The Effect of Direction of Orthogonal Horizontal

8th International Congress on Civil Engineering, May 11-13, 2009, Shiraz University, Shiraz, Iran

The Effect of Direction of Orthogonal Horizontal Components of Earthquake on the Nonlinear Response of Skewed Bridges

Afshin Kalantari1, Mohsen Amjadian2 1- Assistant professor, International Institute of Earthquake Engineering and Structural Dynamics 2- Graduate student, International Institute of Earthquake Engineering and Structural Dynamics [email protected]

Abstract The effects due to the combination of bilateral skewed horizontal components of earthquakes on the nonlinear responses of the skewed bridge piers are investigated using a time domain nonlinear finite element program. Seismic responses of bridge piers are evaluated realistically by simultaneously applying the both horizontal components of earthquake strong ground motions. Analyzes have been done with varying angle of horizontal components of the ground motion from 00 to 900 relative to the bridge deck to find out the effect of direction of components of earthquake on nonlinear response of a bridge piers. A 3D nonlinear model of Foothill Bridge in California was constructed. The plastic hinge formation trends, hysteresis cycles and base shear values of piers have been investigated. Numerical results show that the response of skewed bridge piers are affected by varying the direction of horizontal components of earthquake. Keywords: skewed bridges, direction of earthquake, nonlinear response.

1.

INTRODUCTION

Bridges as one of the elements of transportation systems, depending on the road and site conditions as well as aesthetics considerations, have different geometries. Unlike the normal bridges the special bridges such as cbent bridges, curved bridges or skewed bridges face with various problems during seismic excitations. Furthermore, due to less specific studies on such structures, only a few special criteria and regulations may have been provided in design codes and guidelines. Among these, skewed bridges may find hazardous condition during an earthquake due to the collision of the deck and abutments that may consequently cause torsion in the piers. It has been shown that the bridge piers are subjected to the combination of torsion and bending moments, significant seismic capacity reduction may be observed in them. [1- Hsu, H.-L and Wang, 2- Hsu, H.-L and Liang] Extensive researches have been conducted on the dynamic behavior of skewed bridges. Khaloo and Mirzabozorg (2003) studied about the load distribution factors in simply supported skew bridges. They conducted finite element analysis on five simply supported bridges with i-section concrete girders. The nonlinear dynamic response of columns was not focused in the study. Tirasit and Kawashima (2005) reported that the seismic torsions in skewed bridge pries are larger than those of straight bridge piers. Moreover, skewed bridge piers have higher ductility demands. They also studied the effect of pounding and failure of the bearings on the piers. Malaki (2005) performed a parametric study to investigate the pounding effect of the superstructure on the bearing retainers when a gap is present. He concluded that ignoring the gap in the analysis could cause erroneous non-conservative results. Due to yielding of retainers, the use of nonlinear material modeling for the retainer was also recommended. Here again the ductility of the piers and their nonlinear behavior was not included in the study.


Maleki and Bisadi (2006), studied the orthogonal effects in seismic analysis of skewed bridges. In their studies, they investigated the effects of seismic force direction on the response of slab-girder skewed bridges in response and time history dynamic analysis. They also examined the combination rules for orthogonal earthquake effects such as the 100/30, 100/40 percentage rules and the SRSS method. In their conclusion they mentioned that either the SRSS or the 100/40 percentage rule in the skew direction should be used in the response spectrum analysis. For time history analysis also, they expressed that none of the combination rules provide conservative results. However, during the study they have conducted linear analysis. Nonlinear behavior of piers in skewed bridges may occur during severe earthquakes. The change in the dynamics of the structure due to nonlinear behavior of its elements can change its load-bearing mechanism along the earthquake duration. This is more complicated when different cases of seismic load cases are applied to the structure by means of changing the direction of the excitations. The horizontal seismic excitations are usually modeled by a pair of acceleration time histories that are applied simultaneously as input to the model. Usually two orthogonal components of the earthquake are applied on the parallel to the principle axes of the structure in time history analysis. The skewed bridges are complex structures whose principle axes are not parallel and normal to the deck direction. In this study, the changes in the nonlinear response of piers of a skewed bridge are investigated under various seismic excitations directions. To this end, a nonlinear 3D model of a bridge is modeled in OpenSees software. The characteristics of the structure and dynamic model are introduced and the results of the nonlinear analysis are discussed then.

2.

BRIDGE DESCRIPTION

An 83.82-meter long four span concrete girder skewed bridge illustrated in Figure 1 is the representative bridge in this research. The skew angle is 60°. The details of the piers in different bents are presented in Figures 2c. The deck is taken as a continuous beam with rigid connections to the Columns. The deck is simply supported at the abutments.

a) Bridge plan view (m)

b) Bridge elevation Figure 1: Description of the bridge under study, a) plan b) Elevation

(a)

(b)

Figure 2: a)Bridge section view of bent No.3 (m) b) column sections (m)

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3.

NUMERICAL MODELING

A 3D finite element model of the bridge was constructed in OpenSees software [Ref]. The fiber elements were utilized to introduce the section of the piers. To simulate the nonlinear behavior of the RC section, concrete02 and Steel02 were employed as the materials to model the steel rebar and concrete, respectively. The specifications of the material including the compressive strength of the material of the core and cover as well as steel properties are mentioned in Table 1 and 2, respectively. The nonlinear behavior of the elements are also presented in Figures 2 and 3. Table 1: Concrete material property

Ec(Mpa) Et(Mpa) ρ(kg/m3)

Property

fc(Mpa)

εc

fu(Mpa)

εu

ft(Mpa)

λ

Core Cover

23.302 21

0.00262 0.002

17.842 4.46

0.00703 0.004

2.23 2.1

0.15 0.15

22913 22913

1115 1050

2400

Table 2: Steel material property

fy(Mpa)

b=

270

E Post −Yeild Tangent EInitial − Elastic Tangent 0.01

Es(Mpa) 200000

(a)

(b)

(c) (d) Figure 2: a) Material parameters for Concrete02, b) Hysteresis behavior of Concrete02, c) Material parameters for Steel02, d) Hysteresis behavior of Steel02. [ref]

The nonlinear element dispBeamColumn was used in the model. Table 3 presents the dimensions of the beams and cap beams. Table 3: Equivalent deck beams and cap beams dimensions

Property

As(m2)

Isy(m4)

Isz(m4)

Js(m4)

S(m)

Deck beams

4.232

2.681

0.038

8.133

5.477

Property

Ac(m2)

Icy(m4)

Icz(m4)

Jc(m4)

Cap beams

2.971

0.972

0.557

1.130

A scaled version of 1971 San Fernando earthquake recorded in Pacoima dam is employed for this study. The time history and spectral response of the two components of the record are presented in Figure 3. Several analyses are performed to calculate the seismic response of the introduced model under this excitation with θ value changing from 00 to 900 at 150 intervals.

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Figure 3: Acceleration time history and spectral values for two orthogonal ground motion components

The orthogonal components of ground motion (P as for longitudinal and N as for Normal to the deck direction) are assumed to be applied to the model in different directions expressed by θ as shown in Figure 1.

4.

RESULTS

The preliminary results of the nonlinear dynamic analysis have been shown the following Figures (Fig.4-8). The maximum values of axial force are presented in Figure 4. Figure 4 shows that the maximum axial force of the columns did not occur in the expected Teta=00, but about Teta=750. In case of shear force in the columns although the shear force in Y direction when Teta=00 tends to show a maximum response of the piers but such a conclusion can not be made when the results in X direction are considered. For the bending moment results shown in Figure 6, the maximum value when Teta=00 is observed in X directions. The torsional response of the piers occurred in intermediate pier when Teta=00.

Figure 4: Maximum value of axial force for different angles

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(b)

(a)

Figure 5: Maximum value of shear force for different angles a)Longitudinal direction, b)Transverse direction

(b)

(a)

Figure 6: Maximum value of bending moment for different angles a)About of longitudinal direction, b)About of transverse direction

Figure 7: Maximum value of torsional moment for different angles

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5. CONCLUSIONS Although, in some cases, the maximum time history response of the piers occurred when Teta=00, more study is required to investigate the skewness effects and input seismic motions with different frequency contents. 6.

REFRENCES

1. Hsu, H.-L. and Wang, C.-L.: “Flexural-Torsional Behavior of Steel Reinforced Concrete Members Subjected to Repeated Loading”, Earthquake Engineering and Structural Dynamics, 29, 667-682, 2000. 2. Paiboon Tirasit, Kazuhiko Kawashima, “Seismic Torsion Response of Skewed Bridge Piers”, JSCE Journal of Earthquake Engineering, 2005. 3. Ali R. Khaloo1 And H. Mirzabozorg, “Load Distribution Factors In Simply Supported Skew Bridges”, Journal Of Bridge Engineering, ASCE, Jul/Aug 2003. 4. S. Maleki and V. Bisadi, “Orthogonal Effects In Seismic Analysis Of Skewed Bridges”, Journal of Bridge Engineering, ASCE, January/February 2006. 5. Shervin Maleki, “Seismic Modeling of Skewed Bridges with Elastomeric Bearings and Side Retainers”, Journal of Bridge Engineering, ASCE / July/August, 2005. 6. Mazzoni S., McKenna F., Scott M.H., Fenves G.L., et al, “Open System for Earthquake Engineering Simulation User Command-Language Manual” , Pacific Earthquake Engineering Research Center, University of California, Berkeley, OpenSees version 1.7.5, September 2006.

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