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FINITE ELEMENT ANALYSIS OF EXTERNALLY

PRESTRESSED SEGMENTAL BRIDGES

Prof. Dr.-Ing. G. Rombach, Dipl.-Ing. A. Specker

Department of Concrete Structures Technical University of Hamburg-Harburg, Germany

e-mail: rombach@tu-harburg.de

1 Introduction

Bridges have been built since thousands of years. Nevertheless new innovative construction methods are still required. Precast concrete segmental hollow box girder bridges externally prestressed are one of the major new developments in bridge construction in the last years resulting from the demand for economical design, high durability and fast and versatile construction. The great advantages has made them the preferred structure for many great elevated highways, especially in South East Asia. In contrast to classical monolithic structures a segmental bridge consists of “small” pieces stressed together by external tendons (fig. 1,2).

Fig. 1 Real structure (Second Stage Expressway, Bangkok)

Due to the unreinforced joints the deformation characteristics and the load bearing capacity of a segmental bridge is different from a monolithic construction. In recent years great effort have been made to improve the knowledge of such structures. There are still some areas requiring further investigation like e.g. the behavior of the “dry” joints between the segments. The design of the joints is of critical importance regarding the safety of segmental bridges. Numerical as well as experimental investigations regarding the joint behavior will be presented in this paper. Before discussing this important detail the principal behavior of a single span segmental bridge is demonstrated by a finite element simulation of a full scale experiment.

G.A. Rombach, A. Specker

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Shear Keys

Fig. 2 Standard segment and joint geometry [1]

2 Finite Element Analysis of Segmental Bridges

The behavior of segmental bridges can be studied systematically by means of non-linear finite element calculations. These investigations have to take into account the opening of the joints, the local contact between the tendons and the concrete at the anchorages and the deviators and the non-linear behaviour of the building materials concrete resp. steel. Due to the complexity the numerical model should be verified by experimental data. 2.1 Numerical Calculations of a Single Span with Plain Joints

Figure 3 shows a finite element model of a standard single span of the so-called Second Stage Expressway System in Bangkok, one of the greatest segmental bridge in the world. The dimensions and the cross-section are given in figure 2. The hollow box girder is modeled by four-node shell elements and the tendons by non-linear truss elements. The indentation of the joints is neglected. Various contact algorithms and contact elements had been studied. The real joint can only transfer normal and shear forces under compression. As the normal stress becomes positive e.g. due to bending, the joint opens resp. contact is broken and no force is transmitted. Sliding occurs when the maximum shear force is exceeded. Comparative calculations showed that a linear Coulomb friction model is sufficient to model the real behavior.

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45 m 45 m

Fig. 3 Numerical model – plain shell elements

Further simplifications are justified [2]. The deformation characteristics and bearing capacity of segmental structures are dominated by the behavior of the joints. Therefore a simple non-linear stress-strain relationship is used for concrete according to EC 2 [3] and an ideal elastic - ideal plastic model for the tendons. The single span bridge shown above was chosen because experimental data from a full-scale test carried out in Bangkok in 1990 [4] is available to verify the numerical model. In the test the structure was loaded by steel plates up to failure. The results of the comparison calculations are shown in figure 4, where the mid-span moment is plotted versus the mid-span deflection. A very good agreement between the numerical results and the test data can be seen. This proves the statement of the joints mainly influencing the behavior of segmental structures.

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Fig. 4 Comparison between full-scale test Fig. 5 Stresses in mid-span before and numerical results failure The principal behavior of a segmental bridge under normal bending can be described as follows. As long as the structure is under full compression a segmental bridge behaves linear elastic like a monolithic one. When loading resp. the bending moment is increased, joints start to open and the deflections exhibit a non-linear growth as the overall stiffness decreases. Within a small increase of loading the joints at mid-span open up to the top slab. Then deflections rise again proportionally to the applied load until failure as the lever arm of the internal forces is nearly constant. Failure occurred usually when tendons start to yield and the neutral axis is shifted into the top slab causing the concrete to crush.

G.A. Rombach, A. Specker

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2.2 Numerical Calculations of a Single Span with Shear Keys The numerical investigations shown before are based on plain joints. The shear keys are neglected. This rough simplification has to be verified. For this purpose the numerical model is modified near the relevant joint. The element mesh is refined and the indentation of the joints is considered (figure 6,7). Cubic concrete elements are used which are coupled at the end to the plain shell model described in the chapter before. Different loading arrangements are considered which causes the joint to open at the top resp. at the bottom slab. (figure 7).

Fig. 6 Refined element mesh near the relevant joint

As long as the joint is under compression, the segmental bridge behaves like a monolithic one despite of local effects of the joint and the shear keys. When the joint opens the area to transfer shear loads becomes smaller whereby the normal and shear stresses at the top slab increases (figure 8).

Fig. 7 Joint opening due to positive resp. negative bending moments

Figure 8 shows the normal and shear stress distribution in the webs when the joint is closed and when it is open up to appr. half of the height of the section. It can be seen that shear forces are mainly transmitted in the compression zone. Only a few shear keys are able to transfer shear loads across an opened joint (figure 7,8).

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Fig. 8 Normal and shear stress distribution in the closed and opened joint

These results demonstrate that the indentation of the joints can be neglected in numerical calculations. It should be noted that this is only the case if the structure is under pure bending. When the bridge is un-symmetric loaded resulting in torsion moments the shear keys have to be modeled as other studies showed.

3 Segmental Joints

One of the major areas of uncertainty is the load bearing capacity of the unreinforced joints between the segments. Design and construction of the joints are of critical importance regarding the safety of segmental bridges. The models used in practical design are gained from experiments which are described by simple analytical formulae [5]. Due to the fine indentation of the joints and the complicated interaction between the rough concrete surfaces measurements can hardly be carried out. Numerical calculations are required to investigate the load bearing capacity of the joints [6].

3.1 Verification of the Numerical Model

Experimental and numerical investigations have been conducted. Tests with small specimens (one shear key only, figure 9) similar to that described in [7] have been done to essentially verify the numerical model not to develop further design procedures. The joint geometry and the indentation is representative for segmental bridges. Dry and epoxy glued joints are investigated. Dry joints are modeled by contact elements, the epoxy glue by longitudinal, linear spring elements.

G.A. Rombach, A. Specker

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Shear failure

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Fig. 9 Test specimen Fig. 10 Crack pattern before failure The finite element analysis considers the non-linear behavior of concrete incl. cracking resp. crushing and the interaction between the surfaces (friction, bond, slippage). The specimen is first stressed normal to the joint and then loaded vertically up to failure. Results are shown in figure 11. Numerical and test data show an overall good agreement. Using dry joints there is slippage in the first part of the test because the specimen were not match-cast. This is not considered in the numerical model.

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Fig. 11 Test results versus numerical results for dry and epoxy glued joint

3.2 Finite Element Analysis of Segmental Joints

Based on the verified numerical model, finite element calculations have been conducted with joints having multiple shear keys, different geometries and material properties. Figure 12 shows the vertical load-deflection curves of specimens with different number of shear keys under constant normal pressure. It can be seen that the load bearing capacity is linear to the number of keys. In figure 13 where the bearing capacity of a joint with 3 keys is plotted versus the normal stress, one can see the shear stress – normal stress relation for various normal stresses according to the numerical calculation, the dry joint formula of AASHTO [5] and the conservative estimation in [8] (shear forces are only carried by friction in the compression zone). In contrast to the conservative estimation AASHTO overestimates the shear capacity if normal stresses are high. Both analytical formulae are based on different models and

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assumptions. Therefore further numerical investigations are required to evaluate a consistent model for design of segmental joints.

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Fig. 12 Load carrying capacity of a Fig. 13 Comparison between different joints having multiple shear keys design models and numerical calculations

4 Conclusions

Non-linear finite element models are presented and discussed to study the behaviour of real segmental box girder bridges. The results show that the behaviour of such type of structure is dominated by the un-reinforced joints. The indentation of the shear keys can be neglected in the numerical model if the structure is loaded by bending only. Numerical and experimental investigations of the bearing capacity of the joints show that some analytical design models overestimates the capacity. The objective of the ongoing investigations is to evaluate a simple design model for practical use.

5 References

[1] G. Rombach: Segmental box girder bridges with external prestressing. Conference „Actual Problems in Civil Engineering“ . St. Petersburg, Juli1997

[2] G. Rombach, A: Specker: Numerical modelling of segmental bridges. European Conference on Computational Mechanics, Munich, August 1999

[3] Eurocode 2, Part 1. Design of concrete structures. 1992 [4] T. Takebayashi, K. Deeprasertwong, Y. Leung: A full-scale destructive test of

a precast segmental box girder bridge with dry joints an external tendons, Proceedings of the Institution of Civil Engineers, August 1994, pp. 297-315

[5] AASHTO. Guide specification for the design and construction of segmental concrete bridges. 1998

[6] G. Rombach, A. Specker: Design of segmental joints, in: Externe Vorspannung und Segmentbauweise, Ernst & Sohn, 1998, pp. 303-313

[7] Bakhoum M.M., Buyukozturk, O., Beattie S.M.: Structural Performance of Joints in Precast Concrete Segmental Bridges. MIT Research Report No. R89-26, Massachusetts Institute of Technology, November 1989

[8] Deutscher Beton-Verein: Empfehlungen für Segmentfertigteilbrücken mit externen Spanngliedern. April 1998