Catbas, Darwash, Fadul / 0 0 0 Title Page: Modeling & Load Rating of Two Bridges Designed with AASHTO and Florida I-Beam Girders F.N. Catbas, H. Darwash and M. Fadul Dr. F. Necati Catbas, P.E. Associate Professor & Associate Chair Civil and Environmental Engineering Department University of Central Florida, Orlando, FL Phone: 0--; Fax: 0-- ; e-mail: catbas@ucf.edu (corresponding author) Mr. Haider Darwash Ph.D. Student and Research Assistant Civil and Environmental Engineering Department University of Central Florida, Orlando, FL Phone: 0--; Fax: 0-- Ms. Manar Fadul Ph.D. Student and Research Assistant Civil and Environmental Engineering Department University of Central Florida, Orlando, FL Phone: 0--; Fax: 0-- Word Count: Abstract, Manuscript & References =, Figures and Tables (+) =,0 TOTAL =,
Catbas, Darwash, Fadul / 0 0 0 ABSTRACT Florida I-Beam (FIB) girders provide a number of advantages such as higher load carrying capacity, more efficient fabrication, safer construction, increased lateral stiffness, larger vertical clearance and reduction in the overall cost of bridges. A comparative study incorporating two bridges, one with AASHTO Type III and the other with new Florida I-Beam (FIB) girders is presented. The first bridge is a span bridge designed with AASHTO Type III girders. The second bridge has the same length, width and girder depth; however, it has FIB girders. Both bridges are analyzed using the conventional AASHTO LRFD girder line analysis method and also with a more sophisticated finite element method using a commercial software. The details of the FE model are also presented with the critical considerations of link elements, boundary conditions, pre-stressing tendons. Based on the FE model results, it is shown that it is possible to expect 0% higher live load capacity for interior girders and 0% higher live load capacity for exterior girders using FIB- girders compared to AASHTO Type III girders, while also reducing the cost by about %.
Catbas, Darwash, Fadul / 0 0 0 0 INTRODUCTION Concrete bridges are commonly used in the US. Initially, short and single span bridge superstructures were designed and constructed using concrete girders until the middle of the 0 th century when the pre-stressed bridge girders gained more acceptance and longer spans with prestressed concrete bridges increased dramatically. Today, almost 0% of all the new bridges built in the US are pre-stressed concrete bridges []. Prestressed concrete bridges are considered due to their high strength and durability. Pre-stressed concrete girders perform well for longer spans by the application of a tensile force to reinforcing tendons. This application increases the internal compression in the concrete beam where the tension is anticipated under the given loading conditions. The pre-stressing force can be applied before the concrete is poured (beam is pretensioned) or after the concrete is cured (beam is post-tensioned). There are a number of different pre-stressed concrete girders with a variety of cross-sectional geometries and strands for a required span length and loading. AASHTO I-beams and bulb T-beams have been employed by a many Departments of Transportation as concrete bridge girders. While the AASHTO I-beam and Bulb T-beam girders are commonly used in the state of Florida, Florida Department of Transportation (FDOT), in collaboration with Prof. M. Tadros, developed a new prestressed beam called the Florida I-beam (FIB) to replace these beams in order to enhance the efficiency, to provide a larger vertical clearance and to reduce the overall cost of bridges. FIBs are designed to have higher load carrying capacity, more efficient fabrication, safer construction, increased lateral stiffness because of thicker top and bottom flanges. In addition, FIBs are more economical in comparison to the prestressed beams that are currently being used [,]. FIBs are designed to have high concrete strength, ranging from to 0 ksi, and a large bottom flange compared to the traditional AASHTO and Bulb T-beams, to allow a larger space for more prestressing strands that are usually needed in longer span girders or wider girder spacing. The enhanced design of FIBs is expected to allow bridge designers to reduce the number of beams needed and to reduce the bridge cost. FIBs have improved stability during handling, storage and erection than the other prestressed beams due to a significantly wider bottom flange and low center of gravity. One of the advantages is that FIBs with shallower depth may be used in place of their deeper AASHTO equivalents. This in turn provides a larger vertical clearance that has been a concern for many bridges. In addition, FIBs have identical top and bottom flange shapes for their full range of standard sizes, and since the only varied dimension between FIB standard sizes is the height of the web. The option of using adjustable height forms during fabrication process of all FIB standard sizes is applicable for ease of manufacturing. FIBs can accommodate the largest number of prestressing strands in the USA (up to 0. in diameter strands). Based on the development and progressive studies of FDOT on FIBs, the FDOT developed design bulletins for designers and manufacturers. As a result, FDOT recommended FIBs to be used in all new bridges and bridge widening designs where applicable, while AASHTO beams and Bulb T-beams will no longer be used for any new design []. Objectives and Scope of the Paper FDOT prepared a comparative design of AASHTO Type III beam, which can span approximately 0 feet ( beams with a depth of and spacing of - ) with a FIB ( beams with a depth of and a spacing of - ) which can accomplish the same span by reducing the number of girders. The bridge sections under investigation were used in a comparative cost analysis in the FDOT design bulletin. It was found that estimated savings by
Catbas, Darwash, Fadul / 0 using four FIB girders for this specific structure is about % of the original cost when AASHTO type III girders are used instead [,]. This saving increases when the number of required girders of the bridge increases. Such cost reduction has a significant effect on the overall cost of bridges given that the large number of bridges that are built in Florida state each year. In the study presented in this paper, the structural responses and the load rating factors of these two bridges are presented along with the cost saving information given in the FDOT design bulletin. The first bridge has six AASHTO type III girders (Figure ) and the second bridge with the same general geometry and load-carrying characteristics has four FIBs (Figure ). Both of these bridges are analyzed using the standard AASHTO LRFD girder line analysis as well as using finite element (FE) analysis with a commercial software. The critical details for the appropriate FE modeling of the prestressed sections are presented with the necessary assumptions made for this study. The flexural responses and load rating factors from these analyses are presented in a comparative fashion. Figure : AASHTO Type III Bridge Figure : Florida I-Beam (FIB) Bridge
Catbas, Darwash, Fadul / 0 DESCRIPTION OF THE TWO BRIDGES The bridges, which are studied in this paper, consist of three simply supported spans made up of pre-stressed girders. Each span is 0-ft long and supported by a.- ft long beam cap and this beam cap is supported by three circular columns. The - wide cross section is the same for both bridges as shown in Figure and Figure. Only two -0 lanes are considered to be loaded with an additional 0-0 emergency lane and another -0 pedestrian lane. Both types of girders are in. deep, the first being AASHTO Type III girders, and the second being Florida I-beams. The FIB bridge utilizes four -in. I-beams spaced at -. Each FIB contains - 0. in low-relaxation strands (Figure ). The AASHTO cross section contains six girders spaced at - in each with -0. in low-relaxation prestressing strands (Figure ). The deck is thick and topped with a bituminous wearing surface, and has end barriers that are ft- ½ in. wide. The pretensioned girders have a thick haunched beam in order to control the camber. The prestressing strands are assumed to be straight with eccentricity equal to. in for AASHTO bridge and.0 in for FIB bridge. These eccentricities are computed by the AASHTO LRFD calculation method and all stresses are checked with the allowable stresses. In addition, the moment capacity is also checked to be within the allowable capacity range. The concrete strength is. ksi concrete ( ksi at release) and the ultimate tendon strength is taken as 0 Ksi. 0 Figure : Florida I-Beam (FIB) Typical Cross-Section
Catbas, Darwash, Fadul / 0 0 Figure : AASHTO Type III Girder A generalized cost calculation for these two bridges (one with AASHTO Type III Girder, and other with FIB-) are provided in the FDOT Design Bulletin C0-0 [] as follows: Span Bridge with AASHTO Type III Beams: Total Linear Foot = (0 ft long beams) x ( spans) x ( beams per span) = 0 LF Approximate Cost = (0 LF) x ($ /LF) = $,00 Span Bridge with Florida I-Beams (FIB-): Total Linear Foot = (0 ft long beams) x ( spans) x ( beams per span) = 00 LF Approximate Cost = (00 LF) x ($0 /LF) = $,00 Estimated Savings = % = ($,00-$,00)/$,00 It is noted that costs per linear foot were determined using price estimates from manufacturers and contractors. The values above include only bridge items affected by differing beam types. These items include beam fabrication, beam placement, placed bearing pads, placed diaphragms, placed stay-in-place forms and deck rebar seats []. While the total cost can vary based on many other factors, this calculation provides a reasonably accurate comparison. MODELING AND ANALYSIS OF THE BRIDGES AASHTO Girderline Analysis and Calculations As part of the comparative analysis for the structural responses, the AASHTO methods are utilized as engineers commonly, and in fact, this approach can be used as the first approach in many cases even before detailed modeling methods such as FEMs. In this paper, the authors
Catbas, Darwash, Fadul / 0 0 also conduct calculations and provide results according to the AASHTO LRFD Bridge Design Specifications []. The same loading considerations and assumptions are employed for the analysis of the bridges, which are designed to carry interstate traffic in Florida. The AASHTO and FIB girder sections are evaluated for HL- Design Truck and Design Lane Loads. A dynamic load allowance of % is considered, distribution and load rating factors for moment are calculated according to the AASHTO Guide. Strength I and Service I limit states are considered. The load effects, load rating, and the distribution factors results are all shown later in Tables, and, respectively. Overview of the Full Finite Element Model FE Modeling of pre-stressed girder structures has been shown on a number of studies. In one such study, the author and his colleagues presented pre-stressed and post-tensioned monorail guideway structures by accurately modeling using a FE package for load rating and reliability analyses [,]. In this current paper, AASHTO Type III and FIB girder bridges are modeled using a commercial FE package (CSiBridge) specifically developed for bridge analysis and design [0,]. The two lane loaded case is assumed according to the previous study by the FDOT bulletin. Slab thickness is taken as in with in haunch and in bitumen wearing. Compressive strength of ksi is used for the regular concrete, which is used for the deck, the columns, and the beam cap. For the precast girders,. ksi ( ksi at release) compressive strength is used. Cross diaphragms with in depth and in width also used every one third points of each span with no cross diaphragms at the abutments. Further list of the assumptions considered for the finite elements models can be seen in Table. Table : List of Parameters and Assumptions Value Barrier load 0. kips/ft length Wearing load 0.0 kip/ft Column dimension circular column.ft dia. (0 - # grade 0 steel) Beam Cab dimension Depth ( in), width (0 in) Prestress steel 0. in low relaxation strands fpu 0 ksi Diaphragm Dimensions Depth ( in), Width ( in) Jacking force 0. f!" 0 Modeling of Deck and Girders Shell elements with three degrees of freedom are chosen to model the deck section. Frame elements are used to model the precast pretension girders, the columns, and the beam cap. For the AASHTO type III Bridge, precast pre-tensioned AASHTO type III girders are defined with one hundred and fifty six tendons for the entire length of the bridge. For the FIB Bridge, deep precast FIB girders are defined with one hundred and sixty eight tendons. Each bridge has three piers with. ft long beam cap. The pier and the abutment foundations are assumed to
Catbas, Darwash, Fadul / be fixed for both bridges. Figure and Figure show the finite elements model of AASHTO type III bridge and FIB bridge, respectively with model characteristics and model statistics. Figure : The FE Model of the Bridge with AASHTO Type III Girders Figure : The FE Model of the Bridge with Florida I-Beams
Catbas, Darwash, Fadul / 0 Modeling of the Link Elements The concrete deck and girder connection is a critical detail to be modeled properly for the effective utilization of the composite connection. As a result, rigid links are used to represent the connection between the girders and the deck. The same type of link is used to model the columns and the beam cap connection. Abutment bearings links (link elements) are used to model the abutments by fixing the vertical and transverse translation of the abutment bearings. All other abutment bearing components are modeled as free since the abutment restraint is assumed to be free in the longitudinal direction. Bent bearings links (link elements) are used to model the bearing plates and the connection between the girders and the beam cap by fixing all the translations of the bent bearings. All the other bent bearing components are defined as free, including the rotation along the layout line. To help visualize the abutment geometry, the drawing shown in Figure illustrates the location of the abutment bearings and the substructure. It also shows the location of the action point, which is the location where the bearing will translate or rotate depending on the bearing definitions. 0 Figure : FE Modeling of the Links Modeling of the Tendons Eighteen precast girders are defined in the FE model of the AASHTO type III bridge. Each girder has 0. in low relaxation pre-tensioned strands. On the other hand, twelve precast girders are defined in the FE model of the FIB bridge. Each girder has 0. in low relaxation pre-tensioned strands. Pre-tensioned tendons are modeled as separate elements with kips force embedded in the precast girders to satisfy the design criteria, strength limit state check and for checking the tendon stresses. Because the CSiBridge FEM software provides only bonded posttension tendons, the bonded pre-tensioning tendons are modeled by jacking the post-tensioned
Catbas, Darwash, Fadul 0/ tendons from both sides and specifying zero value for the curvature loss coefficient, wobble loss coefficient, and anchorage slip loss coefficient. Figure shows the distribution of the tendons in AASHTO type III beams and Florida I-Beams. 0 0 Figure : Distribution of the Tendons in AASHTO Type III Beams and Florida I-Beams DISTRIBUTION FACTORS AND LOAD RATING Movable Bridge Load Rating After the completion of the FE model and the simple girder line model, the load rating factors of the bridges are computed. Load rating of the bridges is calculated following the AASHTO Guide []. The load factors rating procedure is commonly used in identifying the live load carrying capacity of bridges. Bending moment capacity of the bridges under investigation is calculated at the critical position of HL- (with design truck and lane load) following the AASHTO Guide. Since each span is considered as a simply supported, the locations of maximum live and dead load moments are located at the midspan section. The load rating can be expressed as the factor of the critical live load effect to the available capacity for a certain limit state. The general formula for the rating factor is []; C γ DC DC γ DW DW ± γ pp RF = () γ LLL( + IM) where C is the factored load carrying capacity, DC is the dead load of structural components, DW is the dead load of the wearing surface, P is a dead load concentrated at a single point, LL is the live load effect, IM is the impact factor, and γ s are the load factors. The calculated load ratings for the critical locations are presented in the following sections. The load factors values depend on the type of load rating, i.e. inventory or operating load rating. The load rating for the girder is calculated at the critical section, located at the midspan.
Catbas, Darwash, Fadul / 0 0 The section moment capacity is calculated for both AASHTO and FIB sections and for the exterior and the interior girders as well. The calculated moment capacity, the moments at the critical section due to live and dead load, and also the load rating factors are all presented in Table and Table. Table : Moment Values Obtained from the FEM and AASHTO LRFD Analyses AASHTO Type III Girder FIB Girder Ext. Girder Int. Girder Ext. Girder Int. Girder Moment Values (K.ft) (K.ft) (K.ft) (K.ft) AASHTO LRFD results (Girderline Analysis) FEM results Section Capacity 0 0 Max. D.L 0 Max. L.L 0 Section Capacity 0 Max. D.L 0 0 Max. L.L Table indicates that the values of the calculated section capacity and the dead load using LRFD method are close to their corresponding values calculated using FEM. The difference in the dead load values is about % on the average. However, the live load values show a significant difference and it is about 0% when the AASHTO LRDF and FEM results are compared. This difference (reduction in LL moments in FEM) can be attributed to better load distribution by means of FE software that represents all the elements of the bridge. When the results of the AASHTO and FIB girder bridges are compared, the FIB has much higher load carrying capacity even though the dead and live load responses are higher for the FIB. Table presents the load rating factors obtained using the capacity and demand calculations presented previously. The results given in Table imply that AASHTO LRFD girderline analysis underestimate the load rating and provides lower load rating factors than those obtained using FE model. The ratios of load rating factors (FEM/girderline) for all types of girders variy between. to., meaning a % to % more live load carrying possibility. It should also be noted that the girderline method underestimates the load rating factors of the FIB girder bridge more than AASHTO Type III girder bridge. A more significant observation is that the bridge with FIB girders has higher load rating factors than the bridge with AASHTO type III girder regardless of the AASHTO LRFD Girderline analysis or FE analysis. When the two bridges are considered, the exterior and interior girders have % and %, respectively, more live load capacity using AASHTO
Catbas, Darwash, Fadul / 0 0 0 girderline analysis. When the two bridges are compared using the FE model results, the exterior and interior girders have % and 0% more live load capacity, respectively. Table : Load Rating of the Bridges Using FEM and AASHTO LRFD FIB Girder AASHTO Type III Girder Load Rating Int. Girder Ext. Girder Int. Girder Ext. Girder AASHTO Inventory..0.0. LRFD results Operating (Girderline. Analysis).0.. Inventory.... FEM results Operating.0.0.. SUMMARY AND CONCLUSIONS Florida I-Beam (FIB) bridges were developed to be the choice for girder type for new designs in Florida. These girders provide a larger vertical clearance and to reduce the overall cost of bridges. FIBs are designed to have higher load carrying capacity, more efficient fabrication, safer construction, increased lateral stiffness because of thicker top and bottom flanges. In this study, a comparative analysis of two bridges is presented. The first bridge is a span bridge designed with AASHTO Type III girders. The second bridge has the same length, width and girder depth; however, it has FIB girders. Both bridges are analyzed using the conventional AASHTO LRFD girderline analysis method and also more sophisticated finite element method using a commercial software. The details of the FE model are also presented with the critical considerations of link elements, boundary conditions, pre-stressing tendons. The cost comparison of these two bridges was presented by FDOT and it is stated that the FIB provides an estimated saving of about %. The results provided in this paper also indicate that the bridge with FIB girders has higher load rating factors than the bridge with AASHTO type III girder regardless of the method (AASHTO LRFD Girderline analysis or FE analysis) to calculate the rating factors. The AASHTO girderline analysis underestimates the load rating factors for both AASHTO Type III girder bridge and the FIB bridge. Based on the FE results, it can be stated that it is possible to expect 0% higher live load capacity for interior girders and 0% higher live load capacity for exterior girders using FIB- girders compared to AASHTO Type III girders, while also reducing the cost by about %. ACKNOWLEDGMENTS The authors would like to thank Mr. Sam Fallaha, P.E. from FDOT Structures Research Center and Mr. Neil Kenis, P.E. from FDOT D Design Office for their feedback and input for the study presented in this paper. The authors would also like to acknowledge the contributions of Ms. Cara Brown for the FE model development at the initial stages of this study.
Catbas, Darwash, Fadul / 0 0 0 The opinions, findings, and conclusions expressed in this publication are those of the authors and do not necessarily reflect the views of the sponsoring or anyother organizations. REFERENCES. PCA (00), Market Research-The Bridge Market, Portland Cement Association, October 00.. Florida department of Transportation (FDOT). Temporary Design Bulletin C0-0. January. 00.. Florida department of Transportation (FDOT). Temporary Design Bulletin C0-0. June. 00.. American Association of State Highway and Transportation Officials (AASHTO). (00). Standard specifications for highway bridges, AASHTO th Ed., Washington, D.C.. AASHTO Guide (00). "Guide Manual for Condition Evaluation and Load and Resistance Factor Rating (LRFR) of Highway Bridges". Barr, P. J., Eberhard, M. O. and Stanton, J. F. Live-Load Distribution Factors in Prestressed Concrete Girder Bridges. Journal of Bridge Engineering, ASCE. September/October. 00.. Shmerling, R.Z. and Catbas, F.N. (00), Load Rating and Reliability Analysis of An Aerial Guideways, Journal of Bridge Engineering, Volume, Issue, pp. - (July/August 00) ASCE, 00.. Shmerling, R.Z. and Catbas, F.N. (00), Visualization, Finite Element Modeling and Analysis of Aerial Guideways, Structure and Infrastructure Engineering Journal, SIE, Structure and Infrastructure Engineering: Maintenance, Management, Life-Cycle Design and Performance, Volume, Issue, First published 00, Pages. Barker, R. M. and Puckett, J. A. (00). Design of Highway Bridges An LRFD Approach, Wiley, N. Y. 0. CSiBridge Introduction to CSiBridge. (). Computers & Structures, Inc. Berkeley, California 0 USA.. CSiBridge Bridge Seismic Design. (). Computers & Structures, Inc. Berkeley, California 0 USA.