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Collapse analysis of externally prestressed structures

Masterarbeit 2001 149 Seiten

Ingenieurwissenschaften - Allgemeines

Leseprobe

Contents

Acknowledgements

Notation

1 Introduction
1.1 Definitions
1.2 Significance of this study
1.3 Scope of the project
1.4 Historical overview and typical characteristics of external prestressing
1.5 Further structural applications of external prestressing

2 Behaviour of externally prestressed structures
2.1 Tendon layout considerations
2.2 Behaviour at serviceability stage
2.3 Fatigue problems
2.4 Behaviour at ultimate limit stage
2.4.1 Influence of tendon slip on the ultimate limit state
2.4.2 Influence of the arrangement of the deviators on the behaviour at ultimate limit state
2.4.3 Influence of simply support and continuous support on the ultimate limit state
2.4.4 Precast segmental and monolithic bridges

3 Collapse analysis
3.1 Investigated bridge types and their differences
3.2 Original bridge data
3.3 Simplified bridge data as basis for the calculations
3.4 FE Calculation
3.4.1 Technical aspects
3.4.2 General approach
3.4.3 Geometric model
3.4.4 Element specifications
3.4.5 Constitutive models
3.4.6 Ordinary reinforcement
3.4.7 Prestress
3.4.8 Material and geometric non-linearity
3.4.9 Kinematic constraints
3.4.10 Discrete crack propagation analysis of the precast segmental type with gap elements
3.4.11 Summary of the dividing features of the different structure types for the FE analysis

4 Results
4.1 Load deflection behaviour
4.2 Tendon stress increase up to failure
4.3 Other results

5 Discussion of the results
5.1 Interpretation of the results
5.2 Discussion of the exactness of the FE calculations by comparing to the full scale test
5.3 Comparison to other FE calculations and test results

6 Conclusion and Recommendations
6.1 Concluding remarks
6.2 Recommendations

References

Codes of practice

Appendix A: Derivation of the simplified tendon layout

Appendix B: Calculation of the minimum reinforcement

Appendix C: ABAQUS Input file for the precast segmental externally prestressed box girder

Acknowledgements

I would like to thank the people, who helped me to do this MSc dissertation. In particular, I would like to thank Tony Thorne, who set up the ABAQUS machine, assisted me with UNIX, and tried to solve patiently all the bugs related with the Pre-processing software, and also Jonathan Hulatt for his useful hints for ABAQUS. Jonathan had also a look at my English writing despite his own work-load. I am grateful to Nigel Hewson, who originally inspired me to the actual topic of this dissertation and gave me some ideas to start with. Mike Ryall and Paul Mullord helped me through useful discussion about prestressing and Finite Element theory.

Jens Tandler

Notation

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Sign convention

All compressive actions are indicated with a minus sign and the tensile actions are shown with a positive sign or no sign respectively. There is one exception: p, the hydrostatic pressure, is negative in tension and positive in compression.

Units

SI units are generally used. However, some values in graphs are given in imperial units.

Abbildung in dieser Leseprobe nicht enthalten

1 Introduction

This dissertation is an investigation into the behaviour of externally prestressed structures, focusing on bridge box girders, at the ultimate limit state. The main objective is the ductility and the tendon stress increase up to failure of externally prestressed structures. Their behaviour will be compared to internally prestressed structures. The dissertation may have valuable information for the first stages of the design process for medium span bridges as the study is concerned about the overall safety and efficiency of prestressed concrete bridges by the means of ductility. The aim is also to provide information about the tendon stress at failure, which is required for the detailed design.

1.1 Definitions

External prestressing is a special technique of post-tensioning. Post-tensioning is used to apply prestress forces to the concrete after hardening. (Hewson, 2000a). External tendons are placed outside of the section being stressed. The forces are only transferred at the anchorage blocks or deviators (Hewson, 2000b).

Abbildung in dieser Leseprobe nicht enthalten

Figure 1‑1: Typical view in box girder bridge with externally deflected tendons (modified from Krautwald, 1998)

Internal prestressing is defined in this dissertation, if tendons lie within the cross-section of the structure. Internal prestressing can be carried out using bond between the structure and the prestressing steel (grouted ducts). The other possibility is internal post-tensioning without bond between the duct and the tendon. The prestressing force is again only transferred through the anchorages and contact pressure against the surface of the duct. Throughout the dissertation only internal post-tensioning with bond and external prestressing is investigated. The figure below outlines the prestressing methods of interest for this dissertation.

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Figure 1-2: Prestressing techniques

The figure shows the pure types. There are more techniques possible, which are the hybrid systems. Hybrid systems are combinations between different pure types. External prestressing in combination with internal post-tensioning is recommended in Germany for launched box girders, although it is not widely used. Pretensioning with internal post-tensioning has been used because of limited stressing capacity for the pretension. All these hybrid systems are only cost-effective in certain situations.

The difference between a monolithic constructions and a precast segmental constructions is thatthe precast segmental constructions have no ordinary reinforcement crossing the joints of the segments whereas monolithic bridge constructions have normal reinforcement along the whole bridge. Precast segmental bridges can be erected by lifting match cast segments into place by the means of different crane types. The segment is then stressed against the rest of the structure or held in place before stressing all segments together. A monolithically cast concrete bridge can be lifted as a whole into place, launched from the abutments, or constructed by balanced cantilever construction with slip form.

1.2 Significance of this study

Recent Problems on external prestressed structures show that there are still problems in the understanding of these structures. Accidents took place in South Africa in 1998 and in Guam in 1996. In the first case a box girder with external straight tendons collapsed during the launching process. The bridge dropped workers and a party of visitors 30m to the ground. 14 people were left dead, including the bridge designer, and 13 were seriously injured (NCE, 1998).

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Figure 1-3: Collapse Injaka Bridge in South Africa (NCE, 1998)

Another example was the catastrophic collapse of what was once the longest post-tensioned balanced cantilever bridge of the world with a span of 241m. The bridge in Guam suffered the destruction after an attempt to strengthen the bridge with external tendons. The project was supervised by an American structural engineer carried out largely by a well-established post-tensioning contractor (NCE, 1996).

A considerable number of scientific papers have been published during the last two decades dealing with ductility and tendon stress increase in externally prestressed bridges. There are differences between the findings. Fundamental research and work in this field was done by B.G. Rabbat and K. Slowat (1987), J. Muller and Y. Gauthier (1989) and MacGregor R.J.G. et al. (1989). Many codes of practice are based on this American research, e.g. the BD 58/94 “Design of concrete highway bridges and structures with external unbonded tendons” for the UK. The connection to the above mentioned research work can be found in Development of BA and BD 58/94 by Jackson P.A. (1995).

There have always been concerns about brittle failure of externally prestressed bridges (Hollingshurst, 1995), because there is only a small increase of the tension in the steel tendons until failure. Another concern was coming from the behaviour of external prestressed segmental structures with no passive reinforcement between the segments (Bruggeling, 1989).

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Figure 1-4: Segmental box girder bridge with deflected external tendons and dry joints under extensive loading in first span (Muller and Gauthier, 1989)

It is possible that there will be a growing demand for externally prestressed structures in Europe because of their likely higher durability, which is obviously attractive to the authorities. An indication of this new demand might be the New Medway Bridge for widening of the M2 in Kent (WS Atkins, 2001). This bridge will be a balanced cantilever prestressed concrete construction with external tendons.

For this reason it is thought to be necessary to make new considerations about the behaviour of these bridges at ultimate limit state with the background of the concerns, the failures, and the latest research. Also the ultimate limit state might govern the check for such structures, because of the low increase of strain up to failure in the tendon. This is in contrast to bonded internally prestressed concrete structures, where the check at service governs the amount of prestressing steel. There might also be important implications regarding the cost efficiency of externally prestressed structures.

1.3 Scope of the project

Three externally prestressed bridge types will be studied; these include an externally prestressed bridge monolithically built, an externally prestressed concrete bridge monolithically built with blocked deviators, and a precast segmental bridge with external tendons. A conventional internally prestressed bridge with bonded tendons monolithically built will also be analysed as a reference. All bridges are box girders. They are simply supported and have a span of 43.25m. The basic bridge data is taken from the Bangkok Second Stage Expressway. As part of this major project a full-scale destructive test was conducted by Takebayashi et al., (1994). The bridge was a precast segmental box girder with external tendons and dry joints. The data collected from this test will also be used to verify the results.

The objectives of this investigation are to determine whether or not externally prestressed bridges fail ductile and the amount of increase in tendon stress up to failure. The analysis will be done by numerical methods using ABAQUS.

Kong 1996 defines ductile failure as followed. ”The failure of an under-reinforced beam is characterised by large steel strains, and hence extensive cracking of the concrete and substantial deflection. The ductility of such a beam provides ample warning of impending failure….” On the other hand brittle failure occurs (Hurst, 1998), if the steel in the tension zone has not reached the yield strain. In this case the concrete crushes suddenly without showing big cracks in the tension zone. Such a section is also described as over-reinforced.

After the introduction, a outline of the recent research will be given explaining the key aspects of the structures concerned. The next section deals with the analysis. This includes the simplification of the original bridge data and statements of all the assumptions made. The explicit explanation of the differences of each of the analysed bridge types are also shown in this section. Thereafter, theoretical background regarding the Finite Element analysis is given together with a description of the actual analysis undertaken. Chapter 4 illustrates the results of the study, which are discussed in Chapter 5. The study will then conclude with the summary of the findings.

1.4 Historical overview and typical characteristics of external prestressing

Looking back to the early days, it is surprising to recognise that the first prestressed concrete bridge was externally post-tensioned. This bridge was built from 1935 to 1937 in Aue, Germany, by Franz Dischinger. Steel with a tensile strength of about 500 N/mm² was used at the time. Considerable losses in the prestressing force have occurred due to the low tensile steel and the bridge was restressed twice in 1962 and 1980 (Virlogeux, 1989). The bridge was demolished in 1994 (Landschaftverband Westfalen-Lippe, 2001).

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Figure 1-5: Elevation and cross-section of the Station Bridge Aue/ Germany with external tendons (Schönberg and Fichtner, 1939)

Although the prestressing bars were not performing so well, the drawback of the low tensile steel has been overcome by the advantage of external prestressing. This construction type allows restressing and replacing of the prestressing strands. The replacement of the strands is even possible without full closure for the traffic crossing over the bridge. Such a replacement under traffic was done at the Braidley Road Bridge in the UK in 1980 (Clark, 1998).The replacement of the tendons was necessary because of corrosion problems. Most of the early externally prestressed bridges suffered from this problem. Corrosion was the main reason for caution to this technique and lead to preference of internal prestressing. In the meantime, reliable corrosion systems have been developed. The strands are commonly encased in high-density polyethylene ducts (HDPE) and the ducts are filled with grease or cement grout. The strand can also be separately encased again in the pipes.

These days external prestressing is mostly used in France and in the USA. The reasons are significantly different. In the USA, external prestressing is used because of its cost-effectiveness, especially if it is used in combination with segmental construction. Major bridges were built with this technique, e.g. the Long key bridge with 101 spans with spans of 36m and an overall length of 3701m (Gallaway, 1980). The believed higher durability of certain types of externally prestressed bridges lead to a massive recovery of this construction technique in France. The French authorities believe, if the corroded tendons can be changed, the bridge will have a longer lifespan. And the possibility of inspection of the tendons should make such bridges more predictable and therefore safer. Virlogeux (1989) states, “…we can master the technique, it is no longer experimental for us, but the normal way of building large concrete bridges”. Although this is quite enthusiastic, it shows that external prestressing might have an important place in bridge construction of the future. The characteristics of this type of bridge construction seems to make them very cost-competitive for very long viaducts, e.g. the Second Severn Approach spans in the UK with about 4km length (NCE, 1994) and the Bangkok Second Stage Expressway with over 60km deck length (Hewson, 1993).

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Figure 1-6: Sunshine Skyway (Florida) – span by span precast segmental, externally post– tensioned approach spans (courtesy of Figg and Muller Engineers Inc.)

1.5 Further structural applications of external prestressing

External prestressing is not only used for bridge construction. It is also used for building constructions. There are reports about the strengthening of silos (Schallwig, 1998 and Hegger, 1998). In both cases cylindrical silos had unacceptable wide vertical cracks due to overloading in their outer vertical concrete walls. This was overcome by the use of external peripheral tendons.

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Figure 1-7: Silo strengthened by external tendons (Schallwig, 1998)

2 Behaviour of externally prestressed structures

2.1 Tendon layout considerations

Although tendon layout considerations are not precisely the topic of the dissertation, it is believed that a short introduction to this field is necessary for a deeper understanding of the actual topic.

Anchorage points have a much higher importance in external prestressed structures than in conventionally prestressed structures. The anchorage is the only point where the tension from the strands is contained. Grouted tendons in bonded prestressed structures transfer their force also along their length and therefore the anchorage is only during construction of such a high importance. Another difference of external prestressed structures is that the prestressing force is not directed towards the concrete mass but produce an eccentric force to the concrete cross-section. Thus, the anchorage points are typically massive concrete blocks.

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Figure 2-1: Deformation of an anchorage point and its surrounding in a box girder bridge (Standfuß et al., 1998)

First attempts leading the external tendons straight through the cross-section lead to a less satisfactory result. There are many anchorage points necessary (marked with triangles in the next figures), which make this construction type uneconomic.

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Figure 2-2: Straight tendons with high number of anchorages (Krautwald, 1998)

Research in behaviour of deflected external tendons allowed the next step. It followed a layout with deflected tendons aiming less anchorage points and a better conformity to the moments from the loads.

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Figure 2-3: Deflected tendons with only few anchorage points

Further optimisation was carried out by improving the positions and numbers of deviators in the span.

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Figure 2-4: Optimised tendon layout (Virlogeux, 1989)

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Figure 2-5: Equivalent design with cross-beams, pseudo parabolic external tendon (Virlogeux, 1989)

Figure 2-4 shows a tendon layout, which is state of the art. Such a position of the tendons produces a moment, which is very close to a parabola and therefore well suited to take effect against moments from loads. Also, it produces a higher shear reduction near the support than a tendon with only one deviator per span. Figure 2-5 shows an arrangement, which has the same effect than the design in Figure 2-4. It has the disadvantage of large cross-beams. It is preferable to deflect the tendons near the web to avoid transverse bending moments. Hence, it is necessary to change their direction also in plan. Always the deflected tendons will be lead to the intersection web bottom slab (see also Figure 2-6).

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Figure 2-6: Deviation in plan and elevation (Virlogeux, 1989)

2.2 Behaviour at serviceability stage

The serviceability check is not of such a high importance for externally prestressed structures than for internally bonded prestressed structures. Traditionally the prestressed concrete is designed by controlling the tensile strength in order to avoid cracking. This is done in order to protect the prestressing cables within the concrete. If the cables are outside the concrete section, there will be no justification for this any longer and partially prestressing (UK: class 3) could be approached. Partially prestressing allows limited cracking under live load. Then, it is very likely that the check at ultimate limit state governs the design prestress force. However, partially prestressing is not permitted in several countries, e.g. the UK, for highway and railway bridges (Jackson, 1995).

The basic calculations at service of externally prestressed structure is very similar to the calculations of bonded post-tensioned structures. The prestressing force is introduced via a normal force along the bridge and via nearly vertical forces due to the sharp changes in tendon geometry at the deviators.

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Figure 2-7: Idealisation of prestressing load

If the tendon arrangement is favourable, the web thickness can be substantially smaller than the webs of conventional prestressed bridges, because the strands are outside the cross-section. It is also notable that losses due to friction are not as high as in internally stressed systems. Friction losses occur at the deviators only. Thus, a higher effective prestress can be reached. It was also found that the tendons do not slip at the deviator under service load (MacGregor et al., 1989).

Cracking tends to be a more controversial aspect. A German research project is often mentioned in this context (Vielhaber, 1988). The following statement is made, “This project has shown that in the case of (pure) prestressing without bond no control of crack width is possible. In such structures, it should be tried to prevent cracking of concrete by increasing the prestressing force“. Although the last part of the statement is maybe a reason for some disagreement, the first part makes a definite comment. But the only reason for no passive reinforcement at certain points in a bridge might be in the case of a precast segmental construction, where the cracks will open at the joints. The reason behind crack control is durability. If there were a crack at the joint, i.e. the joint opens under loading, concrete cover at the longitudinal end of the segment would still protect the passive reinforcement within the precast segment. The situation becomes more difficult with glued joints, where the crack occurs next to the epoxy glue in the concrete.

2.3 Fatigue problems

As far as known by the author, there are only few identified fatigue problems with the external tendons. The tendons tend to swing under load. The vibration produces nearly no measurable prestress force changes (Standfuß et al., 1998). The BD58/94 requires dynamic checks when exceeding 12m between the lateral restraints of the tendon. The German code of practice limits the free length of the tendons to 35m (ARS Nr.28/1998) without further checks.

2.4 Behaviour at ultimate limit stage

The ultimate limit state is for externally prestressed structures much more important than for internally bonded structures, because this check is very likely governed for the amount of prestress force needed. The reasons will be explained later. This is in contrast to internally bonded prestressed concrete structures, where the serviceability check governs the design.

As the load on the section increases beyond the values of the serviceability state, the strain and the stress respectively in the section will increase following the appropriate stress-strain relationship. The constitutive laws from steel and concrete show different characteristics.

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Figure 2-8: Strains, stresses and forces acting on a bonded prestressed concrete section ignoring concrete tension

The strain due to bending in the strand and in the adjacent concrete has the same amount in bonded prestressed concrete structures, because they are directly connected together via the grouted duct. The ultimate moment of resistance is calculated with the equation

Abbildung in dieser Leseprobe nicht enthalten

Furthermore, it is noticeable that

epb (bonded)=Abbildung in dieser Leseprobe nicht enthalten,

where sce’ is the stress in the concrete at the level of the tendon from an applied moment and e’ the eccentricity of the tendon. The situation is different with externally and therefore unbonded prestressed structures. The bending initiated strain in the tendon does not reach the same strain as in the adjacent concrete. The increase in length of the strands can be distributed between two adjacent anchorage points. Hence, the rotation of the beam producing the increase in strain at the bottom side leads not to such a high local prestressing force and ultimate moment of resistances as by bonded structures (Ramos and Aparicio, 1995).

epb (bonded) > epb (unbonded)

The statement above will be investigated later in the analysis. The extension of the external strands can be described as followed.

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Figure 2-9: Extension of tendons under load

Abbildung in dieser Leseprobe nicht enthalten (Ramos and Aparicio, 1995)

LX and LX’ respectively describe the length of the tendons before and after the application of the load. It can be seen that the strain in the strands is not directly connected to the strain in adjacent concrete.

Another interesting characteristic is the second order effect of the tendon eccentricity. With increasing load the eccentricity of the tendon at midspan becomes gradually smaller. The next figure illustrates the fact.

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Figure 2-10: Reduction of eccentricity

Hence, the lever arm of the tendon to the neutral axis of the section decreases, and therefore the ultimate moment of resistance as well (Tan and Ng, 1997).

The two factors described above are the difficult parameters within the calculation of the ultimate moment of resistance. It can already be seen that these influences alter the resistance of section negatively in comparison to a bonded internally prestressed beam.

The other factors influencing the eccentricity and the bending strain are the slip of the tendons at the deviators, the arrangement of the deviators, whether or not the structure is continuous, and whether the structure is a monolithic structure or a precast segmental bridge.

A considerable effort has been made in the last two decades finding ways in order to evaluate all these factors satisfactory. It has been tried to find general solutions trying to include all factors in sufficient way. It is believed that a general solution cannot be found because of the numerous influences. It will be tried to describe a procedure rather than a general solution leading to the ultimate moment of resistance in this dissertation. The importance of the different factors will also be assessed.The general task is to calculate the bending strain in the tendon. Conservatively, it could be assumed that this strain is 0. The calculation is then relatively straightforward. Some codes of practice suggest this approach and sometimes with allowance for a small extra strain subjected to special conditions. The AASHTO 1996 (clause 9.17.4.1), the BD 58/94 (6.3.3.1(f)), and the EC2 part 1.5 (4.3.1.4 P (103)) comply with these specifications. Further increase will be allowed, if a non-linear calculation is conducted. The German code (ARS Nr. 7/1998, clause 8(2)) allows no increase in ultimate limit capacity due to rotation of the structure nor does it mentions a non-linear analysis.

The non-linear analysis of externally prestressed structures at the ultimate limit state in bending is the subject of this dissertation.

Ultimate limit state shear is not a detailed part of this dissertation. However, some facts follow. Shear design tends to be empirical, based on tests carried out on beams with bonded tendons. Bonded tendons contribute to the shear resistance, since they cross the cracks. Concerns have to be expressed as to whether these rules are applicable or not. Alternatively, it could be approached as a reinforced concrete beam or column respectively subjected to external loads (Jackson, 1995).

2.4.1 Influence of tendon slip on the ultimate limit state

It was found that it is reasonable to assume no tendon slip at the deviators at service as already mentioned above. But at ultimate conditions, the tendons move over the deviators (Takebayashi, 1994) or saddles releasing stress of the tendons. The release of stress leads to sudden fall in the strain in the tendon and hence to further deflection of the beam if not to failure. Failure will happen if the neutral axis shifts to high up in the section due to further deflection. The concrete will then fail in compression.

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Figure 2-11: Forces at deviator (MacGregor et al., 1989)

The slippage itself is very difficult to assess. On the one hand, there is the use of cement grouted external tendons and on the other hand, there are grease filled tendon ducts. These different encasements lead to different friction properties between the concrete section and the strand. Cement filled ducts produce a very good connection. The use of them makes sense from the statical point of view, but they are difficult to change in the case of corrosion. Grease filled ducts have a much lower coefficient of friction. It is believed that a full fixity will normally not be reached, as even cement-grouted tendons slipped in a full-scale test (Takebayashi, 1994) at ultimate load. This might be due to the commonly used HDPE duct. An extensive analytical research project was conducted by Rao and Mathew (1996). They produced a finite element model capable of dealing with friction problems at multiple deviators. This is without doubt state of the art in finite element modelling. A model of such complexity is probably far beyond the possibilities of the normal practicing engineer. However, the possibility of the practical application of such solutions seems to be questionable. There will be the need for determination of the statical and dynamic friction coefficient. Rabinowicz (1995) writes on the prediction of the friction coefficient that this is only possible with a deviation of about ± 20%. For reliable calculation, this might be hardly acceptable. In order to produce practical useful solutions, it is decided to use a calculation model, which allowsfree movement of the external tendons for the ultimate limit state at the deviation points. Free movement at the tendon deflection points produces a lower bound solution. Although this is slightly conservative, it is concluded that this is the only safe assumption possible for friction. Fixed connections will be only suitable in the calculation if there are blocking devices used to avoid tendon slip, as done at Second Severn approach spans (Jackson, 1995). Jackson states also that modelling free movement at the deviators is probably demanding. Finding ways of doing this in a satisfactory manner and with reasonable effort will be tried in the project.

2.4.2 Influence of the arrangement of the deviators on the behaviour at ultimate limit state

The arrangement of the deviators mainly influences the change of eccentricity during application of load. Higher losses of eccentricity can be avoided by proper deviator positions, which can be seen below by comparing the eccentricity of the tendon at a deflected beam with different deviator arrangement.

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Figure 2-12: Influence of a middle deviator on the eccentricity

The eccentricity in the first case (e’1) is smaller as in the second case (e’2). The introduction of an additional deviator at mid span helps to avoid higher eccentricity losses. Matupayont et al. (1994) found that the influence of the second order effect is not unimportant especially for longer unsupported tendon length.

2.4.3 Influence of simply support and continuous support on the ultimate limit state

Generally, continuous structures have a higher redundancy and a failure at one section of the structure does not lead necessarily to failure of the whole structure. The released loads will be redistributed to any other point capable carrying this load. Only if enough pins are produced to create a mechanism, the structure will fail. But redistribution of the load is only possible by providing enough rotational capacity. Normally, this is done with an under-reinforced section, which means that the steel has yielded at ultimate limit state before the concrete reaches its load carrying limit. Over reinforced sections fail in simply supported and continuous structures suddenly, because the steel is not able to provide further rotation by yielding. The statements made above are not fully true for externally prestressed structures. Their prestressing steel is less likely to reach yield. The ductility is provided by the rotation characteristics of the whole structure rather than yielding at a certain point in the structure (Takebayashi, 1994 and Muller and Gauthier, 1989).

Also, it was found that the bending strain increase in the tendon at ultimate limit state is much less for continuous bridges than for simply supported bridges (Ramos and Aparicio, 1995).

Although, the question about ductility and deformation will be an important part of this work, continuous structures are beyond the scope of the actual project.

2.4.4 Precast segmental and monolithic bridges

Monolithic bridge types have small cracks almost arbitrary distributed along the length of the structure whereas precast segmental types are characterised by larger cracks propagating through the segment joints. The joints can be dry or glued together with epoxy resin. The use of glue only means that the cracks occur next to the epoxy glued joint because of the higher strength of the connector than the adjacent concrete (MacGregor et al., 1989). The cracks still have the same characteristics.

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Figure 2-13: Joint opening of precast segmental construction with external tendons

Bruggeling (1989) states that the carrying capacity at ultimate state may be reduced due to the behaviour of a precast segmental structure in shear. It was already mentioned above that it is nearly impossible to control the crack width in externally prestressed precast segmental bridges. Shear can then only be transferred at a limited compression zone. He believes that there will be serious reduction in the ultimate carrying capacity. Bruggeling doubts also that there will be enough rotation capacity at ultimate limit state, because there will be no inclined shear cracks.

On the other hand, Muller and Gauthier (1989) write, “It was found that structures prestressed with either internal or external tendons behave essentially in the same way at all loading stages up to ultimate”. This statement includes segmental bridges. They developed a computer program simulating a loading of such structures and made comparisons to tests. They found that both the load carrying capacity and the deformation behaviour are similar.

Looking at the test results from a full-scale destructive test of a precast segmental box girder with dry joints and external tendons (Takebayashi et al., 1994), the failure was occurring at mid span bycrushing of the concretein the top slab. Hence, there was no obvious sign of shear problems. But Rabbat and Sowlat (1989) made different observations in a similar test. In the case of unbonded tendons the joints opened wider in a shear dominated area, and ultimatelyshear compression failureoccurred in the top flange at the joint. However, both found considerable deflection before failure and reasonable ultimate carrying capacity. But the concerns of Bruggeling relating to shear problems might be therefore not unfounded.

3 Collapse analysis

The following chapter describes the measures undertaken in order to evaluate the collapse behaviour of the bridge types of interest.

3.1 Investigated bridge types and their differences

It is the objective of this dissertation to investigate the ultimate behaviour of the following types of bridges,

- an externally prestressed monolithically built bridge with blocked deviators
- an externally prestressed concrete bridge monolithically built
- an externally prestressed concrete bridge consisting of precast segments with dry joints
- and an internally prestressed monolithically built bridge, which is the conventional prestressed bridge with bonded tendons, as a reference.

The following table shows the differences graphically. The table shows a beam elevation including the tendon with their special characteristics. All of these bridge types are currently in use; none of them is an exotic variant. Only the external prestressing with blocking devices at the deviators is not so common.

Table 3-1: Investigated bridge types

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The following figures show the practical application of those different types.Type 1, the conventional version with bonded tendons and monolithic construction, can be seen below. It demonstrates the position of the tendons, which is within the concrete section. The tendons are typically parabolic draped for post-tensioned systems rather than deflected at one certain point. The structural concrete around the tendon allows this favourable arrangement. However, the tendon arrangement in this project is the same for all bridges. The strands will be deflected only at certain points, as it would be typically found in pretensioned beams.

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Figure 3-1: Casting bed for post-tensioned beam (courtesy of Hyder Consulting Ltd.)

The next system illustrated is theType 3,the external version, which allows movement at the deviators. It appears to be favourable to show Type 3 first, because Type 2 can then be easier understood. The Figure 3-2 and Figure 1-1 show the inside of a externally prestressed monolithically built box girder. It can be seen the tendons run through deviators. If the tendon force on one side of the deviator is bigger than the friction force inside the deviator and the tendon force on the other side, the tendon will slip. It is decided to assume zero friction within the deviators. Reasons for this were already comprehensively explained in 2.4.1. Assuming no slippage is a conservative approach.

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Figure 3-2: Bois De Rosset Viaduct (Switzerland), 15-span, 517-m long externally prestressed bridge (courtesy VSL International)

Type 2is a monolithic externally prestressed construction with blocked deviators. This type was used in the UK for Second Severn approach spans. The designer wanted to avoid tendon slippage at any stage of loading at the deviators, because this allows some simplifications in the design calculations (Jackson, 1995). The construction is monolithically, i.e. it has continuous reinforcement throughout the structure.

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Figure 3-3: Construction of the approach spans of the Second Severn crossing (courtesy of Gifford and Partners)

The last type (Type 4) investigated is precast segmental construction with dry joints and external tendons running outside the cross-section. The match cast segments are held in place only by shear connectors coined at the joints of the segments and contact pressure produced by prestressing. There is no continuous ordinary reinforcement throughout the whole bridge. The reinforcement stops before the joints and starts again on the other side within the new segment.

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Figure 3-4: Erection of a precast segmental bridge with overhead truss (courtesy of Hyder Consulting Ltd.)

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Figure 3-5: Segments with shear keys after production in fabrication yard (Rombach, 1995)

3.2 Original bridge data

The bridge data is based on the externally prestressed concrete box girders used for the Bangkok Second Stage Expressway (see also Figure 3-4 and Figure 3-5). The whole bridge structure has a deck length of about 60km. A full-scale destructive test was carried out on a test span (Takebayashi et al, 1994).

The next figures illustrate the original bridge data:

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Abbildung in dieser Leseprobe nicht enthalten

Figure 3-6: Original cross-section and tendon layout (Takebayashi et al, 1994)

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Table 3-2: Material properties (Takebayashi et al, 1994)

The bridge shown above is designed for AASTHO specifications. The relevant codes are the Standard Specifications of 1983 and the Guide Specifications for Segmental Bridges of 1989. It is a precast segmental bridge with external tendons and a span of 43.25m. The segments are typically 3.4m long. There are for different segments, two end diaphragm segments with anchorages, two side deviator segments, one middle deviator segment, and 9 intermediate segments (see Figure 3-6). The two end segments have a length of 1.725m. The bearing’s midpoint has a distance of 0.5m from the edge of the end segment. The cross-section is a typical box girder section. There are 6 pairs of tendons running along the inside of the box girder. Five of them are continuous and running along the whole girder and are deflected three times, two times at the side deviators and one time in the middle. The specification of these five tendons is 19K15. The other pair is anchored between the two the side deviator and is therefore only one time deflected in the middle. The specification is 12K15. They are further described as strands protected with high-density polyethylene ducts (HDPE) and are cement grouted. The total prestressing force was 38443kN after losses. This was found from back calculations of Takebayashi et al. (1994). The whole arrangement had been already installed two years before testing. The long-term losses occurred were 12% over a time period of 2 years. The supports were elastomeric bearings, and the bridge had no surfacing and no parapets (Takebayashi et al, 1994).

The test span was loaded with steel billets as shown in the next figure over a time period of five days. The deflection of the span; several strains, e.g. the tendon strains and concrete strains; joint opening; and slippage at the deviators were measured. The load was being increased until failure.

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Figure 3-7 Test loading arrangement

3.3 Simplified bridge data as basis for the calculations

The bridge data described above has then been simplified for the calculations. These calculations for the simplification of the tendon layout can be exactly followed in Appendix A (Derivation of the simplified tendon layout).

The cross-section was drawn with a CAD program and the section parameters, the area and the second moment of area, were exactly calculated with this program. A hand check followed. Afterwards a simplification to a suitable cross-section for the calculations was carried out. The simplified cross-section together with the area, the second moment of area, and the section modulus are shown in the next figure.

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The final tendon layout consists of 2 pairs of tendons. The originally 5 continuous tendon pairs are grouped together to one pair and the short pair is kept separately. There is no further simplification possible. All the tendon force after losses is given with 38443kN. The exact calculation regarding this topic can be found in Appendix A: Derivation of the simplified tendon layout.

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Figure 3-9: Simplified tendon arrangement in elevation

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Table 3-3: Forces and stresses in tendons

The cross-section of the tendons is chosen in compliance with EN 138-79 and BS 5896: 1980. The 15mm diameter wire is given a 150mm² cross-section. The whole prestressing force of 38443kN, given from the paper about the test, is then distributed to the tendons by weighting their cross-sections. It is assumed all cables have the same stress. The losses given allow a back calculation to the initial stress in the tendons. The losses mentioned by the author of the test paper are long-term losses. Adding these long-term-losses to the tendon stress leads already 1% beyond the maximum tendon stress at the anchorage point of 0.7*fpu (AASHTO; Segmental constructions, 9.1.2). This can only be explained, if the force meant is a force in the tendon further inside the structure. The maximum allowable tendon stress at internal location immediately after transfer is 0.74*fpu (AASHTO; Segmental constructions, 9.1.3). Even in external prestressed structures, there have to be some short-term losses from friction. Hence, this might be a reasonable explanation of this problem. The maximum jacking force can be determined by considering 0.8*fpu tendon stress (AASHTO; Segmental constructions, 9.1.3).

The other parameters needed for the calculations, which are assumption for the material properties, have undergone special consideration due to its importance. A special chapter (3.4.5 Constitutive models) is devoted only to explanations about material assumption in relation with strength and elasticity theory.

3.4 FE Calculation

Finite element analysis is now by far the most used method for calculations of the continuum. The structure could also be simplified to a line model. However, this is deemed to be not satisfying in this case. At collapse stage the structure will leave the elastic structure response. Considering the special case of concrete there will be large cracks, which are impossible to simulate with a line model. Therefore a continuum analysis is the choice for this investigation. FE methods have proved to be successful in many structural applications, especially in linear elastic calculations. However modelling of concrete structures up to collapse seems to be not always successful. One of the main reasons is the complex inelastic behaviour of concrete. Unlike steel components the material response departs at a very early stage from the linear elastic range. The peak stress, especially in tension, is then followed by a very rapid unloading, which makes the use of plastic flow questionable (Kotsovos and Pavlović, 1995). A detailed discussion follows in a later chapter to constitutive modelling for the analysis.The aim of this project is a full non-linear analysis of this kind of concrete structure up to collapse. This includes non-linear material behaviour and geometric non-linearity. Reinforced concrete elements taking into account cracking are used in this analysis as well as the non-linear characteristics of the tendons. The successful modelling of the reinforced concrete in the structure is assumed to be the key for a successful collapse analysis.

3.4.1 Technical aspects

The finite element calculations were carried on a Sun Workstation with 4 GB RAM. The operational system was UNIX in combination with SOLARIS WINOWS.

The geometric model was created with a CAD system. The geometric data was read into PATRAN 2000R2. Meshing and first simple property assignments were then done within PATRAN. Afterwards, an input file for ABAQUS was produced, which was edited with a conventional text editor in order to introduce more difficult elements and other calculation routines. These were the steps used for pre-processing. ABAQUS 5.8 did the calculations and Post-processing was done with ABAQUS POST.

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Figure 3-10: Analysis Process

3.4.2 General approach

This section describes the basic ideas to the configurations of the models. The models shall be able to simulate correct responses to vertical load action. It is not intended to investigate torsional action about the longitudinal axis of the bridge, e.g. warping effects or distorsional effects. The main action causing the failure will be bending, although the structures are also subjected to a high compression because of the prestress. Due to the concrete, the section parts are not slender and therefore not prone to local buckling. It is assumed that the failure will occur either by crushing of the concrete in compression caused by bending or the tension zone of the beam fails. Shear overloading is the other possible failure mode. Capability of real shear failure is not the purpose of the analysis.

These general consideration lead to a model that represents the behaviour in the vertical direction as close as possible. This includes mainly vertical bending in connection with the exact compression representation of the prestress. This is realised firstly by idealising the cross-section in a way that all section properties governing these factors are reproduced in the FE model with very little deviation. These section properties are the second moment of area about the weaker axis, the area, and the position of the neutral axis. Also, the vertical shear area is represented exactly. However, perfect shear behaviour cannot be approached with his data, especially in the case of the precast segmental bridge. The horizontal parameters such as horizontal second moment of area are not represented so close as the vertical one. A line model can satisfy all these parameters.

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Figure 3-11: Line model of externally prestressed beam for a linear analysis

However, as soon as it gets to collapse analysis, local overloading is of interest. This can hardly be done with line model. Local overloading in our case is mainly cracking of the concrete. This causes parts of sections within the models, which are not longer perpendicular to the longitudinal axis. All these requirements can be met by a two dimensional analysis, if vertical bending is off interest. A two-dimensional model for an external prestressed beam is shown below.

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Figure 3-12: Two-dimensional FE model of externally prestressed box girder

The problem with this model is the inaccurate representation of the non-uniform stresses in the top and bottom slab due to shear lag. The shear lag phenomenon is created by the box characteristics of the structure analysed. An externally prestressed solid beam would be perfectly represented by the two-dimensional analysis.

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Figure 3-13: Three-dimensional mesh of the box girder

The four structure types approached in this dissertation have different characteristics of the embedding of the tendons in the model. Besides, the structure consisting of the precast segments has special areas where the cracks propagate. Type 1, the internal bonded tendon version, has grouted tendons. The cement grout is supposed to produce full fixity between the concrete and the duct. The representation is done by connecting the elements of the tendon with every node from the concrete web it passes. The next figure shows the symbol given to this type of bridge and the method how it is realised in the calculation.

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Figure 3-14: Bonded tendon in FE mesh

It can be seen that the tendon determines the position of certain points within the mesh. Thus, the mesh is not always so even as desirable. The tendon is virtually in the same plane as the web. This is not of importance to the FE program. It needs mainly the connectivity data.

The model with external tendons and blocked deviators is a further development of the model before. The tendon is only fixed to the points in the mesh where the tendon is deflected or anchored. The next figure shows this.

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Figure 3-15: External tendon with blocked deviators

The figure shows, that the tendon does not determine the mesh spacing in the same way as with type 1. The mesh can be much more even. A typical characteristic of external tendons is, that they have the same stress between two adjacent deviators. Internal tendons have everywhere different stresses, because the stress is directly related to the curvature in the structure.

The next type with external tendons, which are free to move at the deviators, is modelled by the means of fixity at the anchorages and kinematic constraints at the deviators. The kinematic constraints have the task to transfer vertical forces coming from the tendon to the structure, but it has to allow slip of the tendons at the deviators. This means it does not transfer horizontal force to the structure. The modelling in Finite elements is nearly the same as the symbolic representation (Figure 3-16). A separate point explains the application of the kinematic constraint (3.4.9). It is essentially a release of one degree of freedom to the adjacent node from the web mesh.

[...]

Details

Seiten
149
Erscheinungsform
Originalausgabe
Jahr
2001
ISBN (eBook)
9783836623339
Dateigröße
14.3 MB
Sprache
Englisch
Katalognummer
v226205
Institution / Hochschule
The University of Surrey – Departement of Civil Engineering, MSc Structural Engineering
Note
1,0

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Titel: Collapse analysis of externally prestressed structures