Defining a Baseline Model for Bridge Analysis and Design

Transcription

1 Defining a Baseline Model for Bridge Analysis and Design Brian Brenner Department of Civil & Environmental Engineering Tufts University 200 College Avenue Anderson Hall, Rm. 113 Medford, MA Phone: (617) Fax: (617) brian.brenner@tufts.edu Masoud Sanayei Department of Civil & Environmental Engineering Tufts University 200 College Avenue Anderson Hall, Rm. 113 Medford, MA Phone: (617) Fax: (617) masoud.sanayei@tufts.edu David Lattanzi Gannett Fleming, Inc. Suite 200 Foster Plaza III 601 Holiday Drive Pittsburg, PA Phone: (412) Fax: (412) dlattanzi@gfnet.com Erin Santini Bell Department of Civil Engineering University of New Hampshire 236-D Kingsbury Hall Durham, NH Phone: (603) Fax: (603) erin.bell@unh.edu August 1, 2005 Word count: 4,430 words (footnotes & endnotes: 4,653) Brian Brenner and Masoud Sanayei 1 David Lattanzi 2 Erin Santini Bell 3 1 Tufts University, Department of Civil and Environmental Engineering, Medford MA Gannett Fleming, Suite 200, Foster Plaza III, 601 Holiday Drive, Pittsburg PA University of New Hampshire, Department of Civil and Environmental Engineering, Durham NH 03824

2 2 Abstract In current AASHTO design practices, bridges are designed on an elemental basis. AASHTO code specifies that each structural element is to be designed for the loads it will experience during the life of the bridge. The calculated loads are enveloped to produce maximum loads. This approach, elemental design, is structurally sound, in general conservative, and has resulted in the design and construction of safe and reliable bridges. Designers use a matrix approach to evaluate a set of what are essentially initial-state load conditions. This paper describes development of a baseline bridge model and suggests certain modifications to the traditional bridge design process to take advantage of modern computing capabilities to create a refined baseline model. The baseline model is an analytical model which accounts for the full system behavior of the structure, as opposed to the elemental approach which envelopes loads and conditions to evaluate separate components of the bridge structure. The baseline model is a three-dimensional structural model employing finite element software. A sample baseline model is developed and evaluated for a simple span steel composite concrete stringer bridge. Advantages and challenges for application of the baseline model, as part of a modified overall bridge design process, are presented and discussed.

3 3 INTRODUCTION In current AASHTO design practices, bridge elements are designed on an individual basis. These design practices have developed over a time period pre-dating widespread computer use and analytic methods. In contrast to an elemental analysis approach, structural system analysis can be defined as an analysis in which the structure is not broken into its elements, but is analyzed as a whole, interactive system. This allows the designer to capture the performance benefits and impacts that each element has on other elements. For example, elastomeric bearing pads lessen deflections and stresses in girders by restraining rotations at the supports, in comparison to assumed pure simple span behavior which assumes unrestrained rotation. But this condition is not considered in girder live load estimations. A bridge that is analyzed by modeling the complete structural system would take into account the shell behavior of the deck and its interactions with bridge girders, as opposed to analyzing each girder as an individual beam. As bridges become more sophisticated and more indeterminate, the system level approach becomes more significant. A system level approach can provide a more consistent factor of safety. As a result, instead of arbitrarily strengthening one or two bridge components, all critical structural components are strengthened using the specified factor of safety for each component. The current AASHTO LRFD code (1) represents a significant improvement over previous allowable stress and load factor versions, in that it attempts to systematically measure risk that is quantified as a certain factor of safety between applied loads and provided resistance. The specified factors of safety are determined through a rational, uniform analysis and review. However, the factors are largely applied by the standard elemental approach. Additional factors of safety provided by examining structural system behavior are not rigorously quantified. However, the code does provide some place holders for this quantification, such as specification of a factor for redundancy and structural importance. Recently, research attempts are focused on rigorously defining exactly what these factors of safety should be (2). These attempts have employed system level structural models to evaluate overall performance of bridge structures. While the elemental analysis approach is appropriate for conservative design, it does not result in structural models that accurately evaluate performance of the bridge structural systems. Elemental analysis and design approach is not well-suited for in-service structural health monitoring involving examination of bridge system behavior. Design standards have shied away from system level analysis and design because it is analytically challenging and our current design methodology is based on practices developed before computers became commonplace in most design offices. In most cases although not all ignoring system level behavior is conservative, because it does not include additional factors of safety inherently present in the system performance of the structure. Therefore, design engineers have not felt a need to incorporate it into design. While elemental design is efficient in terms of design, it leaves the designer with no real understanding of a bridge s structural behavior, nor does it provide a tool for accurately measuring the long-term deterioration and performance of a bridge. The benefits gained by having structural elements work together are not quantified and estimations of long term structural performance are never explicitly calculated. Such a design tool would be a baseline analysis model of the structure that more accurately reflects the true structural behavior of the bridge, and serves to conservatively

4 4 envelope behavior for the purpose of conservative elemental design. A baseline model would attempt to capture the designer s understanding of the bridge s actual, system performance, and would have to be sufficiently complex to include all of the major detailing that dictates bridge behavior. Such a model cannot be of the 2D finite element (FE) stick model type currently used in most design offices. These stick models inherently prevent the modeling of system-wide benefits such as parapets, lateral frame stiffness in diaphragms, and other features that are not typically modeled as a part of an enveloped, elemental analysis and design approach. Rehabilitation practices are also limited by current design philosophies. Our rehabilitation methods primarily involve visual inspection of a structure. By estimating allowable loads based on visual damage estimates, two important factors are not evaluated. The first is that certain types of damage can be hidden from view. For example spalling concrete behind stay-in-place forms or delamination in bridge decks are two important examples. The second is that in some instances system level performance has been used to justify an evaluation for a bridge that has remained in service, but would have otherwise been closed. In general, this performance has not been quantified for older structures in a rational, organized manner. By not accounting for system level behavior in aging structures, our understanding of which bridges are most in need of rehabilitation is less objective. Such an understanding is desirable when deciding priorities for the limited funding available for structural rehabilitation. Clearly, we need to alter our fundamental design practices if we want to better evaluate how our bridges behave over their lifecycles. This understanding can help bridge owner s to make more effective and more fiscally responsible decisions regarding rehabilitation and replacement strategies. Bridge designers and owners would also gain a more fundamental understanding of bridge behavior. As mentioned earlier, elemental design practices as specified in the design code do not result in real understanding of bridge behavior. Even a basic knowledge of system level behavior would make engineers more capable of tackling design issues effectively. DEFINITION OF BASELINE STRUCTURAL MODEL This section discusses preparation of a baseline model for a simple span steel stringer composite concrete deck bridge. The basis for the model is the Neponset River Bridge in Quincy, Massachusetts (Figure 1). One typical simply supported span from the nine-span structure was evaluated. The bridge has no skew or other irregularities to consider. A steel stringer composite concrete bridge model was chosen for simplicity and to avoid challenges associated with precise modeling of stiffness and cracking of concrete structures. For the simple span structure, the composite concrete deck is in compression in the longitudinal direction of the span.

5 5 Figure 1. Neponset River Bridge In order to address the research needs of this particular effort, finite element (FE) modeling was used for design verification and long term monitoring. Finite element modeling is readily available to most practicing engineers and is easy to use. If a finite element model can be developed to capture the actual performance of the bridge it could be used to verify the AASHTO based calculations. Such a model would serve as a living document that would remain throughout the life cycle of the bridge in order to document the intentions of the original designers and model the subsequent events. Additionally, NDT data could be compared to the FE model to better comprehend the process of bridge aging, deterioration, and potential damage events. For the Neponset River Bridge, the girders of the baseline model are modeled as frame elements in SAP2000. Using frame elements allowed for the most flexibility in modeling. Several options were considered for the girders, including combinations of shell elements and fully three dimensional elements. Previous research has shown that there is only a slight increase in accuracy with the use of more complex elements and computational demands increase dramatically (3) changes in moments and distribution factors were ±3%. Because shell elements act at the neutral axis of the shell s thickness, assembling shell elements as plate girders requires the use of a method such as offsets and rigid links to account for the thickness. Furthermore, shell elements are not conducive to irregular shapes such as those found in bulb-tee concrete beams (Figure 2), which is commonly used in bridge construction. The simplicity of frame elements allows the designer to input all of the section properties manually if needed, thus accommodating any irregular shapes. Overall, the use of frame elements minimizes model complexity and maximizes model flexibility for the designer, while not subtracting from needed accuracy for evaluation of system performance.

6 6 Figure 2. Typical Bulb Tee Section The deck is modeled using shell elements, with the assumption of a homogeneous concrete slab. While the shell elements neglect the steel reinforcing, this is not a concern for the primary model for the purpose of this research effort. For a simple span structure, the bridge deck is assumed to be in compression under all service cases and the reinforcing is therefore never considered. Deck haunches are not considered as structural elements, but, consistent with traditional bridge design, the gap they provide between the deck and girders is included in the model. The shell elements are 20 inches long by 10 inches (508 mm by 254 mm) wide. This size was chosen so that the model could best verify AASHTO design assumptions such as wheel load distribution factors. AASHTO specifies that design trucks have a tire contact area of 20 inches by 10 inches (508 mm by 254 mm) (1). This specification creates a 2:1 ratio of length to width for shell elements and minimizes inaccuracies due to irregular shell elements ratios. Composite performance between the deck and the girders is modeled by a combination of offsets and reassignment of the cardinal points of the girders. Cardinal points specify where the neutral axis of the section is located relative to the insertion point. The default cardinal point in SAP is at the neutral axis of the girder section. In this model, the cardinal point is assigned to the center of the top flange and is then offset to accommodate the deck haunch. This way the girders can be inserted at the same height as the neutral axis of the deck and then offset to specifications, thereby creating appropriate composite behavior between the deck and the girders. Previous research has utilized rigid links to connect the deck and girders (4). After discussions with SAP software programmers, it was suggested that the large number of rigid links needed to simulate shear studs could create numerical problems in the FE model. The method used in this research minimizes computational effort and avoids this numerical problem. In this model the girders and deck displacements are coupled at 20 inch increments. While they are not considered in traditional design, parapets were considered in this model. Standard design methods classify parapets as superimposed dead loads incapable of supporting vertical loads. However, modern parapets are connected to the bridge deck via grouted dowel rods. This connection integrates the parapets into the structure of the bridges and therefore distributes part of the live loads to the parapets. The spacing of these dowels is according to Massachusetts Highway Department standards is inches ( mm) (5). This spacing is more than enough to create composite behavior between the parapets and the deck. In this model, the parapets are modeled as 2D frame elements. This allows for irregular

7 7 parapets shapes and the inclusion of reinforcing if desired. Shell elements were also considered and a comparison study was performed in order to test both methods. The 2D frame elements were used because of their applicability to irregular shapes. The parapets in this model are 1 foot wide by three feet high (305 mm by 914mm), typical Massachusetts standards for Texas Rail parapets (5), as shown in Figure 3. The assembly method described earlier for the girders using a combination of changing the frame cardinal points and specifying a frame offset is used for the parapets as well. In some cases loads are transferred to the parapets when a girder fails, as shown in Figure 4 Figure 3 MHD Texas Rail Parapet

8 8 Figure 4. Hoan Bridge Girder Failure, Wisconsin In typical, elemental bridge models, bearings are modeled as pins and rollers. This simplifies the model and allows for easy hand analysis. But this modeling assumption does not take into account the elastic behavior of elastomeric bearing pads, nor does it account for the rotational restraint provided by these bearings (Figures 5 and 6). The shortening of the effective length of the bridge via the distributed reaction of the elastomeric pad is accounted for with a combination of axial springs and rotational springs at the centerline of the pad. Elastomeric bearing pads are commonly made of neoprene of varying durometer hardness. Typically they are assembled in layers with steel plates dividing layers of elastomer. The reinforcement with steel plates helps to minimize the bulging of the material and strengthen the pad in shear. Figure 4 displays a traditional elastomeric bearing. Elastomerics are used because they are easy to assemble and minimize lateral and longitudinal restraint in the bridge system while sufficiently supporting vertical loads. The size of the pad is dictated by the required area to resist vertical shear loads and to prevent the girder from slipping off of the support (6). The pads create rotational restraint at the ends of the girders and allow for varying

9 9 vertical deflection, resulting in substantial differences between traditional pin and roller models and actual behavior. In terms of the analytic model, the rotational restraint is essentially a shortening of the effective length of the girder by preventing expected deflections from a simple beam near the supports. One area for future research is the development of a modeling system that is concurrent with the primary model system, but also allows for the deterioration modeling of the bridge. There are several key components to this model that must be considered. The model must be able to capture the performance of cracking and spalling concrete elements. This is a highly nonlinear and complex problem without a definitive solution. However, new FE software is attempting to capture this behavior. The change in bearing pad stiffness should also be considered. Research has shown that as elastomeric bearings age, they increase in stiffness up to 50 times their original stiffness (7). Older bridge systems that incorporate steel bearings lose transverse stiffness and should be modeled as well. Figure 5. Typical Elastomeric Bearing Pad with Steel Plates Exposed Figure 6. Conversion of Elastomeric Bearing Pad to a Combination of Axial and Rotational Springs In order to account for this behavior in the bridge model, non-linear spring elements are used in place of traditional supports. In earlier models for this research, linear springs were used, but these were found not to properly model pad uplift and are therefore inaccurate. Linear springs can resist tension loads in the model, but the actual elastomeric bearings are detailed so they do not resist tension loads. In place of linear springs, non-linear gap spring elements were used. Gap springs allow for full compression resistance and no tension resistance. They are otherwise similar to linear springs. The non-linear gap springs partially restrain the girders in all axial and rotational degrees of freedom. The stiffness of these springs was tested as part of

10 10 the sensitivity study also performed as part of this research. One option that was not included in the model is the use of line springs that act over a specified distance. While these springs more closely model elastomeric bearings, they represent a substantial increase in modeling complexity. The girders must be subdivided and not all FE programs allow for the use of line springs. Given this constraint, a combination of rotational and axial springs provided a more than reasonable representation of actual bearing performance for this research effort. Bearing supports do not act at the centroid of the girders, but at the bottom of the bottom flange. The FE model must account for this line of action. To achieve this, the offset assembly method used to connect the parapets and slab cannot be used for connecting the bearings. Bearings are considered to be nodal restraints in SAP2000 and cannot be assigned offsets. Therefore, two different methods were considered for connecting the bearings to the girders properly. Most previous researchers used a series of rigid links at the ends of girders. Rigid links can be used in this context because only a few links are used and numerical problems are avoided. However they increase computational time and increase the complexity of the model. In this model a series of EQUAL constraints were used in SAP2000 to force translations and rotations at the mid-height of the deck to be equal to translations and rotations at the bearings. This is a simplifying approximation, but deflections and rotations in models using rigid links and in models using the constraint system varied by less that 0.1%. In this single span model there are no piers. However there are two end abutments. Since these end abutments are separated from the superstructure via the bearings they do not need to be modeled in the FE program. Piers that are not integral with the bridge deck can be modeled in the same way. However if piers are integral with the superstructure they can be modeled with frame elements. If the superstructure rests directly against the backfill soil, or if the abutments are integral with the superstructure, the abutment stiffness can be modeled with springs to capture the actual soil and pile stiffness parameters. Diaphragms were modeled as two dimensional frame elements perpendicular to the girders and acting at the mid-height of the girders by assigning a vertical offset. In this bridge, the diaphragms were chosen as C10x25 sections based on as-built drawings from the Neponset River Bridge. The diaphragms were spaced every 20 feet (6096 mm) across the entire length of the bridge (Figure 7). In order to model truss diaphragms, model complexity could be increased, or the trusses could be approximated as beams. The assembly of the diaphragms is straightforward with one exception: the degree of fixity at their connections to the beam elements. Traditionally, designers assume that bolted diaphragms do not transfer moment to the girders. However, bolted connections are partially restrained systems. Both the pinned and fixed conditions were analyzed and differences were compared. Any substantial differences could lead to a study estimating the actual fixity of such connections. As with the parapets, there are a wide range of diaphragm styles and sizes. While the diaphragms dimensions chosen for this model are representative of a wide range of diaphragms, different systems in particular truss bracing should be studied in more depth.

11 11 Figure 7. Framing Plan for Parametric Study Model with Diaphragms (Plan View) Almost all of the assembly for this bridge model was done in an Excel spreadsheet system compatible with SAP2000 (8). This bridge model has a great deal of repetition and was quickly developed within a spreadsheet system. It is conceivable that one could program a Visual Basic module that could automate the procedure. Care should be taken not to assemble everything in Excel without proper understanding of the finite element model being assembled. APPLICATIONS A parametric study was performed evaluating contributions of different parameters to the overall system performance of the bridge structure (8 and 9). Some results from the study are summarized in Table 1. The parametric study compared the impact of secondary structural elements on the total live load moments at the mid-span of the bridge. These moments were compared to the AASHTO estimates for a simple beam (last line of table). The elements tested were a basic 3-D FE model, the inclusion of diaphragms and their fixity, the inclusion of nonlinear and linear springs for elastomeric bearing pads, the effects of older and stiffer bearing pads, and the inclusion of parapets. Three loading cases were analyzed, an off-center HS-20 truck load, a centered HS-20 truck load, and two symmetrical HS-20 truck loads. While a load reduction relative to AASHTO calculations was seen in almost all models, the inclusion of elastomeric bearing stiffness and parapets stiffness had the most impact. The inclusion of

12 12 parapets reduced live load moments by 20%, the inclusion of stiff, old bearings reduced live load moments by 20%. A typical elastomeric pad allowed to experience uplift through non-linear modeling reduced live load moments by 14%. Table 1. Live Load Moments kft (KN mm) at midspan, evaluated for impact of different parameters Loading Type Model Off Center Truck One Centered Truck Two Trucks Basic Model (1334) 974 (1322) 1968 (2671) Fixed Diaphragms (1335) 973 (1321) 1967 (2671) Pinned Diaphragms (1335) 974 (1322) 1968 (2671) Linear Regular Pad 937 (1272) (1258) 1872 (2541) Nonlinear Regular Pad 848 (1150) 857 (1163) 1731 (2349) Linear Older Pad 773 (1049) 763 (1035) 1544 (2095) Nonlinear Older Pad (1069) 778 (1056) 1576 (2139) Parapets (1080) 809 (1098) 1592 (2161) AASHTO 984 (1335) 984 (1335) 1968 (2671) Basic model is baseline. Fixed diaphragms assumes diaphragm connections to main girders are rigid. Pinned diaphragms assumes diaphragm connections to main girders are pinned. Linear regular pad assumes elastomeric bearing pad with linear elastic response with tension allowed. Nonlinear regular pad assumes elastomeric bearing pad with linear elastic response with no tension allowed (compression only). Linear older pad assumes increased modulus of stiffness due aging of elastomeric bearing pad, with tension allowed. Nonlinear older pad assumes increased modulus of stiffness due aging of elastomeric bearing pad, with no tension allowed. Parapets assumes concrete parapets behave compositely with deck section AASHTO calculation of simply supported beam using AASHTO LRFD Code (1) The parametric study, in general, illustrates the general capability of 3D structural model to evaluate impacts to the overall structure of parameters that would not typically be evaluated in this way using standard, elemental design procedures. For example, parapet strength is not normally considered as part of the global bridge structural strength. But when a stringer bridge superstructure is modeled not as individual stingers but as a combined system of stringers and deck, the significant impact of non-structural parapets becomes clear. Development of accurate baseline bridge models will need to account for many complications not present in a simple span steel composite concrete stringer bridge. Even though these models may require a larger initial investment of time and money, they will prove more valuable over the life of the bridge structure by providing an accurate platform for a reasonable structure health monitoring program. By providing bridge owners with a more

13 13 accurate design model, a structural condition assessment program using structural parameter estimation can be more readily and cost-effectively applied. The use of structural parameter estimation would be invaluable in the development of a structural model updating system. Such estimations from NDT data can capture losses in stiffness that are imperceptible during traditional visual bridge inspections. Other structural types, in particular pre-stressed concrete, continuity, skew, curvature, and pier and subsurface conditions must be accurately modeled. In particular, accurate enough models for concrete superstructure performance will be challenging. Current, traditional assumptions for concrete analysis and design are appropriately conservative for elemental design. It is typical to assume a full concrete section, or cracked section for stiffness model. However, a more detailed, realistic model of concrete behavior must account for a complex sequence of change of stiffness during construction staging and loading as the concrete structure cracks, and tensile stress is transferred to reinforcement. MODIFICATION OF THE BRIDGE DESIGN PROCESS Based on current practice, the analytical development and basis of a bridge design is complete on opening day. The design engineer submits a completed design with calculations, drawings and specifications, and this is filed by the bridge owner. The documents may be retrieved at some future date for bridge inspection, load rating, and perhaps special structural evaluation due to an unusual event such as vehicle impact or unexpected deterioration. The documents, in particular design calculations, may or may not be of value to the future engineer dealing with the in-service bridge structure after opening day. The future engineer uses the documents for guidance, but is usually expected to develop an independent analysis model that may or may not take into account the analysis assumptions that formed the basis of the original design. Developing technologies for analysis, data storage and management, make it possible to envision a modified procedure that takes advantage of a baseline bridge model. In the modified procedure, the engineer submits not just elemental design, but a baseline structural model. The baseline model: is developed and submitted in a standardized analysis format is submitted and maintained electronically captures and documents the analytical basis of the bridge design is modified as required to account for any as-built changes to the design is used as the analytical basis for subsequent analysis and evaluation of the structure over its design life- for load rating, structural inspection, and as a baseline model for nondestructive testing and instrumentation response The traditional bridge design process, largely developed and codified in the days before automation, has resulted in the present day gap between the designer and performance of the bridge structure over its service life. Rapidly developing instrumentation, data acquisition, data analysis and management technologies make it possible to close the gap. However, there are many technical and procedural obstacles toward implementation of the above, idealized modified

14 14 bridge design process. A more comprehensive, baseline structural model is more complex to develop than the comparatively simple elemental approach, and thus is prone to concerns for errors and validation. Finite element software, while becoming increasingly usable for production engineering, still has a long way to go. The modified bridge design procedure has many advantages over the current, traditional process: The analytical basis of design does not stop on opening day and get filed away, but becomes more readily available to those who need access to it for future work over the life of the bridge The more refined baseline model is readily adaptable to rapidly developing technology for structural instrumentation and evaluation and integration into a long-term structural health monitoring program The bridge owner is provided with more refined data, that can be updated as needed over the life of the bridge to reflect deterioration and changes to the structure over time. In turn, the more refined modeling can support more objective decision making for maintenance and repair, leading to more efficient use of limited resources The modified design procedure can be argued to be less expensive considering the overall cost of a bridge for its entire design life. However, present day accounting methods still place much greater weight on start-up costs, and increased design requirements before opening day will be perceived to be an increase in cost using this accounting method. Definitions of engineering accountability would also need to be reevaluated using a modified design procedure where the engineer of record delivers a baseline model that is expected to serve as the analytical basis of the bridge, with changes by the bridge owner, over its design life.

15 15 References 1. AASHTO LRFD Bridge Design Specifications (2004). American Association of State Highway Transportation Officials. 2. Ghosn, M. System Factors for Highway Bridges. Proceedings, 6 th International Bridge Engineering Conference, Transportation Research Board, Boston MA., Tarhini, K. M., Mabsout, M., Harajli, M., and C. Tayar. Finite element modeling techniques of steel girder bridges. Proceedings of the 2nd Congress on Computing in Civil Engineering. Part 1 (of 2), Jun , ASCE, New York, NY, USA, Atlanta, GA, USA, Ho, I., and B. M. Shahrooz. Finite element modeling of a deteriorated R.C. slab bridge: Lessons learned and recommendations. Journal of Structural Engineering Mechanics, Vol. 6 No. 3, 1998, pp Massachusetts Highway Department Bridge Manual. Massachusetts Highway Department, Barker, R. and J. Puckett, J. Design of Highway Bridges. Wiley-Interscience, New York, Yazdani, N., Eddy, S. M., and C. S. Cai. Validation of AASHTO bearing stiffness for standard precast concrete bridge girders. ACI Structures Journal, Vol. 97, No.3, 2000, pp Lattanzi, D. Finite Element Modeling for Design Verification and Long Term Health Monitoring of Bridges. Master of Science Thesis, Tufts University, Medford MA., Brenner, B. Sanayei, M., Lattanzi, D. and E. Santini-Bell. Structural Analysis Models Accounting for Bridge Parapet Strength. Proceedings of the 2005 New York City Bridge Conference, New York, September 2005.