding soil. The L-Pile software (2002) was used to compute the P-Y curves, based on the stiff sand soil model with free water at 15

To build an exact computer model of a structure beard against underground elements-piles it is necessary to know how interaction between soil and a pile can be simulated, to get more precise result of the analysis. The p-y curves is a strait interpretation of the relation between deflection of an element and soil pressure on a particular depth. The pressure from the soil on the element is distributed within certain length which depends on the number of springs

A physical definition of the soil resistance *p* is given in Figure 13. There was made an assump‐ tion that the pile has been installed without bending so the initial soil stresses at the depth *xi* are uniformly distributed as shown in Figure 13*b*. If the pile is loaded laterally so that a pile

the soil stresses will become unbalanced as shown in Figure

with units F/L equation 1.

Pushover Analysis of Long Span Bridge Bents

http://dx.doi.org/10.5772/52728

245

drawn sections used in the analysis.

**Piles**

depths.

assigned to it Figure 12.

**Figure 12.** Model of laterally loaded pile

occurs at the depth *xi*

13*c*. Integration of the soil stresses yielding the soil resistance *pi*

deflection *yi*

**Figure 10.** Model of Six-Column Bents

**Figure 11.** Bent Element Cross-Sections

The cross-sections of the cap beam and the column were accurately modeled by using the subprogram offered in SAP2000 called Section Designer. Section Designer lets the user draw the shape of the cross-section and also include the steel reinforcement. Figure 11 shows the drawn sections used in the analysis.
