Identifying Causes for Distress Patterns in ...

Koyuncu, Birgul, Ahlborn, Aktan

1

03-2682 Identifying Causes for Distress Patterns in Prestressed Concrete (PC) I-Girder Bridges Yilmaz Koyuncu Graduate Research Assistant Wayne State University Civil and Environmental Engineering Department 5050 Anthony Wayne Drive, #1305 Detroit, MI, 48202 Phone: (313) 577 3785 Fax: (313) 577 3881 [email protected] Recep Birgul Assistant Professor University of Mugla Mugla Universitesi Rektorlugu 4800 Mugla / Turkey Phone: 01190 252 212 4002 Fax: 01190 252 212 4005 [email protected] Theresa M. Ahlborn Assistant Professor Michigan Technological University Civil and Environmental Engineering Department 1400 Townsend Drive Houghton, MI, 49931 Phone: (906) 487 2625 Fax: (906) 487 1620 [email protected] Haluk M. Aktan Professor Wayne State University Civil and Environmental Engineering Department 5050 Anthony Wayne Drive, #2164 Detroit, MI, 48202 Phone: (313) 577 3825 Fax: (313) 577 3881 [email protected]

Number of Words: 4,557 10 Figures and 1 Table: 11 x 250 =2,750 Total Number of Words: 7,307

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ABSTRACT This study presents an analytical investigation to evaluate the causes of cracking observed near prestressed concrete (PC) I-girder beam-ends and the impact of non-functional bearings on beam-end distress. The cracking potential and their causes are investigated on a PC I-girder near a beam-end using a refined finite element (FE) model. In order to be more realistic the girder modeled is taken from an existing bridge. On this girder, shear stress development due to varying prestressing force within the prestressing force transfer length is evaluated. The model includes three-dimensional solid, continuum elements for the description of the concrete medium, the twodimensional truss elements describing the prestressing tendons. Linear spring elements were used to represent the bond between the concrete medium and the prestressing tendons, and kinematic coupling elements to provide composite behavior between the spring and the truss elements. The analytical study on the girder supported by a deteriorated non-functional elastomeric bearing pad is also performed to assess the significance of their condition on the structural durability of girders. It is observed that recently manufactured PC I-girders are under high shear stress exceeding the shear strength of concrete around the bottom flange and on the web near the beam-end. Another significant result of the analyses is that non-functional elastomeric bearing pads generate distress near the beam-ends of the girders in service. Maintenance of the elastomeric bearing pads is recommended to improve the durability of PC I-girders. Key Words Bursting Cracks, Elastomeric Bearing Pads, Finite Element Analysis, Highway Bridges, Prestressed Concrete IGirders, Transfer Length

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INTRODUCTION Deterioration of in-service civil engineering infrastructure in the United States has become an issue in recent years (1). Due in part to its versatility, availability, and economy, Portland cement concrete has been selected as the building material of choice for roads, bridges, and dams, among other infrastructure elements. Michigan Bridge Design Manual, Section 7.02.03, discusses beam material selection (2). It states that concrete beams are preferable in freeway bridges subjected to severe exposure conditions with Prestressed Concrete (PC) I-girder being the most preferred type. The maximum span lengths and the girder type preferences are related so that PC box beams can be used up to a span of 140-feet. AASHTO type PC I-beams can be used up to a span of 105 feet, and Michigan 1800 I-beams up to a span of 150 feet. The prestressed concrete beam use in Michigan is documented as shown in Table 1, by querying the reconstructed bridges in Pontis, a bridge inventory database used for bridge management by the Michigan Department of Transportation (MDOT) (3). Inventory, operation, inspection, and management data are collected in a relational database for analysis with Pontis. The data in Table 1 shows that the population of PC bridges are increasing such that, during the last decade an average of ten bridges per year are being replaced using prestressed concrete girders (PC I-Girder, PC Box-Girder, or Spread PC Box-Girder). These reconstructed PC bridges are predominantly being rebuilt using PC I-beams (51 of 93). Work performed by others and the field investigations performed in this study have concluded that in midwestern states, such as Michigan, in older PC bridges deterioration induced by corrosion is only near the beamends (1,4). The reasons described are that the beam-ends are located below poorly maintained deck joints and thus exposed to deicing salts draining from the deck surface. Corrosion induced deterioration of PC bridges is more critical than similar deterioration in a conventionally reinforced concrete element for several reasons. One reason is that even minor corrosion of prestressing tendons may affect the load carrying capacity of beams to a greater degree than in conventional reinforced concrete. In addition, because of the relatively small diameter and large number of prestressing tendons compared to the fewer number of larger bars that are used in conventionally reinforced concrete, a greater surface area is available for corrosion. Lastly, the increase in reinforcement density and surface area within a PC section can lead to increased corrosion activity when compared to a conventionally reinforced member. The presence of cracks near the beam-ends is one of the significant parameters in the girder service life (4,5). A second parameter imparting PC I-girder durability is found to be the non-functional elastomeric bearing mechanisms which restrains girder movement. Field studies and literature revealed that PC I-girder end cracks form as early as the precast plant. The moisture ingress increases in a cracked girder as the freezing action widens the cracks. The moisture carries chlorides, which further accelerates tendon corrosion. Consequently, cracking prevention or reduction during manufacture, construction, and operation is essential in order to improve PC girder durability. The cracking and deterioration progression at a beam-end is shown in Figure 1. The initial cracking seen in Figure 1-a and 1-b leads moisture ingress that increases the crack sizes as shown Figure 1-c and 1-d. Further cracking and aggressive agent exposure generates delamination, Figure 1-e, and spall of concrete cover, Figure 1-f, reducing the structural durability performance of the girder. In this study, a discrete beam FE model is developed and analyzed to identify the influence of prestressing loads on beam-end cracking. The Finite Element (FE) model is a beam with straight tendons from a prototype bridge girder in Michigan. The impact of non-functional bearings on beam-end distress is also investigated using the FE model. The stress states and cracking potential at the beam-end zone are evaluated to explore ways to reduce the cracking. RESEARCH OBJECTIVES This research project, “Causes and Cures for PC I-Beam End Deterioration,” was sponsored by the Michigan Department of Transportation (MDOT) and performed by the Center for Structural Durability, a collaborative effort between Michigan Technological University and Wayne State University. Two main objectives for the research program were: • •

Development of an inspection procedure for existing PC I-beams for assessing their vulnerability to tendon corrosion, and Evaluation of repair techniques for existing deteriorated PC I-beam ends.

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An extensive examination of 20 PC I-beam bridges, 2 to 40 years old, was performed to identify and document the distress at the beam-ends. This article presents the FE modeling and analyses are of a discrete PC Igirder under prestressing load. The results of the FE analyses are used to identify the causes of end cracking observed during field inspections. FINITE ELEMENT ANALYSES Field inspections revealed web cracking at the precast plant as shown in Figure 1-a and on girders of bridges recently being constructed, Figure 1-b. During inspection of 375 PC I-beams, a similar cracking pattern was observed on almost every beam-end. Literature describes various mechanisms that can cause beam-end cracking and some are initiated as soon as the girders are cast and the tendons are released (6,7,8,9,10). Earlier studies by Sozen discuss the cracking in I-girders within the anchorage zone (11, 12). The transverse stresses are stated as the main reasons for the bursting and spalling cracking. In this paper, in addition to transverse stresses, cracking within the prestressing load transfer length is investigated. Two additional analyses are presented, one dealing with the effects of non-functional bearings, the second discussing the load-path near the beam-ends. The cracking potential analysis was performed on a discrete I-girder under prestressing load only. The cracking zones were compared to field observations. In addition, the beam was analyzed with non-functional bearings under live and dead loads to document the load path through the beam-end into the support. The interest in the load path analysis is to evaluate the vulnerability of girders with deteriorated ends. In other words, if the load path is clearly described, any girder-end deterioration within the zone of low stress will not necessarily jeopardize girder capacity. The beam modeled is an AASHTO Type-III I-girder (13) from an existing bridge in the Bay Region of Michigan with inventory ID number of 06111-S4, constructed in 1968. This three-span bridge has exterior spans of 31 feet 3 inches and, an interior span of 49 feet. The bridge deck has a uniform 43 feet 2 inches width with two lanes, and the deck thickness is 8 inches. The I-girder modeled is an interior girder on the interior bridge span. Loading Cases, Material Characteristics, and Modeling Assumptions As for loading conditions, three loading states were considered. These states were for beams during production, erection, and service. Accordingly, the specific loads considered in the models were the following: • Prestressing Load: The prestressing load in the tendons was taken into consideration as the only load. The load is incorporated by applying pre-strain to the tendons. • Dead Load: Dead load was applied as distributed load on the discrete beam while retaining the prestressing load. The load path and the stress formation near the beam-ends were examined. • Live Load: The final stage of the analysis was the live load consideration while dead load and prestressing loads were retained. The traffic load, an AASHTO HS20-44 Truck Load (13), was applied to the beam as transversely distributed load on the assumed wheel locations for which the girder was designed to document the beam-end stresses during service. The modulus of elasticity of concrete is calculated from designated concrete compressive strength of 5,000 psi, using the formulation given in ACI 318-02 (14) as Ec=57,000⋅ f ' c , where Ec is the modulus of elasticity of concrete and f c' is the compressive strength of concrete. The modulus for the Grade 250 7-wire strand was assumed equal to the steel modulus elasticity of 29,000 ksi. It needs to be emphasized that this modulus is in reality the tangent modulus at the initial prestressing force, which was 24.5 kips. Certain additional assumptions are made in modeling the girder, for elastic, small deformation, FE analysis. 1. 2. 3. 4. 5.

Symmetrical tendon-cutting pattern was assumed about the vertical axis. Thus, moments generated by unbalanced tendon forces were not included. Time dependent losses such as creep and shrinkage losses were not incorporated. Thermal effects were not included. Only prestressing loss due to elastic shortening of the beam was included. Shrinkage effects of the deck on the girder were not incorporated. Deck was assumed to contribute only to the dead load. The boundary conditions at the both ends were assumed free. The prestressing tendons are modeled as preloaded discrete truss elements attached to the concrete only at the nodes through linear springs.

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6. 7.

5

Tendons are assumed to have only axial stiffness and modeled as line elements with constant in cross-sectional geometry under prestressing forces. The bond properties between the tendons and concrete are modeled using the flexible springs between the two mediums.

Using symmetry only one half of the beam was modeled under the prestressing affect; the self-weight of the beam was not included. The boundary conditions were described as the support at the girder-end, roller in longitudinal direction, and at the mid-span, roller in vertical direction as directed by the symmetry constraints. The Finite Element Model The FE models were developed by a pre-processor and post-processor program HyperMesh and analyzed by a finite element program ABAQUS (14). The finite element mesh and element selection was formed according to the options and analyzing procedures defined by the programs. The FE model of the girder shown in Figure 2 includes 2185 continuum elements with 8 nodes, 342 truss elements with 2 nodes, 342 linear spring elements with 2 nodes, and 342 kinematic coupling elements with 2 nodes for a total of 24,688 degrees of freedom. The three-dimensional continuum elements were used for the concrete portion of the beam. The truss elements defining the prestressing tendons were prestressed, and subsequently prestrained, as an initial force condition. The spring members were utilized to describe the bond between the tendon and concrete. Similar bond-spring analogies and modeling practices were used commonly in the literature (16, 17, 18, 19, 20, 21, 22, 23). These earlier studies mainly dealt with the bond failure and non-linear behavior of the bond stiffness during service. In this research, the elastic bond-spring analogy is used in the girders since maximum loads are limited to service loads. The kinematic coupling elements were utilized due to modeling requirement in ABAQUS (14) as intermediate agents to provide composite action between the spring and truss elements. The geometry used in the model was identical with the prototype AASHTO Type III I-girder. The FE mesh is refined near the beam-end to accurately represent on the girder-end transfer zone stresses. The length of the three-dimensional continuum elements were 4 inches at the beam-end for the first 8 inches, then 6.5 inches for the following 52 inches, and 26 inches for the remaining 234 inches as seen in Figure 2. The bond stress in concrete is proportional to the spring stiffnesses. Assuming strain compatibility between the tendon and the surrounding concrete, the amount of stress developed in concrete should be proportional to the strain. The spring constant for a unit length in this case is proportional to the elasticity modulus of concrete (19). Thus, the stiffness of each spring is proportional to its length which is equal to the length of the concrete element it is tied. Prestressing Force Transfer Length and Stress Pattern near the Beam-end As the prestressing force is transferred from the tendons to the surrounding concrete medium, axial and the flexural stresses gradually develop in the member within a zone termed as the “transfer length”. In developing the FE model of the PC I-girder, the key modeling aspect is the description of force transfer from the tendon to the concrete medium. In forming an analogy between the FE model and the two-dimensional beam model commonly used in design, the nominal compressive stress considered in the PC I-girder design is the summation of flexural stresses with axial stresses calculated at the bottom fiber as shown in Equation 1: fb =

M ⋅ yb P + I A

Equation 1

where; A = Cross-sectional area of the girder, fb = Total uniaxial stress on a fiber below the neutral axis, I = Moment inertia of the section, M = Bending moment due to prestressing load; M=P⋅e, P = Prestressing force, e = Eccentricity of prestressing load measured from neutral axis, yb = Distance of neutral axis to the extreme bottom fiber.

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Equation 2 describes the static equilibrium condition of an incremental element near the beam-end as derived using a simple beam model commonly used in design. The nominal force transferred to the concrete within the force transfer zone increasingly varies near the beam-end. The uniaxial stresses at each side of an incremental element are not equal within the transfer length. Due to this unbalanced condition, shear stress is generated so that static equilibrium is provided. Beyond the development length, the prestressing force in concrete achieves the applied prestressing load less the losses, and the resultant shear stress on the element diminishes. The finite element analysis will give accurate calculation of shear stress at sections. Therefore, the analysis will define the cracking vulnerable zones within the transfer length. v = f b1 − f b2 ( M 1 − M 2 ) y ( P1 − P2 ) v= + I A ∆M ⋅ y ∆P v= + I A

Equation 2

where; v = Shear stress, y = Distance of neutral axis to a fiber on bottom of the section. ANALYSES RESULTS FE analysis using the three-dimensional solid elements, for modeling the beam including tendon and bond elements will give accurate representation of stress distribution. The analysis results are presented as stress contours of axial (longitudinal) and lateral (transversal) stresses. In addition, Von Misses, and principal stresses will be presented. Cracking Potential of a PC I-Girder The axial and shear stress distribution at selected sections along the beam axis are shown in Figure 3 and Figure 4 correspondingly. Each Figure 3-a to Figure 3-i and Figure 4-a to Figure 4-i shows the axial and shear stress distribution at section along x-axis. As seen in Figure 4-i, the prestressing force transfer to concrete is completed, and the axial stress variation became linear. Subsequently, the magnitude of shear stress becomes insignificant after a length between 27.5 and 34 inches and fully diminishes at 47 inches as seen in Figure 4-i. The design transfer length of 7-strand wire is calculated as 26.7 inches according to AASHTO (13). The axial stress variation at a section near the beam-end is the first concern. As seen in Figure 5-a, the axial stress magnitude of 2,970 psi gradually re-distributes until the nominal state is reached at about a transfer length between 27.5 and 34 inches. When the stresses approaches nominal distribution, a maximum compressive stress of 1,740 psi is achieved at the bottom fiber and the stress at the top fiber is tensile at about 100 psi, well below cracking strength of concrete. The axial stress in the z-direction generating from Poisson’s effect, reaches about 600 psi tensile within the web as shown in Figure 5-b. Within this zone, stress exceeds the concrete tensile strength limit of 424 psi calculated using the formulation provided by AASHTO as 6⋅ f ' c simply due to prestressing and confirms previous studies (11, 12) for the concrete with 5,000 psi compressive strength (13,24). The location of web cracking seen in Figure 5-b was also observed during inspection as seen in Figure 1-a, 1-b, 1-c, and 1-d. The shear stress pattern shown in Figure 5-c on half of the girder also indicates a critical location near the bottom flange, within the proximity of the web. The maximum shear stress is around 815 psi and much greater than the design shear strength of concrete, which is calculated as 247 psi according to the limit given as 3.5⋅ f ' c by ACI 318-02 (14). As demonstrated on a newly manufactured girder in Figure 1-b and on a girder in service in Figure 1d, the transition zone between the bottom flange and the web is vulnerable to cracking. The principal stresses shown in Figure 6-a and 6-b demonstrate the cracking potential within the beam-end zone. Principal stress contours as “1”, maximum principal stress, and “3”, minimum principal stress, and their ranges are shown in Figure 6-a and 6-b on half girders correspondingly. The principal stress “1” is compressive with a magnitude reaching 3,000 psi. The principal stress “3” is primarily tensile reaches 765 psi, exceeding the tensile strength of concrete of 424 psi, within the web and bottom flange transition area.

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Load Path Analyses Load path analyses establish the highly stressed portion of the beam-end under the combined action of prestressing, dead, and service loads. This analysis will provide a means of evaluation of the impact of beam-end deterioration to its “load transfer” capability. Also included in the analysis is the impact of a non-functional bearing to the changes in load path. A single girder utilizing the same FE model developed for the prestressing load analysis is utilized. An additional load case is introduced to represent the non-functional elastomeric bearing pad. The deck and girder are considered for the dead load estimation, which is calculated as 0.962 k/ft for a concrete unit weight of 0.150 k/ft3. Superimposed dead load including barrier and wearing surface is 0.335 k/ft. AASHTO HS20-44 truckload (13) is applied at a location to generate the maximum flexural stresses at the midspan. The live load corresponds to a gross truck weight of 72,000 lb, which is an approximated load amount for simulating the largest stress. The dead and superimposed dead loads were uniformly distributed over the top surface of the beam. The truckload was incorporated uniformly in transverse direction on the truck wheel locations. Girder spacing is 91 inches on center; corresponding to a distribution factor of 1.379. The distribution factor is calculated using the formula DF = S 5.5 , where DF is for the distribution factor and S is for the girder spacing. A girder length of 49 feet gives 1.287 for the live load impact factor. The impact factor is calculated by using the formula (1 + I) = (50 ( L + 125 ) + 1) , where I is the impact fraction and L is the span length in feet. The non-functional elastomeric pad behaves rigid as depicted in Figure 7-a. As a result, when the beam bends, the bearing rocks over the pier cap. The effective support area under exaggerated deformation is shown in Figure 7-b. The beam support is modified in the FE model to represent its shape under bending. The effective support area is reduced and shifted towards the center span to represent the non-functional elastomeric bearing pads. The analysis results in Figure 8-a are shown for the combination of prestressing and dead loads and in Figure 8-b prestressing, dead, and live loads. Figure 8-a shows the axial stress distribution under prestressing and dead load. The zone with the stress contour of around 740 psi compressive stress describes the load path to the bearing. The shear stress calculated shown in Figure 8-b reaches 1,640 psi at the bottom flange and 750 psi at the web. The live load is included as shown in Figure 9-a very high tensile stresses are observed near the support area. The shear stress reaches maximum 1,820 psi around the tendons and 560 psi at the web as shown in Figure 9-b. High tensile and shear stress intensities around the support is significant and far beyond the concrete tensile, 424 psi, and shear, 247 psi, strengths. As a result, the region around the support becomes vulnerable to cracking as shown in Figure 8-c, which was a common distress observed during field inspection. Load path to the support region is defined under dead and live load cases using the principal stresses “1” and Von Misses stresses. The principal stresses are 824 psi under dead load and 910 psi including live load. The principal stresses within this contour, the diagonal region between the top flange and the support, are shown in Figure 10-a and 10-b. Von Misses represents the absolute total stresses and may not be used for a qualification of failure conditions, however, if used qualitatively will describe the zones of high stress intensity. The stress intensity will help to describe the load path. Von Misses stresses in Figure 10-c and 10-d describe a similar load path as observed from the principal stresses contours in Figure 10-a and 10-b. The area of the beam-end that is within the stress contours of 1,920 psi under dead load and 2,400 psi under live load are shaded in Figure 10-c and 10-d and assumed to represent the load path. The load path and critical regions near the girder-end are shown in Figure 10-e and 10-f on a real girder correspondingly. Any deterioration that protrudes into the load path increases the vulnerability of the girder-end. CONCLUSIONS This analytical study looked into the influence of prestressing actions, and dead and live loads on girder-end distress. Effort was concentrated on developing the hypothesis for evaluating the causes of beam-end distress. The cracking zones obtained from the analyses correlate with the cracking observed during the field inspection. The major conclusions of this research are described below: 1.

The PC I-beam-ends are often cracked during manufacturing upon tendon release. The initial cracking accelerates the girder-end deterioration with the presence of moisture primarily by accelerating the chloride ingress and corrosion initiation of shear reinforcement and prestressing tendons.

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2.

3. 4.

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Analytical models showed that the cracking potential is very high at PC I-girder ends. Beam-end cracking is due to a high shear stress intensity generated by the deviation in axial loads within the prestressing force transfer length. Cracking from the bursting effect is primarily in the direction of the high longitudinal stress and from transverse (shear) stress due to Poisson’s effect. These loads cannot be eliminated, and the prestressing load transferring mechanism cannot be altered, but cracking can be minimized with the use of confinement steel near beam-ends. Further analysis needs to be performed in order to specify the exact arrangement and size of confinement steel. The load path analysis shows that beam-end vulnerability is a concern for bridge safety. The deteriorated portion of the girder-end is often within the path of dead and live load transfer to the bearings. As the bearing pad loses its flexibility by time and environmental effects, it becomes rigid and ineffective. The poor condition of elastomeric bearing pads affects the support condition, which in turn affects the load path in the girders. Replacement of elastomeric pads should be included in preventive bridge maintenance.

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REFERENCES 1.

2. 3. 4.

5.

6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16.

17. 18.

19.

20. 21. 22. 23. 24.

Whiting, D.A., Stejskal, B.G., and M.A. Nagi. Rehabilitation of Prestressed Concrete Bridge Components by Non-Electrical (Conventional) Methods. FHWA-RD-98-189. Federal Highway Administration, Washington, D.C., 1998. Michigan Department of Transportation. Bridge Design Manual, 2001. http://www.michigan.gov/mdot/0,1607,7-151-9622_11044_11367---,00.html. Accessed July 29, 2002. “Pontis” (Version 3.4.3). Computer Software, American Association of State Highway and Transportation Officials, Washington, D.C., 2001. Aktan, H.M., Ahlborn, T.M., Koyuncu, Y., and J.M. Kasper. Inspection Based Health Monitoring of Prestressed Concrete Bridges in Michigan. 1st FIB Congress: Concrete Structures in the 21st century, Osaka, Japan, October 13-19, 2002. Ahlborn, T.M., Ovanesova, A.V., Kasper, J.M., and H.M. Aktan. Prestressed Concrete Bridge Beam Health Monitoring in Michigan. First International Conference on Bridge Maintenance, Safety and Management, Barcelona, Spain, July 14-17,2002, pp. 283-284. Buckner, C.D. A Review of Strand Development Length for Pretensioned Concrete Members. PCI Journal, March-April 1995, pp. 84-99. Russell, B.W., and N.H. Burns. Measured Transfer Lengths of 0.5 and 0.6 in. Strands in Pretensioned Concrete. PCI Journal, Sep-Oct 1996, pp. 44-65. Russell, B.W., and N.H. Burns. Measurement of Transfer Lengths on Pretensioned Concrete Elements. Journal of Structural Engineering, May 1997, pp. 541-549. Kannel, J., French, C., and H. Stolarski. Release Methodology of Strands to Reduce End Cracking in Pretensioned Concrete Girders. PCI Journal, Jan-Feb. 1997, pp. 42-54. Leonhardt, F. Prestressed Concrete Design and Construction. Wilhelm Ernst & Sohn, Berlin, 1964. Lenschow, R.J., and M.A. Sozen. Practical Analysis of the Anchorage Zone Problem in Prestressed Beams. Journal of the American Concrete Institute, November 1965, pp. 1421-1439. Gergely, P., and M.A. Sozen. Design of Anchorage-Zone Reinforcement in Prestressed Concrete Beams. PCI Journal, April 1967, pp. 63-75. Standard Specifications for Highway Bridges, 16th Edition, America Association of State Highway and Transportation Officials. Washington, D.C., 1996. ABAQUS/Standard User’s Manual (Version 5.8), Hibbitt, Karlsson and Sorensen, Inc., USA, 1998. Building Code Requirements for Structural Concrete, ACI 318-02, and Commentary. ACI 318R-02, American Concrete Institute, Farmington Hills, MI, 2002. Mehlhorn, G., and M. Keuser. Isoparametric Contact Elements for Analysis of Reinforced Concrete Structures. Proceedings of Finite Element Analysis of Reinforced Concrete Structures Seminar. ASCE. Tokyo, Japan, May 21-24, 1985, pp. 329-347. Morita, S., and S. Fujii, Bond-Slip Models in Finite Element Analysis. Proceedings of Finite Element Analysis of Reinforced Concrete Structures Seminar. ASCE. Tokyo, Japan, May 21-24, 1985, pp. 348-363. Niwa J., Chou, L.L., Shima, H., and H. Okamura. Nonlinear Spring Element for Strain-Relationship of a Deformed Bar. Proceedings of Finite Element Analysis of Reinforced Concrete Structures Seminar. ASCE. Tokyo, Japan, May 21-24, 1985, pp. 374-383. Eligehausen, R., Popov, E.P., V.V. Bertero. Local Bond Stress-Slip Relationships of Deformed Bars Under Generalized Excitations. UCB/EERC-83/23. Earthquake Engineering Research Center, California, October 1983. Limkatanyu, S., and E. Spacone. Reinforced Concrete Frame Element with Bond Interfaces. I: DisplacementBased, Force-Based, and Mixed Formulations. Journal of Structural Engineering, March 2002, pp. 346-355. Wu, X.H., Otani, S., and H. Shiohara. Tendon Model for Nonlinear Analysis of Prestressed Concrete Structures. Journal of Structural Engineering, April 2001, pp. 398-404. Kwak, H.G., and S.P. Kim. Bond-Slip Behavior Under Monotonic Uniaxial Loads. Engineering Structures, 2001, pp. 298-309. Padmarajaiah, S.K., and A. Ramaswamy. A Finite Element Assessment of Flexural Strength of Prestressed Concrete Beams with Fiber Reinforcement. Cement and Concrete Composites, 2002, pp. 229-241. Leet, K.M., and D. Bernal. Reinforced Concrete Design. McGraw-Hill, 3rd Edition, 1997.

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LIST OF TABLES TABLE 1 Material Selection in Reconstructed Bridges............................................................................................. 11 LIST OF FIGURES FIGURE 1 (a) Cracking at the web zone at the precast plant; (b) cracking within the proximity of bottom flange of a girder for a bridge under construction; (c) cracking observed on the web and around the bottom flange of girders in-service bridge; (d) moisture presence around cracking on the web; (e) delamination and spalling on a girder; (f) spalling of cover concrete and exposed rebar. .................................................... 12 FIGURE 2 PC I-girder Finite Element model............................................................................................................ 13 FIGURE 3 Axial stress distribution at sections near the beam-end under prestressing loads. ................................... 14 FIGURE 4 Shear stress distribution at sections near the beam-end under prestressing loads.................................... 15 FIGURE 5 (a) Axial stress in X-direction (longitudinal, ksi); (b) axial stress in the Z-direction (vertical, ksi); (c) shear stress on X-Z plane (ksi) near the beam-end. .................................................................................. 16 FIGURE 6 (a) Principal Stress “1” (ksi); (b) Principal Stress “3” Near the End Zone (ksi). ..................................... 17 FIGURE 7 (a) Non-functional bearing observed during field inspection; (b) the form of the bearing under flexural bending. .................................................................................................................................................... 18 FIGURE 8 (a) Axial stress under prestressing and dead load (ksi); (b) shear stress under prestressing and dead loads (ksi); (c) common distress at the bearings observed in PC I-girder bridges. ............................................ 19 FIGURE 9 (a) Axial stress under prestressing, dead, and live loads (ksi); (b) shear stress under prestressing, dead, and live loads (ksi).................................................................................................................................... 20 FIGURE 10 (a) Principal stress-1 for dead load (ksi); (b) principal stress-1 for live load (ksi); (c) Von Misses stress for dead load (ksi); (d) Von Misses stress for live load (ksi); (e) load path on a PC I-girder; (f) critical regions near the girder ends...................................................................................................................... 21

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TABLE 1 Material Selection in Reconstructed Bridges Years

Superstructure or Deck Replacement

PC I-Girder

PC Box-Girder

Spread PC Box-Girder

1960-70

69

2

2

None

1970-80

127

4

9

None

1980-90

161

18

6

None

1990-00

261

51

24

18

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a

b

c

d

41029- S16-3 (1964)

41029- S16-4 (1964)

25042- S12-4 (1969)

e

f

FIGURE 1 (a) Cracking in the web zone at the precast plant; (b) cracking within the proximity of the bottom flange of a girder for a bridge under construction; (c) cracking observed on the web and around the bottom flange of girders in an in-service bridge; (d) moisture presence around cracking on the web; (e) delamination and spalling of a girder; (f) spalling of cover concrete and exposed rebar.

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Z Y

X FIGURE 2 PC I-girder Finite Element model

TRB 2003 Annual Meeting CD-ROM

Paper revised from original submittal.

Koyuncu, Birgul, Ahlborn, Aktan

14

FIGURE 3 Axial stress distribution at sections near the beam-end under prestressing loads.

TRB 2003 Annual Meeting CD-ROM

Paper revised from original submittal.

Koyuncu, Birgul, Ahlborn, Aktan

15

FIGURE 4 Shear stress distribution at sections near the beam-end under prestressing loads.

TRB 2003 Annual Meeting CD-ROM

Paper revised from original submittal.

Koyuncu, Birgul, Ahlborn, Aktan

16

a

b

c

FIGURE 5 (a) Axial stress in X-direction under prestress only (longitudinal, ksi); (b) axial stress in the Zdirection (vertical, ksi); (c) shear stress on X-Z plane (ksi) near the beam-end.

TRB 2003 Annual Meeting CD-ROM

Paper revised from original submittal.

Koyuncu, Birgul, Ahlborn, Aktan

Y

Z X

17

a

Y

Z X

b

FIGURE 6 (a) Principal Stress “1” (ksi); (b) Principal Stress “3” Near the End Zone (ksi).

TRB 2003 Annual Meeting CD-ROM

Paper revised from original submittal.

Koyuncu, Birgul, Ahlborn, Aktan

18

41029-S16-3 (1964)

a Distributed Service Loads

Pier Cap

Steel Sole Plate

Elastomeric Pad

Pier Cap

b FIGURE 7 (a) Non-functional bearing observed during field inspection; (b) the form of the bearing under flexural bending.

TRB 2003 Annual Meeting CD-ROM

Paper revised from original submittal.

Koyuncu, Birgul, Ahlborn, Aktan

Y

19

Z X

Y

a

c

Z

b

X

25042- S12-4 (1969)

FIGURE 8 (a) Axial stress under prestressing and dead loads (ksi); (b) shear stress under prestressing and dead loads (ksi); (c) common distress at the bearings observed in PC I-girder bridges.

TRB 2003 Annual Meeting CD-ROM

Paper revised from original submittal.

Koyuncu, Birgul, Ahlborn, Aktan

Y

Z

20

a X

Y

b

Z X

FIGURE 9 (a) Axial stress under prestressing, dead, and live loads (ksi); (b) shear stress under prestressing, dead, and live loads (ksi).

TRB 2003 Annual Meeting CD-ROM

Paper revised from original submittal.

Koyuncu, Birgul, Ahlborn, Aktan

Z

Y

Y

21

a X

Z X

Z

Y

c

Y

e

b X

Z X

d

f

FIGURE 10 (a) Principal stress-1 for dead load (ksi); (b) principal stress-1 for live load (ksi); (c) Von Misses stress for dead load (ksi); (d) Von Misses stress for live load (ksi); (e) load path on a PC I-girder; (f) critical regions near the girder ends.

TRB 2003 Annual Meeting CD-ROM

Paper revised from original submittal.