RELIABILITY BASED BRIDGE RATING SOFTWARE

Transcription

1 RELIABILITY BASED BRIDGE RATING SOFTWARE Michael H. Scott, Christopher C. Higgins, Gregory Esch Oregon State University, Corvallis, OR, USA Abstract This paper summarizes the implementation and use of bridge rating software developed at Oregon State University for reinforced concrete deck girder (RCDG) bridges. An overview of the software is presented along with an example rating of an RCDG bridge. The computational steps taken by the software are outlined and visualization tools and output formats for the rating results are shown. 1. Introduction Many of Oregon s conventionally reinforced concrete deck girder (RCDG) bridges built in the 1950 s were designed to permit higher shear stress in the concrete than permitted by current AASHTO standards. Compounding this problem are increased traffic volume and truck load magnitudes. These bridges are nearing the end of their originally intended design lives and they have been exposed to millions of load cycles from traffic. As a result, Oregon highways have nearly 500 bridges exhibiting diagonal cracks due to overload, environmental conditions, or some combination of these factors. Diagonal cracks have been identified in both the main girders and the bent caps. To address the question of the capacity and estimate the remaining life of diagonally cracked RCDG bridges, a research program was undertaken at Oregon State University that incorporated field testing, vehicle load data collection, laboratory testing, and analysis. An outcome of the research program was the development of a reliability based assessment methodology for RCDG bridges. An analysis of moving loads is required to identify the critical moment-shear combination for comparison with available momentshear interaction capacity. The methodology enables flexible input scenarios including field inspection information for damage locations, field test data for load distribution and impact factors, specification based distribution and impact factors, and alternative capacity estimation methods (AASHTO-MCFT and Response-2000 TM ). Further, the methodology permits the updating of vehicle load data and owner selectable reliability SCOTT, Bridge Rating Software, 1/7

2 index values. The new methodology is a departure from past practice and involves a number of additional steps that can be time consuming. 2. Bridge Rating Methodology The reliability based rating of a bridge girder is accomplished by comparison of the load effects induced at each critical section with the available moment-shear resistance at that section. The computation of internal bending moment and shear forces at sections identified as critical along each span is accomplished by structural analysis methods. The critical sections coincide with locations of bar cut-offs, splices, and changes in stirrup spacing, all of which may control the bridge capacity. The second moment reliability index, β, is used as a means of quantifying the safety of a bridge girder. The moment-shear capacity (resistance) at each section is treated as uncertain while the load (demand) is considered to be deterministic. Full details of the rating methodology are given by Higgins et al (2006) AASHTO-99 Nominal Capacity Rating Vehicle Controlling Load Effects Controlling Vehicle History Shear (kips) 100 p f 50 Nominal 0 3σ 2σ 1σ Avg Moment (kip-ft) Figure 1 Moment-shear capacity and demand comparison to determine the reliability index, β, at a critical girder section. The calculation of β at a critical section is shown in Figure 1, where the nominal moment-shear capacity is computed by the AASHTO-MCFT procedure (AASHTO 2003), which is a simplified form of the modified compression field theory (Vecchio and Collins 1986). Also shown are the average capacity and standard deviations of one, two, SCOTT, Bridge Rating Software, 2/7

3 and three σ. The comparison of 23 full-scale conventionally reinforced concrete girders with the capacity predicted by the simplified AASHTO-MCFT procedure generated a normal distribution with an average experimental-to-predicted shear strength ratio of 1.1 and a 7.4% coefficient of variation (Higgins et al 2004). The probability of failure, p f, is the area under the normal curve to the left of the controlling (M,V) coordinate, and is related to the reliability index by the standard normal cumulative distribution function, i.e., p f = Φ(- β). Eleven vehicles were used for the rating shown in Figure 1, where the entire moment-shear history is shown for the controlling vehicle and only the controlling moment-shear combination is shown for the remaining ten vehicles. 3. Software Implementation The live load moment-shear interaction at each critical section is determined from linearelastic structural analysis by incrementally moving the rating vehicle axle loads across the bridge. Several approaches to compute structural demands exist; however, the software utilizes an efficient FORTRAN subroutine based on slope-deflection equations to compute the internal forces at each section for the moving loads. This approach enables the use of closed-form expressions for the internal forces in prismatic bridge girders of up to five spans of arbitrary length, thereby bypassing the need to form and solve matrix equations. The software implementation, however, is independent of the specific details of the structural analysis method, which is considered a black box to the remaining modules of program. The two-dimensional analysis of a bridge girder for vehicle loading requires the use of distribution factors to account for three-dimensional effects owing to the location and spacing of axles across the bridge deck. The program described in this paper considers only conventionally reinforced concrete deck girder bridges, such as the one shown in Figure 2. The program computes distribution factors for moment and shear in the exterior and interior girders shown in Figure 2 according to the procedures outlined in AASHTO-LRFR (AASHTO 2003). Figure 2 Conventionally reinforced concrete (CRC) bridge deck geometry. The input of the bridge data can be interactive through the graphical user interface (GUI) shown in Figure 3 or through the use of a formatted input file. The input menus are built SCOTT, Bridge Rating Software, 3/7

4 with modules from the GLUT library and the rendering of the bridge is done through use of the OpenGL graphics library (Wright and Sweet, 2000). Information for each rating vehicle is read from an external file. Currently, the program reads vehicle load data (axle weights and spacings) and lane loads by parsing a BRASS-GIRDER TM formatted library file (Watters 2005). The geometric specification of the bridge (span lengths and approach boundary conditions), as well as the critical section locations and capacity information, is tokenized from the input file using standard parsing routines. The three span bridge model shown in Figure 3 represents the McKenzie River Bridge on Interstate 5 northbound, just north or Eugene, OR. The critical locations (indicated by vertical lines on the bridge) were determined from design drawings and field inspection data to locations that control the bridge capacity. These locations correspond to changes in stirrup spacing, longitudinal bar cut-off locations, and changes in web dimensions. The bridge rating results shown herein are for the McKenzie River Bridge. Figure 3 Visualization of bridge girder with the locations of critical sections indicated by vertical lines. The moment-shear capacity at each section is specified in one of two ways. First, the capacity may be read directly from an external file that contains moment-shear values for each point on the capacity curve. This option allows the user to import capacity information computed from Response-2000 TM (Bentz 2000) or any other section analysis program. Second, the user can specify concrete and steel material properties and dimensions for each section in order to compute the moment-shear capacity according to the AASHTO-MCFT procedure. Regardless of the source of the moment-shear capacity, the program renders the capacity envelope at each critical section, as shown in Figure 4. SCOTT, Bridge Rating Software, 4/7

5 (a) AASHTO-MCFT (b) External File Figure 4 Description of M-V section capacity information: (a) computed from section reinforcing details using AASHTO-MCFT procedure; (b) read from external files. Data structures, programmed in C++ (Stroustrup 1997), link the input information from the GUI to the structural analysis module and the results of the structural reliability analysis to the GUI output. A standard template library (STL) list (Musser and Saini 1996) stores the moment-shear capacity information at each critical section identified by the user. The associated STL list iterators traverse the sections to compute the reliability index from the moment-shear capacity and demands. An option is available in the program to export the reliability indices and rating factors shown in Figure 5 to a comma separated output file for further post-processing. (a) Reliability index (b) Rating factor Figure 5 Visualization of the (a) reliability index and (b) rating factor at each critical section along the bridge girder. 4. Future Extensions Future extensions of the software will be to bridge girders of arbitrary number and span lengths, internal boundary conditions (hinges), and variations in cross-section SCOTT, Bridge Rating Software, 5/7

6 dimensions (tapered and haunched spans). Standard finite element computations will be employed to calculate the internal demands in such bridge models. The extension to finite element analysis will also lend the rating methodology to 3D bridge models, as well as to the use of 3D visualization tools for the GUI. The software design permits the future inclusion of moment-shear capacity modules for other types of bridges, such as those composed of steel or prestressed concrete. This will require either the comparison of experimental to predicted moment-shear capacity for the materials particular to these bridge types or the inclusion of known material statistics (distribution type, mean, and standard deviation) in order to determine the section moment-shear capacity in a probabilistic sense. Additional extensions of the reliability based bridge rating methodology and software will be to account for uncertainties in the bridge geometry (span length, skew, section dimensions) and in the vehicle loadings. This all-encompassing assessment of sources of uncertainty in bridge rating will require a general finite element reliability analysis (FERA) setting, such as OpenSees (McKenna et al 2000) where the sources of uncertainty are characterized by random variable distributions directly in the finite element analysis. 5. References 1. Higgins, C., Daniels, T.K., Rosowsky, D.V., Miller, T.H., and Yim, S.C., Reliability based assessment of conventionally reinforced concrete bridges for shear, Journal of the Transportation Research Board, approved for publication (2006). 2. AASHTO, Manual for Condition Evaluation and Load and Resistance Factor Rating (LRFR) of Highway Bridges, American Association of State Highway and Transportation Officials (Washington, D.C., 2003). 3. Vecchio, F.J. and Collins, M.P., The modified compression field theory for reinforced concrete elements subjected to shear, ACI Journal, 83(2): (1986). 4. Higgins, C., Miller, T.H., Rosowsky, D.V., Yim, S.C., Potisuk, T., Daniels, T.K., Nicholas, B.S., Robelo, M.J., Lee, A-Y., Forrest, R.W., Reliability based assessment methodology for diagonally cracked conventionally reinforced concrete deck girder bridges: An integrated approach, SPR 350 Final Report (Oregon Department of Transportation, Salem, OR, 2004). 5. Wright, R.S. and Sweet, M., OpenGL SuperBible, 2 nd Edn (Waite Group Press, Indianapolis, IN, 2000). 6. Watters, M.J., Bridge Rating and Analysis of Structural Systems (BRASS), (Wyoming Department of Transportation, Cheyenne, WY, 2005). 7. Bentz, E.C., Sectional analysis of reinforced concrete members, Ph.D. Thesis, Department of Civil Engineering (University of Toronto, 2000). SCOTT, Bridge Rating Software, 6/7

7 8. Stroustrup, B., The C++ Programming Language, 3 rd Edn (Addison-Wesley, Reading, MA, 1997). 9. Musser, D.R. and Saini, A., STL Tutorial and Reference Guide, (Addison- Wesley, Reading, MA, 1996). 10. McKenna, F., Fenves, G.L., and Scott, M.H., Open System for Earthquake Engineering Simulation, (University of California, Berkeley, CA, 2000). SCOTT, Bridge Rating Software, 7/7