ANALYSIS OF SHEAR STRENGTH IN THE END PANELS OF STEEL BRIDGE PLATE GIRDERS

Transcription

1 ANALYSIS OF SHEAR STRENGTH IN THE END PANELS OF STEEL BRIDGE PLATE GIRDERS Date of Submission: September 27, 2013 Jessica Boakye, University of Massachusetts Amherst REU Site: University of California San Diego Principal Investigator: Dr. Chia-Ming Uang Graduate Advisor: Dong-Won Kim

2 Abstract Current AASHTO design code equations for the shear strength of steel plate girder end panels do not account for tension field action. Tension field action in steel plate girders was first modeled by Basler in 1961 and provides the girder with post-buckling shear strength. Additionally, the effect of a concrete slab for a composite specimen is not accounted for in current equations. Physical full scale tests are being conducted at the University of California San Diego on bare and composite steel plate girders. This REU assignment focuses on the physical testing and modeling of specimen SG2 which was tested on July 2, A finite-element model was developed in ABAQUS and compared to the physical test results. Also, a parametric study on SG2 was conducted to monitor the effects of varying web steel grade, flange thickness, and bearing stiffener thickness. It was found that SG2 experienced substantial post-buckling strength. Additionally, the parametric study showed that increasing web steel grade and flange/bearing stiffener thickness increases the shear strength of the girder. Further work needs to be done on composite testing and ultimately a new set of code equations need to be developed. ii

3 Table of Contents Abstract... ii Introduction... 1 Literature Review... 2 Methods... 3 Experimental Testing... 3 Finite Element Modeling... 4 Results... 6 Experimental Testing... 6 Finite Element Modeling... 9 Failure Mechanism Conclusions Further Work Contact Information Acknowledgements References iii

4 Introduction Steel plate girders were introduced into construction as a cost effective alternative to rolled beams for large spans. The girder is built up from plates welded or bolted together. The behavior of a plate girder is typical of an I-shaped section where the web carries most of the shear while the flanges carry the moment. Since the flexural demand is usually higher in the web, it is usually thinner than the flanges. The slender web makes buckling the primary failure mode. To help increase stability transverse and sometimes longitudinal stiffeners are added. The transverse stiffener on the outer edge of the end panel is referred to as a bearing stiffener. A sketch of a typical plate girder is shown in Figure 1 below. Figure 1: Typical Plate Girder (Source: Boakye) The buckled web panel behaves similar to a Pratt truss with the diagonal tension field acting as the diagonal tension member of the truss. This provides the web with post-buckling strength. The truss like behavior is referred to as tension-field action (T.F.A). Interior panels are bounded by neighbor panels and stiffeners which create a rigid boundary. The exterior panels only have a small extended web as their boundary which creates a weaker condition. Current T.F.A formulas are for the interior panel only which would overestimate the strength for an end panel. As a result, the current AASHTO design codes (AASHTO 2010) include tension field action for the interior panels but exclude it for the end panels. Additionally, the code neglects the composite action that occurs when a concrete slab is used in conjunction with the plate girder. Because of the thin webs, elastic buckling occurs at a relatively low percentage of the applied shear load making the post-buckling strength critical. When plate girder bridges are re-evaluated according to current standards, the shear demand may exceed the capacity leading to unnecessary bridge retrofit. The long term goal of the project is to develop an analytical formula to accurately quantify the shear strength of the end panels that can be applied to various design codes in order to avoid excessive retrofit. As part of this research both composite and steel plate girders will undergo shear testing in the Powell Lab at UC San Diego over the next two years. Finite-element models and subsequent parametric studies will be completed with ABAQUS. 1

5 Literature Review Due to a failing infrastructure, the structural integrity of many bridges has come into question. As a result, many state transportation departments are forced to reevaluate the bridges in their area. California alone has an estimated $6 billion in bridge repair needs (ASCE 2013). Steel plate girders have been used for bridge construction as a cost effective alternative to rolled beams. In plate girders, the thin web makes buckling a concern. Undesirably, their strength may be underestimated in current design codes. This may lead to unnecessary retrofits which states like California cannot afford. Current design codes do not include the post-buckling strength of the girder end panels when calculating the shear strength (AASHTO 2010) which can lead to a bridge being inappropriately designated as structurally deficient. In plate girders, the web is designed to provide shear strength while the flange is supposed to resist flexure. Since the flexure load is usually higher, the web is usually thinner than the flanges. Because of the thin webs, elastic buckling occurs at a relatively low percentage of the applied shear load (Lee and Yoo 1998). Therefore, if post-buckling strength exists, it is important to include it in design codes. Post-buckling strength, or tension field action, is the diagonal tension that forms in a buckled web panel. The buckled web panel behaves similar to a Pratt truss with the diagonal tension field acting as the diagonal tension member of the truss. This tension field action provides the girder with additional strength before failure is reached. Unfortunately, postbuckling strength is inelastic which makes it hard to explain in an analytical formula. In 1961, the first extensive study on steel plate girders was conducted by Basler. Basler conducted a series of tests on steel plate girders at the Fritz Engineering Laboratory at Lehigh University and observed post-buckling strength. The physical tests showed that the girders continued to resist shear strength after elastic buckling had been reached (Basler 1961). He then developed formulas to quantify the total shear strength including elastic buckling strength and post-buckling strength that were later incorporated into design codes. To simplify the equation derivations, Basler assumed the flanges were completely flexible. This assumption seems to be true for the interior panels but is not true for the exterior panels, which leads to an overprediction of the post-buckling strength on the end panels (Baskar et al., 2002). Therefore, the design codes only include the elastic buckling strength for the end panel. One important aspect of research into steel plate girders is to develop finite element models to avoid costly physical testing. Due to fabrication inconsistencies, a field specimen can be slightly damaged before construction begins which is hard to incorporate into a field model. Researchers have been able to incorporate these fabrication inconsistencies into their models by running a buckling analysis on the girder. The buckled shape that results is then applied to the model and an initial imperfection value is assigned. It has been found that by increasing initial imperfections, the post-buckling strength decreases (Lee and Yoo 1998). By modeling the initial imperfections correctly, finite element programs such as ABAQUS provide extremely accurate results when compared to physical testing. Composite construction has been introduced into plate-girder bridges to reduce cost. Composite action is achieved by eliminating or minimizing the slip between the steel and concrete surfaces. 2

6 The resulting increase in strength and stiffness depends on the amount of slip eliminated. The composite action with plate girders is achieved through the use of shear studs (shear connectors). The studs are welded on the upper flange of the steel girder and then embedded into the concrete deck slab (Baskar et al., 2002). Initial studies have found that the composite action increases the post-buckling strength (Baskar et al., 2002). Methods Experimental Testing The experimental testing program called for four simply supported girders to be tested in summer All girders are to be fabricated and tested in the Powell Structures Laboratory at the University of California San Diego. Two bare plate girder models (SG1 and SG2) were tested first. The composite models (CG1 and CG2) have plate girders identical to SG1 and SG2, respectively, so that the concrete slab effect can be easily quantified. Table 1 gives detailed information on the dimensions of all four models. Table 1: Specimen Dimensions Specimen d 0 /D D/t w D (in.) t w (in.) t f (in.) b f (in.) F y (ksi) F c (ksi) V n1 (kips) V n2 (kips) SG N/A A572 SG N/A Grade CG CG where: d 0 : Web Panel Width D: Web Panel Depth t w : Web Thickness t f : Flange Thickness b f: Flange Width F y : Steel Yield Stress for Flange and Web V n1 : End Panel Shear Strength (AASHTO) V n2 : Interior Panel Shear Strength (AASHTO) F c : Concrete Compressive Stress AASHTO (2010) gives two different equations for the end panel shear capacity and the interior panel shear capacity. Both of these equations can be simplified to a factor multiplied by shear capacity V p which is a function of the shear yield strength of the web. For the end panel, the factor is simply C and only accounts for the buckling strength. The interior panel equation is more complicated but it can be simplified to V p multiplied by the sum of C BA (from buckling action) and C TFA (from tension field action). The AASHTO equations are displayed in Equations

7 V p = 0.58F y Dt w (1) C = buckling shear stress shear yeild stress V n1 = CV p (3) (2) V n2 = V p C (1 C) (1+ d 0 D 2 = V p[c BA + C TFA ] (4) The same test set up was used for all tests and is shown in Figure 2. As shown, the girders were initially painted white. Once the steel yielded, the paint would chip off making yielding more visible. In order to introduce load, two 500-kip actuators were used in conjunction with a loading beam. To prevent an unexpected failure mode, lateral bracing was included on the backside of the specimen as shown in Figure 3. Figure 2: Test Set Up Figure 3: Lateral Bracing Finite Element Modeling Finite element models were produced using ABAQUS. ABAQUS was chosen because of its ability to capture the nonlinear behavior of the specimen and the relatively short run time. For this particular REU assignment, SG2 was modeled. Shell elements (S4R) were used to construct the models for time efficiency. A buckling analysis is conducted first to simulate fabrication inconsistency. The buckled shape is then applied to the static analysis so that the imperfection is included in the model. For this analysis, the maximum magnitude of an initial imperfection of D/500 was applied. The steel material properties were taken from the mill certificate. The ABAQUS model for SG2 is shown in Figure 4 and the results of the buckling analysis for SG2 are shown in Figure 5. 4

8 Figure 4: ABAQUS Model - SG2 (Source: Boakye) Figure 5: SG2 Buckle Analysis (Source: Boakye) The blue represents no stress while red and orange represent an area of high stress. This particular analysis shows local web buckling on the left side of the specimen. When the static analysis begins, this initial stress is applied to the model making failure on the left panel more likely. A parametric study for SG2 was also completed using ABAQUS to evaluate the effect of different design decisions on the flange thickness, bearing stiffener thickness, and the web steel grade. They are detailed in Table 2. The highlighted rows indicate the actual values for SG2. For the parametric study different aspect ratios (end panel width-to-depth ratios) needed to be studied. To avoid flexural failure, two of the interior panels were removed from the model. The base models for the end panel aspect ratios of 0.5, 0.75, and 1 are shown in Figure 6. Table 2: Parameters 5

9 (a) (b) (c) Figure 6: Base Models (Source: Boakye) The modes for aspect ratios of 1, 0.75, and 0.5 are shown in Figures (a), (b), and (c) respectively. Results Experimental Testing Specimen SG2 was tested on July 2, The global response (the load felt by the loading beam vs. vertical displacement) is shown in Figure 7. Since each end panel takes half of the applied load, the end panel shear strength would be half of the applied load. The specimen showed minimal damage at the AASHTO limit and continued to resist applied loads. Figure 8 is a picture of the specimen at the AASHTO limit and a zoomed in picture of an interior panel. The buckling observed in the interior panel displayed was present in all four panels. Little to no yielding was observed at this point. At maximum applied load, the buckling became more severe and some yielding was observed (Figure 9). At this point the stiffeners seemed to still be intact and more displacement needed to be applied to better observe the failure mechanism. Figure 10 shows the specimen at 1.4 inches vertical displacement where the deformed shape became clear and the yielding of the web became more pronounced. 6

10 Figure 7: Global Response for SG2 Test Total Applied Load vs. Displacement (Source: Boakye) Figure 8: Deformed Shape at AASHTO Predicted Shear Strength 7

11 Figure 9: Deformed Shape at Maximum Load Figure 10: Deformed Shape at Maximum Displacement Figure 11 shows a graphical representation of Equation (3) and Equation (4). The strengths were normalized by divided by V p. The blue line represents the Equation (3) while the red line equation (4). The maximum applied load for SG2, shown by a black triangle in Figure 11, was found to be in between the AASHTO (2010) strength for the end panel and the interior panel. 8

12 Figure 11: SG2 Strength Results (Source: Boakye) Finite Element Modeling The finite element model for SG2 was analyzed and the final deformed shape is shown in Figure 12. Next, the global response for the model is plotted against the experimental data which is shown in Figure 13. Figure 12: Deformed Shape FEM Model The blue represents no stress while red and orange represent an area of high stress. This particular analysis shows shear failure on the left side of the specimen. Figure 13: Global Response Correlation 9

13 The results from the parametric study are shown in Figures for end panel aspect ratios of 0.5, 0.75, and 1.0 respectively. The strength increased with all three parameters. The biggest increases came from the change in flange thickness. As expected, increasing the aspect ratio decreased the overall strength. This is reflected in Equation (1). For each parameter, the overstrength factor (FEM prediction/aashto prediction) for the end panel is calculated. The overstrength factor increased with increasing bearing stiffener thickness, flange thickness, web steel grade. Figure 14: Parametric Study, Aspect Ratio = 0.5 (Source: Boakye) End Panel Shear Strength (kips) End Panel Shear Strength (kips) Figure 15: Parametric Study, Aspect Ratio = 0.75 (Source: Boakye) 10

14 End Panel Shear Strength (kips) Failure Mechanism Figure 16: Parametric Study, Aspect Ratio = 1.0 (Source: Boakye) Through the experimental and analytical testing, it was found that the girder seems to have the same failure mechanism each time. In the failed end panel: first, the web buckles, then plastic hinges form on the flanges and bearing stiffener. More research will be conducted to identify the location of these hinges and the effect they have on the shear strength. Figure 17 shows a detailed sketch of the failure mechanism observed. Figure 17: Failure Mechanism (Source: Boakye) 11

15 Conclusions Experimental results on SG2 showed a large amount of post-buckling strength and proved the AASHTO equations for the shear strength of the end panel are too conservative. Since the AASHTO interior panel shear strength equations overpredict the shear strength, this implies that the end panel undergoes partial tension field action. A separate equation, which accounts for partial tension field action, needs to be developed for the end panel. The finite element model seems to be overpredicting the girder strength. The specimen still needs to be coupon tested so that exact materials properties can be input into ABAQUS. The finite element model s deformed shape mirrors the observed failure from experimental testing. The parametric study demonstrated that increasing bearing stiffener and/or flange thickness tends to increase the shear capacity of the panel. This may be due to the stiffened boundary that occurs when either of these parameters is increased. More research needs to be done on how to incorporate these factors into shear strength equations. Further Work Although substantial progress has been made on the project this summer, there is still more work that needs to be done. The finite element models need to be calibrated after coupon testing. Also, a mathematical model should be established. Finally, a comprehensive equation needs to be developed in order to make the AASHTO end panel shear strength equation more accurate. Contact Information For future information on this project please contact: REU Student Jessica Boakye: jboakye@umass.edu UCSD PhD Candidate: Dong-Won Kim: dwk008@ucsd.edu UCSD Principal Investigator: Dr. Chia-Ming Uang: cmu@ucsd.edu 12

16 Acknowledgements The author would like to thank Dr. Chia-Ming Uang, Dong-Won Kim, Gulen Ozukula, and the Powell lab staff for their guidance and support through the REU program. The testing program for this project was sponsored by the California Department of Transportation. This project was partially supported by the National Science Foundation through the Research Experience for Undergraduates program (EEC ) and the George E. Brown Jr. Network for Earthquake Engineering Simulation (NEES) Cooperative Agreement CMMI Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation. References AASHTO. "AASHTO LRFD Bridge Design Specifications, Customary U.S. Units." (2010) ASCE Report Card for America's Infrastructure. March (July 6, 2013). Baskar, K., and N.E. Shanmugam. (2003) "Steel concrete composite plate girders subject to combined shear and bending." Journal of Constructional Steel Research, Baskar, K., Shanmugam, N., and Thevendran, V. (2002). Finite-Element Analysis of Steel Concrete Composite Plate Girder. Journal of Structural Engineering, 128(9), Basler, K., (1961). "Strength of plate girders in shear, Proc. ASCE, 87, (ST7), Reprint No. 186 (61-13)". Fritz Laboratory Reports. Paper 70. < (July 1, 2013). Lee, Sung C., and Chai H. Yoo. (1998). "Strength of Plate Girder Web Panels Under Pure Shear." Journal of Structural Engineering, 124(2),