Advances in Bridge Engineering, March 24 - 25, 2006
FINITE ELEMENT ANALYSIS OF SKEW-CURVED RC BOX GIRDER BRIDGES Vishal S. Jawanjal and Manoj Kumar Birla Institute of Technology & Science, Pilani ABSTRACT
Bridges are the key elements in any road network. Use of box girder bridges is gaining popularity in bridge engineering fraternity because of its better stability, serviceability, economy, aesthetic appearance and structural efficiency. Its rigidity against torsion under asymmetrical loads makes it an optimum choice for bridges curved in plan or elevation. The curved and skew box-girder bridges are common sight nowadays, however, some times the site situation demands to go for intricate spans geometries such as skewedcurved spans. The present paper deals with the Finite Element Analysis of simply supported box-girder bridge curved in plan with skewed supports. In this study the finite element analysis has been carried out using the 9-node degenerated shell element, however, the geometry of the bridge has been modeled with the help of STAAD Pro. In order to study the behavior of skewed-curved box-girder bridge, a 20m span Reinforced Concrete (RC) bridge has been considered and the degrees of curvature and skewness has been varied to study the effect of curvature and skewness on deflection, longitudinal bending stress and and shear lag. Keywords: Box Keywords: Box Girder, skew-curved bridge, Finite Element Analysis, coefficient of shear lag INTRODUCTION
Over the last few decades, the enormous growth in traffic volume has resulted into the congested roads, reduced speed and long traffic traffic jams specially in areas. In urban dense areas, for smooth flow of traffic, there is a growing need to place new highways in existing transportation corridors in order to minimize disruption and land acquisition. This results in grade-separated intersections where the structures may be curved and skew. The use of curved and skew spans is common in the flyover construction but sometimes the situation demands to go for intricate span geometry such as a span, which is curved in plan and supported on skew supports. In New Delhi, two noted examples were found out for skew-curved category viz. the Dhaula Kuan Interchange and Mass Rapid Transit System (MRTS) flyover at GT r oad [Tandon, 2003]. The analysis of bridge curved in plan is complex, however, the presence of skewness in the bridge curved in plan makes the analysis more complicated. complicated. The bridges curved in plan are subjected to high torsional loading in addition to longitudinal and transverse bending due to eccentric vehicular loading and thus changing the initial geometry of the structure due to deformations in the section. The use of the concrete box girders in highway and flyover bridge construction has proven to be very efficient structural solution. Box girder sectrions are commonly used in curved bridges due its rigidity and stability to keep the original geometry intact in the presence of high torsional moments. Moreover, in addition of its structural behavior, economy and
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aesthetics makes it an optimum choice for bridges curved in plan or elevation. [Sennah and Kennedy, 2002] Present paper is concerned with the investigation of the deflection, longitudinal bending compressive stress and coefficient of shear lag in curved, skewed, and skewedcurved box-girder bridges due to its self-weight and live load. To this end, single cell vertical web reinforced concrete (RC) box-girders with various curvature and skewness have been analyzed using the Finite Element Method. Finite element analysis of the bridge is carried out using the 9-node degenerated shell element, however, the geometry of the bridge has been modeled with the help of STAAD Pro. STRUCTURAL BEHAVIOR OF BOX GIRDERS
The structural response of a box girder bridge consists of five primary actions, viz., longitudinal bending, transverse bending, torsion, distortion or deformation and warping. Under the self-weight and other symmetrical loadings the section primarily experiences longitudinal and transverse bending, however, all of the above responses are combinedly present in case of asymmetrical loads, which is common in box girder bridges. It may be noted that deformational stresses (resulting from torsion and distortion) can occur even under symmetrical loading if the supports are skewed or if the bridge is curved in plan [Chapman, et al., 1971]. In general, the shape of the cross section deforms by transverse bending of walls arising due to absence or insufficient rigidity of diaphragms. Deformation of cross section is resisted by diaphragms, which also significantly effect the distortional moment. Warping is the out of plane displacement of fibers of the cross sections in longitudinal direction and occurs under torsional loading. Moreover, in box-girder bridges, the longitudinal bending stresses in the regions close to the webs are found greater than those in the flange remote from the web due to shear deformation and this phenomenon is called shear lag. Shear lag is an important parameter in the study of box girders and is represented in the form of Coefficient of Shear Lag (CSL). CSL is defined as the ratio of longitudinal stresses obtained by finite element analysis and those obtained by simple bending theory. GEOMETRIC CONFIGURATION OF THE BRIDGES ANALYZED
In order to demonstrate the behaviour of curved, skewed and skewed-curved boxgirder bridge, a 20m long two-lane single cell box girder with vertical webs is considered. The section of the bridge considered is shown in Fig. 1. In order to study the behaviour of curved, skewed, and skew-curved, six models of bridge as shown in Figure 2 have been analyzed. The first section is straight without any curvature and skewness. To investigate the effect of skewness and curvature on behaviour of box girder, two skew bridges with skew angle 150 (skew-15) and 300 (skew30) and two bridges curved in plan with angle 30 0 (Cur-30) and 600 (Cur-60) have been considered. Moreover, to study the behaviour of skew-curved bridge, a 300 curved bridge with 300 skew (SkCur-30) has been considered. All the bridges have been analyzed for its self-weight and live load. In this study live load is considered as IRC class 70R tracked vehicle [IRC-6, 1997] at mid span. It may be added that the issue pertaining the position of the live load is quiet important for the design point of view the IRC tracked vehicle has been placed at maximum eccentricity at mid-span as per the guidelines of IRC guidelines [IRC-21, 1997]. 184
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METHOD OF ANALYSIS
The linear finite element analysis carried out in this study is based on the threedimensional, degenerated, layered shell element formulation. Each element has nine nodes with five degrees of freedom at each node (three translation and two rotational degrees of freedom) [Hinton et al. 1984] and has been used for spatial discretization of the bridge. All the bridges were discretized into 60 elements. It becomes tedious to generate the input data for curved and skew bridges; therefore, the geometry of the bridge was first modeled in STAAD Pro to generate the coordinates of each node point. The formulation of the element and validation of the computer program used in this study are given by Kumar [Kumar, 1997]. ANALYTICAL INVESTIGATION 1
For the analytical investigation of structural behavior of straight, curved, skewed, and skewed-curved bridges, a two lane bridge of twenty-meter span box-girder as shown in Fig.1 has been considered. A detailed study on influence of geometry of bridge on its structural behaviour has been made by Jawanjal [Jawanjal, 2004], however, this paper deals with the influence of geometry of the bridge on deflection, longitudinal compressive stress and coefficient of shear lag. Influence of Geometry on Deflection
Deflection of bridge at mid-span is an important parameter, which governs the serviceability requirement of the bridge. In this study, the influence of geometry of the bridge on the deflection under the outer web (i.e. web near the live load) and on inner web has been investigated. Fig 3 shows the variation of deflection along the span for the straight, skew, curved, and skew-curved cases for outer and inner webs. Fig 3a shows the effect of skewness on deflection under outer and inner webs. It is evident from Fig 3a that the deflection of the bridge under the outer web slightly decreases in the presence of skewness, however, there is no significant effect of skewness on deflection under the inner web. The study conducted suggested that deflection is highly influenced by curvature. As the angle of curvature increases, deflection under both the webs increases. For the bridge with curved in plan by 60 0, the deflection under the outer web was found approximately 2.8 times of that for straight bridge, however, this factor was found to decrease to 1.6 for inner web [Fig. 3b]. The variation of deflection along the span for straight, cur30, skew30 and sk-cur30 is shown in Fig 3c. Fig 3c shows that the deflection 0 at mid-span under the outer web f or the bridge curved in plan by 30 is approximately 1.5 times as compared to straight bridge and this factor reduces to approximately 1.3 for 0 0 bridge curved in plan by 30 and skewed by 30 . In other words, deflection of curved bridge (under both the webs) decreases in the presence of skewness in the bridge. Influence of Geometry on Compressive Stress in Top slab
Fig. 4 shows the variation of longitudinal compressive stress along the width of the top slab. Fig 4a clearly indicates that up to skew angle 15 0, there was no significant effect of skew angle on the compressive stresses in top slab. However, at skew angle 300, the longitudinal compressive stress in the top slab was observed to decrease by approximately 14% for both the webs i.e. outer web (near the live load) and inner webs. Fig 4b shows the influence of angle of curvature on compressive stress in the top slab. It
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can be observed from the Fig 4b that, the longitudinal stress in top slab is not much affected by curvature in plan., however, near the inner web the stress was found to decrease with increase in angle of curvature. It can be easily observed from the Fig 4b 0 that the compressive stress for 60 -curved bridge is 40% lower than that for straight bridge. A comparison of longitudinal compressive stress for straight, skewed, curved, and skew-curved bridge is shown in Fig 4c. The figure indicates that longitudinal compressive stress near outer web for 300 curved bridge is approximately 8% higher in comparison to straight bridge, however, for 30 0 skew bridge the stress is 22% lower than that for straight bridge. For the locations near the inner web, the trend of stress was found reverse as compared to outer web. For outer web, the stress for curved, skewd and skewcurved bridge was found lower than that for straight bridge. Influence of Geometry on Coefficient of Shear Lag (CSL)
Figure 5 shows the variation of Coefficient of Shear Lag (CSL) along the width of the bridge for skew, curved and skew-curved bridges. It can be observed from the Fig 5a, that CSL decreases with increase in the skew angle. On the other hand, Figure 5b shows that as the angle of curvature increases, CSL near the outer web increases, however, it decreases tremendously near the inner web. A comparison of CSL for straight, skew-30, curved-30 and ske-curv-30 is shown in Fig 5c. From the figure, it may be noted that for curved and skew-curved bridge, CSL near the outer web is close to CSL for straight bridge, however, for skewed bridge CSL reduces in comparison to straight bridge. Moreover, the trend for CSL near inner web was observed reverse as compared to outer web. For the skew-30 bridge the CSL near inner web is found approximately 23% lower than that for straight bridge, however this factor was approximately 25% for skcur30 bridge. CONCLUSIONS
In this paper, finite element analysis of the simply supported reinforced bridge was carried out to investigate the influence of geometry on deflection, longitudinal compressive stresses and the Coefficient of Shear Lag (CSL). This limited study can be concluded with the following significant observations: •
•
•
On the basis of study made it was observed that the deflection of the bridge is not much affected by skewness of the bridge supports. However, the angle of curvature significantly affects the deflection of the bridge. Furthermore, the study suggested that the deflection of curved bridge decreases in presence of skewness. For skew bridges with skew angle up to 15 0, the variation in the longitudinal stress was not significant, however, it increases for highly skewed supports. For bridges curved plan the longitudinal stress near the outer web was not much affect by angle of curvature, however, the stress near the inner web decreases with increase in angle of curvature. Further, for bridges curved in plan with skewed supports, the longitudinal stress decreases in near the outer web and increases outer web in comparison to straight bridge. The study suggested that the CSL decreases as the skewness of the support increases. Similar trend was observed for curved bridges near the inner web, however, for outer web the trend was reverse. Moreover, for bridges curved in plan with skewed
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supports, CSL is approximately same as for straight bridge, however, near the inner web, CSL decreases as compared to straight bridge. REFERENCES
1. Chapman, J. C., Dowling, P. J., Lim, P. T. K., and Billington, C. J., The Structural Behaviour of Steel and Concrete Bridges, The Structural Engineer, Vol. 49, No. 3, pp. 111-120, 1971. 2. Hinton E. and Owen, D. R. J. (1984). “Finite Element Software For Plates and Shells” Pineridge Press, Swansea, U. K. 3. IRC:6. (1997). Standard Specifications and Code of Practice for Road Bridges, Section II– Loads and Stresses, Indian Road Congress. 4. IRC:21. (1997). Standard Specifications and Code of Practice for Road Bridges, Section III– Cement Concrete (Plain and Reinforced), Indian Road Congress. 5. Krishnamoorthy, C. S. (1994). “Finite Element Analysis Theory and Programming” Tata-Mc-Graw-Hill Publishing Limited, New Delhi. 6. Jawanjal V. (2004) “Finite Element Analysis of Skew Curved Box Girder Bridge” ME Thesis, Birla Institute of Technology & Science, Pilani, India. 7. Kumar, Manoj (1997). “Analysis of Box-girder Bridges Using Finite Element Method”, M.E Thesis, University of Roorkee, India. 8. Scordelis A.C., Wasti, S. T., and Seible, F. (1982) “Structural Response of Skew RC Box Girder Bridge”, “Journal of Structural Engineering”, Vol. 108, 89-104 9. Sennah, K., and Kennedy, J. (2002). “Literature Review in Analysis of Box-Girder Bridges.” J. Bridge Eng., 7(2), 134-143. 10. Tandon M. (2003) “Aesthetics and technologies for urban bridges”, Indian Concrete Journal, July 2003, 1191-1196
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FIGURES & GRAPHS
Skew-30
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Figure 2. Models of Skewed (skew), Curved (Cur) and skewedCurved (Sk-Cur) bridges
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Advances in Bridge Engineering, March 24 - 25, 2006
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Fig. 1 Section of the bridge considered in study Span (m)
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Fig. 3: Influence of geometry of Box-Girder on deflection along the span
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Fig. 4: Influence of geometry on compressive Stress in top slab
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Fig. 5: Influence of geometry on Coefficient of Shear Lag (CSL)
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