Collapse analysis of externally prestressed structures

Transcription

1 University of Surrey Department of Civil Engineering Collapse analysis of externally prestressed structures Jens Tandler A dissertation submitted in partial fulfilment of the requirements for the Degree of Master of Science in Structural Engineering August 2001

2 Abstract The use of external prestressing is becoming more popular throughout Europe due to their expected higher durability and the possibility of active maintenance of the prestressing cables. Questions have been raised about the behaviour of these structures beyond service loads. A comprehensive numerical analysis has been carried out comparing the behaviour of three different types of externally prestressed bridges to a conventionally internally prestressed bridge. The external types are a monolithically built bridge with external tendons, a monolithically built bridge with external tendons and blocked deviators, and a precast segmental bridge with external tendons. The internally prestressed bridge is monolithic. The primary objectives are to determine whether or not ductile failure occurs, i.e. the load-deflection response, and the tendon stress increase at ultimate stage. The results show that the monolithically built bridges have a considerable higher ultimate moment capacity as well as deflection. This shows the advantage of using continuous ordinary reinforcement. All externally prestressed types did not reach the capacities of the internally prestressed bridge. It was found that ductility depends mostly on the reinforcement within the cross-section. Externally prestressed girders have no prestressing cables in the cross-section and need sufficient ordinary reinforcement in order to deform ductile. Although the tendon stress increase up to failure in the actual analysis is remarkable, the discussion shows that the magnitude varies greatly depending on the layout of the whole structure. KEYWORDS: EXTERNAL PRESTRESS, DUCTILITY, TENDON STRESS INCREASE, FINITE ELEMENT ANALYSIS

3 Jens Tandler 2001

4 TO ALL MY SUPPORTERS, ESPECIALLY TO KRISTIN

5 Contents at a Glance 1 Introduction Behaviour of externally prestressed structures Collapse analysis Results Discussion of the results Conclusion and Recommendations Jens Tandler 2001 V

6 Contents Acknowledgements...VIII Notation...IX 1 Introduction Definitions Significance of this study Scope of the project Historical overview and typical characteristics of external prestressing Further structural applications of external prestressing Behaviour of externally prestressed structures Tendon layout considerations Behaviour at serviceability stage Fatigue problems Behaviour at ultimate limit stage Influence of tendon slip on the ultimate limit state Influence of the arrangement of the deviators on the behaviour at ultimate limit state Influence of simply support and continuous support on the ultimate limit state Precast segmental and monolithic bridges Collapse analysis Investigated bridge types and their differences Original bridge data Simplified bridge data as basis for the calculations FE Calculation Technical aspects General approach Geometric model Jens Tandler 2001 VI

7 3.4.4 Element specifications Constitutive models Ordinary reinforcement Prestress Material and geometric non-linearity Kinematic constraints Discrete crack propagation analysis of the precast segmental type with gap elements Summary of the dividing features of the different structure types for the FE analysis Results Load deflection behaviour Tendon stress increase up to failure Other results Discussion of the results Interpretation of the results Discussion of the exactness of the FE calculations by comparing to the full scale test Comparison to other FE calculations and test results Conclusion and Recommendations Concluding remarks Recommendations References Codes of practice Appendix A: Derivation of the simplified tendon layout 107 Appendix B: Calculation of the minimum reinforcement 115 Appendix C: ABAQUS Input file for the precast segmental externally prestressed box girder 120 Jens Tandler 2001 VII

8 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 workload. 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 Jens Tandler 2001 VIII

9 Notation Symbols Subscripts b c m p u x,y,z Biaxial Concrete Mean, hydrostatic Prestressing steel Ultimate x,y,z directions Main symbols ε Strain σ Normal stress τ Shear stress σ 1, σ 2, σ 3 Principal stresses σ bp τ c λ c σ cb σ ce ε pb σ pb ε pe σ pe σ s ρ s σ t bu σ t σ te Stress at bottom fibre of section caused by prestress Part of a term describing pure shear strength Hardening parameter from the concrete compression yield surface Negative principal stress Concrete stress at level of tendon from applied moment Bending initiated strain Bending initiated stress Direct strain from prestress in tendon Direct stress from prestress in tendon Stress in ordinary reinforcement Percentage ordinary reinforcement Hardening parameter of the crack detection surface Biaxial tensile strength of the concrete Applied tensile stress Jens Tandler 2001 IX

10 σ tp φ xx σ y a o b o DL E e Stress at top fibre of section caused by prestress Deflection angle of the tendon Uniaxial yield strength Constant Constant Dead load Young s modulus Tendon eccentricity before application of load e Tendon eccentricity after load application e b F f c f ctm f cu f pu f t G f Distance from tendon to the bottom of the section Force Compression yield function of the concrete Concrete tensile strength Uniaxial concrete compression strength Ultimate strength of the tendon Crack detection surface function of the concrete Concrete fracture constant h x Coefficient EC2 DD ENV :2001 I Second moment of area k Coefficient EC2 DD ENV :2001 k 1 Coefficient EC2 DD ENV :2001 k c Coefficient EC2 DD ENV :2001 M Moment M applied M crbf, M crtf M e N sd p q r bc σ Applied moment Cracking moment bottom flange/ top flange Moment introduced form tendons into the end diaphragm Axial force on part of the section from the quasi permanent load and prestress Hydrostatic pressure Distorsional stress Ratio of the maximum biaxial compression strength to the maximum uniaxial compression strength of the concrete Jens Tandler 2001 X

11 σ r t T xx u z Z b, Z t Ratio of the negative uniaxial tensile strength to uniaxial compression strength of the concrete Deflection force from the tendon Crack width Lever arm Section modulus bottom fibre and top fibre 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. 1 in = 25.4 mm 1 ft = m 1 kip force = 4448 N 1 psi = 1/145 N/mm² Jens Tandler 2001 XI

12 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. Posttensioning 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). Figure 1-1: Typical view in box girder bridge with externally deflected tendons (modified from Krautwald, 1998) Jens Tandler

13 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. 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 that the 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 Jens Tandler

14 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 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). 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 Jens Tandler

15 American structural engineer carried out largely by a well-established posttensioning 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). 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 Jens Tandler

16 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 underreinforced 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. Jens Tandler

17 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). 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. Jens Tandler

18 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). Jens Tandler

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

20 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. Figure 1-7: Silo strengthened by external tendons (Schallwig, 1998) Jens Tandler